Neutrinos & Neŭtrinoj

Okay, let’s just go hell for leather on this. Most of it is just going to come out of my head.

When I was seven, I was really interested in nuclear physics. I had this naive idea that if I knew everything all matter and forces were made of down to the smallest level, I would effectively know everything, full stop. The error of this thought was borne in upon me when I realised I had no idea what the scientific name of the freshwater shrimp was, anything about that animal’s anatomy and so on, and more broadly that just because you knew everything about the building blocks of everything in the Universe didn’t mean you knew much about the things that were made of ’em. Seven year olds, eh?

However, one thing that did impinge upon my learning was that atoms were made up of electrons orbiting a nucleus made of neutrons and protons, that the nuclei were held together by the strong nuclear force carried by pions, light was made up of photons, and protons and neutrons were part of a larger class of fairly massive particles called hadrons, which were generally composed of smaller particles called quarks held together by gluons. This is now such a long time ago that nuclear physics has changed considerably since then and some of the ideas are very outdated. For instance, at one point it was thought that quarks were made up of smaller particles called “rishons”, whose number of types enabled the standard model to be simplified by seeing them as pairs of rishons of a few kinds. Only two types of rishons would be needed for there to be four types of quark. Also back then, the top and bottom quarks had yet to be detected, so people mainly talked about up, down, strangeness and charm, and it hasn’t been lost on me that that’s the title of a Hawkwind album. This was, however, about three years before the album came out and at the time I would’ve been entirely contemptuous and condescending about this piece of music with pretentions to be high art. I should hastily add that I’m not like that any more.

Now it was quite easy for my undeveloped child’s mind to understand all this. Basically, each particle had mass, charge (or no charge) and spin, and these properties defined what that particle was. They were divided into bosons and fermions, and also leptons, mesons and baryons according to their mass from light to heavy. I was for some reason particularly excited about mesons. Many of these particles are unstable, and when they break up their mass, charge and spin need to be conserved. To take a completely wrong example, say there’s a meson with a mass five hundred times that of an electron. If it broke up into two smaller particles, if each has a mass 250 times that of an electron, that would conserve mass. However, this is totally wrong because some of a particle’s mass is lost in binding energy, so each of the pair would actually have a mass more than half of the meson’s. That’s not in any way a real example but because I’m ploughing on at a rate of knots, I’m not looking any details up and can’t remember the properties of a pion, for example. Leptons, incidentally, are not like that. They’re stable, lighter and not made of anything smaller. This is about mesons and baryons. If you asked my seven-year old self, I’d be able to give you the properties, but my late middle-aged and addled brain can no longer so do.

But, more simply, if a neutral particle emits an electron it will become positively charged because electrons are negatively charged and that needs to be preserved.

Not all objects have mass at all. If an object has a mass of zero, it has no choice but to move at the speed of light, which is actually not the specific speed of light but just the fastest speed there is, to quote Monty Python. Neither must every object have charge. Most objects we come across in everyday life, such as combs and loo rolls, tend to have no charge most of the time although if you comb hair with a comb it will become charged and be able to pick up small bits of loo roll, so it does happen. On a subatomic scale, though, there are essentially charged particles, namely the electrons and protons making up atoms, but there also have to be the uncharged neutrons which balance out the nucleus and prevent it exploding. Both protons and neutrons are made up of charged quarks which together add up to one unit of positive charge or no charge because they cancel each other out or they don’t. So that’s also simple.

Spin is however really not simple. Although this makes no sense to our macroscopic brains, spin is quantised and a property like charge and mass. Also, even more strangely, a particle can have non-integral spin, and if it does, it needs to be flipped over twice to reverse its spin. Look at it this way: there’s a gyroscope spinning in a clockwise direction when viewed from above. Usually, to make it spin anticlockwise all you need to do is turn it upside down. If, however, it had non-integral spin, if you turned it upside down, it still wouldn’t be spinning anticlockwise and you’d have to flip it over again to make it spin the other way. This is very weird and as I’m typing this I wonder if I’ve got it wrong but it’s been said that if you think you understand quantum mechanics, you don’t understand it, so presumably I do understand this because I don’t.

So why am I bothering to mention this little detail? Well, it was discovered some time ago that the way subatomic particles break down must conserve mass (taking into account that some of their mass is converted to energy when they’re stuck together), electrical charge and also this other property, spin. In order for this to work properly, there must be massless and chargeless particles. These particles seem to be nothing, but they aren’t because they have spin. These are neutrinos, and they come in various types because they’re leptons and they have corresponding more tangible particles, so there are for example muon’s neutrinos and electron’s neutrinos. They are of course bloody weird. The way they’re detected is by filling enormous buried underground tanks with dry cleaning fluid and trying to detect the tiny number of atoms which are changed by interaction with them. Since they’re produced in nuclear reactions, the Sun emits them. It’s been said that a million neutrinos passed through a wall of lead a light year thick, almost all of them would come out the other side. They virtually do not interact with matter. About forty-odd years ago, there was a problem understanding the Sun because it wasn’t producing enough neutrinos. In other words, the massive tanks of dry-cleaning fluid under the Alps or wherever they were kept were not producing detectable numbers of different atoms. I mean, I don’t know how you detect a couple of altered atoms in six hundred tonnes of dry cleaning fluid, but apparently you can. I’ve probably missed the point. Incidentally, I don’t want to go off on too much of a tangent but I find it kind of annoying that there is a thing called “dry-cleaning fluid“. How is it dry-cleaning then, eh? And while I’m at it, it used to be used to decaffeinate coffee, or something similar did, and it always used to give me a stomach ache when I drank it. Tangent alert!

Okay, so my point is that for whatever reason I didn’t have any problem accepting that neutrinos existed even though they were massless and practically didn’t interact with matter, at the age of seven. In fact, in 1987 it turned out that neutrinos did in fact have some mass because a couple of hundred thousand years ago, a star exploded in one of the Milky Way’s satellite galaxies and the neutrinos took a few seconds longer to get here than the light, implying that they were travelling more slowly than light and must therefore have mass.

Now for the famous problem.

Centuries ago, Johannes Kepler worked out that the time it takes a planet to orbit the Sun can be worked out straightforwardly from its distance. To quote Kepler’s Third Law, “the squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits”. Semi-major axis is the mean distance of a planet’s orbit from the Sun. Isaac Newton generalised this law to come up with the law of gravity, and it’s supposed to apply to everything in the Universe. There’s a lot more, but this is the important bit. It means that if you look, for example, at the triple star system next to the Sun, you can work out from the masses of Proxima Centauri, α Centauri A and B and their distances from each other how long it takes them all to orbit each other. The much closer A and B are close in mass to each other and take eighty years to orbit and Proxima, which is eleven thousand times the distance of Earth from the Sun, takes 550 thousand years to orbit the other two, whose total mass is what matters. However, it doesn’t stay this simple.

If you look at a galaxy, you might think you can calculate its mass from the number of stars in it and their sizes. Galaxies rotate very, very slowly: our solar system takes something like 225 million years to orbit its centre. It ought therefore to be expected that the time taken for a star twice as far out from the centre to orbit this galaxy should be the square root of the cube of twice as long as 225 million years, i.e. a little under three times as long. However, it actually only takes about twice as long. Why?

Obviously you can’t see everything in the Galaxy. If you were looking at this solar system from α Centauri, even with a fantastically powerful telescope, you wouldn’t be able to see Jupiter, any of the other planets or moons, any of the dwarf planets or any of the asteroids, and between the stars there are also rogue planets wandering in interstellar space, dust, maybe black holes and brown dwarf “stars” too dim to see as well as potential comets very slowly orbiting sheer light months from the Sun, so there definitely is missing mass which means galaxies would seem to rotate faster than just counting up the stars would predict, and also, coming back to neutrinos, they also increase the mass of galaxies somewhat. However, for this to work as a way of accounting for how fast galaxies spin, and also how quickly galaxies “near” each other affect each others’ motion, well over three-quarters of the mass of a galaxy would have to consist of this sort of stuff. Maybe it does, but it probably doesn’t because for example 99.8% of the mass of our solar system is the Sun. Therefore it probably isn’t lots of ordinary invisible matter doing this.

Therefore, scientists decided that there must be something called WIMPs – Weakly Interacting Massive Particles. This is by contrast with MACHOs – MAssively Compact Halo Objects – which is the idea that there’s a roughly spherical cloud of massive ordinary matter also orbiting galaxies outside the plane of the arms. I’m about to come to the point by the way. To me, and to a lot of other people, WIMPs seem to be invented just to explain the problem. They’re most of the matter in the Universe, but they conveniently do not interact with the matter we’re familiar with. I paused there because I almost wrote “do not interact with ordinary matter”, but in fact if this is true they actually are “ordinary” matter, and it’s atoms, molecules and light which aren’t, in other words all the stuff which can be detected. Hence I think this is silly and go with a different hypothesis, which is MoND – Modified Newtonian Dynamics. This is the idea that the explanation is that Newton’s laws of gravity only work on relatively small scales and break down if you consider them over thousands of light years or further.

All this said, I am perfectly well aware that I’m no physicist. I did have my doubts about the cosmological constant as a teenager but just thought it was because I didn’t understand physics, then it turned out Albert Einstein had the same doubts and found it embarrassing, so maybe I should listen to my intuition more. Maybe people can be too embedded in their area of expertise to realise the flaws in their thoughts. Or, maybe an outsider just doesn’t understand properly and only thinks she does.

But my point is not about this but ageing and how people accept and reject things as they get older. As a child, I liked the idea of neutrinos because they were absurd and weird, and therefore fascinating. As a fifty-seven year old, and in fact even when I was quite a bit younger, I find the idea of dark matter, which is what I’ve just described, hard to accept even though it’s quite similar in a lot of ways to neutrinos. And that’s the process of becoming more conservative as you get older, and therefore this now becomes not an abstruse argument about physics or cosmology but personality and maturity.

There has been a pattern where young people start off left wing and become right wing old people. This is apparently less true than it used to be. Why this happens is another question. It may be that as one acquires wealth and possessions, one realises that one’s position of poverty and the apparent need to depend on the state for financial support was temporary and would also be for other people, and therefore things will get better or easier if one takes responsibility for things. Or, it could be that as one’s career advances, one makes moral compromises and therefore descends into self-deception and rationalisation for them. Or, again, maybe it’s cognitive decline and an inevitable process of being more easily duped by politicians and media-based propaganda. Conservative ideas are more appealing because they’re about the “good old days”. If this last one is so, the answer to a drift to the right may be just to decide that one was more likely to have been correct before one started losing one’s marbles and freeze one’s political opinions at that stage, but when new situations arise it can be harder to apply those principles than it used to be.

Why has this image appeared at this point on this blog post? Well. . .

I accept that neutrinos exist. Once upon a time, in 1887 CE, a guy called Lazarus Zamenhoff living in Poland invented a language called Esperanto, which I’m sure you’ve heard of. It was designed to be simple and logical, and was specifically constructed in a Europe where the various powers had been at each others’ throats for centuries, so the vocabulary was mainly based on Romance, Germanic, Greek and Slavic roots, plus a few completely invented words. In order to make learning it easier, Zamenhoff introduced the idea that words could be plugged together to change their meaning in a completely regular way, so for example the prefix “mal-” would turn a word into its opposite: “bona” means “good”, “malbona” means “bad”, and more controversially, “knabo” means “boy” and “knabino” girl, and in fact in the original version of the language all the gendered terms are unmarked when masculine and marked when feminine in this way. This is sexist but there are practical reasons for it. As in natural languages which mark this kind of gender, there are ways of working round it.

One of the possible flaws in the language is what this approach to word building does to words which are similar in many languages. For instance, take the English word “school”. In French this is «école», in German ,,Schule”, in Indonesian “sekola” and so on. All words which look and sound similar. In Esperanto, the word for school is “lernejo” – “learn-place”. This is easy to form and break down, and it reduces the need to learn a more opaque word, but the chances are that in many cases the word will already exist in the learner’s native language and there may at least initially be some puzzlement.

Germaine Greer’s famous book is called ‘The Female Eunuch’ in English, the language it was written in. The Esperanto word for “eunuch” is the rather logical word “neŭtro”, related to the adjective “neŭtra”, meaning “neuter”. However, since unmarked nouns in Esperanto usually refer to males or inanimate items, “neŭtro” means “male eunuch”. “-Ino” is the feminising ending. Hence the Esperanto word for “female eunuch” is “neŭtrino”! I don’t know whether Greer’s book has been translated into Esperanto or what its title is if it has, and I also don’t know what the Esperanto word for the elementary particle is, but logic suggests that neutrinos are called something else in Esperanto and the word “neŭtrino” does in fact mean “female eunuch”. If not, the chances are that when Esperantists talk about fundamental particles they say that there are vast tanks of dry-cleaning fluid under the Alps intended to detect female eunuchs and that when scientists detected Supernova 1987A, they noticed that female eunuchs don’t move at the speed of light. Well I could’ve told ’em that.

So what’s my point? Do I have one? Surprisingly, yes. As I’ve got older, like many other people my acceptance of novelty has become less flexible and although I was fine with neutrinos I wasn’t fine with dark matter. Neutrinos were discovered in 1956, though they were theorised earlier. ‘The Female Eunuch’ was published in 1970. Esperanto had its rules laid down in 1887, and although better-designed versions of the language have been proposed since, it’s difficult to accept them because the whole point of Esperanto was that it was supposed to be a single language which everyone could use. I actually think Esperantido is loads better but I wouldn’t use it because it isn’t the original. This rigid design is reflected in the fact that these two concepts, the female eunuch and the neutrino, have happened in the world getting on for a century after the language was devised, but it isn’t open to accepting new ideas in that way. As such, Esperanto represents exactly what happens to us as we get older, but not because we compromise or become more conservative, but simply because we were designed for an earlier age, in the case of Esperanto, one where neutrinos were unknown and second-wave feminism was unthought of.

It occurs to me also that second-wave feminism itself has also been superceded and may be in the same position, but that’s another story.

A Post-Truth Test Tube

I’m currently a recovering addict. A few months ago on a whim I joined a FB group to debate Earth’s shape. I’ve come across flat Earthers before, online at least. Whether I’ve encountered adult Westerners who believe Earth is flat, I don’t know. Finding the group highly addictive, I became one of the main posters and enjoyed it a lot, but it isn’t really the best employment of one’s time. That said, it does constitute an interesting case study of the way we think and behave.

The useful thing about looking at flat Earther psychology is that it’s firmly established that Earth is spheroidal. The room for doubt is practically submicroscopic on this matter, so there’s no risk of being wrong or being drawn into believing that it’s flat, and because of that, rather than becoming embroiled in arguments which might persuade one, one can instead just examine how flat Earthers justify their position. Positions plural, actually. Most flat Earthers seem to believe we are on an almost flat surface under a transparent dome with the Sun going round us, but there are other views. For instance, some believe Earth as we know it is surrounded by broader rings of continents and oceans to which we have no access, and to be honest that is a really fascinating and appealing view which might go some way towards addressing the claustrophobia of the more restricted version, and a few of them seem to believe we are on an infinite plane. I say “seem to” because this is one of the problems with trying to work out what’s pagoing on: are they serious about this or just kidding around?

The answer to this is probably that it depends. This is one thing about groups seen from a distance as opposed to groups examined more closely: the details of individual differences become clearer. As far as I can tell, there seem to be several categories of “flat Earther”. There certainly are people who are just joking, and in fact when the flat Earth society was reëstablished in I think the ‘noughties, it appears to have been a joke. There are also trolls, which is a slightly different thing because I suspect the people concerned enjoy either tweaking the feathers of people they see as nerds or deceiving people into thinking it’s flat for fun. This seems to blend into a group of people who are trying to make money out of gullible people and present themselves as serious campaigners and investigators on the issue. Then there are their followers, who have bought into the whole thing, which is where the conspiracy theories start. There are few people who think independently on the issue, and there are then religiously-motivated people and people who are simply persuaded but not particularly religious. Finally, there are enquiring people who don’t seem to be skilled at fact-checking and simply feel that the two views, flat and round Earth, are equally open to question: kind of “false balance” people who think there is enough evidence for it to be a fair fight.

I can certainly vouch for the power of the force of gravity here, because I couldn’t leave it alone. Rather than manifesting itself as concluding Earth was flat for me, it came across as a compulsion to post and address issues even though I knew it wouldn’t persuade anyone to do it. It may be worth asking myself questions about why I felt the draw of the belief system and attempting to change it, and why “flat Eartherism” in particular has this pull. I know that I have obsessive-compulsive tendencies although I’m not going to pathologise that or embrace a self-diagnosis, but it is there and it probably is a factor for me. But it was also very time-consuming. Cutting my ties with it is also a judgement call, because it’s possible for some people actually to make a living out of addressing the issue. There are, for example, YouTube channels devoted to debunking flat Eartherism as well as all the so-called “Truth” channels focussing on promoting it. Pushing it far enough might in theory have brought some money in although I’m small fry in that pond,so probably not.

This raises the question of whether it’s harmless. In a way, this is beside the point. It’s more that the occurrence of the belief, which often seems to be a long way down the line for many people who have come to question other widely-held beliefs such as how genuine the Apollo program was, is symptomatic of poor fact-checking abilities, and when I say “ability” I do believe critical thinking can be developed in most people. They could even develop it themselves, although it may be difficult to overcome emotional and social attachment to a belief. It is also true that believing Earth is flat is going to exclude people from certain lines of work, or at least make it difficult for them to pursue them, such as on large engineering projects or piloting international aircraft, so maybe human resources are lost to society because of this belief. More broadly, however, there are the issues of overvalued ideas, vulnerability to more negative consequences from other beliefs (anti-vaccination comes to mind) and the general feeling of distrust and fear which may arise from the idea that there is a vast conspiracy to keep all this from the public. The size of this effort would be a lot bigger in this case than any other conspiracy I can think of, because so much more depends on the shape of the planet than other things.

Looking at the trolls, and here I presume that trolls exist and I’d expect there to be at least a few, an outsider would see them as pretending to be of low intelligence and poorly-educated, which is an odd thing to do to one’s reputation. I imagine that they are deriving entertainment from successfully deceiving others or annoying people they may see as nerds. I have in common with these people that I’m drawn into wasting my time and energy on a project which is not very productive and a bit of a pointless endeavour. Trolling is something I don’t fully understand and I sometimes wonder if trolls even know what their real motivations are, because it’s so easy to develop an online persona unintentionally. Beyond this, I can even develop a little conspiracy hypothesis of my own that the whole exercise is a distraction from more consequential issues for all of us, not just the flat Earthers. It’s possible to drop the whole intentional fallacy from this idea and just say, this is what it does and it doesn’t matter if it’s a concerted effort or not. This is one reason why I’ve given up on them, because it really is a bit of a waste of time.

There’s also something like the “sunk cost fallacy” operating here, perhaps on both sides. The sunk cost fallacy is the feeling that because you’ve spent a lot of time and resources, and have perhaps lost a lot in your own life socially and otherwise by pursuing a particular goal, it’s hard to back out of it. If you’ve become a flat Earther, you may value the comradeship of the people around you, online or off, and in many sallies away from majority opinion, people can lose friends and acquaintances, and also opportunities, and all of these things amount to costs. Another form of cost is the embarrassment one may experience from admitting one was wrong.

All that said, we should avoid “othering” people whose beliefs we’re confident are incorrect. One reason for this is that having delusions is part of the healthy human psyche, and even where they don’t serve a positive purpose they may nonetheless exist. Failure to acknowledge that we rationalise our beliefs, even if they’re correct and well-supported by evidence, is lack of self-awareness. Our beliefs also have functions beyond the practical. They can be like interests which bind a club together, and of course this is a substantial part of the function of religious beliefs. I have long maintained that religious belief of some kind is inevitable and therefore that we shouldn’t always resist it, as it can play a valuable part in maintaining good mental health. The question here is whether believing Earth is flat is worthwhile enough for the cost paid through lack of contact with reality.

I have an acquaintance who used to be quite a close family friend. We even went on holiday together and attempted some joint business ventures. Quite some time back, they expressed the view that the Apollo missions were a hoax. I engaged with them on this but they didn’t change their mind. I should point out at this stage that this person was a faithful Green Party voter and possibly even a member of the party. They were also an alternative medicine practitioner. This particular category of work has a lot of variation in it and can be stigmatised. It’s also how many people see me. Nonetheless there is a perceived issue of evidence supporting efficaciousness or otherwise which plainly does apply to some modalities. During the lockdown, they expressed support for Trump, not just regarding his approach to the pandemic but more widely. I could make a link between belief that Apollo was a hoax and this later conclusion. I found the incident very saddening and disappointing.

It seems that a lot of the more vocal flat Earthers nowadays connect their beliefs to the Apollo hoax idea, which makes sense if you think Earth is flat, and also to anthropogenic climate change denial, the New World Order conspiracy theory and anti-vaccination. Of all of these, I should point out that in the 1990s I was close to being anti-vaxx, although my problem was that as usual my opinion wasn’t similar to that of others. I tended to get lumped in with anti-vaxx people even though my actual position was that I wanted some vaccinations to be given by inhaler or nebuliser, not injection, rather than being opposed to vaccinations as such, and as such wasn’t opposed to the single tetanus jab or OPV per se. Now that this is being done routinely with children, I no longer have that objection although I am still concerned about the evolution of slow viruses by attenuation. However, I’ve long felt that the real problem with vaccination resistance is that much of the population doesn’t feel respected or listened to, and I wonder also if this is a factor here. This is one conspiracy theory I’ve seen from the inside. I get the impression also that flat Eartherism is the “hard drug” as it were. It’s the last thing people end up believing in once they’ve accepted all the others.

Due to the universal nature of delusions, a more useful marker for mental illness may be the overvalued idea. It isn’t so much that people believe Earth is flat as that they’re preoccupied with the idea and it comes to dominate their lives. It is understandable that if you think something so fundamental is different than how it’s presented publicly, you probably would think it was quite important to do something about it, and are also likely to think there may be a sinister reason behind the deception. Is it an overvalued idea for a starving person to focus on finding something to eat?

According to the conspiracy theory, the rationale behind persuading the world that Earth is round is to dislodge humans from the centre of creation and lose Earth in the vastness of an impersonal Universe, thereby undermining theism. If that were the aim, it seems like overkill. Why would it be necessary to keep “building” the Universe in the way they would have had to have been doing, for instance initially portraying distant galaxies as nebulæ within our own and likewise with quasars, before promoting them to enormous distances? There’s another perspective within this one that the Big Bang theory, evolution and flat Earthism are all part of a plot to do this, and are associated with the Illuminati, the Masons and unfortunately sometimes the Jews. This last association probably indicates why all this might be dangerous.

I actually find the bog-standard flat Earther view to be claustrophobic and think it makes the world feel like a prison. It also seems to guarantee that there is no life anywhere except on Earth, which for me is a deal-breaker for theistic prayer and worship. If God chooses to sustain a Universe where we are the only sentient beings in a single biosphere, it seems like God cannot be related to by humans on an emotional level. This makes more sense if one does see the Universe as vast, but it still works to some extent on the prison world hypothesis because whereas God could have chosen to sustain a vast Universe, she chose not to, which means we’re trapped conceptually. Of course, we could still be literally trapped on Earth in a vast Universe, but at least the way things are we do know how enormous the world is and the contrast with the largely lifeless Universe in which we’re embedded emphasises the specialness of this planet. This would be less true of an infinite plane Universe though there is still the problem of apparently being at its centre, since it is supposed to be infinite and therefore has either no centre or a ubiquitous one.

Of course one might be forgiven for asking why this matters given the current world situation, and that’s a valid question. It would be easy to come up with a conspiracy theory of one’s own here, that fine minds are being distracted from what matters in order that atrocities can be committed, but in response to that I would say that many of the minds which are being distracted, mine included, are rather far from fine and wouldn’t make much of a contribution anyway, and also that it’s a basic principle to focus on the consequences of a set of circumstances more than the cause, which is a distraction in itself and also symptomatic rather than the more general underlying cause of the problem, which would be worth addressing. The question remains, then, of whether one should bother with this at all. Unfortunately the answer seems to be yes, because analysis of how the issue has arisen allows insight into how other more serious issues have, or might do in future. It’s a kind of model for how, for example, Russian trolls might influence voting in elections or how the Rohingya genocide was engineered.

The idea of conspiracy has tended to centre on NASA as a major actor in this realm. This is peculiar as the sphericality of the planet seems to have been first suggested by Pythagoras in the sixth century BCE, its circumference measured by Eratosthenes in the third century BCE and it was then accepted by the Church into the European Middle Ages, to the extent that they used to discuss whether it was possible that God would have created land on the opposite side of the globe from Christendom because if it were inhabited, it might not be feasible for the Word of God to reach them. I have to admit to being a little confused by this as it seems to imply their view of gravity was quite modern, but it is nonetheless so.

This does, however, raise the question of what kinds of people accepted Earth as round at the time. It does seem quite likely that the average European peasant would not have had an explicit view of Earth’s shape at the time, as they had more pressing concerns, but that might be to underestimate their mentality. Likewise, it also seems entirely feasible that even today many peoples who have not had contact with Western civilisation would assume Earth is flat. The rather startling figure of seven percent of Brazilians, though, appears to refer to Europeanised Brazilians rather than the likes of the Yanomami.

I’ve noticed also that some flat Earthers are merely repeating claims without checking up on them. Two of these in particular are that until the 1920s, US public schools taught that the world was flat. This does not tally well with discoverable facts about history. It was the work of a couple of minutes to locate a digital archive of nineteenth century school geography textbooks, on whose first page it was stated categorically that Earth is round and we live on its exterior. This particular work was published in 1889. It is possible that children were being taught that the world was flat at a later date, for a couple of reasons. One is that teachers don’t necessarily teach what is on the curriculum, and could be either poorly educated themselves or believe that it’s flat, in which case they would presumably teach that if the issue arose. Another is that it isn’t clear how far such textbooks had penetrated by this time. A second, less consequential, claim is that Eratosthenes was inserted into textbooks in the 1980s. I am in the happy position of being able to refute this. I first read of his experiment in ‘The Collins New World Of Knowledge Encyclopedia Of Science And Technology’, published I think in 1973. It’s quite an audacious claim that it was added more recently than that, and I expect that if I were to bother to look, I would find earlier examples. These two claims make me feel that it’s almost Last Thursdayism. A rather similar claim is that NASA pictures taken in the 1960s are CGI, which is very peculiar as there would’ve been many other ways to fake images at that time.

Getting back to NASA, there are two oddities about this particular focus. One is that their existence is completely superfluous to the evidence Earth is round, which as I said is millennia old. Another is that they are only one of many space agencies, which I think probably reflects the US-centric nature of Flat Earthism. There are around sixteen space agencies with launch capability and several times that number capable of doing things like building satellites to be launched by others. These two aspects seem to reveal a considerable degree of ignorance about general knowledge. This is coupled with two other aspects of how flat Earthers view education. They often view mathematics with suspicion and are unwilling to apply the scientific method, often engaging in ad hominem attacks when these are used. All of this taken together had led me to feel that they have been poorly served by the schooling system. They seem to regard belief in a round Earth to result from indoctrination when well-expressed scientifically based tests which are easily reproduced by someone without elaborate equipment are actively avoided. This makes it more likely that their beliefs are motivated by religious sensibilities, but unfortunately not open-minded or progressive ones.

The Bible does seem to imply that its human writers tended to assume Earth was flat. Apart from references to “the four corners of the Earth” in the Tanakh, Jesus is depicted as rising into heaven above Earth, which suggests a sandwich-like cosmology with heaven constituting an entirely horizontal layer above the terrestrial realm. It also raises a question in my mind which I’ve been unable to answer so far. If Biblically literalist Christians (and also many Muslims but not religious Jews on the whole) are often young Earth creationists due to their approach to their sacred texts, why is it less common for them to be flat Earthers? Such a view is clearly assumed by Biblical authors just as creationism is, yet the view is much less popular. If I could crack this conundrum, it might lead me towards better arguments against creationism. This might also be a massive waste of time of course, like the rest of it.

A major problem with how flat Earthers interact with the rest of humanity is that we who have an accurate view of Earth’s shape are often guilty of ridicule and insult towards them. This leads to entrenched positions which are defended and attacked not by reasoned argument but through largely emotional interaction. I can imagine a flat Earther becoming more relaxed about her beliefs and getting on with her lives in other ways, and then eventually not caring much about Earth’s shape or quietly conceding she was wrong, but if that day does dawn in their lives, it will do so a lot later if they’ve been pummeled for their beliefs in this way. They’re likely to thrive on persecution, and it is in any case wrong to behave thusly towards them. This may fuel the retention of the beliefs in question.

Flat Earthers, oddly, seem to see the rest of us as indoctrinated “sheeple”. Both sides seem to accuse the other of the same things, and for once because we are able to state confidently that Earth is not flat and back that up with evidence, it’s possible to separate the accusations from the reality, but it is still interesting that they perceive us as we perceive them. Unlike us, sadly in a way, the evidence they present is not remotely convincing and could only be believed by someone who was both unaware of science in the sense of it being a body of information and of the scientific method. They often think of scientists as having their views dictated by monetary interests, and to be honest this has been known to happen, as with medical research into the consequences of smoking tobacco, but in the case of investigating Earth’s shape this is easily reproducible. I have, as mentioned here before, suggested that in order to avoid accusations of manipulation, they come up with their own falsifiable test but I have never known one to do that.

It only takes one reliable falsification for a hypothesis to be rejected. In the case of Earth being flat, many falsifications are available. It would be interesting if the hypothesis that Earth is round could be falsified, but apart from minor details such as its oblateness this has not happened so far and nothing offered by flat Earthers that I’m aware of has succeeded in doing so. Good quality evidence would be most welcome, but is not forthcoming. The closest they get is objects being visible which seem to be beyond the line of sight, but when this is definitely testable it can be explained by refraction of light by the atmosphere, which can only make objects appear higher, i.e. visible if somewhat beyond the horizon, than they would be if no atmosphere was present. Other, similar attempts have been made, such as the claim that RADAR works beyond the horizon. It does, but that’s a special kind of RADAR called, appropriately, “over the horizon RADAR” and works by bouncing short wave radio waves off the ionosphere. Similarly, a microwave mast in Cyprus can communicate with one in the Lebanon, and since microwaves only work by line of sight this would only be possible if each is above the horizon from the other’s perspective, but in fact Lebanon is quite a mountainous country and this is not at all problematic.

I’ve also noticed quite basic misunderstandings which seem to result from not reading sources closely. One flat Earther claimed that my own claim that seismic waves indicated that there was an apparently spheroidal core centred six thousand odd kilometres below the surface was outdated because Earth’s core was not made of iron and nickel but of ionised light elements such as hydrogen and oxygen, and provided a link. What they actually linked to, if followed, reveals a paper which was scientifically quite rigorous but didn’t make this claim. Rather, it claimed that seismic waves appeared to show that Earth’s core was an alloy of iron and nickel combined with ionised hydrogen and oxygen which behaved differently due to the high pressure. This particular flat Earther said they were an ex-engineer who had accepted all their life that the planet was round, but changed their mind later on. Although I’m not questioning that, I do wonder if it’s a sign of cognitive decline, because the paper did not claim anything like they said it did. There were also many spelling mistakes not similar to autocomplete errors in their writing, which again doesn’t show for sure that they’re mistaken but does suggest something regarding their reliability.

All of this, then, seems to be the consequence of something characteristic of our time, perhaps like the Targeted Individual community, where people diagnosable as in a markèdly delusional condition meet others online who reinforce their beliefs of persecution, but combined with poor educational attainment and critical thinking skills. However, we can’t feel all superior about this because not only is it partly about bad luck with the education system, but it’s also nothing more than a delusion we happen not to share, unlike the individual delusions the rest of us happen to have.

If you’re a flat Earther reading this, I want to say the following to you. Although you’re wrong, I will also inevitably be wrong about some of my beliefs, and the reason you’re wrong is not connected to you being in the minority. Even if only a single person in the world believes something, the mere fact that it’s just the one person has no bearing on whether it’s true or not. I don’t want you to feel I treat you with contempt, and if any of what I’ve written has made you feel this way, I sincerely apologise. It takes courage to stick to a belief which the whole world is against, and I respect you for that. Who knows what else we might have in common outside this area?

“Janus, Mimas, Enceladus. . .”

When I was six, I set myself the task of memorising the then known moons of Saturn, and it stuck. Even today I can easily reel off “Janus, Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion, Iapetus, Phoebe”. Several times that number of moons are known to orbit Saturn today, but even ten sounds like a lot. There are a couple of oddities on this list, but today I’m actually going to be talking about Janus. Sort of.

“Sort of” because Janus is not necessarily what we thought it was. It was sometimes, but at others it wasn’t. Janus was discovered in 1966 CE but although it had an unofficial name, it wasn’t officially called that until 1983. In the meantime, it had been discovered that “Janus” wasn’t what everyone thought it was. In the opposite situation to Venus, which had previously been called the morning and evening star (Phosphoros and Hesperos) and in ancient times was not recognised as the same thing, Janus turned out to be two separate moons. This led to confusion about the nature of its orbit, since it would appear to “jump around”. On arrival at Saturn, the Voyager probes were able to take a picture of two moons which seemed to be on a collision course with each other but were obviously still there in spite of previous apparent collisions, and it emerged that “Janus” was in fact two moons sharing the same orbit and swapping over when they got close to each other. Hence another name was needed, and one moon kept the name and the other was called Epimetheus. Epimetheus was in a sense the first Saturnian moon to be discovered by the Voyager missions and therefore has the number XI, but it had been seen before and just not recognised for what it was. Janus is considerably larger than Epimetheus, at three million cubic kilometres as opposed to 820 000, and since both are too small to be round it makes more sense to refer to their size by their volumes. Janus is in fact 203 by 185 by 152.6 kilometres, whereas Epimetheus is 129.8 by 114 by 106.2 kilometres. Neither are drastically far from being spherical and are, like a lot of other bodies of that size, potato-like in appearance, if potatoes have craters.

The situation with Janus and Epimetheus was the first time I realised that gravity doesn’t just attract. Janus and Epimetheus zoom around Saturn at around sixteen kilometres per second, kind of treating their common orbit like a race track. The inner moon catches up with the other, at which point they swing around each other and the inner becomes the outer. This works because the gravitational attraction between the moon in front and the one behind causes one to speed up and enter a higher orbit and the other to slow down and enter a lower one, after which they separate, i.e. move away from each other. In other words, the acceleration due to one moon “falling” towards the other leads to it being “pushed” away, so to speak. It would be interesting if some kind of jiggery-pokery from this happening could be harnessed to provide something which looks like anti-gravity, but it’s a very special case and I really don’t think it could be.

At their minimum distance, Janus and Epimetheus are only fifty kilometres apart. Since they are actually larger than that even in their minimum dimensions, each would practically fill the other’s sky at these times. Larger moons approaching at this sort of distance would smash each other to bits with their gravity, and it’s possible that this has already happened and caused the situation to arise in the first place. Maybe the two used to be a single dumb bell-shaped moon back in the day. The exchange occurs once every four years or so because at other times they aren’t close enough to have that influence on each other.

This is Janus itself:

Since the moon is only two hundred kilometres across, an individual pixel in this image would have a width of about two hundred metres. It isn’t minute, but it is fairly small. On the other hand, it’s also large enough to approach being round and doesn’t give the impression of being “cute” like some small moons and asteroids do because the features on its surface are not out of proportion. I only realised in the last couple of days that it was (kind of) discovered in 1966 because to me it’s always been there, which of course it sort of has, but it’s also a bit surprising that it was only discovered eight months before I was born, just after the Beach Boys’ ‘Good Vibrations’ had slipped off the number one spot (it was actually Tom Jones but I’ll breeze over that. He’s okay, but – well, you know).

There are four named features on Janus, named after characters from the legend of the twins Castor and Pollux, like other features on Epimetheus. These are Castor, Idas, Lynceus and Phoibe, all craters. There is a faint dust ring, about five thousand kilometres across, around the orbits, which isn’t surprising as they presumably claw at each other wildly every four years as they pass each other, which is bound to raise some dust, although it’s attributed to meteoroid impacts. They’re also shepherd moons, which isn’t just an album by Eithne but also refers to moons which keep rings in place and maintain their neat edges. Janus does a slightly better job than Epimetheus because it’s more massive, so the A Ring, which they shepherd, is neater when Janus is closer than when it’s the other way round. It’s also probably a rubble pile, hence the ring, and it’s quite icy. These two things together make it very light for its size, rather like Saturn, at sixty-three percent that of water, so it’s actually less dense than Saturn. It’s possible to measure this from the moons’ gravitational influence on each other. Surface gravity varies due to the irregular shape but is around a six hundredth of ours. It’s reddish-brown.

I might as well do Epimetheus while I’m at it. Epimetheus I would’ve expected to be paired with a moon called Prometheus as they were brothers, but apparently not. I also knew a cat called that so it’s a bit weird typing that name here. Here it is, seen from a pole:

It looks a lot more “moony” than Janus to me, because it has proper-looking craters. In fact I’m surprised how different they look. It was realised in about 1978 that astronomers were probably dealing with two different moons, and one of the Pioneer probes might have taken a picture of Epimetheus but it was too vague to enable it to have its orbit plotted. The craters are called Hilaeira and Pollux, which figures. There’s actually a photo of it with the shadow of the F Ring across it:

That’s it, more or less. Not a lot to say about such tiny moons. Oh, just that Janus used to be the god of doors and has a face on both sides of his head, which makes you think Janus the moon is special because it always has one face looking at Saturn and the other out into the rest of the system, but actually that’s normal for moons, in Saturn’s case all the way out to Titan.

Mimas next time.

For The High Jump

This is going to be a bit of a departure for me, since I have practically no interest in sport. I run, more in the breach than the observance there, enjoyed (field) hockey at school, and was actually good at it, but my involvement in sport is exceedingly limited. Maybe you have to be born into a sporting family or something, as nobody in my nuclear or extended family was remotely into it. However, today I’ve decided to write something on the question of the high jump, as it happens to be relevant to a physical phenomenon.

Earth is of course round, but it isn’t spherical. That is, not only does it have an irregular surface, with valleys and mountains, continents and abyssal plains, but even considered in a “smoothed out” kind of way it is not spherical. Its diameter is forty-three kilometres greater at the Equator than between the poles. There are also some smaller deviations. The Equator itself is slightly elliptical and one pole, I think the North, is further away from the centre than the other. Then there are some even more minor deviations which have led to it being described as “lumpy shaped”. Another description is “pear-shaped”, but both of these can give the impression that it deviates radically from the spherical, which it really doesn’t.

Measuring Earth’s dimensions in terms of the metric system reveals a slightly unusual relationship between the planet and its units, because a metre was initially defined as a ten millionth of the distance between the North Pole and the Equator on a quadrant passing through Calais, if I recall correctly. In any case, this means that a spherical Earth would be exactly forty million metres in circumference, or more sensibly expressed, 40 000 kilometres, and that there are also a mathematically derivable diameter and radius for this ideal shape – Earth “should” be 12 732 kilometres and 395 metres, forty-five centimetres in diameter and 6 366.197724 kilometres in radius. However, this is not the case. It wasn’t, as far as I know, possible to survey that meridian with that accuracy along the whole of its length and in any case land expands and contracts seasonally. The metre is no longer defined in this way but by the distance travelled in vacuo by light in 1/299 792 458 of a second.

In fact, the diameter at the Equator is 12 742 kilometres and between the poles 12 713.6 kilometres. I learnt the first figure as 12 756, so I wonder what’s happened there. Therefore the question arises of how much difference this makes to gravity, to which the answer is quite easy to calculate. Simply divide 12 742 by 12 713.6 and square it. This yields 0.447%, rounded down. It also means that a cubic decimetre of distilled water at 4°C will weigh a kilogramme at the Equator and a little over 1 004 grammes at the poles. Both of these are assumed to be at sea level, and this raises a further complication.

The heights of mountains can be measured in a number of ways, one of which is to measure how high above sea level the peaks are, but another is distance from the centre of the planet, and in this case that second number is more relevant. Although Mount Everest is the highest point on land above sea level, the highest point from Earth’s centre is actually Mount Chimborazo in the Andes, even though it’s only the thirty-ninth highest peak in the Andes. This is, I’m guessing, because Chimborazo is close to the Equator. It’s 6 384.4 kilometres from Earth’s centre, and if you halve our equatorial diameter you get 6 371 kilometres. This suggests that South America straddles a bulge in the Equator, suggesting there’s another one off the east coast of Asia, and this is important because another location, quite a long way off the east coast of Asia is the deepest point on Earth’s solid surface, the Challenger Deep in the Marianas Trench. Hence the Challenger Deep is potentially not the closest location to the centre, and in fact it isn’t. The closest point to Earth’s centre is unsurprisingly in the Arctic Ocean at the Litke Deep, which is 6 351.61 kilometres from it. Taking these two together leads to a difference in gravity, all other things being equal, of one percent. The actual height difference is thirty-two and three-quarters kilometres.

However, all other things are not equal. There are gravitational anomalies. Hudson Bay in Canada has unusually low gravity, for example, because geologically speaking it was recently covered in a thick and heavy ice sheet. Once this melted, just as in Europe, the rocks of the crust beneath began to spring upwards and are therefore less dense than they would be in a tropical area. Parts of the crust have also been squeezed out sideways. This has led to the gravity there being lower, but it isn’t the only factor. Convection currents in the magma mantle underneath the crust also pull the rocks downward in the area. The greatest gravitational anomaly on the planet is in the Indian Ocean south of Sri Lanka, which may be due to the plate carrying the Subcontinent moving particularly fast. There will also inevitably be slight variations in gravity all over the planet due to the

The reason Earth bulges slightly around the Equator is that it’s spinning, which pulls the substance outwards. This rotation also influences how heavy things are, although gravity is not different because of that alone, because of the centrifugal effect. This leads to something called the Eötvös Effect, where objects weigh slightly less if they’re moving east at a constant velocity relative to Earth’s surface than they are if they’re moving west. However, even a stationary object feels the centrifugal effect, which is unsurprisingly most pronounced at the Equator. A line graph for this effect on a ten kilogramme mass looks like this:

By Crystallizedcarbon – Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=42890848

This is at the Equator. A newton amounts to about a hundred grammes if it’s thought of as a unit of weight. Added to the effect of gravity, it means that gravity combined with rotation will reduce the weight of an object by 0.9% at the Equator at sea level assuming no gravitational anomaly compared to the North Pole at sea level.

Now I’ve done all that, I’m finally ready to consider the male high jump record. A few preliminary remarks are in order here. One is that I’m aware that both the land and water speed records went from dramatic improvements to increasingly small incremental improvements as they approached the sound barrier, but this can be put down to technological progress. It isn’t so clear that this would, at least legally, be the case with human athletic records, although it’s conceivable that training or selection of athletes might improve. I’ve chosen the male high jump records because they’re higher than the female ones, which would magnify any observed difference. My question, then, is this: is there any discernible difference between high jump records achieved at high and low latitudes? That is, is it easier to jump near the Equator because of being assisted by the lower gravity and the rotation of the planet? Another question, which I think is probably exceedingly hard to answer, is: is it easier to jump if one does so to the east? In order to answer that, I’d need to know the minutiæ of the sites where the records were made. There is another factor which acts against the altitude issue – there is less oxygen higher up. This will be further confounded by oxygen doping, and would also be by the presumably illegal practice of using drugs to promote the production of red blood corpuscles or receiving a self transfusion of banked blood.

Anyway, here is a map of Olympic sites since 1896:

(Unfortunately this is Mercator but I have shifted it to put the Pacific in the middle). It’s interesting to note how uneven the distribution is. They had apparently never been held in the Middle East, South America or Afrika up to whenever this was compiled, but they took place in Rio de Janeiro in 2016. The closest to the Equator they’ve ever been held is Mexico City in 1968, and the furthest seems to be Helsinki. Then there’s the list of progressive men’s high jump records, in teeny-tiny writing:

This is from here.

What one could expect would be that the same person could jump two metres at the North Pole but 2.02 metres at sea level at the Equator. Another problem is that the above list doesn’t seem to correspond to Olympic high jump records. Interestingly, though, all of these records are sufficiently close to each other to be influenced by such a change in gravitational strength in the limiting cases. The biggest difference between latitudes of successive records is Malmö and Los Angeles, which is twenty-one and a half degrees. The difference in those results is 0.9%, and since the difference is smaller than the extremes, it wouldn’t’ve meant the record would not have been broken if the two were swapped, all other things being equal.

Unfortunately, therefore, this is inconclusive because it isn’t possible to isolate the factors involved sufficiently, but if it ever happens that there is a less than one percent difference in records, gravity and the centrifugal effect will be at least approaching significance. The question arises of how close or far from the Equator it’s sensible to hold the Summer Olympics or high jump competitions. There seems to be a series of sports zones determined partly by latitude, so it’s impossible to compare like with like, and altitude could be expected to make a bigger difference.

The Solar Mass Transit System

Space is in a sense mostly empty. In another sense it really isn’t because there are virtual particles everywhere, the quantum vacuum may not be at its lowest energy state and there are at least a couple of atoms per litre of space. Also, everywhere feels the pull of gravity. There is nowhere in the Universe you can go to escape any object’s gravitational pull. Actually, I question that, for this reason. Suppose you are orbiting a lorry floating in space in an otherwise entirely empty Universe a billion light years away. Someone sitting in the lorry reaches out, breaks off its driver’s side wing mirror and flings it into space. This will alter the number of objects in the Universe and the wing mirror will change the gravity acting upon you. How much difference would that make to your path? I suspect it will make so little that your accomplice may as well not have bothered, to the extent that it may actually be smaller than the grain of the Universe as expressed by Planck units, although I haven’t done the maths. If the Universe is big enough, there will definitely come a point where the influence a particular mass has on another will never add up to more than the Planck length, and this, to me, seems to mean zero influence. Then again, maybe this is the kind of quantum gravity thing which physicists have been slaving away for decades to solve and it’s more complicated than I think.

All of this notwithstanding, the Solar System is practically a point compared to the Universe, so the gravitational forces acting within it are considerable. There are of course nine major bodies the mass of Mercury or higher plus a further seven moons of planetary size, and various other smaller but still quite massive worlds such as Ceres and Vesta.

By Lagrange_points.jpg: created by NASAderivative work: Xander89 (talk) – Lagrange_points.jpg, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=7547312

Each pair of these bodies has five points in space around it which, assuming they’re the only two bodies in the Universe, have balanced gravity. Objects placed at these points are stable. Either side, they will tend to fall towards these points. Something similar was mentioned by Jules Verne in his ‘Round The Moon’ («Autour de la Lune») whose astronauts’ weights drop to zero five-sixths of the way to their destination. Perhaps surprisingly, I haven’t read «De la Terre à la Lune», so for all I know it’s mentioned in there as well.

Given the eight planets and the Sun, there are of course five Lagrange points associated with each at any one time. This gives a total of forty. There are also five for every planet-moon pair, although not all are significant, so for example Jupiter and the Galileans have twenty as well as the five associated with Jupiter and the Sun. Some of these points are very close to each other and all are in constant motion relative to other frames of reference. There should also be similar balanced points between any two objects, such as, to be silly, Chiron and Hidalgo, or Ariel and Phobos.

All this means that in order to reach another world in the system, you don’t actually need to expend the energy necessary to get all the way from, for example, Earth to Mars because you’ll get help on the way. There will be a point following Earth in its orbit but further whither spacecraft might be aimed rather than Mars itself, and since there’s an increasing tendency for objects to fall towards these points, even the energy required to get there is less than it might be. Once in that location, it would be necessary to thrust a little further in order to approach the destination. The locations of the Lagrange points are along a line passing through the centre of gravity of the system and also forming the third point of an equilateral triangle with the two masses. Hence for the Sun and Earth, there’s a point between Earth and Venus, another between Earth and Mars, another where Antichthon would be, and one each 60° ahead and behind on our orbit. They would presumably also shift their positions slightly as Earth moves around its elliptical orbit. For immediate transport, the most useful locations for the Earth-Sun system are L1 and L2, which are both 1.5 million kilometres from Earth. Venus approaches Earth to about forty million kilometres, and of course it will have its own L2 point with the Sun at around a million kilometres closer. There will also be an equilibrium point about halfway between the two planets due to their masses being roughly equal, at twenty million kilometres, and the cis and trans lunar L1 and L2, 61 350 kilometres either side of Cynthia. Hence there’s a kind of “ladder” between Earth and Venus, with the lunar L1 and L2, the Earth-Sun L1, the midpoint between Earth and Venus and Venus’s L2. The respective distances are:

• Earth to L1: 323 050 km.
• L1 to Cynthia: 61 350 km.
• Cynthia to L2: 61 350 km.
• Translunar L2 to Earth-Sun L1: 1 054 250 km.
• Earth-Sun L1 to Earth Venus equilibrium: approximately nineteen million km. This one will be slightly closer to Venus than Earth.
• Venus equilibrium to Venus-Sun L2: approximately nineteen million km.
• Venus-Sun L2 to Venus: approximately a million kilometres.

Hence there are seven rungs to this ladder, and yes there are issues with what happens when you get to Venus but I’ll go into those when this blog gets there! Each of these stages can be aimed at without using anywhere near as much fuel as would be required otherwise, partly because the spacecraft would be drawn towards them in any case. The difficult one is the equilibrium point, which is constantly circling the Sun and is influenced by its gravity too. A slingshot manoeuvre around Cynthia would accelerate the craft to some extent, but it’s hardly worth it as the escape velocity is lower than Earth’s so the speed would already have been moving that fast.

Mars is a more popular imaginary destination than Venus of course, and it too has a ladder of this kind. In its case, the Martian L1 is much closer to Mars but there are also the translunar and Earth-Sun L2s. The equilibrium point is also closer to Mars and since the gap between the orbits is larger, considerably further away. There would also be Lagrange points associated with the Martian moons but they wouldn’t be very useful as they’d be very close to the moons, but with the two moons rather than one, we start to get a hint of the complicated situation seen further out in the system. Venus has an almost perfectly circular orbit and Mars quite an elliptical one, to the extent that the seasons in the northern and southern hemispheres are very different and of different lengths, hence the larger southern ice cap. For the Lagrange points, this means they would move around quite a lot, and in doing so would move objects within them around too. All of these points would move by as much as 42 million kilometres over the 687-day Martian year, and that amounts to free travel, though only at 2600 kph, which isn’t significant over solar system scale distances although it is more than twice the speed of sound at sea level, and if you just care about getting there eventually rather than how long it takes you, it can help. This kind of “shuttle service” exists in equilibrium points between planets all over the Solar System, and technically there are eighty-seven of them overall, although not all are useful. They’re most concentrated in the inner system, where there are two dozen between the local planets and several more between them and the outer ones.

As well as all this, there are four planetary examples of L3 in the inner system, three of which move past Earth regularly and once again this is free travel, sometimes very fast. In Mercury’s case it can be almost 60 kps, and it would be possible to hop between them as well, carrying you closer to your destination with very little expenditure of energy. The question might arise in your mind of how this doesn’t violate the laws of thermodynamics, because it looks like a free lunch. The answer is that it isn’t because although there is a huge difference between the mass of a spacecraft and a planet, these activities do in fact ultimately add up to making minuscule differences to the planets’ orbits, but not significantly.

The equilateral points are often considered because they have features not often found elsewhere. There is a series of short stories called ‘Venus Equilateral’ written in the ’40s CE by George O. Smith about a radio relay station at the L4 point of the Venus-Sun system. Another well-known set of stories in this vein includes one by Asimov, all based on the same setting, where there are two stars of different spectral types (colours) occupying two points of the triangle and an Earth-like planet occupying the third. This gives it a day lasting two-thirds of its rotation period because it’s illuminated by both suns at a 60° angle to each other. In the real world, the most striking example of L4 and L5 are found in Jupiter’s orbit, where the Trojan asteroids are situated 60° ahead and behind Jupiter itself. This has led to the points themselves being referred to as “trojan”. For Jupiter there’s a “Greek” and a “Trojan” camp, although the actual names are mixed up between the two so that Greek characters from the Illiad are found in the Trojan camp and vice versa. The first of these to be discovered was Achilles, which is a dark red D-type asteroid, roughly spherical and around 133 kilometres in diameter. L4 is the leading point, and is referred to as the Greek camp because Achilles is there. There are more than six thousand asteroids here, the largest of which in either camp is Hektor, averaging at 225 kilometres across, which even has its own twelve kilometre wide moon called Skamandrios. Hektor is cylindrical and a lot longer than it is broad. The Trojan camp follows Jupiter at L5 and includes just over four thousand asteroids. Neptune also has Trojans, two of which are called Otrera and Clete. Twenty-two are known but of these only three are at the L5 location. They’re centaurs rather than asteroids, a category of object intermediate between asteroid and comet.

L5 was first introduced to me in 1976 when I heard about the Stanford Summer Torus Project (I may have got that name wrong). In the ’70s, a plan was devised to build a mile-wide wheel in space at the terrestrial-lunar L5 point which constituted a permanent space habitat. The July 1976 National Geographic includes a popularised version of the plan written by Asimov but the documents themselves made interesting reading. The general idea was to construct a six-spoked spinning wheel around 1 800 metres in diameter protected from radiation with a two metre layer of lunar regolith and have alternating agricultural and residential sectors with industrial processes and research carried out in the spokes, which constitute something like skyscrapers with lift shafts running along to the hub, which is a docking station and a low gravity environment. In the article this was envisaged as happening by 2026. Clearly it won’t be. Yet another space-related disappointment.

Another more serious omission is the possibility of building a solar power station at L5, which would solve all out energy and most of our climate problems at a stroke. I’ve mentioned orbital solar power elsewhere though, so I won’t be going into detail here. As it stands, these L4 and L5 locations are occupied by the Kordylewski Clouds, which are collections of dust. Their existence has been confirmed but there’s some confusion because when the Japanese lunar spacecraft Hiten flew through both as a form of gravitational assist, basically the same manoeuvre as I described for Venus, it didn’t detect an increase in dust concentration. However, it’s claimed that they can be visible to the naked eye, as they’re a dozen times the width of the Sun and slightly reddish compared to most other visible dust. There are a number of spacecraft situated at various Lagrange points.

The moons of Saturn, apparently unlike those of Jupiter, are sometimes in trojan relationships with each other. Tethys and Dione have a pair of them each: Telesto, Calypso, Helene and Polydeuces. However, Saturn is for another time on here, so for now I’ll leave it at that. However, the same kind of “rapid transit system” that I outlined in the inner Solar system would operate for the four complex satellite systems of the gas giants. Technically they would have a very large number of Lagrange points, but for most of the moons these would be unimportant because they are so small compared to their planets. For Jupiter’s four Galilean satellites, though, there are two dozen equilibrium points and twenty Lagrange points, and for Saturn’s seven roughly spherical moons, which excludes the rather large Hyperion, there would be over five thousand equilibrium points and thirty-five Lagrange points. This is more significant than it might appear, as by making the two regions around the planets more navigable, not only does it ease travel within those systems, but it also aids travel across them, particularly when one bears in mind that there will also be equilibrium points between the systems.

To conclude then, the Solar System is riven with locations which ease space travel, although sometimes they would mean that spacecraft traversing it would have to do so rather slowly. Another option is to hop onto an Earth grazer asteroid and hitch a lift to another part of the system, although again this could be rather slow. Some spacecraft have already taken advantage of the former approach, though not the latter, and it’s worth bearing in mind that when you look out into the system, there are many invisible but rather special points orbiting along with the visible planets and moons.

Vulcan And Vulcan

If you say “Vulcan” to most people nowadays in an Outer Space context, the chances are they’ll think of Spock, and that’s an entirely valid thing to do. However, if you were to say it to anyone with much knowledge of astronomy in the nineteenth century, it would’ve called something completely different to mind: a planet which orbits the Sun even more closely than Mercury. I’m going to cover both in this post.

Firstly, the ‘Star Trek’ Vulcan, whose Vulcan name is Ni’Var. This is reputed to orbit the star 40 Eridani A, a member of a trinary star system also known as ο² Eridani (Omicron-2 Eridani – that isn’t an “O”) sixteen and one quarter light years from here, and therefore also quite close to 82 Eridani, which is said to be one of the most suitable nearby stars for life, around which a possibly habitable planet orbits in real life. Of the stars, A is an orange dwarf, B a white dwarf and C a red dwarf which is also a flare star. Because B would previously have been a red giant and exploded, the chances are that any habitable planets orbiting A would have been sterilised by B’s outburst, and since C is a flare star, this is also unsuitable, although there would be nothing to stop an interstellar civilisation settling a planet in A’s habitable zone, which would of course be Vulcan.

As I’ve mentioned, I don’t pay much attention to either ‘Discovery’ or the new ‘Star Trek’ films, but I’m aware that Vulcan has been destroyed in revenge for the destruction of Romulus. I find this a bit annoying and I’m not sure what the point of it was plot-wise, but it doesn’t alter the in-universe fact that Vulcan was the homeworld of the first species to make open contact with humans when Zefram Cochrane first activated the warp drive. I’m also aware that that is inconsistent with the depiction of Cochrane in TOS. It is interesting, though, that any real planet in the habitable zone of 40 Eridani A would have been severely damaged by the 40 Eridani B supernova.

I understand Vulcan to have no moons, higher gravity than Earth and no surface oceans. I’m also aware that Romulans and Vulcans are the same species. It irritates me that they’re humanoid but also interests me that some of their anatomy and physiology is known, such as their copper-based respiratory pigment. Then again, although the in-universe explanation of widespread humanoid aliens is that we are all descended from humanoid ancestors who existed around the time our own Solar System formed, it’s also conceivable that convergent evolution would lead to similar body forms among sentient tool-using species. Back to Vulcan itself though. It has a thinner atmosphere than Earth’s, which I think justifies the copper-based blood pigment, and the sky and much of the surface is red. There are seas, i.e. large landlocked lakes, rather than oceans continuous with each other. Depending on the total surface coverage of bodies of water, I think this would probably make the planet uninhabitable for humans although clearly not for native life. 40 Eridani A is a K-type star, with a longer lifetime than the Sun’s in terms of being able to support a habitable planet, which, if orbiting at the distance necessary to receive the same quantity of light and head from its primary as we do from our Sun as a planet, would have a mean orbital radius of about 0.68 AU, i.e. sixty-eight percent of Earth’s distance from the Sun, and 223-day year. However, Vulcan is supposed to be hotter than Earth and might therefore be closer to its sun or have more greenhouse gases in its atmosphere, or it could just reflect less heat back into space, and in fact it probably would due to less ice on its surface. The difficult thing to account for with Vulcan is the combined higher gravity and thinner atmosphere, but there is another reason than gravity why a body might lose some of the gas surrounding it, which is consistent with what we “know” about Vulcan. Earth’s strong magnetic field is generated by our own large moon, Cynthia, which raises tides in our iron-nickel core and magnetises it like stroking a bar of iron with a magnet does, and that generates our magnetosphere, which traps ionising radiation from the solar wind which might otherwise reach Earth’s surface and strip away our atmosphere. Hence Vulcan, with no pre-existing satellites, would not have this benefit but would on the other hand still be able to hold on to some atmosphere because of its higher gravity, so maybe that is in fact realistic. Venus has no magnetic field but an extremely dense atmosphere, although not one hospitable to life at the solid surface, due to photolysis – the action of light on rocks releasing carbon dioxide gas. However, we’re basically aware that Vulcan’s atmosphere has enough oxygen to support human life without their own oxygen supply, and not enough carbon dioxide to poison us, which is 0.5% at our own atmospheric pressure. 170 millibars partial pressure of oxygen is required for this and CO₂ cannot be making a significant contribution to the pressure, so we can surmise that the rest of Vulcan’s atmosphere substantially consists of other gases. It isn’t pure oxygen. In fact, it’s quite likely to be nitrogen if Vulcan physiology is anything like ours and their bodies consist partly of protein, as the nitrogen has to come from somewhere, so I’m going to say the mean surface air pressure is about 0.25 bars. I’ve plucked this figure out of the air, so to speak. There probably is no such thing as sea level there because of the various lakes with different presumed depths and heights, so this would be defined as some kind of mean distance from the centre of the planet or a level at which gravitational pull is close to a particular standard. The boiling point of water on Vulcan is therefore about 60°C, but we know from McCoy’s mouth that Vulcan is very hot compared to Earth, so this puts an upper limit on its surface temperature unless it’s so hot at the equator that it causes water to evaporate.

40 Eridani A is orange. The sky is likely to be close to a complementary colour, such as teal, given that, but because of the dusty surface it’s entirely feasible that it would in fact be pinkish due to small particles high in the atmosphere. Also, the general ruddiness of the planet as shown on screen gives the impression of heat and dryness, so artistically that does seem to be a good decision. The same features make some people think of Mars as a hot planet when in fact it’s often colder than Antarctica. Regarding sparse water cover, a thin atmosphere might make sense here too, particularly if water is regularly evaporating from the surface at the equator, since some might then be lost into space.

Vulcan would also lack plate tectonics if it’s like this, since that’s fuelled by water. The planet has no continents as such, but it does have active volcanoes and lava fields, which is to some extent to be expected as it corresponds to the “hot spot” situation in the centre of the Pacific plate on Earth, where magma seems to need to vent. Here, this results in Hawaiʻi, but on Vulcan a mountain range could be expected because there are no oceans. There would be nothing like the Pacific Ring Of Fire, and also no fold mountains because those are caused by the collision of continental plates.

Vulcan’s colour is depicted differently in different manifestations of the series. In TOS and Enterprise, it’s red. In TAS it’s yellower, and in TNG brownish. However, on Mars there is variation in colour from space due to a dust storm season, and this can be imagined on Vulcan too. Maybe one way to think of Vulcan is as a larger, hotter version of Mars.

The real 40 Eridani A does have a planet. This is, as usual, called “b”, and orbits much closer to the star than the inner edge of the habitable zone. It has a roughly circular orbit 0.22 AU from the star and a mass estimated at 8.5 times Earth’s (both those figures are rounded off). At Earth’s density, this would give it a diameter of around 25 000 kilometres, which is a type of planet unknown in our own solar system at any distance from us, and it’s classed as a “Super-Earth”, but it has a period of 43 days and would be like Mercury on its surface during the day, if it rotates at all. It’s also the closest known Super-Earth. Its orbit differs considerably from Mercury’s, which will become relevant later in this post, in being much less elliptical, which to me, in my probable naïveté, suggests there are no planets larger than it in at least the inner solar system.

This brings me to the other Vulcan. In the nineteenth Christian century, the French astronomer Urbain Le Verrier came up with a particularly accurate model of planetary motion within the Solar System. It had been noted that the most recently discovered planet, Uranus, tended to drift slightly behind and ahead of its predicted position given its distance from the Sun and shape of its orbit. From this, Le Verrier calculated mathematically that there was likely to be another planet further out pulling at it, and predicted its position, which turned out to be correct. In fact he almost had it named after him, but they eventually decided to call it Neptune. This established his reputation and consequently, when he turned his attention to the orbit of Mercury, people paid attention and took his views seriously.

Mercury’s orbit is quite unusual compared to the other planets, particularly if you ignore the period of time when Pluto was regarded as one. It’s the most eccentric orbit by a long way compared to the others, with a variation in distance from the Sun of around twenty percent. Le Verrier also noted that the movement of the “points” of the orbit precessed around the Sun much faster even when compared to its year of eighty-eight days than those of other planets. Just as he had with Neptune, Le Verrier proposed that there was either an as-yet undiscovered planet even closer to the Sun or a number of smaller bodies like asteroids within the orbit of Mercury, and since it would’ve been so close and so hot, he called it Vulcan after the Roman god of fire, Vulcanus. The planet’s existence could be confirmed in two ways. Either it could be detected in transit, as most planets are detected at the moment, or it could possibly be glimpsed during a total solar eclipse. A number of astronomers then reported that they had indeed seen this planet transiting the Sun. For instance, Edmond Lescarbault, a doctor, described a tiny black spot moving across the Sun faster than a sunspot, moving with the rotation of the Sun, would, and also lacking a sunspot’s penumbra. The observations even seemed to confirm Le Verrier’s prediction of Vulcan’s size and orbit. However, it was difficult to predict when these transits would occur because that depended on the tilt of Vulcan’s orbit compared to ours. Mercury, for example, can only be seen to transit the Sun in May or November because only then is the tilt of both its and our orbits aligned such that it can get between us and the Sun. The observations did seem to occur fairly randomly, but at first glance Mercury’s do as well, if you didn’t know anything about its movements already.

There was a total eclipse of the Sun in 1883, shortly after Le Verrier’s death in 1877, during which Vulcan was not observed. It was still possible that the planet was either behind or transiting the Sun at the time, but six further such observations, the last in 1908, also failed to turn it up, making it increasingly improbable that the planet existed. However since that time astronomers have claimed that close ups of the Sun’s surface do sometimes show small black dots which are not sunspots, although these may be imperfections of photographic plates, and there are asteroids which approach the Sun more closely than Mercury does, such as Icarus. It strikes me that it’s not only possible but probable that there are asteroids which orbit entirely within the orbit of Mercury, although they would have to be very small and would be difficult to observe or confirm. These are known as Vulcanoids, and would have to be between six kilometres and a couple of hundred metres in diameter. Every region of the Solar System which is not severely perturbed by the gravity of known objects has been found to contain objects like asteroids or comets, so if the innermost region of the system doesn’t have any this must be due to a non-gravitational effect. It is in fact possible that the light from the Sun is so strong at that distance that it would push smaller bodies away from it over a long period of time, so this may be the explanation. This might sound far-fetched, but it’s been proposed that this effect could be used to divert asteroids which would otherwise crash into Earth by painting them white in order that the pressure of light from the Sun would change their orbits, and this is also the principle used in a solar sail. The MESSENGER probe took photographs of the region but this was limited because damage from sunlight needed to be avoided. Much closer in than Mercury, asteroids are likely to vaporise of course.

Vulcan was considered to orbit 26 million kilometres from the Sun, giving it a sidereal period (“year”) of twenty-six days. At another point, observations appeared to show it had a year of 38.5 days. I think it was also supposed to be very small but I can’t track this down: possibly about a thirtieth the mass of Mercury, which with the same density would’ve given it a diameter of around 1 600 kilometres, probably meaning that if it had been found to exist it would’ve been demoted from planethood by now in the same way as Pluto was. In fact, if it did exist, it would indeed have perturbed the orbit of Mercury but the other factors which turned out to be the explanation for this phenomenon would still be in play, meaning that there would’ve been an even greater anomaly unless the planet happened to be exactly the right mass and in exactly the right place, and possibly retrograde. Some kind of pointless immense astroengineering project could probably achieve that to some extent, but why? Possibly to prevent us from being aware of relativity?

The fact is that the planets don’t simply orbit the Sun alone without influencing one another and the Sun. This is the famous three-body problem, that it’s impossible to work out in almost all cases how three bodies would orbit each other, and even more so the much larger number of massive bodies in the Solar System. It’s possible to work out how much gravitational influence the planets would have on each other if they were the only two bodies in the Universe though, and if initial conditions are known. For instance, Venus and Earth approach each other to within fifty million kilometres and have roughly the same mass, so left to themselves they would orbit each other at roughly twenty-five million kilometres from their centre of gravity once in forty-five millennia if I’ve calculated that correctly, and at the closest approach, which would be during a transit of Venus, that’s the gravitational pull we’re exerting on each other – about forty-five thousand times less than the Sun’s. Mercury is the least massive planet, being just over half the mass of Mars, the next smallest. Pluto is of course far lower in mass, and if Cynthia is considered a planet in its own right, that would be considerably less massive. Anyway, this means that Mercury is pulled around a lot by the other planets. Venus approaches it to within about 38 million kilometres but without doing the maths it isn’t clear if that’s the biggest gravitational influence because of Jupiter being so much more massive than the other planets, even though it’s far further away. Jupiter is over three hundred times the mass of Earth but would get within 4.8 AU of Mercury, which actually gives it roughly the same influence as Venus. But this is not the only reason Mercury’s orbit precesses as much as it does.

Albert Einstein listed a number of ways to test his theory of general relativity, one of which was the orbit of Mercury. The pull of the other planets is insufficient to explain precession in Newtonian terms. There’s still a bit left over if you try to do this. It’s at least seven percent larger than it “should” be. The explanation for this was instrumental in getting general relativity accepted. Einstein made three suggestions about how general relativity could be corroborated. One was that light would be red shifted if it passed through a gravity well. Remarkably, although it took something like four decades, the observation of 40 Eridani B eventually showed that this was so, I’m guessing because of the other stars in its system. Gravity stretches light because it distorts space. The second proposition was that stars observed near the Sun during a total solar eclipse (Again! They’re useful things) would appear to be in a different position because their light would be bent by the solar gravity, and this was indeed found to be so a few years later. However, the world had to wait for these two findings. The other one was that Mercury’s orbit would precess at the rate it did having taken into account the perturbations of all the other planets, and again this was found to be so, but in this case it was already known that this happened because Le Verrier had observed it in the previous century and the existence of Vulcan had been refuted. The reason this happens, I have to admit, I don’t really understand, but I can provide a kind of visual model of it which could show this.

The Rubber Sheet Theory is a model of space as if it’s two dimensional left to itself with weights representing stars and planets which, if placed on such a sheet would create dents in it. Obviously this is not an adequate explanation as such of general relativity for several reasons, one of which is that it uses gravity to explain gravity – that’s what’s pulling down the weights. It also makes space appear to be a substance, something which physicists had worked heavily against when they disproved the existence of the luminiferous æther, which since it was supposed to be extremely rigid wouldn’t work in this situation anyway. It shouldn’t be mistaken for Einstein’s theory itself, but it is a useful way of looking at it. In any case, if you imagine the kind of dent which shows up in the title sequence of Disney’s ‘The Black Hole’:

. . . which is like one of those charity coin collection things, space around the Sun is distorted to a limited extent like that, and attempting to do a “wall of death”-style orbit around it, which would in any case be elliptical rather than perfectly circular because the Universe is imperfect like that, would lead to your bike describing a series of ellipses which were not perfectly congruent with each other but were more like a spirograph pattern. Having written that paragraph with its references to a number of very ’70s things makes me wonder if it’s going to make any sense to someone born after Generation X.

Now I can see that this does happen, but I am also puzzled by it. Whereas I’m sure that I couldn’t aim a coin at one of those charity collection things in such a way that it would just circle around at the same level until friction interfered, and that at best if I could make it describe an elliptical path for a few revolutions, the bits of the ellipse furthest from and closest to the hole would precess, I would put that down to the fact that I, and anyone else to a lesser extent, can’t aim perfectly rather than simply due to the geometry of the hole. Nevertheless, this appears to be what I’m being asked to believe with this: that it isn’t only one’s inability to aim perfectly, or for that matter the friction the coin (or ball bearing – let’s take the instability of the coin out of the picture), that leads to this precession. But apparently not. Apparently, if you were to have too much time on your hands and designed some kind of precision ball bearing throwing machine for charity coin collectors, and it wouldn’t be popular because they want coins, not ball bearings, it would do the wobble thing even if it stayed circular enough not to fall down the hole immediately, and it would wobble more the closer it was to the whole. So they say, and this is what got general relativity accepted.

There have been other Vulcans. For instance, one of the many hypothetical planets in Western astrology is the intramercurial Vulcan, seen as the soul ruler of Taurus and orbiting once every twenty days. This Vulcan would go retrograde more often than Mercury. It’s fiery and urges the individual to look for non-physical knowledge, which makes sense given its history in astronomy. It was also suggested in a poll as the name of one of the moons of Pluto, and actually won the most votes but that was then named Kerberos after the Hadean dog, which was the runner up. Vulcan actually doesn’t seem like a very good name for a moon of an icy planet way out in the outer reaches of the Solar System, but I don’t know the reasons it wasn’t used. Maybe the IAU just didn’t want to be reminded of what they might regard as an embarrassing phase in the recent history of their science. In the Second Doctor story ‘The Power Of The Daleks’, there’s a planet called Vulcan which is settled by humans and highly volcanic with pools of fuming mercury on its surface. Doesn’t sound very nice at all really. There does not, however, seem to be an asteroid named Vulcan, which is quite surprising.

I’ve sometimes wondered if there’s a story behind the naming of the ‘Star Trek’ Vulcan and if it’s in any way connected to the hypothetical planet, but I don’t know. How about you?

Super-Habitability

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Yesterday I mentioned in passing the concept of super-habitability. I’m happy to say that ‘Handbook For Space Pioneers‘ introduced this concept, although it may have passed unnoticed. In this book, which describes the eight habitable planets available for human settlement in 2376 CETC (Common Era Terrestrial Calendar), the final planet, Athena, 77.6 light years from Earth in the HR 7345 system, is actually more habitable than Earth. The book rates the different planets according to their habitability using the ‘Von Roenstadt Habitability Factor’, with the least habitable, Mammon, having one of 0.79. This is a largely desert planet with a thin atmosphere which was largely settled due to its rare earth metals, which are useful in matter-antimatter reactors. Earth has a factor of 1.0, and Athena one of 1.09. This is because Athena is not only similar to Earth but lacks a polar continent, meaning that more of its land is hospitable to human settlement. Therefore it was this book that came up with the idea. Ahead of its time.

The search for exoplanets tends to be biassed in various ways as I’ve previously mentioned. One of these is that the ideal planet to be detected would be a super-Jupiter orbiting very close to its rather dim star, orbiting parallel to the line of sight. This is indeed a very common type of planet to be found but not at all Earth-like. It also gets a bit depressing after a while because the planets concerned may make their systems unsuitable for more hospitable planets further out. This situation has been somewhat remedied more recently and many somewhat Earth-like planets have now been found.

However, it’s been suggested that we may be setting the bar too low here. I mentioned the Copernican principle yesterday, also known as the principle of mediocrity, that it’s often informative to look at the world with the assumption that there’s nothing special about us as a species, and perhaps more closely, apply the same principle to ourselves as individuals (e.g. “accidents always happen to someone else until they happen to you” – this is not some kind of exaggerated humility and self-effacement). When we look for Earth-like planets, we are in a sense only looking for worlds which are good enough, and also good enough for humans, as opposed to worlds which are fantastic. That is, Earth is all very well, and yes it is precious and rare and all the other stuff, but there could in principle be worlds which are even more hospitable to life than this one. Super-habitable planets, in other words.

I feel a sense of hesitancy here because it’s like insulting my own mother, but the fact is that this planet may be particularly suitable for humans, but it could have, and has been in the past, more comfortable for life than it was when we first evolved as anatomically modern humans. At that point, it was plagued by regular ice ages, had larger deserts and had little in the way of continental shelves, meaning that fishing, for example, would’ve been very difficult without boats in most places. Not that I care, as a vegan, but there is a theory that I accept that we went through an amphibious phase when we depended on sea food, which could be relevant to the development of the our brains and ability to speak. Even now there are issues with this planet regardless of the influence of humans on it. Looking beyond humanity confronts us with the fact that although this planet is really quite a nice place to live, it may not be ideal for other life. There are two aspects to this as well. One is “life as we know it”. That is, life which breathes oxygen, drinks water, uses sunlight to synthesise food, is carbon-based and depends on biochemistry, which may not be the only kind of life. We don’t know that there cannot be other forms of life which are very different, to which Earth would seem a very hostile place. For instance, it’s easy to imagine aliens detecting the high level of corrosive and hyper-reactive free oxygen in our atmosphere and concluding that this is not the best abode for life because they have simply never encountered body chemistry which actually requires that. They might feel the same way about this place as we would about a planet whose atmosphere was high in elemental fluorine or chlorine and had seas of aquæous hydrofluoric or hydrochloric acid. Or, if there were life forms based on plasma, and I strongly suspect this can happen, they might wish to avoid anywhere with even a trace of liquid water in its atmosphere or on its surface and only survive in the very driest deserts here. But the current popular conception of superhabitability is to be biocentric in the sense of looking for the ideal conditions for life to begin, develop and thrive on it. Perhaps surprisingly, Earth is not currently ideal for this, and it isn’t even entirely due to human technological development. Moreover, Earth has been more habitable in the past that it currently is.

Seventy-one percent of Earth’s surface is underwater, and of that most of it is so deeply so that no daylight ever reaches the ocean bed. This doesn’t rule life out at all of course – there is life in the deepest part of the ocean – but it does reduce the energy available and there is less diversity down there than elsewhere. It relies on food raining down from further up, sometimes including dead whales, which provide a huge amount of nutrition for quite some time. The water column above the beds is also rich in life, getting richer the closer to the surface it gets, and there are of course ecosystems around hot water vents at the bottom of the ocean. However, the euphotic zone, where there’s enough light for photosynthesis to take place, is only two hundred metres deep, and that’s where the ocean teems with life. Shallow seas are much richer in life and more diverse for that reason. Hence, withough being disrespectful of the ecosystems of the trenches, abysses and abyssal plains, more than half of the surface of this planet could be said to be “wasted”. Two ways in which things could be different here are for the seas to be shallower. The shallow sea biome is quite rare nowadays on Earth, but in the past has been much more extensive, and would mean that plants could grow on the bottom of the sea and support many other organisms. The same could apply to another possible situation, where the Sun was either brighter or we were closer to it, meaning that although there might still be extensive abyssal plains, the light would penetrate further down. Alternatively, photosynthesis, which currently operates using red light, could possibly be based on shorter wavelengths which penetrate further. A planet with a red photosynthetic pigment, for example, might have seaweed growing deeper. It’s possible that chlorophyll only appeared on this planet because a preceding purple pigment used by another taxon of organisms meant that only red light was available to plants, and if that second stage hadn’t happened, “plants” would now mainly be purple.

Stars are also different colours. From the viewpoint of photosynthesis, this could also have implications for the colour of the pigments. Habitable planets were long thought only to be possible for worlds associated with F-, G- or K-type stars but it’s now thought that red dwarfs may be more suitable (for a summary of spectral types, look here). K-type stars last longer on the Main Sequence and are orange, so I presume a planet orbiting one would be in a constant “rosy-fingered dawn” situation, though much brighter, but this gives life longer to evolve than it does here. Our own planet will be able to support microörganisms for up to 2 800 million years in the future, but these will to some extent resemble the æons when only microbes existed here. Large multicellular life is likely to become extinct only about 800 million years hence when there won’t be enough carbon dioxide in the atmosphere to support photosynthesis, which will happen due to the increasing brightness of the Sun. This is also driven by plate tectonics, as carbonate rocks are forced from the sea bed into the mantle where they react and release carbon dioxide while forming silicates. This means that a fainter, more long-lived star or more active continental drift would make this planet more hospitable to life for longer.

A larger planet would often have a number of advantages for life. Here I’m talking about rocky planets rather than gas giants. This is where the biocentric approach becomes more evident. The definition of a “superhabitable” planet here is to do with how suitable it would be for life of the kind we’re currently familiar with rather than humans, because large, dense planets would have higher gravity than Earth. LHS 1140b, for example, may be superhabitable, but not for us. It’s seven times the mass of Earth and 40% larger in diameter, giving it a surface gravity more than three times ours. This is beyond the capacity of human beings to survive unaided without some form of modification, but its dense atmosphere may provide it with a greenhouse effect which heats it to a temperature compatible with life as found here. Larger rocky planets will take longer to cool, meaning that there will be more active plate tectonics and more carbon dioxide recycling, although there may be a limit here because higher gravity would slow it beyond a certain point due to the weight of the continental plates. Larger planets, particularly fast-rotating ones, would have stronger magnetic fields and therefore be more easily able to hang on to their atmospheres and protect the surface from ionising radiation.

When Earth has been warmer, there has been more biodiversity, although just to comment on anthropogenic climate change that doesn’t work out now because it’s a rapid change and also unstable. Evolution might eventually fill in the gaps of course. This planet has a tendency to edge into colder conditions rather than hotter ones, for instance the current spate of ice ages and the Snowball Earth scenario in the late Cryptozoic Eon, but most of the time it’s been hotter on average than it is today. Consequently we’d’ve done better if we were somewhat closer to the Sun, although it’s not clear how much, at least to me. Another circumstance where there’s been more diodiversity and larger animals has been when oxygen was higher in the atmosphere, although this has a limit above which there would be devastating fires and other oxidative damage. The highest partial pressure of oxygen ever on this planet has been 350 millibars, amounting to 35% of the atmosphere, but in a denser atmosphere this proportion would be smaller because the absolute quantity of oxygen is what matters, not the proportion.

The final helpful criterion is a combination of about the same water cover combined with a larger number of landmasses. Earth currently has six continents, one of which is circumpolar. At other times it’s had as few as one. I’m not sure why this is considered advantageous but I can make a few guesses. It would mean that evolution would take place in isolation on each of the continents, as it has here with Australia, South America and the rest of the non-polar continents taken together, and that arid areas would tend to be smaller, although rain shadow deserts would still exist. Those, however, would be less common as well because there would be fewer mountain ranges due to fewer continents crashing together. There would also be more land near the coast than there currently is here, and more shallow sea areas on continental shelves. I’m reminded of Douglas Adams and his description of Ursa Minor Beta as consisting largely of beaches.

Some of these characteristics are impossible to detect with existing technology. For instance, although I think there is a way of finding continents and mapping them crudely by measuring fluctuations in brightness and colour, only a very few planets have even been imaged as points of light so far and they’re much larger than Earth. There’s probably a way of coördinating and processing telescope images taken in different parts of the Solar System to simulate the effect of an enormously magnifying lens, but I’m just guessing there. Nonetheless, there are certain known planets which do appear to satisfy some of these conditions. One is Kepler-442b. Incidentally, many of these planets have rather boring, monotonous names at present because they were all found by the same project. This planet, also known as KOI-4742.01 orbits its K-type sun at a distance of 61 200 000 kilometres once every 112.3 days, has a mass 2.3 times Earth’s and a diameter of around 17 100 kilometres. This gives it a surface gravity twenty-eight percent higher than ours, which is just about bearable. Without other factors being involved, its surface temperature would be about -40, but it could easily be warmer due to the Greenhouse Effect, low albedo and so forth. This last factor is of course the way in which it isn’t super-habitable, if it’s so.

It’s possible that there are more super-habitable planets than strictly Earth-like ones because there are more orange dwarfs than yellow dwarfs. Nine percent of stars in the Galaxy are of this kind as opposed to seven percent of the Sun’s spectral type, and several of the criteria simply follow from a planet being more massive than Earth. For instance, higher gravity could make the oceans shallower and give the planets more tectonic activity, and as a personal interjection continents on larger planets have more chance of being widely separated and having different evolutionary histories. A planet 1.4 times the diameter of the Earth whose surface is 29% covered in land, i.e. proportionately the same as Earth’s at the moment, has almost twice as much land, which if the average continent size were the same would be represented by a dozen continents. Likewise, we currently have five oceans here but there could be more there, although oceans are not well-defined and in a sense there is only one ocean. Planets with more than fifty percent land coverage could have landlocked oceans, and even worlds with less land due to quirks of geography, but this won’t apply to planets of this kind.

What might such a planet be like? Here I’m going to choose an example which satisfies all the criteria. There will be many others, if they exist at all that is. The average temperature would be somewhat higher than Earth’s and there would be no permanent ice caps at the poles, although snow-covered mountains and glaciers could easily exist. The climate would be warm and humid, with more cloud cover than Earth. Tropical rain forest vegetation would cover much of the land and there would be smaller desert areas. The oceans would be shallower and there would be copious vegetation on the sea beds. Atmospheric oxygen content would be higher in absolute terms but lower in terms of percentage than Earth’s. The denser atmosphere would mean stronger winds and more devastating rotary storms such as tornados and hurricanes. Also, these planets are likely to be more similar to each other than strictly Earth-like planets would be. The general picture is a little similar to the way Earth was at the climax of the age of dinosaurs or during the Carboniferous, although the higher gravity would limit the size of terrestrial megafauna.

These larger planets have a kind of momentum to them, which allows them to continue with fairly stable climatic conditions for many æons. By contrast, Earth-like planets run the risk of becoming permanently ice-covered, tipping into runaway Greenhouse effects and ending up like Venus, losing much of their atmospheres or relying more on large moons to maintain their magnetic fields, and therefore perhaps the ones that don’t have them or something else to raise internal tides only have thin atmospheres and no land life.

However, this does raise another question in my mind. As far as we know, we are the first technological civilisation to arise on this planet, although there’s tantalising evidence that there may have been advanced industrial processes here during the Eocene, maybe not from terrestrial species. If that’s so, it means that the periods of time during which Earth was more hospitable to life than it is today didn’t give rise to tool-using species. Therefore, is it possible that a more hospitable habitat is like the Swiss with their cuckoo clocks? Would stability end up providing little challenge to species and prevent it from evolving humanoid intelligence? Are these planets too comfortable? And there’s another question. Although these planets seem stable, they would be nearer a set of limits for biological habitability. Our planet has issues, but maybe that’s a sign of it being able to endure change. If something happened to one of these planets, like a large asteroid impact or a change in the luminosity of the sun, would this proce too much for life to handle? For instance, on this planet the life could be replenished by that surrounding undersea vents even if it died elsewhere, but I’m not sure whether there’d be many extremophiles – organisms who prefer hostile conditions – on such a world. Also, these planets are superhabitable by the needs of life as we know it in general, but not by human standards. We’d do okay, probably, on a planet which was somewhat larger and warmer than Earth although we’d have to be wary of the storms, but these super-habitable worlds wouldn’t be pleasant places to live for us. There’s a potential second set of hypothetical planets which are super-habitable for us, for instance with the Galactic Association example of Athena, a planet with no polar continent. Some of the characteristics would be similar, such as smaller but more numerous continents, but the set of criteria is not the same.

Taking this the other way is even more speculative because we’re only aware of one example of how life can arise and evolve, which is based on chemistry, organic matter, water and to a lesser extent oxygen for respiration. If there are other ways for life to exist, there could be whole other sets of “habitable” environments – I hesitate to say “planets” here because for all I know this would be happening on the surfaces of neutron stars, in nebulæ or the photospheres of “ordinary” stars. This is rather more difficult to discuss, but if life can exist in different ways it would seem to multiply the probability of life in the Universe, and also of the types of world which could support it. But I can only really leave this as a possibility thus far, or at least without making this post really long.

To conclude then, all this looks rather cheerful as regards the possibility of life as we know it in the Universe, but it also kind of pushes us Earthlings into a corner, as if all of this is true, we’re quite atypical of life in the Universe and our planet’s a bit weird. So who knows?

The Expanding Earth Theory

Some time ago, I had a Peters Projection map of the world from ‘New Internationalist’ magazine. The idea behind the Gall-Peters Projection (it wasn’t originally Peters) is that it’s supposed to show all the land in correct proportion as to its size, which I presume it does, but the problem is that it doesn’t preserve compass direction and considerably distorts the shapes. As far as I can work out, it’s a cylindrical projection that differs from Mercator by progressively reducing the north-south lengths to zero as they approach the poles. There is a lot to be written about this map projection in particular and political correctness, but not here.

No, where I’m going with this is the reaction one of my friends had to the maps of continental drift in the book. There were a couple of pages showing the evolution of this planet’s appearance from the supercontinent Pangæa in the late Permian to its current appearance. Pangæa looked roughly like this:

There are certain issues with this map, such as the fact that Antarctica is ice-covered in it, which it wasn’t at the time, but it succeeds in roughly illustrating the supercontinent and the condition of the surrounding tectonic plates at that time. Again, Pangæa and the general idea of supercontinents is interesting but still not quite what I’m going to talk about today.

My friend made a rather disparaging comment regarding the map of Pangæa along the lines of it just being guesswork and “how the hell could they know this is what happened?” I explained to him about the continents fitting together, the presence of symmetrical bands of magnetic minerals on the floor of the Atlantic, the continuation of coal seams across continents which match the jigsaw and the presence of fossils of the same species in widely separated parts of the world. Incidentally, today I might add that Earth’s interior has now been found to be cooling faster on one side than the other, indicating that something large was blocking the heat for a long time in the distant past, and this is thought to be the above supercontinent. His response, after I’d said all this, was “yeah, but how the hell could they know this is what happened?”! It was like I hadn’t said anything!

To some extent, I think his attitude is a healthy one, and I presume it was based in distrust for authority of any kind. He’s an intelligent, well-educated guy and I’m not disparaging him for his opinion. It’s just that I feel that it illustrates something which I doubtless also do, where I reject counter-intuitive and novel ideas, sometimes just because they’re new. It’s a widespread phenomenon for people to receive a new idea, perhaps not listen very closely to the evidence cited in support of it and proceed to pick holes in it and reject it out of hand. This is all the more so when immediate observation seems to contradict it, as can be seen today with Flat Earthers. They have an approach they describe as “Zetetic Cosmology”, which is the idea that one should always depend on what can be directly observed oneself, and in many ways this is commendable, and like my friend involves distrust of authority, which is again to be encouraged. However, there comes a point when one either has to trust experts in a field other than one’s own or find an example of something which would prove one’s assumption wrong if it turned out to be true when tested. In the case of the Flat Earth, my answer is to use railway timetables in distant parts of the world and online traffic cams to observe daylight, because in both cases these being fake would involve a ridiculously vast conspiracy, lots of people missing important appointments and a whole load of RTCs. Other examples of this would include the idea that the Apollo missions were a hoax and the various Covid-19 conspiracy theories.

At the same time, it’s uncomfortable to have one’s world view challenged on the other side. I don’t know how far back my acceptance of continental drift goes, but I remember mentioning a piece of evidence for it in school in 1976, which is currently forty-five years ago when I was nine, so it’s one of those things which forms a kind of cherished part of the jigsaw I use to make sense of life, and it’s disturbing to have that questioned. Consequently, although I’m aware of lots of evidence supporting it, I probably use that evidence more as a comfort blanket to confirm that my beliefs about the world are correct rather than actually enquiring into it in any great depth. That does also mean I trust experts in this area. But there’s a psychological urge to force people into believing what I believe which is more about competition and perhaps aggression than altruism, and that’s not a good motive.

Alfred Wegener was an early proponent of the theory of continental drift. He noted that South America and Afrika seemed to fit into each other neatly, with Brazil jutting out in a shape very close to how the Gulf of Guinea “juts in”, and the Great Australian Bight matching the coastline of Victoria Land in Antarctica. He thought of this in around 1911.

Prior to this, and in fact for many decades after, the prevailing wisdom was that land bridges rose and sank between the different continents, causing flora and fauna to mix, which is for example why the continent of Lemuria in the Indian Ocean was posited. There are prosimians (non-simian primates such as tarsiers and bush babies) in Madagascar, continental Afrika and Indonesia, so how did they get to be in such widely separated places? The answer was supposed to be Lemuria, named after lemurs. Oddly, although this idea has now been discarded, there was in fact formerly a fairly large landmass in the Indian Ocean and in a few million years time there will be again, when the Afrikan Rift Valley opens up and East Afrika splits off. The descriptions of changes in geography in Olaf Stapledon’s ‘Last And First Men’ also relate land bridges rising and falling, as was generally believed in the 1930s. I even have a book from the late 1940s with a map of them as they were supposed to be in the Mesozoic, shown above.

Land bridges don’t really work though, because they violate the principle that crustal rocks generally float at the same level above the mantle depending on its depth and density. For land bridges to appear and disappear in that way, their density or thickness would have to change.

The problem with continental drift was that there didn’t seem to be a mechanism for them to move around. Wegener proposed something called Polflucht – “pole flight”. His idea was that the centrifugal effect of Earth’s rotation pulls the land masses away from the poles and causes them to break apart as they approach the equator. If this idea worked, it would make sense to a certain extent because we’re in a situation where the Tethys, an ocean which used to stretch all the way round the equator, has now closed due to the collision of Afrika and Eurasia and the formation of the Isthmus of Panama, and Australia has also moved north from its prior connection with Antarctica. The problem is, however, that the crust is far too sturdy to allow this to happen. It’s also interesting that Wegener, who was mainly an expert on polar geology, would focus on this aspect of the planet to explain.

At this time, as far as I can tell, there wasn’t any idea of a supercontinent cycle, where continents collide together and are broken up, only to join together again in a different configuration hundreds of millions of years later. The reason I say this is that the explanation which was proposed after this was rejected seems to suppose that Pangæa was the one and only original supercontinent which then broke up and the continents formed then drifted into their current positions. The idea proposed was of course the Expanding Earth Theory:

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The idea here is that all the land was joined together when Earth was first formed, and this planet was considerably smaller back then. Then Earth expanded and the single landmass cracked apart, creating today’s world map. There were various hypotheses about how this might have happened, one of which I find a lot more interesting than the others. One is that Earth started off as the rocky core of a gas giant like Jupiter and was therefore compressed and under a lot of pressure. The Sun gradually boiled off the atmosphere and as the pressure reduced, the planet “sprang out” and expanded due to its release. Another theory is based on the idea of the luminiferous æther, which in itself probably could do with an explanation. It used to be thought that just as sound or waves in water need a medium to carry them, so did light, radio waves and the like, and this was referred to as the æther. Although this idea is not completely dead for complicated reasons which slip my mind right now, the æther’s existence was refuted by the Michelson-Morley experiment, which showed that light travels at the same speed whether or not it’s moving in the direction of our planet’s orbit or at right angles to it, meaning that there was no static medium carrying it and ultimately ushering in Einsteins theory of relativity. Incidentally this experiment is also used by Flat Earthers to “prove” that Earth does not orbit the Sun or rotate. Isaac Newton believed that gravity was caused by a condensation of the æther combined with its rarefaction, which was eventually applied to the idea of the atmosphere doing the same thing, thereby providing the basic theory for powered heavier-than-air flight by explaining lift. Æther was later demonstrated to be necessarily incompressible and it was thought that matter was a sink in this æther, an idea which was clearly on its way to becoming Einsteins theory of general relativity and in fact something I used to believe myself up until I was about thirteen. This was then elaborated by Ivan Yarkovsky into the suggestion that Earth gradually accumulated matter from the transmutation of the æther into atomic matter and therfore slowly expanded.

Those are the less interesting explanations. The one which I feel drawn to, although it isn’t true, is Dirac’s. Paul Dirac was one of the most important physicists of the last century and is extremely respected. He proposed that the gravitational constant was slowly decreasing, causing the planet to expand gradually. Once again this explains continental drift, and seems to develop fairly naturally out of Newton’s and Yarkovsky’s theories of gravitation, but it also does something else which is very interesting. It amounts to an explanation for the expansion of space, and therefore is quite economical and elegant in its explanatory power. It isn’t just about Earth but the whole cosmos.

There is an odd parallel between the Expanding Earth Theory and theories of the evolution of the Universe. Over the past century there have basically been four of these. One of the best supported is now refuted, which is the Steady State Theory. This is the idea that space is infinite and constantly expanding, with matter being generated slowly within it, so that at any one time the visible part of the Universe looks roughly the same. In this view, there was no beginning to the Universe and it will always exist. The established and widely accepted theory today is more or less the Big Bang Theory, which is that the Universe expanded out from a single point around 13 800 million years ago and will continue to expand forever. I have my issues with this but I won’t mention them today. If there was only slightly more mass than there in fact seems to be in the Universe, it would also end up collapsing into a similar state to the early Universe in the distant future. Finally, there is the “oscillating Universe”. This involves an endless series of collapses and expansions, and raises the philosophical question of whether time is cyclical or each instance of the Universe is a new one. Although the Big Bang Theory is the only really acceptable one among scientists at the moment, there is also a theory that the Big Bang was preceded by a collapsing Universe made of antimatter when time was running backwards, which sounds pretty similar to the oscillating Universe to me.

Just as there was an oscillating Universe theory, later discredited, there was also an oscillating Earth theory. This involved the planet going through alternating phases of expansion and contraction which explained the phenomena on this planet which look like they’re caused by contraction. I imagine this includes mountain ranges but that’s just my guess. I find it interesting that there were two cyclical expansion-contraction theories about the world, one involving Earth and the other the Universe.

It is of course very appealing that there should be a single explanation combining continental drift and the Big Bang Theory based on weakening gravity. I don’t know if this has ever been done, but it also strikes me as a good explanation for the fact that fossils of extinct life forms tend to be much bigger than the life forms around today, such as dinosaurs and giant insects. Maybe this is because the fossils themselves have expanded over time and back in the day, the animals and plants who became them were of relatively modest size. However, this is not so because the Expanding Earth Theory is refuted, and in science you have to be brutal about your emotional attachments. Dirac’s idea is absolutely lovely, but it’s also dead wrong.

I mentioned train timetables earlier as a way to refute the Flat Earth hypothesis. This works because a sphere cannot be mapped onto a flat surface without distortion, as illustrated by Peters Projection. This means that two distant train routes of the same length would in some cases be distorted on a map. The Flat Earth is effectively a map of the real Earth, because it’s a curved surface forced into a flattened shape. This means that somewhere on this flat Earth, notably in Canada and Australia according to the main idea Flat Earthers have Earth’s shape, it ought to take a lot longer to go the distance the route is supposed to cover than it actually does. Now it could simply be that the map shown above is wrong, but there will always be routes whose length is dramatically distorted if Earth has a continuous flat surface and Euclidean geometry is roughly applicable, because every map distorts the planet’s surface. This is a particularly reliable reason for saying Earth cannot be flat.

As it happens, the same kind of idea can be applied to the Expanding Earth theory. I mentioned previously that there are stripes of magnetic minerals on the floor of the Atlantic. These are generated when the ocean floor spreads out from the central ridge, which is volcanic. As magnetic materials float in the lava, they get lined up with Earth’s magnetic field, which varies in its direction and strength. These then solidify with their alignments pointing in particular directions, and they line up symmetrically because the ocean is spreading from a ridge running roughly down the middle in both directions. If Earth was expanding, these magnetic materials would line up as if they’re on a smaller planet the older they are, meaning that it would be like attempting to project a globe onto a larger one without changing the sizes of the map. They would not line up according to longitude.

Satellites are now able to measure the size of the planet to within two hundred microns and there is no expansion faster than that. Continental drift is faster than that at about an inch a year in some places, so the idea that Earth is expanding is redundant, as it fails to explain what’s going on. The continents are also moving in different directions. For instance, the Pacific is gradually narrowing, as is the Mediterranean, so there isn’t a general trend towards expansion.

The trouble with this evidence is that it starts to become a little abstract and therefore lays itself open to being distrusted. As soon as it becomes difficult to follow a line of argument, or where it involves trusting an expert in a different discipline from one’s own experience, the possibility of error or perhaps conspiracy arises. This isn’t necessarily something to be distrusted, but at the same time questioning and distrust is important. The ultimate solution may be to become as well-informed as possible on certain matters, and perhaps to be self-aware when one is overly attached to a particular view, and maybe question one’s motives. Because whatever else is true, Dirac’s version of the expanding Earth and its link with an expanding Universe is truly appealing, but it’s still turned out to be wrong. But it’s tough to accept this.

“What Is The Universe Expanding Into?”

Steve, I wrote this with you in mind.

Yahoo Answers is, as I mentioned previously, about to die, although it’s a death by a thousand cuts. In the past I’ve used this blog to put more thoroughly thought-out answers to frequently-asked questions on the site, so I’ve probably addressed this before, but right now I have a different and perhaps less dogmatic take on this question than I usually adopt. Before I go on, I should probably insert the standard diagram people put in nowadays when talking about the Big Bang:

Strictly speaking, this diagram is inaccurate because it shows a two-dimensional projection of a three-dimensional model of a four-dimensional set of circumstances. Take the barred spiral galaxy at top right. If the X-axis is supposed to be time, we should be concluding that the left hand arm of that galaxy happens first, then the end of the right hand arm and the nucleus, and finally the middle of the right hand arm. Also, space is two-dimensional in this picture when for most practical large-scale purposes it really has three dimensions. In other words, this isn’t so much a diagram as an illustration intended to communicate the history of the Universe since the Big Bang. You can’t take it too seriously. It has an artistic, creative aspect.

One possibly inaccurate, because it isn’t really intended to be that accurate, feature of this diagram is the way it shows space. It’s a black rectangle into which the Universe is expanding. There is an outside to this Universe, and at that point you’d be forgiven for asking, if the Universe is everything, what’s the blackness outside it supposed to be? Why is that not also the Universe? The Jains, of all people, had an answer to this. They believed that the Universe as we know it was suffused with a substance which made movement possible, but was surrounded by infinite space from which this was absent. Nowadays, maybe we could do something similar with the idea of dark energy, the apparent force which causes the Universe’s expansion to accelerate. The above picture has a literal “bell end”. It flares out rather than widening steadily or perhaps slowing down from left to right. This is the influence of dark energy, as it represents accelerating expansion. I suppose it’s possible to think of the Universe as infinite space with at least one region where dark energy is active. However, this is neither how I think of it nor, as far as I know, the way scientists do.

Before I go on, I want to make a point about the nature of science at this scale. In certain circumstances, rational thought is “bigger” than science. Maths is one example of that. There’s plenty of pure mathematics which seems to have no practical application and even applied maths doesn’t need to be tested by observation if it’s proper pure maths. For instance, it’s a mathematical truth that any roughly spherical planet covered by an atmosphere must have at least two points on its surface where there’s no wind at any moment, although these points may move. However, our oceans needn’t have any points where there’s no current because there’s land on this planet. Likewise, a doughnut-shaped planet needn’t have any such locations, nor need any planet with at least two mountains high enough to stick up into the stratosphere. There’s no need to observe any planets to prove this because it’s a mathematical fact. I’m not entirely sure about this, but I suspect that cosmology may also have aspects of this: it may not be possible to approach the nature of the Universe entirely scientifically because there’s by definition only one example of the Universe and it can’t be compared to others. This is a particular view of the nature of the Universe which either includes the Multiverse as part of the Universe or in some way demonstrates that this Universe is all there is. There are a number of conceivable ways in which there could be other universes, but some of the arguments for it not only rely on logic and maths but also require that they cannot be observed even in principle. For this reason, without disrespecting the field, there’s a way in which cosmology cannot be scientific. James Muirden once said:

The Universe is a dangerous place – a sort of abstract wilderness embracing the worlds of physics, astronomy, metaphysics, biology and theology. These all subscribe to the super-world of cosmology, to which students of these various sciences can contribute. Strictly speaking there is no such person as a ‘cosmologist,’ for the simple reason that nobody can be physicist, astronomer, metaphysicist, biologist and theologian at the same time.

James Muriden, ‘The Handbook Of Astronomy’ 1964.

It isn’t clear though whether something which is outside the realm of science will always remain there, and in this view, it may be that there’s not in principle something imponderable about cosmology if the mind pondering it is sufficiently powerful, but simply that the span of disciplines is too broad for anyone to grasp. There certainly seem to be cosmologists nowadays, but maybe they’re cosmologians.

Although I don’t want to dwell on that, I do want to point out that it isn’t immediately obvious what space and time are. The nature of space in particular seems to depend on observation. It’s possible to doubt the existence of space but not the passage of time, since as far as we know we are disembodied viewpoints imagining the world but we can only do that imagining if time passes. This is in spite of the fact that spacetime is unified, so it isn’t clear how we’re immediately confronted with time but not space. Maybe there are more advanced minds in the Universe who experience both with the same immediacy. But there are, in any case, at least two different ways of thinking of space and this is what I usually based my answer on.

Space can be thought of as a thing or a relationship. That is, it could be understood as a container, as it were, in which objects are located, but also an object in itself. The Universe clearly is an object, but that doesn’t mean it’s made of space and studded with galaxies like spotted dick. There is a famous “balloon” analogy applied to space, which views the galaxies as spots on the surface which move apart from each other as the balloon inflates. This makes it sound like there’s a hyperspace into which the Universe is expanding, but this may not be the case.

In maths and physics, the concept of space is often used to make arcane ideas simpler. For instance, up, down, top and bottom quarks seem to refer to direction and location, but of course they don’t. They’re just called that to indicate that they are related to each other more closely than they are to other quarks. Likewise, we might talk about the temperature rising and falling, but that doesn’t mean there’s a spatial dimension called temperature. This can even be taken into the realm of space itself. We impose the idea of several dimensions on the idea of direction and temporal precedence, but there are reasons to suppose that this is mere convenience.

Suppose space is an actual thing. What would happen if there was a tear in it? It would surely mean that one could go into that tear, wouldn’t it? But how could that happen if there was no space there, since it’s torn? Does it mean anything to say that you can take a one metre sphere out of space? What happens when you move “into” it? How would it be different from a point? This suggests that there’s a flaw in thinking of space as the fabric of the Universe.

Consequently, space can be thought of as a combination of direction and location. Location can be described, more or less, using three numbers, although since there are higher dimensions this doesn’t work perfectly. It is, however, true, that relative to one’s current position a list of numbers is sufficient to describe where something else is. This tells you how far away something else is and in what direction. However, there is no absolute position. The Universe has no centre, or its centre is everywhere. This would also be true if space is infinite but it isn’t. However, as I’ve just said, space cannot have an outside, so how can this be?

The answer is that there is a maximum distance between two points, after which the direction between them reverses. This follows from the fact that the parallel postulate is incorrect: parallel lines do in fact meet at an enormous distance in most circumstances, and nearer than that in special circumstances to do with extremely high gravity. These are just properties of that group of qualities we refer to as space or spacetime, in a similar sense to addition working the same way either way round and subtraction not. When it’s said that space is expanding, all that means is that the maximum possible distance between two locations is increasing. That doesn’t imply that any actual object is expanding. A further clue to this being so is that although it’s impossible to travel faster than light, sufficiently distant objects do recede from each other at superluminal speeds. This would be impossible if space was an object unless the mass of such an object could only be expressed by a number on the complex number plane, but the distance between nearby locations increases at less than the speed of light, at a specific distance at the speed of light and at a greater distance greater than the speed of light. This is impossible for a single object because it would have to have real mass in small quantities, zero mass at the volume of the observable Universe and imaginary mass at greater than that volume. I have to say that’s an interesting set of properties and I’m not sure if it really is impossible.

The point is that in this view the Universe has no outside or, in terms of hyperspace, no interior. It clearly does have a three-dimensional interior, but not an interior in terms of a larger set of large dimensions. This account is slightly complicated by the fact that as well as time there are tiny further dimensions, but it usually makes more sense to measure the length of a pencil line than its area.

That’s an expanded version of my usual answer to the question “what is the Universe expanding into?” but it could be wrong. The reason it might be wrong is fascinating, and therefore probably not valid, but here it is anyway: ‘Brane Theory.

You might think at first that Brane Theory is just “Brain Theory” spelt wrong. That would be funny, but sadly it’s not so. Brane Theory is an extension of string theory and although I’m not afraid of maths, I can’t understand it fully. I’ve already mentioned the issue of extra dimensions which are, however, tiny. Brane theory uses this idea to explain why gravity is so much weaker than the other forces, if indeed it is a force. It isn’t immediately clear to observation, but there seem to be three major forces in the Universe plus gravity: electromagnetism, the strong force and the weak force. Of these, electromagnetism is obvious except that it may not be realised that light is part of electromagnetism. The strong force prevents atoms other than hydrogen from exploding as soon as they form, since their nuclei are made up of positively charged particles which repel each other. The weak force is a bit more obscure, and might be better described as the weak interaction because it doesn’t involve attraction or repulsion. It amounts to a tiny force field which occurs when radioactive decay involves atoms emitting beta particles, which are fast electrons. When a nucleus releases an electron, because it’s negatively charged and there are no negatively charged particles in the nucleus, a neutron becomes a proton, or the nucleus emits a positron and a proton becomes a neutron. In the former case it means the element moves one place up the periodic table. But nothing is pushing or pulling, which makes it confusing. The strong and weak nuclear forces are very small scale in their range, only operating within atomic nuclei, and for some reason the strong nuclear force is 128 times weaker at double the distance. Electromagnetism is more straightforward, probably because we experience it ourselves directly and obviously in the form of light, current, magnets, compasses, lightning and so on, and it diminishes like gravity, following the inverse square law. That is, for example, a light source emitting light all around it such as the Sun will do so in a sphere and because a sphere twice the size has four times the volume, it will be a quarter as bright from twice as far away. Gravity may not even be a force at all, but the distortion of spacetime by mass, and is anomalously weak. A magnet can pick up a piece of iron against gravity even if the magnet only has a mass of one gramme, yet Earth’s mass is nearly six quintillion (long scale) times the mass of the magnet. That’s ridiculously weak.

Brane theory, at least sometimes, attempts to solve the problem of gravity being as weak as it is by using extra dimensions. Instead of exerting a force in three-dimensional space, gravity may be doing so in hyperspace, which means that instead of weakening due to the geometry of a sphere, it does so due to the geometry of a higher, multidimensional cousin of a sphere, but the other forces are confined to three-dimensional space, in a thin membrane, hence the name “Brane Theory”, which is of course expanding in hyperspace. It’s also theorised that just after the Big Bang, in the part of the above diagram labelled “inflation”, this Universe collided with another one, causing this inflation.

So in other words, perhaps it isn’t a silly question to ask what the Universe is expanding into. This still doesn’t require space to be a thing, but makes the galaxies and stars into a thin, three-dimensional skin on a four-dimensional or multidimensional bubble. The answer is therefore possibly that the Universe is expanding in hyperspace, which is also not a thing but a way of describing distances and directions which need more than three numbers relative to where you are.

A few bits and pieces I want to clear up. This might all be thrown up in the air by the recent discovery of the way muons precess, because that suggests that the standard model of particle physics is wrong. And finally, I may have got this wrong myself. That is, what I just said might turn out to be nothing like what Brane Theory actually is. But note this: it’s maths and I’m not afraid of it. Lots of people are afraid of maths, and think they’re no good at it. I may well also be no good at maths, but I’m not afraid of it. This is a tangential point but very important, and probably has more bearing on everyday life that Calabi-Yau manifolds and stuff have anyway.