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.

The 19A0s

As usual, it isn’t clear to me whether people have heard of a particular thing, so I may or may not be telling you about something you already know, but here goes anyway.

I’ll start with the Phantom Time Hypothesis. This is the belief, promoted by the Bavarian historian Heribert Illig, that the years 611-914 CE are fabricated and that we therefore currently live not in the year 2021 but the early eighteenth century. This is a conspiracy “theory” that Otto III of the Holy Roman Empire persuaded the Pope to alter the year in order to put them in the year 2000 AD, and I use Anno Domini rather than Common Era here deliberately because they were said to have fabricated this system themselves. Further, Illig claims that the Emperor Charlemagne never existed, which is a bit of a blow to every European because we’re all supposed to be descended from him, so presumably we don’t exist? Evidence supporting this hypothesis include the relative scarcity of archaeological finds from the seventh to the tenth century CE, the similarity between architecture of Late Antiquity and the Middle Ages and the failure of the Gregorian calendar to line up with the Julian calendar as it was in Roman times despite being corrected from 1582 onwards. There are huge problems with this hypothesis which amount to sound refutation. Outside Europe, the calendars match up absolutely fine, for instance the Mayan, Muslim and Jewish calendars, astronomical events such as conjunctions and eclipses still occur when they’d be expected and tree rings from the alleged period also fit the consensus view of history. For instance, on 3rd May 1715 there was a total eclipse of the Sun in Britain, which should’ve been three years ago according to this idea. There is indeed a discrepancy between the eleven days lost to the calendar when we adopted it in Britain, but that’s because it was intended to align with the Council of Nicea in 325 CE and not the start of the Christian era and some days had already been lost by that point.

Heribert Illig has connections with Immanuel Velikovsky’s beliefs that Venus used to be a comet that became a planet during the Bronze Age. Velikovsky was a psychiatrist born in Tsarist Russia to a Lithuanian Jewish family who practiced psychiatry in the British Mandate of Palestine. I was a fan of his ideas as a child but later came to realise that they make absolutely no sense, although it is interesting that he made various predictions about the solar system which turned out to be correct. Velikovsky sought to refute Freud’s claim that the Pharaoh Akhnaton was the founder of Judaism, an idea which incidentally I have wondered about myself because of Psalm 104, which is also why Freud thought this was so. This led him to investigate the chronology of Ancient Egypt and because of the apparent discrepancy between the apparently dateable events in the Hebrew Bible, he chose to revise that to resolve the problem, so it’s based on a faith-based approach to history. In order to explain events such as the destruction of Sodom and Gomorrah and the Plagues of Egypt, he posited that various astronomical catastrophes had taken place which led to happenings such as rains of burning hydrocarbons, and further, revised geology to make the claim that crude oil deposits were of recent origin and came from Venus.

So that’s two movements which seek to revise history. I don’t really understand why Illig should have made his revisions under the influence of Velikovsky. Maybe having come to question the idea of historical records being accurate, he ended up being unable to leave history alone and it planted the seeds of doubt in his mind about another period. I also don’t know what Illig now thinks about Velikovsky’s ideas, that is, whether he also believes history followed the accounts in the Hebrew Bible rather than other evidence or whether he just thinks the Dark Ages never happened.

Now there is a joke “belief” called “Last Thursdayism” which is taken from an earlier hypothesis called the Omphalos Theory. There are in fact two major schools of thought referred to as the Omphalos Hypothesis: this is the one which has nothing to do with psychogeography, Christopher Marlowe or the Isle of Dogs. This Omphalos “Theory” originated in the mid-nineteenth century and is named after the Greek word for navel, ομφαλος, because the fundamental question he attempted to answer can be summed up thus: did Eve and Adam have navels, since they weren’t born? It’s a response to the theory of evolution and amounts to the belief that God created the world in medias res, with wear on the teeth of hippos, all the fossils in place, the first humans as adults with navels and all their teeth and so on, a few thousand years ago. There’s an obvious theological problem with this, which is that one is supposed to believe that God doesn’t lie but this would basically have made the world one big lie. It’s still believed to some extent by creationists who hold that light from distant stars and galaxies was created in transit, although there are a couple of alternative hypotheses here that space is hyperbolic and we’re near the centre and that the speed of light is slowing down, which they also evoke to explain how Methuselah and his contemporaries came to live so much longer than we do nowadays. Of course the simple thing would be just to accept the findings of science, but no, apparently not. I actually used to know a geneticist who believed all this, and it saddened me that anyone could get a PhD in a life science while accepting this rubbish, when probably quite talented, previously well-educated and intelligent people probably didn’t even get bachelor’s degrees in biology. There’s no justice.

Last Thursdayism is a joke, and as its name suggests is the idea that the Universe was created last Thursday, with apparently consistent but false memories intact. This is of course possible in the sense that it doesn’t actually contradict any evidence whatsoever, just as it wouldn’t if it was last Wednesday or a few moments ago, but of course it’s untestable and nobody takes it seriously anyway. It’s generally used as a rejoinder to Young Earth Creationists, although it has strong affinities with Descartes’ method of radical doubt because it would also be very much his kind of thing to attempt to disprove (and he’d be bound to use the ontological argument to do so).

There’s another, rather niche, claim made along similar lines to the Phantom Time Hypothesis on a much smaller scale, which I assume also to be a joke attempting to parody it, referred to as “The 19A0s”. Before I go into that, it reminds me a little of the difficulty I used to have in accepting that there were years after 1984, which if I’m honest still feels like the present to me, and everything after it is just made up. This is of course due to the influence of a certain dystopian novel which I’ve written about elsewhere on this blog. It would be rather Orwellian either to make up extra years which never happened or to convince everyone that it will always be 1984 in the same way as “Oceania has always been at war with Eastasia”. This is just an unusually long December. I think the reason I find 1984 so magnetic isn’t so much to do with anything particularly major that happened during that year as that it was very much focussed on in advance at George Orwell’s instigation, and that it’s in the early part of my reminiscence bump and was the last full calendar year before I became adult, so maybe it isn’t entirely mentally healthy that I do this, although of course it is only a joke. Frankie Goes To Hollywood aren’t in the charts any more, Thatcher and Reagan are no longer in office and the ZX Spectrum is not currently the most popular microcomputer in the UK. Strange but true.

The 19A0s is kind of vaguely similar to this idea. I’m not sure where it originates, but it may be here. It isn’t a massively popular idea but a few people have taken it up and run with it. This page (which at least on this browser-machine-O/S is screwed up a little) mentions the Phantom Time Hypothesis, so I think it probably is inspired by it. The idea is that there is a lost decade between the late 1970s and the early 1980s, although it doesn’t seem to have lasted ten years. The dates in question are 28th February 1978 and 15th December 1983, a 2116-day period which for me includes the start of my own reminiscence bump. The language used in these links is rather obscurantist and I think pseudo-intellectual, but I think I can glean a few ideas from it. One is that whatever happened during this time was so traumatic that we’ve all been induced to forget it. Another is that it seems to be a psychogeographical project, or at least something like one. Psychogeography is a kind of playful, nomadic, surrealist, situationist approach to walking around a town or city which attempts to construct a new realistic narrative, perhaps to experience the urban landscape as art, but in this case by making associations between cultural artifacts such as the video Elpe by the Norwegian group Röyksopp and the DVNO video:

I’m not sure this is actually succeeding in saying something or if it’s more a kind of playful pseudo-intellectual chewing gum, but I do find myself drawn to it. What I’d project onto it would be the impression of a break between the post-war era and the “greed is good” world, which as I never tire of reminding you I went into here. As you can gather from the link, the apparent dislocation of 1979 is not in fact as abrupt as it seems. To make the post-war consensus, Keynesian world continue past 1979, I had to posit no less than seven changes in history, one of which was pre-Victorian. The seeds of the 1980s were sown more than a century and a half previously, and even that could be seen as the chains of cause and effect merely becoming discernible rather than an initial change.

One difference between the 19A0s and Phantom Time is that whereas the latter supposes unreal time which was inserted, the former imagines that there was a real period which was removed. I think one reason for the project is a kind of nostalgia which attempts to extend the period of a particular kind of design and iconography to more than it occupied in reality. Again, I have a lot of sympathy with this, and after all, it has nostalgia value for me too.

One suggestion made in the BoingBoing link is to search for the string “19A0”, which is phonetically identical to the year “1980”. In hexadecimal this string corresponds to the decimal number 6560, and it will occur from place to place. The idea is to treat this as “residue” in the Mandela Effect sense of the word. At the moment, in the personalised view of Google I’m presented with, many of the links I’m served with are in fact to do with the project, but I also get a spanner, a Thai letter like an sideways S, some two-coloured irregular shapes and references to the ‘Dune’ universe (Duniverse?).

To summarise then, this appears to be a parody art project a bit like the K Foundation or the Illuminati Trilogy, somewhat influenced by psychogeography and Situationism, and satire on the Phantom Time Hypothesis, but there’s remarkably little material available. It doesn’t seem to have been very successful, which I think is a pity because it really looks like it could’ve ridden on the coat tails of Vaporwave, but sadly it didn’t. It amounts to another of those things which I find interesting but is for some reason not appealing to most other people.