A Short, Grim Future?

This is going to be a mite depressing, but to put it in perspective it’s probably not as bad as the collapse of the false vacuum, so I’ll talk about that first and then it may even seem quite cheerful.

Some physicists have managed to construct themselves a bit of a nightmare scenario about the Universe. This involves the possibility that the Universe as we know it, i.e. the one we’re living in, is in a higher energy state than it could be in. It’s like a diamond or the metal tungsten, in that it isn’t stable but is quite durable, to the extent that we’re fooled into thinking it will last forever due to human life being much shorter, and in tungsten’s case the whole age of the Universe so far being much shorter than the period it needs to break down significantly. Regarding the false vacuum, all the energy in the entire Universe might not be as low as it could be. It is in fact all the energy because if it wasn’t, i.e. if any tiny region of space was actually in a lower state, that would immediately drag everything around it into a lower state, destroying all matter and structure around it and spreading out at the speed of light until the whole Universe ceases to exist, i.e. it would become a true vacuum, in which nothing could ever exist, so it isn’t even like it could be replaced by anything other than eternal emptiness – endless nothingness. If this is true, we wouldn’t see it coming because it would move out at the speed of light, although it might end up looking like a cosmic mirror for a while. We might see our own beautiful planet reflected in that mirror for a few seconds knowing that we and it and everything we have ever done was about to wink out of existence, so maybe it’d be better if we didn’t have any warning. If any intelligent life form, or other intelligence, or for that matter any kind of blind unthinking process like something to do with black holes or something, ever manages to lower any point anywhere below the energy level of a false vacuum, it will trigger this series of events which will end everything forever, with nothing ever able to replace it.

I sometimes wonder if this is what would happen if we ever tried to exploit zero-point energy. That is, there is energy stored in empty space which can sometimes be detected. For instance, if two metal plates are placed microscopically close to each other, this energy will pull them towards each other. Much energy can be extracted from this, and at first this might seem to be a marvellous solution to the energy crisis which would perhaps lead us to fume and rail against the fossil fuel industry – more about them later by the way – but if you think anthropogenic climate change and the like is a bad thing, just imagine comparing it to this extraction of zero-point energy which, well, would be very clean indeed, with no radioactivity or pollution whatever, so that sounds absolutely great, except for one thing: it might bring about the collapse of the false vacuum and the end of everything. If this happened as a result of an experiment on Earth, it would destroy the whole planet within about a twentieth of a second, go on to destroy our moon a second and a half later, the Sun eight minutes after that, every planet in the Solar System a few hours after that and so on. The Galaxy would be gone after seventy millennia, but nothing living in it would be able to stop it and after a few billion years the whole observable Universe would be gone.

So that’s not good. On the other hand, it might not be true. I personally suspect that if it could happen it already would’ve done, because given the size of the Universe it’s hard to imagine that somewhere, some form of alien life would’ve experimented this and caused this to happen. On the other hand, maybe it can happen but hasn’t because the whole Universe is absolutely empty of any intelligent being at all beyond this planet and one day we’ll just do something silly and all go fring like a dying filament light bulb.

The collapse of the false vacuum into the true vacuum is one of the worst things that could ever happen, but there are many worse conceivable things. For instance, the infinite and eternal suffering of all consciousness would probably be worse, and if that was the alternative it would be a kindness to cause it to collapse. But this collapse into nothingness works quite well as a comparison to what I’ll eventually be talking about in this post.

While I’m at it, there’s another bad thing which constitutes a cognitohazard and isn’t really connected. A cognitohazard is a set of sensory or mental phenomena which harms someone physically or mentally who experiences it. This idea became prominent in 1988 in David Langford’s ‘Interzone’ story ‘BLIT’, which was about an image which destroyed the consciousness of anyone who saw it. Later on, another science fiction story called ‘Basilisk’, I think, told of a world where all online images had been banned because of the possibility of this cognitohazard being posted by bad actors.

Unfortunately, it turns out that something similar to this image definitely exists in the form of the McCollough effect. This is going to sound incredible but it isn’t. It’s also a bit difficult to describe because I’ve decided not to risk it, but it involves something like looking at a series of horizontal green stripes for several minutes, then a series of vertical red stripes for several minutes. If you do this, and I really don’t recommend it, the result is apparently that any series of black and white stripes will then look pink for up to three months. This is obviously a lot milder than the fictional image in ‘BLIT’. Personally, and at this point I’m going to mention something which leads into a whole world of personal stuff I never talk about but I’ll hint at it here, I have very good reason to suppose that if I ever tried this the result would be a lot worse for me than it would for most other people. This probably sounds like one of those game-playing things which people do to intrigue others, but, again unfortunately, I can assure you that it’s anything but.

Somewhere out there in conceptual space, there could be some other kind of visual or other sensory cognitohazard which is worse than this, which exploits a vulnerability of the human mind but has not been discovered yet.

I’m going to ask you now not to search for the following idea: Roko’s Basilisk. I’m not going to say what it is. Once again unfortunately, I do know what it is. It’s probably nothing to worry about but just in case it is and you don’t already know it, please don’t try to find out. It’s another cognitohazard. Maybe it’s nothing.

That, then, is another category of bad stuff, but it’s quite cerebral and more something which might worry you but can probably be set aside without it being much of an issue. I’ve mentioned these things because they’re pretty bad, and enable one to contrast them with a much more realistic, possibly inevitable and very worrying possibility which it doesn’t seem likely that we can stop happening well within a human lifetime, which will affect all of us.

You might think anthropogenic climate change is bad enough, and of course it is pretty bad. Sadly, the same processes involved in climate change could also have a much more serious and urgent set of consequences next to which global warming is a picnic in the park. I can’t really overestimate the seriousness of this possibility. It’s been haunting me for months now. Maybe the very seriousness is causing people not to want to think about it and put it out of their minds. I don’t know how someone could not be motivated to do something about it.

Here it is. You might not want to read on. You might wish I hadn’t told you about this, so feel free to stop at this point, but on the other hand please do continue, because this really bothers me and I don’t want it to happen.

Anthropogenic climate change is happening. I realise there are deniers out there so I’m briefly going to spend time showing why we can be confident this is going on. If you still have questions, please look online for more information. Basically, the position is this. Most elements occur in atoms with slightly different weights because their nuclei have different numbers of neutrons. With carbon, there’s carbon-12, carbon-13 and the radioactive carbon-14. These are called isotopes. Biochemical processes prefer a particular ratio of these isotopes, and carbon-12 and -13 are stable, so they don’t turn into anything else. Volcanoes and other non-living processes don’t have this preference. Therefore it’s always possible to tell where carbon comes from – whether it was processed by living things or not. Fossil fuels are from coal, natural gas and oil, which used to be living things, so it has a particular ratio of carbon isotopes. The extra carbon dioxide in the atmosphere has this ratio of isotopes, so it’s from life, and in fact from fossil fuels. It isn’t from volcanoes or other non-living sources. Some people suggest that the Sun is heating the planet as part of a cycle, and this cycle does exist. However, the upper atmosphere is getting cooler and the lower atmosphere hotter, so it isn’t the Sun which is causing this heat. Water vapour is a much stronger greenhouse gas than carbon dioxide. This doesn’t help us though, because carbon dioxide heats the lower atmosphere and increases its humidity by increasing evaporation, so there will be more heating because of the water vapour due to the carbon dioxide causing it to form. There was a cluster of weather events early in the history of climate records which were unprecedented, making it seem that there was an extreme climate in the nineteenth century. This, though, was because it was easier to break records when there hadn’t been many kept. Today’s records are still records even though climate has been recorded for well over a century now. Other stars said to be sun-like are less like the Sun that they seem to be, so the fluctuations in their brightness are not comparable to ours. Climate change is actually milder than it would be if this was happening at a time when the Sun was giving out more radiation.

That’s very brief and sketchy of course, but climate scientists are generally satisfied that anthropogenic climate change is real, now and dangerous. I don’t want to focus on this right now though, but something much more threatening that’s connected to carbon dioxide and not to climate change.

Some time ago, a marine biologist collected living shelled molluscs on an ocean exhibition and kept them in an enclosed container. Unsurprisingly, she found that carbon dioxide built up in this container and it dissolved in the sea water. On looking at them again, she found that their shells had dissolved in the water because the carbon dioxide had made the water more acidic, by forming carbonic acid. This observation, I’m afraid, is absolutely crucial and has absolutely catastrophic consequences.

We already know that carbon dioxide is rising in the atmosphere, and it’s also dissolving from the atmosphere into the oceans, making them more acidic. This means that marine organisms with calcium carbonate shells, i.e. rather a lot of them, will have those shells dissolve, which will usually kill them in one way or another. For instance, it makes them more vulnerable to predators, which is often what caused the shells to evolve in the first place. It doesn’t even seem to take much acidification to cause this to happen. This does very obviously imperil coral and shelled molluscs such as whelks and oysters in the sea, and this is not good, but that’s not the main issue. The main issue is this: the marine food chains are very often based on calcium carbonate shelled plankton called foraminifera. There are thousands of these per cubic metre in the seas on continental shelves for instance. If these are killed en masse, the very specific dietary needs of many of the other species eating them will not be satisfied and they will starve, die and not reproduce. This does not, however, mean that their biomasse will disappear or affect all other organisms equally, and that might sound cheery and a relief, but it really isn’t, because of the nature of the organisms that will survive, and it’s not good at all.

Algal blooms and red tides are two phenomena resulting from anthropogenic environmental imbalances. Algal blooms are often misnamed, as they’re actually caused by blue-green algae, which are not actually algae but more like bacteria capable of photosynthesis. The excess of dead animals and plants floating in the sea will effectively fertilise it with nitrogen and phosphorus and due to the lack of shelly organisms able to consume it, this will feed blue green algae, causing deeper water to be blocked off from sunlight, leading to lack of oxygen further down. Anoxic oceans are usually a major factor in mass extinctions, as in, if they happen there just will be a mass extinction.

We think this planet is ours, and when I say ours, I mean that we think it belongs to plants and animals. It’s actually more like microörganisms grudgingly allowing us to exist provided we aren’t too much trouble to them. Blue-green algae have been around for thousands of millions of years and probably initially evolved because their colour allowed them to fit in between all the purple bacteria which did most of the photosynthesis at the time. They incorporated themselves into the cells of algae and still exist inside them as chloroplasts. They aren’t really algae – they’re the older organisms. Likewise, mitochondria, found in both plant and animal cells, have a similar history, having been microbes which became part of more complex cells, including our own. They run the Krebs Cycle, which is how we use oxygen to extract energy from sugar, and are the reason we breathe oxygen, just as blue-green algae produce that oxygen in the first place.

So they produce oxygen, sounds okay right? Well no, because that’s not all blue-green algae do and the fact that they deprive the deeper sea of oxygen is not the only problem. Firstly, yes, they use up the oxygen and this will cause fish everywhere in the ocean to suffocate, causing what they call a “dead zone”. That isn’t all. They also produce powerful toxins. One of these was a cause célèbre among biological sciences students when I was at uni because if you come in contact with it, it makes you cry blood within a few seconds and will kill you in two minutes. It’s spectacularly poisonous. And there’s another one, which I need to move on to red tides to talk about.

Red tides are another likely consequence of ocean acidification, and they happen for the same reason. These are the so-called “red tides”. Not all red tides are harmful, and they aren’t all red either, but they’re called that because of dinoflagellates. The “dino-” prefix should be attended for because it means the same thing here as it does in “dinosaur”, i.e. “terrible” or “monstrous”. Dinoflagellates come in all sorts of forms, but the ones to worry about are those which produce saxitoxin, which is also produced by blue-green algae. Saxitoxin is the substance which causes paralytic shellfish poisoning and is one of the most powerful organic toxins in existence. It’s basically a bio-weapon. Incidentally, the pufferfish which don’t produce the notorious tetrodotoxin sometimes produce this instead. Saxitoxin can’t be inactivated by heating or acid, so it will stay active in the water. It kills by paralysing the skeletal muscles, which of course include the muscles mammals, birds and reptiles use to breathe, so it leads to suffocation.

That sounds bad, but actually it’s worse. This won’t just be something happening in the oceans which we can find a way around. Saxitoxin is, as I’ve said, a particularly powerful toxin, to the extent that there will be enough to make the atmosphere itself toxic even though it starts in the sea. If we breathe it, it will kill us, and those people left around when this happens. Anyone who wants to go on breathing after about 2065 is going to have to be choosy about their air. Sorry to be flippant.

This will be followed by a mass die-off of the algal blooms and their composition, which will consume more oxygen. This process is part of what happened at the end of the Permian, which apart from the oxygen catastrophe and snowball Earth is probably the worst thing ever to happen to life on this planet and killed off 96% of all life. The extinction of the dinosaurs was pretty trivial compared to that.

If this happens, it will mean the extinction of humans, all other mammals, birds, reptiles, fish, most molluscs, coral, various types of plankton, brachiopods and a lot of other animals I haven’t thought of. Insects, actually, might be okay. And if this happens, children born today will only be in their early forties by then. And you can also easily imagine that in this situation where atmospheric air is poisonous, some megacorp will start charging us to breathe. I mean, there’s profit to be made and people will be very motivated to buy their product, so why not?

I want to point out that this wouldn’t be good. It can be prevented of course, but nobody seems to want to do that. In fact nobody seems to want to think about it or take it seriously. I don’t know why this is. It seems quite important to me, and I thought people cared about their children and grandchildren. Maybe I was wrong.

Star-tling Thoughts

I don’t know where to start with this one! The reason for this picture will eventually become clearer.

You probably know I’m panpsychist, which is linked to my veganism. I suppose the best place to begin is to account for this connection and the reasons for this belief, and also to describe what that belief actually is first of all, so here goes.

Panpsychism is the belief that matter is inherently conscious. In fact I’m not so sure about this definition because it might also be that space itself is conscious. I should point out further that my own version of panpsychism might differ from the usual version, and that it isn’t the same as hylozoism or pantheism. I usually employ an analogy with ferromagnetism, thus. Many elementary particles carry an electrical charge, including in particular quarks and some leptons. All such particles have magnetic fields, and a north and south pole which means they can be lined up by applying a magnetic field to them. However, most materials, though they’re largely made up of such particles, are not magnets. Only certain arrangements of matter are, the most familiar of which are lumps of iron whose magnetic domains are aligned. In this situation, the essential magnetic character of most matter comes to express itself in a macroscopic way which can be observed easily. There are other arrangements which are also magnets, such as the rare earth pickups used in electric guitars.

Consciousness is, in my view, similar. At least many and possibly all elementary particles are conscious, and in fact possibly all of space because of virtual particles. However, most materials, though they’re largely made up of such particles, are not minds. Only certain arrangements of matter are, the most familiar of which are wakeful humans with their particular bodily form and functions. In this situation, the essential conscious character of most matter comes to express itself in a macroscopic way which can be observed easily. There are other arrangements which are also minds.

There may also be a need to contrast this with pantheism and hylozoism. Hylozoism is the belief that everything is alive. This is not the same thing as most people would probably say that not all living things are conscious, such as bacteria and plants. It’s more like the belief that the Cosmos is an immense living organism, which to some extent I can get on board with because it’s a bit like the very liberal definition of acid which interprets almost all chemical reactions as reactions involving the action of an acid. It’s fine, but it’s not panpsychism. The other thing panpsychism isn’t, although I have some sympathy with it, is pantheism, which is the idea that God is everything. One issue with that belief is that it can be a kind of squeamish version of atheism which is afraid to call a spade a spade. I am personally not pantheist because God is unlike and not dependent upon any created (or sustained) thing. That doesn’t mean the Universe isn’t worthy of respect or that God is more like a human than the Universe. I don’t want to dwell on these distinctions, but it’s important they be made because many people think this is the claim I’m making.

Okay, so why do I believe this? Because there’s no other way of accounting for consciousness. All the other models – behaviourism, physicalism, psychophysical dualism, functionalism, idealism and anomalous monism – have massive flaws. I don’t want to go into them in depth right now because although I’m staking out a vague claim here, this isn’t the main point of this post. The claim that panpsychism isn’t a solution to the mind-body problem either is also fair, because it attempts to solve the problem by assuming what it’s trying to account for. Why would matter be like that?

This belief of mine has certain consequences. For instance, it makes me vegan but in a way my veganism is more extreme and sadder than most people’s because I accept that plants are also conscious and suffer. Hence veganism is just a kind of utilitarianism where suffering is minimised rather than a particularly positive way of life where no avoidable suffering and death is wrought upon the world. I constantly destroy bacteria too. We cannot be entirely non-violent but we should still strive to be as non-violent as possible, and partly for that reason it’s not my place to judge others. The world is a practically endless cycle of carnage in which we are all complicit. I’m vegan because eating animals or dairy products would involve an unnecessary extra step which would involve the death of more plants than just eating plants.

All this doesn’t generally occupy my mind much. However, a couple of things have come to light in the past week. One was that I met up with my ex and was presented with a first draft of an essay I wrote for my Masters:

I’ve already talked about my time at Warwick. The above essay is a reaction to a comment made by Christine Battersby near the beginning of that year. The reason I did my MA was to further pursue radical philosophy and help to provide a theoretical basis for progressive politics, and as I must surely have said elsewhere, it turned out that Warwick University’s primary activity seemed to be manufacturing excuses for why the political state of affairs was inevitable – capitalist realism in other words. I hoped that the Women’s Studies contingent would be better but although I very much liked their transphobia, they were also speciesist. Battersby claimed that consciousness depends on language use, so in other words if you don’t have a voice it doesn’t matter what happens to you. She was utterly focussed on humans and didn’t care about anything else. I’m not going to rubbish everything she says, because for example ‘Gender And Genius’ is a very interesting book, but there were a number of problems with her belief system, not least its incompatibility with more than a very limited anthropocentric version of veganism. If you can’t see what’s wrong with that, you need to check your privilege. Yes, I know that’s a cliché.

So that’s one. The other one is more widely interesting but no less personal. It starts, as so many things do, with Olaf Stapledon, “W.O.S”, whose name is associated with the works ‘Last And First Men’ and ‘Star Maker’. The second is more relevant here. Neither of these books is really a novel, and in fact this statement is made at the beginning of the first. They are, however, both science fiction. The first describes the two thousand million year-long future history of the human race from 1930 onward. The second covers the entire history of the Multiverse, focussing mainly on our own Universe. Yeah yeah, big canvas, vast scope, origin of the adjective Stapledonian, but that isn’t what I want to concentrate on right now. The relevant bit at the moment is the way stars are portrayed. And I quote:

It isn’t clear whether W.O.S. actually believed this, but then again it isn’t even clear whether W.O.S. considered himself the author of these words for reasons I can’t be bothered to go into here, but there are two ways of looking at this taken at face value. One is hylozoism – stars are living organisms. In fact, in ‘Star Maker’, various things are living and sentient organisms which might not be considered so by most earthlings. The other is something close to panpsychism, at least if the star itself is considered a world. The outer layers of the star are conscious. The chapter goes on to claim that the voluntary movements of stars are identified by astrophysics as their normal movements as predicted by scientific laws and theories.

This sounds fanciful and outlandish, not to say unscientific and perhaps even superstitious. We don’t generally look at the stars at night and think of them moving around deliberately. In fact, apart from the fact of Earth’s rotation, most of the time non-astronomers don’t think about the stars’ proper motion at all. Eppur si muoveno – pardon my Italian. The formation and rotation of galactic arms is confounding in various ways. The most obvious of these is the one dark matter is evoked to explain. The velocity of objects in the outer margins of galaxies does not compare to those further in according to the mass of the visible portion of those galaxies, so it’s claimed that there must be invisible matter causing them to rotate faster than they should. Moreover, the spiral arms of galaxies are more like the bunches of vehicles in traffic jams, separated by sparsely-populated stretches of road, through which individual motorists move, than a kind of “formation dance” arrangement. Finally, and this is a more significant fact than may at first appear, stars of different spectral classes move at different velocities around the galaxy. At this point I should probably fish out the Hertzsprung-Russell Diagram:

By Richard Powell – The Hertzsprung Russell Diagram, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=1736396

It can be seen that stars are not randomly distributed by these criteria. There are, for instance, no small hot stars other than white dwarfs and there’s a general correlation between brightness and heat, the hottest stars being on the left of the diagram – O-type stars like Rigel. Hence their size and mass can be taken into consideration if need be. The cooler stars are on the right, and these are the interesting ones from the viewpoint of the very peculiar statement that has been quite recently been made about them by a respectable astrophysicist.

So here’s the thing: cooler stars move faster around the Galaxy than hotter ones at the same distance from the centre. This is called Parenago’s Discontinuity. More specifically, stars of spectral type F8 and hotter “orbit” faster. A few explanations have been offered for this apart from the rather obvious one I’m going to mention in a bit. One is that stars might be shining more brightly on one side than the other, and although light has no mass, it does have momentum and therefore can be used as a method of propulsion:

Another “sensible” explanation is that the stars emit jets of plasma which have the same effect, and there seems to be a third one that it’s to do with stars being slowed down as they move through nebulæ.

Okay, so another explanation has been offered by one Gregory Matloff. Matloff is a pretty respectable guy. He has a doctorate in meteorology and oceanography, a Masters in astronautics and aeronautics and a BA in physics. He’s authored various books, such as one on solar sails with Eugene Mallove – this is the very real technology of using reflective mylar sheets as a form of space propulsion by sunlight pushing on the “sail” thus formed, because as I said above, starlight has momentum which can be used as a power source. He’s currently a professor of physics. So this guy is not exactly like a Sasquatch chaser or UFOlogist – he has been involved in SETI but in a very dry, scientific kind of way – but has some respectable credentials. It should also be said that just because someone is an expert in their own field, it doesn’t mean their opinions are worthy of respect in other fields about which they know less. Immanuel Velikovsky seems to have been a competent psychiatrist but his claims about the recent origin of Venus as a comet are completely ridiculous and seem also to be motivated reasoning. Matloff is not like that so far as I can tell.

So why am I going on about this bloke then? Because he’s a panpsychist. Not only that, but he reckons panpsychism is a testable explanation for why cooler stars circle around the Galaxy more quickly than hotter ones. He believes that such stars are conscious and move around of their own volition. They don’t obey the laws of physics as we know them as precisely as they’d be expected to, but the extent to which they don’t is only like someone running for a hundred years and changing their velocity over that time by a couple of centimetres a second. This minimal degree of involvement reminds me of the Steady State Theory, which saw matter as continuously springing into existence at the rate of about two hydrogen atoms a year in a volume the size of the Empire State Building. Although, so far as I can tell, Matloff is open to the idea that the stars in question are adjusting their speed and direction using jets or changing their luminosity, he’s also open to the much more controversial idea that not only are they doing it deliberately but that they’re doing it by psychokinesis.

There comes a point in certain conversations where the “argument by incredulous stare” is deployed. This happens in a couple of philosophical areas, one of which is panpsychism and another of which is modal realism (the idea that the Multiverse is real). However, mere outlandishness doesn’t make something false and doesn’t constitute an argument against it. This is the fallacy of the argument from incredulity, much beloved of flat Earthers and Apollo mission deniers. It is, though, true that extraordinary claims require extraordinary evidence.

A relatively good piece of evidence that this is in fact going on is found in the fact that only cooler stars do this. There are a number of ways to account for consciousness, one of which is the behaviour of the rings making up some of the molecules in nerve cell microtubules. These are part of the cytoskeleton, and it’s been suggested that quantum events associated with the p orbitals in aromatic moieties within tubulin, the protein they’re made of, is what consciousness is. If this is so, only similar phenomena would be able to manifest consciousness, although this could be functionally equivalent and not be made of the same stuff. If it actually does require that stuff though, stars couldn’t be conscious. Maybe they aren’t. Actually this needs restating: even if panpsychism is true, it doesn’t mean that consciousness would be manifest in stars, though stars could still be impotently conscious.

Matloff prefers to evoke the Casimir Effect. An example of this is the tendency of two metal plates very close to each other to pull towards each other. It’s an example of zero-point energy, which is the “free energy” supposèdly present in empty space. Whereas this energy undoubtedly exists, it doesn’t follow that it can be extracted and used, or that if it can that that would be a good idea – my naïve mind suspects that this would cause collapse of the false vacuum and the end of the Universe, but that’s just me and I might be catastrophising. If that’s true, though, depending on the size of the Universe and how common technological cultures are within it, it seems guaranteed that that can’t happen because we’re still here. Matloff claims that the Casimir Effect’s contribution to molecular bonds makes cooler stars conscious.

This next bit is going to sound like W.O.S. again. Stars are often too hot for chemistry. Atoms as such have trouble existing in many of them because they’re too hot for electrons to stay in orbitals around them, so the idea of microtubule p orbitals being associated with consciousness is a non-starter here. However, the upper layers of stars are cooler than their interiors and molecules can form in the cooler stars, i.e. those of spectral class F8 or below. Hence the proposition that consciousness becomes operable at the energy level below which molecular bonds exist because they are involved with certain molecular bonds implies that volitional behaviour in entities below that temperature would not be found in similar entities hotter than it. In a very crude sense, all living humans have body temperatures below 6300 Kelvin, or 6000°C. This is actually true. A human running a temperature above 6000°C would not be conscious but be superheated gas. Or would she? I don’t know. It’s counterintuitive that she’d be in good mental health.

Okay, so the idea is that stars cool enough to have molecules are conscious and have volition. They act deliberately. Evidence for this is that cooler stars travel through the Galaxy faster than they should. Incidentally, this also means the Sun is conscious, because it’s a G2V star, well below the threshold where consciousness is extinguished at this stage.

Now, unfortunately I have completely forgotten how I came to this conclusion but three dozen years ago or so, I realised that if panpsychism is true, psychokinesis must also be possible. I have racked my brains about this and cannot for the life of me recall my train of thought regarding this. It isn’t to do with anything like psychophysical dualism, although that would also strongly suggest psychokinesis in the most straightforward version of that model (bodies and souls). So I apologise for this irritating omission. This also means that my reasoning can’t be examined for this belief. I might just have been wrong. Also, it makes panpsychism testable: if it could be shown that psychokinesis is impossible, it would also refute panpsychism.

Stars being conscious isn’t the same thing as panpsychism being true or psychokinesis being possible. It could be that one of the other methods of transportation they could use is under their voluntary control, and that an alternative arrangement of matter found in cooler stars also confers consciousness, but merely in functional terms like a human being is often conscious.

The problem I have with all this is that I can’t decide if Matloff is serious, or if he is, whether he’s sensible. It’s true that I am panpsychist and nowadays I take it on faith that this implies that psychokinesis is possible even though I can’t remember why. However, there is a problem with this set of claims. There’s a thing called “God Of The Gaps”, which is the idea that God is simply used to explain anything we don’t understand. Thus before the theory of evolution was popular, people believed God created all species more or less as they are in historical times. This is not a good way to believe in God. Likewise, panpsychism could be evoked to explain a lot of things we don’t have good scientific theories for. For instance, dark matter is the usual explanation for why galaxies rotate faster than the visible mass in them suggests they should. Another one is Modified Newtonian Dynamics (MoND). I don’t like the first explanation because it seems to me that dark matter is a conveniently inactive substance which has just been made up to plug the gaps in the model, although I am open to the idea that it might just be ordinary matter which can’t be seen such as rogue planets, dust, neutrinos and so on. However, it would be equally possible to say that stars simply move around galaxies faster than the ordinary laws of physics suggest because they’re using psychokinesis. In fact, maybe I’ll just decide that’s what I believe.

I can’t imagine these views being taken seriously in the astrophysics community. However, it is interesting that they are the same views as W.O.S. expressed in ‘Star Maker’ in 1937. ’Star Maker’ is a work of fiction. It gets certain things about astronomy and astrophysics completely wrong. At the time, it used to be thought that planets were formed when stars came close to each other and pulled elongated cylinders of gas out of their photospheres, which then condensed into gaseous or solid bodies, and that red giants were young stars in the process of forming. There’s clearly no omniscient authority telling W.O.S. what to write, or if there is it’s an unreliable narrator. W.O.S. does, however, portray himself as the true author of neither ‘Last And First Men’ nor ‘Star Maker’. He also narrates his own experiences in the third person in some stories, and the continuity between ‘Last Men In London’ and ‘Odd John’ suggests that he is not who he says he is. Is it possible, then, that certain ideas arrive in fiction from another source? Did W.O.S. somehow intuit that stars were conscious and did their own thing? I do have a very good reason for suspecting that this is true because of a certain paragraph in his ‘Odd John’, but because it suggests an ontological paradox and would cease to be useful as a message if I said what it was, you’re just going to have to trust me on this.

Leaving all that aside, I find it very hopeful to think of stars as living organisms, or as conscious beings. If that’s true, it means that whatever happens to this planet’s life because of what humans are doing to it, mind will continue to exist in the Universe, and in fact life, at least until the end of the Stelliferous Era, roughly one hundred million million years from now. After that, W.O.S. suggests other ways in which life and consciousness might survive and there are other suggestions about what might be possible in the very long term, but for now, if I can persuade myself that stars are conscious, I find the future to be very bright indeed.

Two Pieces Of Evidence For Evolution, And The Nature of the Bible

This post tries to do the same for evolution as this did for the Earth being a globe, but with an additional bit on the nature of sacred texts in general, focussing on the Bible. It isn’t supposed to be a thoroughgoing survey of evidence for evolution so much as just a couple of tests which can be done fairly easily which demonstrate that it’s fantastically improbable that evolution didn’t happen. I’m also going to mention a couple of other things supporting evolution. This is A-level biology stuff. It isn’t so sophisticated as to be hard to understand for a lay person. I’m also repeating myself here but it’s worth it for the sake of a more targetted post.

Immunological Studies

I should point out first of all that there is a major ethical issue with this one, and possibly also with the other one depending on the organisms on which it’s carried out. Most vertebrates have an immune response somewhat similar to memory. When we’re exposed to certain substances, our bodies come to recognise them and deploy defences against them. This is often more harmful than helpful, but the way it’s done is for the immune system to manufacture large molecules called antibodies whose surfaces match the molecular structure of the surfaces of the molecules they neutralise, like jigsaw pieces fitting together. They also match other molecules with sufficiently similar shapes. There’s an example of this in vaccination. The BCG vaccine, used against tuberculosis bacteria, also works against the leprosy pathogen because the two are closely related and have similar compounds on their surfaces. Both are in the genus Mycobacterium and are about as closely related as horses and donkeys.

In fact you can even use horses and donkeys to demonstrate this. If you take a blood sample from a horse and inoculate a rabbit with it, not only have you done something extremely unethical but you’ve also caused the rabbit’s immune response to recognise a particular set of molecular patterns as found in the blood of a horse. If you then take a blood sample from the rabbit and combine it with the blood of a donkey or zebra, it will similarly show an immune response but not as strong as it would to a horse. It would show a weaker response to the blood of a tapir or rhino and a much weaker response to a more distantly related animal such as a human. Incidentally, you could do this with any set of mammals. The rabbit is not crucial here. Inoculating a human with horse blood in the same way would produce an immune response which would be steadily weaker with more distantly related animals.

This happens because the proteins found in animals tend to vary in detail from species to species, but these variations are usually not directly related to their function, which means that random mutations in their DNA often result in different amino acids in the chains. I should probably explain this a bit better.

DNA codes for proteins. That’s what genes are: instructions for building proteins from amino acids. Amino acids have small molecules with groups at either end which can bond to each other quite easily. These form chains known as polypeptides. Some amino acids can also bond at their sides using sulphur atoms, which enable the chains to fold into particular shapes. If one of these changes, it’s unlikely to preserve the function of the protein, but it often doesn’t matter much what the chain of amino acids other than the ones which link is made of in detail. Consequently there is no pressure for them to conform, and organisms simply will tend to become more chemically different from each other if they don’t form part of a single breeding population. This means that these immune responses are effectively using an animal’s immune system to measure how closely related to each other two organisms are, and the variations are not normally anything to do with how the organisms have been “designed”. They’re simply random differences.

DNA Strand Bonding And Temperature

This can be carried out more ethically than the immune system, although it’s practiced differently. This one basically looks at the code for making the proteins rather than the proteins themselves, but has the advantage of including an organism’s entire genome rather than just the proteins produced by its genes. Most DNA is non-coding. Actually, you know what? I’m going to introduce the nature of DNA here.

DNA is the molecule which stores genetic information in most organisms. The exceptions are certain viruses which use RNA instead. DNA is arranged like a ladder, with the sides consisting of a sugar called deoxyribose and a phosphate group. These are linked to the half-rungs, consisting of four compounds, two with a pair of rings and two with single rings. These are cytosine, guanine, thymine and adenine, known as bases. Each can only bond with one of the others, cytosine with guanine and adenine with thymine. The whole assemblage twists in a double helix like a spiral staircase. On a larger scale, the DNA molecule coils again like a telephone handset cable, and several times again, packing the whole molecule into a small space. There are also globules of protein which help it stay in this arrangement. On a higher level the molecules are organised into two larger systems visible under a light microscope. These are chromosomes and plasmids. Plasmids are loops of DNA not found in the nuclei of cells but found in the likes of bacteria, mitochondria and chloroplasts. Chromosomes are usually paired in most organisms, or at least animals, but they can also either be single or in groups of several such as threes or sixes. Humans usually have forty-six chromosomes. Most of the time they’re invisible because they’re packed away but sometimes there are giant chromosomes, as in the salivary glands of fruit flies, and they become discernible when cells divide.

DNA encodes genes in the “rungs”. Every amino acid has a three-base code, or several codes, and there is also a “stop” codon which ends protein transcription. Every gene codes for a protein, but further down the line these proteins are responsible for the manufacture of other chemicals and structures, or for their acquisition and movement from the external environment, so living things are not just made of protein.

Most DNA is non-coding. That isn’t the same as non-functional. For instance, the centromere some way through the chromosome has a certain pattern of bases which makes it easier for the spindles to pull on the chromosome during cell division and the telomeres at the ends of the chromosomes stop the genes towards those ends becoming deleted or damaged when cells divide. Much of it has no clear function, which is of course not the same as it having no actual function. In a way, non-coding DNA is like dark matter is supposed to be, in that it constitutes the majority of the genome but is “invisible” in that it doesn’t turn into proteins. This means that whereas it could constitute the design of an organism if you’re going to go all teleological on us, it probably doesn’t. It could be anything most of the time. Something like 99% of the human genome is thought to be non-coding. Some other organisms have much more coding DNA than humans. For instance, there’s a species of seaweed with only three percent.

Protein transcription occurs when the strand is unravelled by a protein (the purple blob in this clip, which shows replication rather than transcription). It’s possible to use these enzymes to separate DNA into single strands. If you did this with a human sample and put it into solution, the corresponding bases in the DNA would tend to align and recombine. If that solution were then heated sufficiently, it would separate again. However, if single-stranded DNA samples were to be made from a chimpanzee and a human, they would combine to a certain extent but maybe about one percent of them would not bond, and when heated in solution will separate at a lower temperature. This trend continues with increasingly distant relatives, such as humans and cats, humans and kangaroos, humans (let’s just stick with ourselves for now) and cobras, humans and fruit flies, humans and bananas and so on. Each of these will separate at lower temperatures than its predecessor. This is because they have fewer and fewer bases in common.

Now, it’s possible to imagine that organisms that occupy similar ecological niches will be genetically similarly “designed”, so you might expect, for example, that an aardvark and an anteater would, if designed, have a lot of genes in common, such as genes for a long snout, powerful claws and digestive enzymes for breaking down insect cuticles. This would make sense if the animals in question were designed. However, studies such as this and the immunological technique mentioned before show that aardvarks are not closely related to any other mammals although they are somewhat related to manatees and elephants, that is, that they have more DNA and genes in common with them than anteaters. By contrast, anteaters can be shown by the same methods to be quite closely related to armadillos and sloths, and as a group these three clades are only very distantly related to all other mammals. It has nothing to do with design. The non-coding DNA underlines this as there is no reason for it to be faithfully copied if it has no function. All it does is indicate how closely related organisms are.

My own genome shows that I am mainly Scottish and Irish (i.e. I’m ethnically a Gael) with some apparently Mestiço ancestry originating in West Afrika or the nearby islands. This corresponds with what I know about my family history and health and isn’t even slightly surprising. Established genome sequencing techniques confirm what I already knew or strongly suspected. It’s just a way of tracing family history, among other things, and it works beyond our own species to establish common ancestry all the way back to LUCA – the Last Universal Common Ancestor, thought to have lived somewhere between 3 480 and 4 280 million years ago. I imagine it wouldn’t work on viruses to link them to other organisms usefully, as they might have RNA genomes or genes which have been transcribed into the genomes of hosts. But there is no qualitative difference between me discovering I have West Afrikan relatives and a scientist discovering armadillos and pangolins are not closely related but armadillos and anteaters are.

A Couple Of Miscellaneous Points

There used to be a sea urchin whose madreporite (the orifice urchins and their relatives use to ferry sea water in and out of their bodies) started off in the centre of its shell and it gradually moved towards the edge. There are plentiful fossils of this sea urchin in chalk cliffs, and the further up you climb from the beach in, say, Dover, the closer the madreporites on these fossils are towards their edges. This is clear visual evidence for evolution, although it uses fossils, which leads some people to doubt. Therefore here’s another. Mammals have a nerve supplying their larynxes called the recurrent laryngeal nerve. This travels down the neck, loops round the collar bone and then comes up towards the larynx. In most mammals this is fine and a slightly odd but functional arrangement. It’s also true of giraffes with their almost two metre long necks. They have a nerve whose only function is to move the larynx which is three and a half metres long, when it need only be well under a metre in length. This may actually be one reason giraffes are so quiet. They can make a low grunting noise and that’s it. This may or may not be useful. One thing which is clear, though, is that this is not a sensible way to design an animal. The only reason giraffes’ recurrent laryngeal nerves are this way is that they’re descended from okapi-like animals with much shorter necks. I find this to be one of the best pieces of easily stated evidence available to support evolution.

The Bible

This came up twice recently, once in connection with flat Earthers and once with young Earth creationists. It’s notable that historically, young Earth creationists have tended not to believe Earth is flat, although more recently more of them seem to. Before that, for a long period there was only a tiny minority of Christians who were flat Earthers, although more seemed to have a problem with evolution. To an extent it’s a waste of time to engage with them, for a couple of reasons. One is that there are more pressing concerns in most people’s lives, and another is that they don’t seem to be willing to listen. It’s also very difficult to determine if they’re in earnest, but there are people who spend a lot of money and resources into promoting the idea that Earth is flat, suggesting that they really do believe that.

The Bible, and here I’m including both the Tanakh and the New Testament as I get the impression that Christians proportionately outweigh faithful Jews among flat Earthers, is a collection of disparate texts. If you are a faithful follower of either or both parts, the chances are that the main reason you take it seriously is that you regard it as a guide to living righteously. Because it’s so varied, it can’t be categorically said that none of it is a science textbook, particularly Torah. Torah has what appear to some to be instructions on hygiene, for instance with respect to infectious diseases, and dietary prohibitions which it’s often been argued are linked to avoiding parasites. That may or may not be what they’re about. Jewish traditions often seem to involve disputations about the true import of a text and as a Goy I probably shouldn’t comment. I am, however, aware that that view exists, and consequently it isn’t entirely true to say that the Tanakh is never supposed to be taken to refer to something like science, accurately or otherwise. All that said, the chances are that such a wide-ranging and enormous corpus as the Tanakh and the New Testament would end up revealing something about the human writers’ views on the nature of the physical Universe. Jewish cosmology seems to look something like this:

By Tom-L – Own work Based on File:Early Hebrew Conception of the Universe.png and several other depictions, including Understanding the Bible, Stephen L. Harris, 2003., CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=99817773

That’s all entirely clear, or rather can be gleaned from various parts of the text. The New Testament view seems to be somewhat different, as from Paul’s comments about the Seventh Heaven it seems to have incorporated the Greek view of a cosmos consisting of nested spheres, each bearing a planet or the fixed stars. At that time, the Jews were largely Hellenised, some of the authors, such as Luke, were well-educated and it seems that such ideas as those of Eratosthenes and Aristarchus had filtered through. However, the gospels refer to Satan taking Jesus to a high place where all the nations of the world could be seen, and the risen Jesus ascends into Heaven, which strongly suggests a “sandwich”-type cosmology of a flat Earth and heaven. Even Luke mentions these, and they seem to imply Earth’s flatness. However, what’s more important about the incidents? What do they communicate? Surely that Satan tempted Jesus with great Earthly power in return for submission to him, which Jesus rejected, isn’t it? The Ascension is harder to account for, and to me at least the suggestion that it’s an “acted parable” is not convincing. Even so, the idea communicated is that Jesus Christ is God. Focussing on Earth’s shape because scientifically ignorant people, which basically everyone was at the time anyway by the way, is utterly beside the point.

This can be seen elsewhere in the Bible. For instance, there’s a passage which refers to plants forming a barrier which have either stings or thorns. The details are not important. Torah refers to insects using a word translatable as “quadruped”, as it contains the Hebrew term for “four”. I’ve seen Christians attempt to argue that it refers to locusts because their hind legs are for hopping and don’t count as legs, which I find silly and pointless.

Conclusion

Not only is it unnecessary to be creationist or a flat Earther to be a faithful member of the Christian or Jewish faith, but in the case of the former it’s actually questionable to be due to the fact that unlike Judaism, Christianity is an evangelising faith, and to insist on creationism or belief in a flat Earth is both a barrier to evangelism and a refusal to use the divine gift of reason. Anti-theists would possibly be very happy with Christian flat Earthers because they give Christianity such a bad image. However, it just isn’t necessary to believe either absurdity to be Christian.

Could Science End?

Yesterday I considered the question of what civilisation would be like if nobody could do mathematics “as we know it”, which is one fairly minor suggestion for an answer to the Fermi Paradox of “where are all the aliens?”. Of course the simplest answer to this is that there aren’t any and probably haven’t ever been any, but there are also multitudinous other possibilities, many of which have interesting implications for us even if we never make contact with any. Yesterday, the fault was in ourselves, but what if the fault was in not our stars, but the stars? What if the issue is not that other intelligent life forms lack a capacity we do have, but that there is a realistic, external but still conceptual problem which prevents anyone from getting out there into interstellar space in a reasonable period of time? What if, so to speak, science “runs out”?

Even if there are no aliens, this possibility is still important. It’s entirely possible that they are in fact completely absent but science will still stop, and that would be a major issue. It would be rather like the way Moore’s Law has apparently run up against the buffers due to thermal noise and electron tunnelling. Ever since 1961, when the first integrated circuit was invented, there’s been an approximate doubling of transistors per unit area of silicon (or germanium of course) every two years or so, which may be partly driven by commercial considerations. However, as they get smaller, the probability of an electron on one side of a barrier teleporting to the other and thereby interfering with the operation of transistors increases. In 2002, it was theorised that the law would break down by the end of the decade due to Johnson-Nyquist noise, which is the disturbance of electrical signals due to the vibration of atoms and molecules tending to drown out weak signals, which is what nanoscale computing processes amount to. It isn’t clear whether Moore’s Law has stopped operating or not because if it does, it would have consequences for IT companies and therefore their profitability and share values, so the difficulty in ascertaining whether it has is a good example of how capitalism distorts processes and research which would ideally operate in a more neutral environment, and there’s also a tendency for people to suppose that scientific change will not persist indefinitely because of being “set in their ways” as it were, so it’s hard to tell if it actually has stopped happening. It’s been forecast, in a possibly rather sensationalist way, that once Moore’s Law does stop, there will be a major economic recession or depression and complete social chaos resulting from the inability of IT companies to make enough money to continue, but I don’t really know about that. It seems like catastrophising.

More widely, there are areas of “crisis”, to be sensationalist myself for a moment, in science, particularly in physics but as I’ve mentioned previously also perhaps in chemistry. The Moore’s Law analogy is imperfect because it isn’t pure scientific discovery but the application of science to technology where it can be established that a particular technique for manufacturing transistors has a lower size limit. This is actually a successful prediction made by physics rather than the end of a scientific road. However, the consequences may be similar in some ways because it means, for example, that technological solutions relying on microminiaturisation of digital electronics would have to change or be solved in a different way, which is of course what quantum computers are for. The end of science is somewhat different, and can be considered in two ways.

The first of these is that the means of testing hypotheses may outgrow human ability to do so. For instance, one possible time travel technique involves an infinitely long cylinder of black holes but there is no way to build such a cylinder as far as can be seen, particularly if the Universe is spatially finite. Another example is the increasing size and energy required to build particle colliders. The point may come when the only way to test an hypothesis of this kind would be to construct a collider in space, and right now we can’t do this and probably never will be able to. There would be an extra special “gotcha” if it turned out that in order to test a particular hypothesis involving space travel it would be necessary to have the engines built on those principles in the first place to get to a place where it could be falsified.

Another way it might happen is that there could be two or more equally valid theories which fit all the data and are equally parsimonious and there is no way of choosing among them. It kind of makes sense to choose a simpler theory, but on this level it becomes an æsthetic choice rather than a rational one because nothing will happen as a result of one theory being true but not the other. If all the data means all the observable data, this is the impasse in which science will find itself.

It also seems to be very difficult to arrive at a theory of quantum gravity. Relativity and quantum physics are at loggerheads with each other and there seems to be no sign of resolution. There “ought to be” some kind of underlying explanation for the two both being true, but it doesn’t seem to be happening. Every force except gravity is explained using the idea that particles carry the message of that force, such as photons for electromagnetism and gluons for the strong nuclear force, but gravity is explained using the idea that mass distorts space instead, meaning that gravity isn’t really a force at all. I’ve often wondered why they don’t try to go the other way and use the concept of higher dimensions to explain the other forces instead of using particles, but they didn’t and I presume there’s a good reason for that. It wouldn’t explain the weak force I suppose. However, there does seem to be a geometrical element in the weak force because it can only convert between up and down quarks if their spin does not align with their direction of motion, so maybe. But so far as I know it’s never been tried this way round, which puzzles me. There’s something I don’t know.

There may also be a difference between science running out and our ability to understand it being exceeded. Already, quantum mechanics is said to be incomprehensible on some level, but is that due to merely human limitations or is it fundamentally mysterious? This is also an issue evoked with the mind-body problem, in that perhaps the reason we can’t seem to reconcile the existence of consciousness with anything we can observe is that the problem is just too hard for humans to grasp.

People often imagine the ability to build a space elevator, which is a cable reaching thousands of kilometres into space to geostationary orbit up and down which lifts can move, making it far easier to reach space, but there doesn’t appear to be a substance strong enough to support that on Earth, although it would be feasible on many other planets, moons and asteroids using existing technology. We might imagine it’s just round the corner, but maybe it isn’t. Likewise, another common idea is the Dyson sphere, actually acknowledged by Freeman Dyson himself as having originally been thought of by Olaf Stapledon, which encloses a sun in a solid sphere of extremely strong matter to exploit all of its energy, which again may not exist. And the obvious third idea is faster than light travel, which is generally taken to be impossible in any useful way. One way the search for extraterrestrial intelligence (SETI) could be conducted is to look for evidence of megastructures like Dyson spheres around stars, and in one case a few people believed they’d actually found one, but what if they turn out to be impossible? Dyson’s original idea was a swarm of space stations orbiting the Sun rather than a rigid body, which seems feasible, but an actual solid sphere seems much less so. Our plans of people in suspended animation or generation ships crossing the void, or spacecraft accelerated to almost the speed of light may all just be pipe dreams. Our lazy teenage boasts will be high precision ghosts, to quote Prefab Sprout. Something isn’t known to be possible until it’s actually done.

If non-baryonic dark matter exists, the beautiful symmetries of elementary particles which the Standard Model of physics has constructed do not include it. And despite my doubts, it may exist, and even if it doesn’t there’s an issue with explaining how galaxies rotate at the rate they do. However, at any point in the history of science there were probably gaps in knowledge which seemed unlikely to be filled, so I’m not sure things are any different today. It reminds me of the story about closing the US patent office in 1899 CE, which is apparently apocryphal, because everything had been invented. However, there is also the claim that technological progress is slowing down rather than accelerating, because the changes wrought in society by the immediate aftermath of the Industrial Revolution were much larger than what has happened more recently. At the end of the nineteenth century, there seemed to be just two unresolved problems in physics: the ultraviolet catastrophe and the detection of the luminiferous æther. These two problems ended up turning physics completely upside down. Now it may be possible to explain any kind of observation, with the rather major exceptions which Constructor Theory tries to address but these seem to be qualitatively different. The incompleteness of these theories, such as the Uncertainty Principle and the apparent impossibility of reconciling relativity with quantum mechanics, could still be permanent because of the difficulty of testing these theories. Dark matter would also fall under this heading, or rather, the discrepancy in the speed of galactic movement and rotation does.

This is primarily about physics of course, because there’s a strong tendency to think everything can be reduced to it, but biocentrism is another possible approach, although how far that can be taken is another question. Also, this is the “trajectory and particles” version of physics rather than something like constructor theory, and I’m not sure what bearing that has on things. Cosmology faces a crisis right now as well because two different precise and apparently reliable methods of measuring the rate of expansion of the Universe give two different results. Though I could go on finding holes, which may well end up being plugged, I want to move on to the question of what happens if science “stops”.

The Singularity is a well-known idea, described as “the Rapture for nerds”. It’s based on the perceived trend that scientific and technological progress accelerate exponentially until they are practically a vertical line, usually understood to be the point at which artificial intelligence goes off the IQ scale through being able to redesign itself. Things like that have happened to some extent. For instance, AlphaGo played the board game Go (AKA Weichi, 围棋) and became the best 围棋 player in the world shortly after, and was followed by AlphaGo Zero, which only played games with itself to start with and still became better than any human player of the game. This was a game previously considered impossible to computerise due to the fact that each move had hundreds of possible options, unlike chess with its couple of dozen or fewer, meaning that the game tree would branch vastly very early on. But the Singularity was first named, by Ray Kurzweil, two and a half dozen years ago now, and before that the SF writer Murray Leinster based a story on the idea in 1946, and it hasn’t happened. Of course a lot of other things have been predicted far in advance which have in fact come to pass in the end, but many are sceptical. The usual scenario involves transhumanism or AI, so to an extent it seems to depend on Moore’s Law in the latter case although quantum computing may far exceed that, but for it to happen regardless of the nature of the intelligence which drove it, genuine limits to science might still be expected to prevent it from happening in the way people imagine. For this reason, the perceived unending exponential growth in scientific progress and associated technological change could be more like a sigmoid graph:

I can’t relabel this graph, so I should explain that this is supposed to represent technological and scientific progress up to the Singularity, which occurs where the Y-axis reads zero.

There’s a difference between science and technology of course. It’s notable, for example, that the development of new drugs usually seems to involve tinkering with the molecular structure of old drugs to alter their function rather than using novel compounds, and there seems to be excessive reliance in digital electronics on a wide variety of relatively scarce elements rather than the use of easily obtained common ones in new ways. And the thing is, in both those cases we do know it’s often possible to do things in other ways. For instance, antibacterial compounds and anti-inflammatories are potentially very varied, meaning for example that antibiotic resistance need not develop anything like as quickly as it does, even if they continue to be used irresponsibly in animal husbandry, and there are plenty of steps in the inflammatory process which can be modified without the use of either steroids or so-called non-steroidal anti-inflammatories, all of which are in fact cycloöygenase inhibitors, and there are biological solutions to problems such as touchscreen displays and information processing such as flatfish and cuttlefish camouflage which imply that there is another way to solve the problem without using rare earths or relatively uncommon transition metals. So the solutions are out there, unexploited, possibly because of capitalism. This would therefore mean that if the Singularity did take place, it might end up accelerating technological progress for quite a while through the replacement of current technology by something more sustainable and appropriate to the needs of the human race. Such areas of scientific research are somewhat neglected, meaning that in those particular directions the chances are we really have not run out of science. They could still, in fact, have implications for the likes of space travel and robotics, but it’s a very different kind of singularity than what Kurzweil and his friends seem to be imagining. It’s more like the Isley Brothers:

Having said that, I don’t want to come across as a Luddite or anti-intellectual. I appreciate the beauty of the likes of the Standard Model and other aspects of cutting edge physics and cosmology. I’m not sure they’re fundamental though, for various reasons. The advent of constructor theory, for example, shows that there may be other ways of thinking about physics than how it has been considered in recent centuries, whether or not it’s just a passing trend. Biocentrism is another way, although it has its own limits. This is the practice of considering biology as fundamental rather than physics. The issue of chemistry in this respect is more complex.

Returning to the initial reason this was mentioned, as a solution to the Fermi Paradox, it’s hard to imagine that this would actually make visiting other star systems technologically unfeasible. If we’re actually talking about human beings travelling to other star systems and either settling worlds or constructing artificial habitats to live in there, that doesn’t seem like it would be ruled out using existing tech. The Dædalus Project, for example, used a starship engine based on the regular detonation of nuclear bombs to accelerate a craft to a twelfth of the speed of light, though not with humans on board, and another option is a solar sail, either using sunlight alone or driven by a laser. Besides that, there is the possibility of using low doses of hydrogen sulphide to induce suspended animation, or keeping a well-sealed cyclical ecosystem going for generations while people travel the distances between the stars. There are plenty of reasons why these things won’t happen, but technology doesn’t seem to be a barrier at all here because methods of doing so have been on the drawing board since the 1970s. Something might come up of course, such as the maximum possible intensity of a laser beam or the possibility of causing brain damage in suspended animation, but it seems far-fetched that every possible technique for spreading through the Galaxy is ruled out unless somewhere out there in that other space of scientific theory there is some kind of perpetual motion-like or cosmic speed limit physical law which prevents intelligent life forms or machines from doing so.

All that said, the idea that science might run out is intriguing. It means that there could be a whole class of phenomena which are literally inexplicable. It also means humans, and for that matter any intelligent life form, are not so powerful as to be able to “conquer” the Cosmos, which is a salutory lesson in humility. It also solves another peculiarity that somehow we, who evolved on the savannah running away from predators, parenting and gathering nuts and berries for food and having the evolutionary adaptations to do so, have developed the capacity to understand the Universe, because in this scenario we actually haven’t.

Counter-Earth

You could be forgiven for thinking that, provided you accept Earth is roughly spherical, the two options for understanding the Solar System are either that the Sun and planets orbit us or we orbit the Sun. Both of these seem like quite simple solutions for how the Universe, or this bit of it at least, works. However, these are not in fact the only options. Tycho Brahe, for example, thought this was an accurate portrayal of the state of affairs:

Tycho held that Earth is too heavy and slow to be in motion, and therefore that it must be stationary, but accepted that the movements of the planets when they went retrograde was best explained by the idea that they orbited the Sun, so he concluded that the Sun orbits Earth but the other planets orbit it, except for our own satellite. Before that, the geocentric system included the idea that everything orbited us but also described little circles in its own orbit to explain how planets go retrograde.

Two thousand years before Tycho, Πυθαγορας (Pythagoras) founded a school or cult which had a whole host of unusual ideas, while including elements which have persisted to the present day. The trouble with the figure of Pythagoras is that it isn’t entirely evident that he existed, something he has in common with many of his near-contemporaries. Nonetheless, the ideas associated with him and his cult are quite clearly delineated, and one of those was the first model of the Solar System which dislodged Earth from the centre and asserted that we were in orbit like the other planets. The Pythagoreans also believed that all things were made up of numbers, so if you happen to believe in the simulation theory, that’s kind of what they thought too, in their own way, which just shows how old the ideas expressed in ‘The Matrix’ really are. Not wanting to go too far off track though, Φιλόλαος (Philolaos) came up with the actual cosmology. The initial idea was that the planets were in spheres whose motion produced a sound inaudible to human ears but which was in perfect harmony, meaning that the ratios of their orbits had to be harmonious in musical terms. The Cosmos, which is spherical, expanded out from a central point at a steady speed in all directions. At this centre is situated the central fire of the Cosmos, which is both an unlimited element and central. The Sun is a mirror, reflecting this fire, and Earth rotates once a year as it orbits, meaning that the central fire is constantly visible in the antipodes but not from Greece. Also, and this is where the Counter-Earth comes in, there is a twin Earth on the other side of the fire which is also invisible due to the way Earth rotates.

Why is there a twin Earth though? Two reasons: it makes the number of orbiting bodies plus the central fire up to ten, which according to Pythagoras is a perfect number, and because only Earth and Counter-Earth were massive, enabling the Solar System to be balanced. All the other orbiting bodies are made of fire and therefore fairly insubstantial. So the reason is partly numerological. Although this theory is wrong, it’s not completely wrong, and it might also be noted that according to this our planet is round. You have to go back an extremely long way before the idea of Earth being flat was dominant among the intellectual élite of Western culture. This planet, in any case, is referred to as “Antichthon”.

This idea of a Counter-Earth has been very persistent. It does at first seem to make sense to think that for all we know, there’s another Earth on the other side of the Sun which we never see because it takes exactly the same amount of time to orbit and is always behind it. It’s also a very appealing idea. It is, however, impossible without enormous forces being deployed to keep it or us hidden, and it must be them because we can’t detect any. Here’s an illustration of the problem:

We orbit the Sun in a slightly elliptical path with the Sun at one focus, or rather, the barycentre of the Earth-Sun system there. To a very limited extent, the Sun is also orbiting us but not significantly – it’s just slightly off-centre. Although it takes roughly 365¼ days to get round the Sun, it doesn’t happen at a constant speed. Kepler’s laws of planetary motion include the most influential of all, the third, which was to give rise to Newton’s theory of universal gravitation. This states that the square of the sidereal period (year) of a planet is directly proportional to the cube of its mean distance from the Sun. This is easiest to work out with Saturn, since it takes about thirty years to orbit and is about ten times the distance of Earth from the Sun. The cube of ten is a thousand and that’s square root is close to thirty, thirty squared being of course nine hundred. Now Earth is between 1.01675 and 0.9832899 AU from the Sun-Earth baycentre, so it can be calculated to reach a maximum velocity of 30.29 kps and minimum of 29.29 kps, meaning that if Earth was at aphelion and Antichthon perihelion and a line drawn through their centres passed through the barycentre of the Sun-Earth system, Antichthon would be due to appear from behind the Sun after about six hours. Also, the barycentre would be at the centre of the Sun rather than to one side because, as the Pythagoreans correctly surmised, the system would be balanced between the two planets pulling the Sun in opposite directions.

The stable locations in an orbit between two bodies are referred to as Langrangian Points, and they do not correspond to where one might at first expect them to be. L1 is where the pulls of the Sun and Earth are equal, and since the surface gravity of the Sun is 109 times ours, it will be about 1.5 million kilometres above the equator at noon on an equinox. Likewise L2 on the other side at midnight, at the same distance. Jupiter has a collection of asteroids situated at L5 and L4 known as the Trojans, sixty degrees ahead and behind. It’s also possible that there are dust clouds in cis lunar space in the same places, L4 and L5, referred to as Kordalewski Clouds. If Antichthon was the same size and mass as Earth, it would have influenced the trajectories of spacecraft aimed at Venus and Mars to the extent that they would not have taken their predicted courses and would have failed to enter orbit, failed to land or crashed into their targets. At this distance from Antichthon, the gravitational influence would be equivalent to 0.46 parts per thousand million, but it’s possible to land rovers and landers precisely on the surface, which would not be the case if Antichthon was of the same size as Earth. The L3 point on our orbit is also unstable in this star system because Venus would come within about thirty million kilometres of it and has a gravitational pull similar to ours. This also influences the position of Earth itself. Hence there can be no Antichthon in the sense of being a planet the same size as ours. However, so far as I can think nothing rules out the possibility of a much smaller body or perhaps a dust cloud in that position, which is too small to detect from here and is difficult to detect due to the Sun’s glare, and in fact I think such an object very probably does exist. It could be an asteroid, a group of asteroids, a rubble pile or a dust cloud, but the chances are it is there, just as there are likely to be objects in the other four locations. The same applies to the other planets, meaning that there are forty such spots in the Solar System, plus innumerable others associated with moons.

Antichthon has cropped up a lot in fiction. Probably the most famous example is Mondas, the Cybermen’s home world, which is in ‘Doctor Who’. In the final William Hartnell adventure, ‘The Tenth Planet’, an Antarctic tracking station finds that the Zeus IV spacecraft is being pulled off course by an unknown force. This is in fact what would happen if Antichthon actually existed, and it’s also described as having left its previous orbit due to the arrival of Cynthia (“The Moon”), which led to inhospitable conditions and the need to use prosthetics on the inhabitants. Mondas is shown as identical to Earth. This is actually quite plausible for a ‘Doctor Who’ story and it also explains why Mondas hasn’t been detected, except that nowadays it’s not where the Whoniverse ended up going because the revival decided to put them in a parallel universe instead. This is one use for Antichthon in fiction: it enables a single “parallel timeline” compared to factual history, though only one. It’s also feasible that a previously stable orbit could be disrupted by the arrival of a large moon on this side.

The 2011 film ‘Another Earth’ is based on the parallel universe premise, in that so far as I can tell it seems to posit the idea that the new Earth encountered in the film is absolutely identical down to individuals, whose lives may however have taken different courses, so this is a kind of “what if?”/”if only” scenario. Back in the Anderson ‘verse, there’s a film called ‘Doppelgänger’, also known as ‘Journey To The Far Side Of The Sun’, which (spoilers follow but this is pretty obscure nowadays) involves the discovery of a mirror world on the other side of the Sun, where everything, including apparently organic molecules, has reverse chirality. As I haven’t seen it, I don’t know if this means food on the other planet turns out to be poisonous or non-nutritious to the astronaut, or much about it at all.

I have vague memories of a children’s sci-fi book where Antichthon was still populated by non-avian dinosaurs, but I haven’t tracked it down.

The most notorious use of Antichthon is in John Norman’s ‘Gor’ series, which raises all sorts of political and ethical questions due partly to the writing itself and also due to the public response to it. I’m probably going to go into this in greater depth in a post of its own, but for now I’ll just cover it sketchily. In the ‘Gor’ series, Antichthon is called Gor, which apparently means “rock” in the lingua franca, and has been populated by advanced aliens abducting humans through history and forcing them into a technologically primitive state. There are other aspects which I’m reluctant to mention, although I will in future, but the whole thing strikes me as a bit of a wasted scenario because of what Norman did with it. Here once again, though, is an attempt to portray a single alternate history and in this case an alternate scenario which the author very disturbingly regards as utopian. There’s so much to say about this that it deserves a post of its own, but for now I will say that, the appallingly extreme sexism notwithstanding, I can empathise with an attempt to anchor a fantasy in reality and plausibility this way, although even saying that feels like I’m being too kind to him about these atrocious novels. I also get the impression that the fact that there is just one alternative suits Norman quite nicely.

That, then, is all I want to say about the matter. I think it would be interesting to send a space probe to our Lagrangian points to discover what’s actually going on there. It would be particularly nice to know that there was a Pluto-sized body there, although I’m not sure what the maximum diameter and mass possible for it not to be detected would be. Even a few pebbles would be good. But what are the chances of that getting paid for?

Small – Far Away

Until I was about thirteen, it used to mystify me why distant objects look smaller than close ones. Why wasn’t everything like tunnel vision? If there’s a castle in the middle distance which looks like a mathbox at arms length, why would they seem to be the same size? If they weren’t, vision would be very cluttered. There is, though, probably no way that could happen.

The answer, which it took me a silly amount of time to work out, is of course that the further away your field of vision is, the larger area it occupies, and therefore the smaller the portion of that area is occupied by objects within that field at that distance. I actually had to read Jacob Bronowski’s ‘Ascent Of Man’ before I realised how it worked. I presume practically everyone else who can see has worked it out before they were able to use language, but for some reason not me. It might be due to my poor eyesight, as I’ve been short-sighted for as long as I can remember. My early visual memories are literally blurry.

There’s a famous scene in ‘Father Ted’ about this:

After reaching adulthood, I did have one strange experience on travelling past a field of sheep on a train and not getting any visual cues regarding how distant it was, where they somehow ended up looking about the size of cauliflowers to me. This is odd because there are cues such as mistiness, how you need to focus your eyes and the relative angles of your pupils which ought to tell you what’s going on. Nonetheless, and perhaps mildly embarrassingly, these didn’t come into play on this occasion for some reason. Of course I didn’t actually think they were the size of caulis, but the impression was vivid.

And yes, I hereby acknowledge that I still find Graham Linehan’s writing hilarious.

Another place where “small – far away” comes into play is of course ‘Doctor Who’:

I think there’s a history of dimensional transcendentalism in British children’s literature. Actually that’s quite a pretentious way of saying it, and it’s probably fairer to say that C S Lewis’s 1950 novel ‘The Lion, The Witch And The Wardrobe’ kind of invented it, not ‘Doctor Who’. The wardrobe seems to be bigger on the inside, although it’s because it’s a portal to another universe. Looking at it that way, the TARDIS is dimensionally transcendental because it’s a pocket universe, although ‘Who’ already uses that term to mean something else. As a child, I saw the TARDIS as kind of mushroom-like, in that the physical exterior of the vehicle contained a kind of stalk extending into hyperspace and expanding to a size bigger than the three dimensions of the Police Box. This is similar to the First Doctor’s explanation of the feature. I’ve always presumed that the word “transcendental” turns up in that in the mathematical sense rather than “transcendental meditation” or something else. A transcendental number is one which cannot be expressed using the four standard arithmetical operations or raising to a whole number power. All transcendental numbers are also irrational, since a ratio is one integer divided by another. There is an uncountably infinite set of transcendental numbers, as opposed to integers which are only countably infinite. I’m left with the impression that the dimensional transcendentalism of the TARDIS is achieved by exploiting the points in space between the ones accessible to us in ordinary space, but these two versions can be combined if you imagine the TARDIS to have a kind of four-dimensionally “rough” space along the lines of “If Wales were flattened out it’d be bigger than England” kinda thing. This ignores the Planck Length though.

‘Doctor Who’ is, to say the least, fiction. However, some things really are bigger on the inside. One example is a sphere exactly half the diameter of the Universe. The Universe is said to be 93 thousand million light years across, which reducing it to more manageable units is a diameter of 28.5 gigaparsecs. In Euclidean space, a sphere of half this size would have a volume of a little over 1515 cubic gigaparsecs. However, since space is not Euclidean, this is incorrect and the actual volume of such a sphere is 18 181 cubic gigaparsecs. It actually has a dozen times the volume. This is like the forty-five centimetre diameter Pilates ball in the corner of this room having an internal volume of a ball more than twice its diameter, which would make it a lot slower to inflate and deflate. You’d wonder where all the air was going or coming from.

It isn’t confined to the Universe as a whole either. The distance between the event horizon and the centre of a black hole is greater than the apparent radius of that event horizon. In fact, technically any object with mass is larger on the inside because gravity is a distortion of space, although I don’t think anyone has worked out how much it’s done so. It can’t be significant on the scale of Earth’s mass though because that’s been measured so precisely that the discrepancy is so small that placing the apparent size of the planet in the same volume as if space were Euclidean would not lead to any visible difference even on our comparatively minute scale. Nonetheless it is technically true.

Great Britain, which could possibly do with another name (Albion?) is the eighth largest island, and is accompanied to its west by the twentieth largest, Ireland. There is then, as usual, a kind of power law of islands of diminishing size and variable isolation. I was recently rather shocked to find that I’d been completely unaware of Portsea Island, which is the third largest in terms of population in these isles at two hundred thousand. Or rather, I knew it existed and I’ve even been there, but I failed to recognise the significance of the fact that a large town was largely built on it. Some of the smaller islands are far away, but still count as part of the archipelago: Rockall comes to mind, but also the islands of St Kilda. The question of whether the Faroe Islands count as part of this collection of bits sticking up out of the water also arises. Pear’s Cyclopædia used to say they were part of Scotland, although that was not meant in political terms but geographically. The reason I bring this up here is the evolutionary processes known as island dwarfism and island gigantism, together known as the “island effect” or “island rule”. This is the tendency for small animals to become larger on islands and large animals to become smaller. What, though, do “small” and “large” mean here?

The Canadian biologist J. Foster was one of the first people to study the island effect thoroughly in the 1960s, looking at various groups of mammals, and found that species of subspecies varied in size according to their taxon. Carnivores were smaller, rodents larger, even-toed ungulates smaller and insectivores and lagomorphs smaller. He didn’t look at creatures other than mammals, but the effect does apply to them, as with the Komodo dragon and giant tortoises at the large end and pygmy frogs at the other. One explanation is that smaller creatures get larger due to the lack of predators, whereas larger ones get smaller because of the lack of food. If this is so, the factors involved don’t just apply to islands. I’m personally wondering two things right now: does it apply to lakes, and does it affect plants? And the third thing is, how small does an island have to be before this starts to happen? Does it apply to Great Britain? Are animals and plants on islands far away from the English East Midlands smaller or larger in these islands? It should help to look at more distant examples first.

Possibly the most famous incidence of insular dwarfism is of the Flores Straits Islanders, who were humans of unusually small stature, currently classified as a different species, being around 110 centimetres tall. They died out early in the last Ice Age, although there appear to be folk tales of them still around in the area. Humans currently living in the area are also unusually short, but not to the same extent. They seem to have been a sister species to Homo habilis, the “handy man”, who lived in Afrika about two million years ago. Once again, we’re in the Coral Triangle as Flores Island is in Eastern Indonesia. The island of Komodo itself, where Komodo dragons live, is nearby. On Flores Island there are other examples of dwarfism. As far as the humans were concerned, it was hypothesised that their size was not an adaptation but was associated with pathology, such as Down Syndrome or iodine deficiency. Other primates in this category include an extinct species of macaque who lived on Sardinia and a colobus monkey native to Zanzibar. There was also a dwarf wolf native to Honshu, Kyushu and Shikoku, which strike me as rather large compared to some others, but it’s been claimed that the size of island is not the main factor, which makes no sense to me because in a sense a continent is an island.

Dodos are a good example of island gigantism, and unfortunately also an illustration of island tameness. It’s possible that small herbivores find it easier to hide from large predators, so they become larger in their absence. There were a number of species of giant primate on Madagascar, which is getting on for three times the size of Great Britain. The Pleistocene extinction event, which may or may not be linked to human activity, has led to a lot of larger species dying out. It seems to me also that they may be occupying vacant niches due to lower biodiversity.

There are examples of island gigantism in these isles. For instance, there’s an endangered vole in the Orkeys who is unusually large, a fairly large subspecies of field mouse on St Kilda, but I’m not aware of any insular dwarfism. That said, it does actually seem that the species of animals living in these islands are often smaller than their continental counterparts, and this may be a form of dwarfism. For instance, there are three very small species of native cockroach in the genus Ectobius, each only about a third to a quarter of the length of Blatta orientalis or the larger Periplaneta americana. Likewise with cicadas, native to the New Forest. Cicadetta montana is around a centimetre long, but cicadas elsewhere can be up to five centimetres in length. As is usual with evolution, the size difference probably already existed but became significant in Britain due to the pressure from human activity. That’s just my guess though.

The thing about these islands, though, is that they’ve only been islands at all for the past seven thousand years and are still very close to France and Benelux, so the isolation which might apply to other islands may not pertain to us. Then again, the Orkneys are pretty close to Great Britain too. The Orcadian example, though, might illustrate something about genetics more generally. Orcadians are generally the most distinct population of humans in Ireland and Britain in terms of ancient ancestry here, and the voles of the Orkneys may partly reflect a similar distinction. That does raise another issue for me though: is there another scale factor? Rodents like voles are liable to stay on their islands rather than often surviving to mix with the mainland population, except where they’re helped by humans, but a beaver or capybara is living in a smaller world and less likely to be distinct for that reason. Again, this is just me.

Probably the most shocking example of the island effect is what happened on Haţeg Island in the late Cretaceous. Here, pterosaurs became giants and sauropods (i.e. the likes of Diplodocus and Brachiosaurus) dwarfs. I’ve mentioned the place before. Haţeg Island was about the size of Ireland and was situated in the northern Tethys in today’s Romania. Its pterosaurs were extremely large. Hatzegopteryx, for example, had a twelve metre wingspan. Magyarosaurus and Paludititan, by contrast, were dwarf sauropods, both about six metres long and weighing about a tonne. They might have been preyed upon by the pterosaurs.

Presumably, if at some time in the future Britain was able to stay isolated, after we’ve become extinct, it might be expected to show the island effect, but that would depend on it remaining an island. Although the immediate likelihood of us staying isolated is high due to anthropogenic global warming raising the sea level, in the long term Doggerland, currently below sea level in the German Ocean/North Sea, will rebound against the pressure of the ice sheets and the whole region is likely to return to being a peninsula. Consequently we probably won’t ever be affected much by island gigantism or insular dwarfism, meaning that living in these islands is long going to be like it is now: looking through the wrong end of a telescope and seeing tiny animals here, but giant ones abroad.

The Anti-Universe

A prominent mythological theme is that of time being cyclical. For instance, in Hinduism there is a detailed chronology which repeats endlessly. Bearing in mind that the numbers used in mythological contexts are often mainly there to indicate enormity or tininess, there is the kalpa, which lasts 4 320 million years and is equivalent to a day in Brahma’s life. There are three hundred and sixty of these days in a Brahman year, and a hundred Brahman years in a Brahman lifetime, after which the cycle repeats. Within a Brahman Day, human history also repeats a cycle known as the Yuga Cycle, which consists of four ages, Satya, Treta, Dvapara and Kali. The names refer to the proportion of virtue and vice characterising each age, so Satya is perfect, life is long, everyone is kind to each other, wise, healthy and so on, satya meaning “truth” or “sincerity”, Treta is “third” in the sense of being three quarters virtue and one quarter vice, Dvapara is two quarters of each and Kali, unsurprisingly the current age, is the age of evil and destruction. Humans start off as giants and end as dwarfs. Then the cycle repeats. Thus there are cycles within cycles in Hindu cosmology.

The Maya also have a cyclical chronology, including the Long Count, in a cycle lasting 63 million years. Probably the most important cycle in Mesoamerican calendars is the fifty-two year one, during which the two different calendars cycle in and out of sync with each other. The Aztecs used to give away all their possessions at the end of that period in the expectation that the world might come to an end.

The Jewish tradition has a few similar features as well. Firstly, it appears to use the ages of people to indicate their health and the decline of virtue. The patriarchs named in the Book of Genesis tend to have shorter and shorter lives leading up to the Flood, which ends the lives of the last few generations before it, including the 969-year old Methuselah. Giants are also mentioned in the form of the Nephilim, although they are seen as evil. I wonder if this reflects the inversion of good and evil which took place when Zoroastrianism began, where previously lauded deities were demonised. There is also a cycle in the practice of the Jubilee, consisting of a forty-nine year Golden Jubilee and a shorter seven year Jubilee, and obviously there are the seven-day weeks, which we still have in the West.

The Hindu series of Yugas also reflects the Greek tradition of Golden, Silver, Bronze and Iron Ages, which was ultimately adopted into modern archæology in modified form as the Three-Age System of Stone, Bronze and Iron. The crucial difference between the Hindu and Greek age system and our own ideas of history is that they both believed in steady decline whereas we tend to be more mixed. We tend to believe in progress, although our ideas of what constitutes that do vary quite a lot. In a way, it makes more sense to suppose that everything will get worse, although since history is meant to be cyclical it can also be expected to get better, because of the operation of entropy. Things age, wear out, run down, burn out and so on, and this is the regular experience for everyone, no matter when they’re living in history, and it makes sense that the world might be going in the same direction. On the longest timescale of course it is, because the Sun will burn out, followed by all other stars and so on.

Twentieth century cosmology included a similar theory, that of the oscillating Universe. It was considered possible that the quantity of mass in the Universe was sufficient that once it got past a certain age, gravity acting between all the masses in existence would start to pull everything back together again until it collapsed into the same hot, dense state which started the Universe in the first place. There then emerge a couple of issues. Would the Universe then bounce back and be reborn, only to do it again in an endless cycle? If each cycle is an exact repetition, does it even mean anything to say it’s a different Universe, or is it just the same Universe with time passing in a loop?

This is not currently a popular idea because it turns out that there isn’t enough mass in the Universe to cause it to collapse against the Dark Energy which is pushing everything apart, so ultimately the objects in the Universe are expected to become increasingly isolated until there is only one galaxy visible in each region of the Universe where space is expanding relatively more slowly than the speed of light. This has a significant consequence. A species living in a galaxy at that time would be unaware that things had ever been different. There would be no evidence available to suggest that it was because we can currently see the galaxies receding, and therefore we can know that things will be like that one day, but they would have no way to discover that they hadn’t always been like this. This raises the question of what we might have lost. We reconstruct the history of the Universe based on the data available to us, and we’re aware that we’re surrounded by galaxies which, on the very large scale, are receding from each other, so we can imagine the film rewinding and all the stars and galaxies, or what will become them, starting off in the same place. But at that time, how do we know there wasn’t evidence of something we can no longer recover which is crucial to our own understanding of the Universe?

Physics has been in a bit of a strange state in recent decades. Because the levels of energy required cannot be achieved using current technology, the likes of the Large Hadron Collider are not powerful enough to provide more than a glimpse of the fundamental nature of physical reality. Consequently, physicists are having to engage in guesswork without much feedback, and this applies also to their conception of the entire Universe. I’ve long been very suspicious about the very existence of non-baryonic dark matter. Dark matter was originally proposed as a way to explain why galaxies rotate as if they have much more gravity than their visible matter, i.e. stars, is exerting. In fact, if gravity operates over a long range in the same way as it does over short distances, such as within this solar system or between binary stars, something like nine-tenths of the mass is invisible. To some extent this can be explained by ordinary matter such as dust, planets or very dim stars, and there are also known subatomic particles such as the neutrinos which are very common but virtually undetectable. The issue I have with non-baryonic dark matter, and I’ve been into this before on here, is that it seems to be a specially invented kind of matter to fill the gap in the model which, however, is practically undetectable. There’s another possible solution. What makes this worse is that dark matter is now being used to argue for flaws in the general theory of relativity, when it seems very clear that the problem is actually that physicists have proposed the existence of a kind of substance which is basically magic.

If you go back to the first moment of the Universe, there is a similar issue. Just after the grand unification epoch, a sextillionth (long scale) of a second after the Big Bang, an event is supposed to have taken place which increased each of the three extensive dimensions of the Universe by a factor of the order of one hundred quintillion in a millionth of a yoctosecond. If you don’t recognise these words, the reason is that these are unusually large and small quantities, so their values aren’t that important. Some physicists think this is fishy, because again something seems to have been simply invented to account for what happened in those circumstances without there being other reasons for supposing it to be so. They therefore decided to see what would happen if they used established principles to recreate the early Universe, and in particular they focussed on CPT symmetry

CPT symmetry is Charge, Parity and Temporal symmetry, and can be explained thus, starting with time. Imagine a video of two billiard balls hitting and bouncing off each other out of context. It would be difficult to tell whether that video was being played forwards or backwards. This works well on a small scale, perhaps with two neutrons colliding at about the speed of sound at an angle to each other, or a laser beam reflecting off a mirror. Charge symmetry means that if you observe two equally positively and negatively charged objects interacting, you could swap the charges and still observe the same thing, or for that matter two objects with the same charge could have the opposite charges and still do the same thing. Finally, parity symmetry is the fact that you can’t tell whether what you’re seeing is the right way up or upside down, or reflected. All of these things don’t work in the complicated situations we tend to observe because of pesky things like gravity and accidentally burning things out by sticking batteries in the wrong way round or miswiring plugs, but in sufficiently simple situations all of these things are symmetrical.

But there is a problem. The Universe as a whole doesn’t seem to obey these laws of symmetry. For instance, almost everything we come across seems to be made of matter even though there doesn’t seem to be any reason why there should be more matter than antimatter or the other way round, and time tends to go forwards rather than backwards on the whole. One attempt to explain why matter seems to dominate the Universe is that for some reason in the early Universe more matter was created than antimatter, and since matter meeting antimatter annihilates both, matter is all that’s left. Of course antimatter does crop up from time to time, for instance in bananas and thunderstorms, but it doesn’t last long because it pretty soon comes across an antiparticle in the form of, say, an electron, and the two wipe each other off the map in a burst of energy.

These physicists proposed a solution which does respect this symmetry and allows time to move both forwards and backwards. They propose that the Big Bang created not one but two universes, one where time runs forwards and mainly made of matter and the other where time goes backwards and is mainly made of antimatter, and also either of these universes is geometrically speaking a reflection of the other, such as all the left-handed people in one being right-handed in the other. This explains away the supposèd excess of matter. There’s actually just as much antimatter as matter, but it swapped over at the Big Bang. Before the Big Bang, time was running backwards and the Universe was collapsing.

In a manner rather similar to the thought that an oscillating Universe could be practically the same as time running in a circle because each cycle might be identical and there’s no outside to see it from, the reversed, mirror image antimatter Universe is simply this one running backwards with, again, nothing on the outside to observe it with, and therefore for all intents and purposes there just is this one Universe running forwards after the Big Bang, because it’s indistinguishable from the antimatter one running backwards. On the other hand, the time dimension involved is the same as this one, and therefore it could just be seen as the distant past, which answers the question of what there was before the Big Bang: there was another universe, or rather there was this universe. It also means everything has already happened.

But a further question arises in my head too, and this is by no means what these physicists are claiming. As mentioned above, one model of the Universe is that it repeats itself in a cycle. What we may have here is theoretical support for the idea of a Universe collapsing in on itself before expanding again. That’s the bit we can see or deduce given currently available evidence. However, in the future, certain evidence will be lost because there will only be one visible galaxy observable, and the idea of space expanding will be impossible to support even though it is. What if one of the bits of evidence we’ve already lost is of time looping? Or, what if time just does loop anyway? What if time runs forwards until the Universe reaches a maximum size and then runs backwards again as it contracts? There is an issue with this. There isn’t enough mass in the Universe for it to collapse given the strength of dark energy pushing it apart, but of course elsewhere in the Multiverse there could be looping universes due to different physical constants such as the strength of dark energy or the increased quantity of matter in them, because in fact as has been mentioned before there are possible worlds where this does take place. Another question then arises: how does time work between universes? Are these looping universes doing so now in endless cycles, or are they repeating the same stretch of time? Does time even work that way in the Multiverse, or is it like in Narnia, where time runs at different speeds relative to our world?

It may seem like I’ve become highly speculative. In my defence, I’d say this. I have taken pains to ignore my intuition in the past because I believed it was misleading. However, there appears to be an intuition among many cultures that time does run in a cycle, and the numbers these cultures produce are oddly similar. The Mayan calendar’s longest time period is the Alautun, which lasts 63 081 429 years, close to the number of years it’s been since the Chicxulub Impact, which coincidentally was nearby and wiped out the non-avian dinosaurs. The Indian kalpa is 4 320 million years in length, which is again quite close to the age of this planet. Earth is 4 543 million years old and the Cretaceous ended 66 million years ago, so these figures are 4.6% out in the case of the Maya and 5% for the kalpa. Of course it may be coincidence, and the idea of time being cyclical may simply be based on something like the cycle of the day and night or the seasons through the year, but since I believe intuitive truths are available in Torah and the rest of the Tanakh, I don’t necessarily have a problem with other sources. Parallels have of course been made between ancient philosophies and today’s physics before, for example by Fritjof Capra in his ‘The Tao [sic] Of Physics’. Although much of what he says has been rubbished by physicists since, there is a statue of Dancing Shiva in the lobby at CERN and one quote from Capra is widely accepted:

“Science does not need mysticism and mysticism does not need science. But man needs both.”

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:

Author
en:user:MichaelNetzer
This image is copyrighted; however, the copyright holder User:MichaelNetzer allows the image to be freely redistributed, modified, used commercially and for any other purpose, provided that their authorship is attributed.

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.

Balbides And A Cold Sun?

a soccer goal, shot on the German »Chambers League« 2005, the annual football tournament of the german Chambers of commerce in the Sport School in Grünberg, Hesse, Germany
Date
created 21. Mayıs 2005
Source
Own work
Author
Manuel Heinrich Emha

The other day a bloke turned up at our front door with what looked like a scythe wrapped in brown paper. It was easy to distinguish him from the Grim Reaper because he wasn’t wearing a robe and had a lot more flesh on his bones than one might expect. It was in fact my dad’s hoist. Rather taken aback that there didn’t seem to be a base, I asked him about the contents of his truck and he replied that there was a second piece whose shape he had difficulty in describing. I then realised, suddenly, that this was an opportunity to use a word which practically nobody knew, although it would not be an aid in communication. He was attempting to describe a rectangular balbis!

For some reason, although it’s a common shape the word is almost never used, and as far as I know has only been written about once in geometry. There are two types of balbides (that’s the plural). One is in the shape of a capital H, which is the “common” balbis, and the other is like a rectangle with one side missing, the rectangular balbis. They might at first be considered to be different shapes, but depending on the form of geometry used, they may or may not be the same. Remarkably, only one mathematician ever seems to have studied and written about this shape and it’s generally dismissed or ignored, but like other mathematical figures it has properties of its own which seem just as significant as others.

In geometry, a literal line is infinite in length. It’s a line segment which isn’t. In Euclidean geometry, parallel lines never meet, but it emerged in the nineteenth century that Euclidean geometry doesn’t apply to our Universe and in fact parallel lines do meet at a distance of many gigaparsecs. Now consider both types of balbis. In Euclidean space, a rectangular balbis can be thought of as a triangle with two right angles whose apex is at infinity. It’s a limiting case of a triangle which can only exist in Euclidean space. In space as it actually is, or seems to be, there can be no absolute rectangular balbis because space ultimately curves round on itself, so the only possible type of balbis is the H-shaped version, whose sides come back round the Universe to meet at their starting point. However, there can be a shape very close indeed to a rectangular balbis in the form of an isosceles triangle which is very nearly a rectangular balbis but in fact has an apex higher than the distance between the base and the edge of the observable Universe. It’s hard to imagine any practical purpose for this, and also hard to imagine any observable property this triangle might have that distinguishes it from a rectangular balbis.

As I’ve mentioned, there has so far as I can tell only ever been one mathematician who has studied or written about balbides. His name was the Reverend P H Francis, he held a Masters from Cambridge in Mathematics and he is remarkable among the people I might describe as fringe thinkers for being a proper scientist, in a way. His work focussed on three areas. Two of these were the analysis of games in a non-game theory kind of way and the mathematics of infinity, particularly in connection with balbides. His understanding of games is that they are an outgrowth of the human instinct for hunting and are all connected to the idea of aiming for a target, which it occurs to me might be interesting from a theological viewpoint in view of the fact that the generic Hebrew word for sin, עבירה, literally means missing the target, and I note the guy was a vicar. His mathematics presumably makes sense and is up to a certain academic standard. From what I’ve read of his work, it made sense to my twelve-year old mind, bearing in mind that I have no particular aptitude in that field. He certainly seems to have been a respectable mathematician, if somewhat isolated because of his idiosyncratic interests. His third field is where it gets weird. He believed that the nature of infinity offered a solution to Olber’s Paradox, and his solution was utterly bizarre. Before I get to that, I should go into what Olbers’ Paradox is.

Olbers’ Paradox can be summed up by the question, why is the sky black? That is, if we live in an infinite Universe (and we probably don’t but bear with me because it’s still odd) which is homogenous, i.e. there are stars and galaxies in all directions, when we look up at the night sky it ought to be blue-white at a colour temperature of around 40 000°C, and in fact the temperature of most of the Universe should be at around that level. This is because, space being infinite in this view, any straight line from any point should intersect with the surface of one of the hottest possible stars at some point, so the entire “surface” of the sky should be that bright and that hot. But it isn’t. Why?

Some of the assumptions on which this is based are now outdated. In the early twentieth century, the Steady State theory held that space was infinite and eternal, and this view was remarkably well-supported by the evidence available at the time. Once it was realised that space was constantly expanding it became clear that another solution to the paradox was that over sufficient distances, space was expanding faster than light and therefore light would never reach us. Incidentally, the issue is also present to some extent in a finite but static Universe, since if space is curved light is going to travel a lot. This also means that if the Universe was contracting rather than expanding, it would also heat up for the same reason and life would become impossible – every point would catch up with all the blue-shifted light. For this reason, it’s been stated that “I think therefore I am, and therefore the Universe is expanding”, which is probably the second thing Deep Thought realised.

P H Francis came up with a different solution to Olbers’ Paradox, apparently partly based on his views of infinity. I’m straining my memory here, but I seem to recall that he believed that the real number line was in fact a loop, reaching positive infinity before reversing its sign and becoming negative infinity, so for him a truly infinite number was both positive and negative. Consequently, for him too a balbis would be an example of a shape which meets itself in the middle, but for different reasons. It also seems to mean for him that at infinity, light reverses its direction, meaning that space is not exactly limited but reflects like a mirror. This next bit I have to admit I find utterly baffling. Francis also believed that infinity could be at any distance, possibly because the Universe is an irregular apeirohedron. This is going to need some explaining, and I may be wrong. An apeirogon is a polygon with countably infinite sides. An apeirohedron is the three-dimensional version, and is not the same as a sphere or spheroid because these have uncountably infinite faces. Instead, an irregular apeirohedron would consist of an infinite number of convex and concave polygons, and I’m guessing that this is what Francis has in mind. Because infinity is in a sense undefinable, it means that there are many possible values. Note that I don’t believe this is true, but in making that statement, if my guess is correct, I am contradicting a qualified mathematician who presumably knew what he was talking about.

And there’s more. Francis claimed further that the only star in the Universe is the Sun itself. What we see as stars in the night sky are in fact reflections of the Sun at various distances as its light “bounces off infinity”. This is his solution to Olbers’ Paradox. Moreover, the Sun is not hot. He believed that “the popular notion that the Sun is on fire is rubbish, and merely a hoary superstition on a par with a belief in a flat earth, an Earth resting on the back of a tortoise or an elephant, or a sun revolving around a stationary earth.” Of course people don’t literally believe that the Sun is on fire, but his target is more the idea that the Sun is hot at all. He gives several reasons for supposing the Sun is not a hot ball of gas. Firstly, the Sun is roughly spherical, and if it were a ball of gas or plasma, it would not have a smooth surface. Secondly, space is a vacuum, and heat cannot travel through a vacuum, hence thermos flasks. Thirdly, heat can be generated by cold objects. An electric fire, for example, is hot, but the generator which provides the current to be converted to heat needn’t be. He believed instead that the Sun is an electrically-charged light source whose electricity warms Earth’s atmosphere, and therefore the surface, and one piece of evidence for this is that at higher altitudes it’s colder, because the molecules of the atmosphere are further apart and therefore the heating effect is weaker. Earth is also reflective, and this prevents the radiation of heat into space because, and I may not be following this exactly, silvered surfaces do not radiate heat but prevent it from being radiated.

All of this is very odd. Whereas I don’t believe it for a second, that isn’t really what’s odd about it. The Rev. Francis reached his own conclusions which were well-founded, as he saw it, in mathematics, and there are clear links between his interests. A rectangular balbis is a goal mouth that never ends and he was interested in games. He saw games as centred on the idea of achieving a target, which he also saw as an evolutionary imperative connected with survival via hunting. At the same time, he was a vicar so he may have had similar views on Christianity as a useful strategy for playing the game of life, which involves meeting a moral target. Then there’s the issue of what happens if a balbis goes on forever and reverses into itself – infinity. Then there’s Olbers’ Paradox, which he seems to have solved by using the concept of infinity as he saw it and the reflection of light in an undefined distance. In fact the only bit of his thought which seems not to be part of this coherent whole is the temperate Sun. Even so, it has an internal consistency to it. What’s odd about it is him. He’s a qualified mathematician who managed nonetheless to draw the same kind of conclusions about the nature of reality as might be reached by a Flat Earther, someone who believes we are within a hollow earth, that Venus was a comet, that aliens visited humans in prehistoric times or that there is phantom time and the dark ages never happened. Some of the people involved in these claims are educated and intelligent to be sure. For instance, Velikovsky (the Venus guy) was a psychiatrist, Illig (phantom time) seems to have been his acolyte, Von Däniken was a hotel manager who, however, probably originally got his ideas from Carl Sagan and doesn’t appear to be sincere, and Flat Earthers are a whole plethora of people who, however, tend not to be scientifically trained. P H Francis is not like this. The profession followed by Velikovsky is potentially scientific but he seems mainly to have been a Freudian psychoanalyst which is clearly not. But Francis was a respectable mathematician, although many of his works are self-published. How did it happen that he reached such heterodox conclusions about cosmology?

He isn’t, in fact, alone in this. Fred Hoyle also ended up drawing unexpected conclusions and sticking with them, although they were somewhat more in keeping with mainstream cosmology. Hoyle was the first person to hypothesise that heavy elements were formed by nuclear fusion in stars, something which Francis, incidentally, definitely would not be on board with. This is now accepted more or less universally. However, he rejected the Big Bang theory and stuck with the Steady State, claiming that the apparent red shift of receding objects was not caused by the expansion of space but the presence of microörganisms in the interstellar medium absorbing other wavelengths of light. Hoyle in fact coined the term “Big Bang Theory”, in 1949, and meant it to be pejorative. He believed that the Roman Catholic priest Georges Lemaître who originally came up with the idea that because space was expanding it must have originally been in a hot, dense state at the beginning of time to be akin to the cosmological argument for the existence of God, and to be honest I find it hard not to agree with him there. But those are my issues and not those of someone more versed in cosmology than I. Hoyle did, however, believe in the fine-tuning argument, as he held that the existence of the carbon atom in particular seemed suspicious in an arbitrary Universe.

One significant difference between Hoyle and Francis seems to be that Hoyle was inside his profession and Francis outside it. Consequently Hoyle is not perceived as a “crank” in the same way as someone like Velikovsky or Illig, whereas Francis probably is. After all, he did self-publish and doesn’t seem to have had academic peers. It’s also interesting that there are two priests here involved in cosmology, one an Anglican, the other a Roman Catholic, and I think this perhaps illustrates how cosmology itself, as James Muirden claimed, is not a purely scientific profession but attracts people who would seek non-scientific but nonetheless valid answers to ultimate questions about reality. It’s substantially about reputation and being linked to some kind of social network, and that isn’t just to say it’s an “old boy network”, although I think it is, but that we all need to bounce our ideas off people to remain sane. Nonetheless, the takeaway from this is that the Reverend P H Francis stands out among “cranks” by being so very heretical in spite of being scientifically and mathematically literate, and I think this makes him unique.