Deducing The Existence Of Rice Pudding And Income Tax

This post will not be entirely about ‘The Hitch-Hiker’s’ Guide To The Galaxy’. And incidentally, the rest of the ingredients list includes a teaspoon of cinnamon, presumably powder, in case you were wondering, and the next bit reads as follows (and has started to transition to live-action):

(apparently it couldn’t deduce the spelling of “yields”).

Just to put this in context, this is naturally from H2G2 and regards the operation of the second greatest computer in all of space and time, Deep Thought, who started from first principles with ‘I Think, Therefore I Am’ and managed to deduce the existence of rice pudding and income tax before anyone managed to turn it off. It does this without any RAM incidentally. Is it just me, or is anyone else reminded of the bomb in ‘Dark Star’?

This is the second time, to my knowledge, Douglas Adams chooses to parody Descartes in the series. The first time is with the Babel Fish proving God exists and therefore doesn’t exist. This one involves Descartes method of doubting as much as possible until all he’s left with is the Cogito, id est, “I think, therefore I am”, and then using the Cosmological and Ontological Arguments for the existence of God to fill in everything he’s just rejected as open to doubt. He could’ve gone further, but didn’t. Isaac Asimov did something similar in ‘Reason’, where a robot on an orbital solar power station deduces that there is no Universe outside the station and that humans are brought into existence in the airlock when they arrive and are killed when they re-enter the airlock to leave. Incidentally there are problems with his presentation of the Three Laws in this story because it was written before he’d fully formulated them.

In terms of the two deductions above, Adams has a version of the Universe which strongly resembles the English-speaking world of the late 1970s, perhaps even the Home Counties, and Deep Thought is therefore able to deduce the existence of rice pudding relatively easily. In fact I think income tax is a more probable deduction than rice pudding, although that still involves the existence of what may be a uniquely human institution, namely money. As a side note, the idea that cinnamon exists is reminiscent of ‘The Dune Encyclopedia’, where the spice Melange, secreted by the sandworms of Arrakis and enabling humans who take it to fold space and travel between the stars without moving, an ability known here as  קְפִיצַת הַדֶּרֶךְ or Qephitzat Ha-Derech, turns out to be similar in composition to cinnamic acid, as seen at the top of this diagram:

Molecular structure of the spice Melange. Note the copper atoms in the porphyrin ring, conferring its distinctive blue hue

Hence at least in the Dune universe, a cinnamon-like substance does exist off Earth.

As mentioned a few posts back, Fred Hoyle used the Anthropic Principle to conjecture that the bonding energy of the carbon-12 nucleus was of a certain value. Starting from the first principle that organic, carbon-based life exists, he predicted the triple-alpha process. In the early Universe, almost all atomic matter was either simple hydrogen (protium – just a proton and an electron) or helium-4, with two protons and two neutrons. If two helium-4 atoms combine, they form a beryllium-8 atom, and if that then collides with a further helium-4 atom, carbon-12 is formed. In most circumstances, the probability of this happening is very low but it so happens that the energy of three helium-4 atoms colliding is unusually close to the energy of a carbon-12 atom, meaning that they are more likely to stay together than they would be otherwise. This is an example of the so-called “fine tuning” which appears to show that either a Creator exists or that we are living in one of an innumerable number of parallel universes where the conditions happen to be exactly right. By a happy “accident”, conditions in this universe happen to favour the existence of carbon, upon which life can be built.

This is an unusual path of reasoning that turned out to lead to a successful prediction and is therefore similar to the deduction that rice pudding exists in H2G2. It goes roughly like this:

1. I think, therefore I am
2. Physical conditions in the Universe must allow thought to occur
3. For thought to occur, organic life must have existed at some stage
4. For organic life to exist, carbon must be an abundant element
5. For carbon to exist, the triple alpha process must be favoured

There’s a humungous number of steps missing from that argument of course, but it’s a fair sketch of how you get from the Cogito to the strength of the strong nuclear force and the existence of organic life. Note that Deep Thought was not an organic life form, but in order for computers to be invented, organic life forms are assumed to be necessary at some stage.

I was once very impressed indeed by an a priori idea that seems to prove that the atmosphere of any roughly spherical planet must have at least two locations where there is no wind. This sounds very much like the kind of thing which could only be demonstrated by observation. One can imagine looking at endless detailed global weather charts and finding at least two spots on each of them which are completely calm, and then making the inductive inference that it was very likely always to be the case. However, this isn’t necessary and in fact the proof can be demonstrated by means of imagining you’re trying to comb a tribble:

exhibit in the New Mexico Museum of Space History
21 August 2017, 14:59:27
Own work
Stilfehler

Each of the hairs on a tribble can be thought of as arrows indicating wind direction. No matter which way that hair is combed, there will always be at least two points on the animal’s surface from which all the hairs radiate. Of course it makes more sense to give a tribble a parting or whatever, but the fact remains that there have to be two such locations, and that’s a topological truth. Extend this to a globe showing wind direction on any approximately spherical planet or moon, and the fact remains true, except of course that the atmosphere has depth. This, however, simply means that each individual layer must also have two still spots. It doesn’t work if the world has mountains on it high enough to leave the atmosphere because then the supposed stationary spots could be lined up to be where the air would be if the mountains weren’t there, and this means that a toroidal world is exempt from this fact. It also means it doesn’t apply to ocean currents unless there’s no land on the world. Therefore it already becomes possible to conclude from the premise that there are round planets completely enveloped in atmospheres that this is so without actually going there and checking them out.

Yesterday’s post on landlocked countries led me to similar conclusions, although they’re probabilistic and rely heavily on the idea that there are other planets with territorial intelligent life forms using a money-based economy on them. In fact that’s not entirely true. There are two sets of implied facts about such worlds, one relying on the existence of beings like us in those respects, the other not. We have already divided Mars, Venus and other worlds geographically into smaller areas, which are however not that relevant to this issue because there are no open bodies of liquid on those planets, but if, for example, Venus looked like this, and the land masses were divided up geographically, they would have certain predictable features.

I made the following claims yesterday about landlocked territories. They are likely to:

• Be arid
• Have extremes of temperature
• Include high mountains, perhaps near or on their borders
• Be located on the largest continent
• Contain the point furthest from the land on that continent

The last point is not in fact true of Kazakhstan, Bolivia or Paraguay, but it is true of the Central African Republic. Except for the third, these are all consequence of the physical features of lines on a map separating bits of land, although not below a certain number. For instance, Hispaniola simply has a line drawn down the middle of it separating Haïti and the Dominican Republic and I have no knowledge concerning where the highest point on that island is, although it’s obviously more likely to be in the larger country. And to test that hypothesis without foreknowledge, the Dominican Republic is larger than Hispaniola and therefore more likely to contain the island’s highest point. And indeed the highest point on Hispaniola, and in fact in the whole of the Caribbean, is Pico Duarte. The reason for assuming that landlocked states are likely to have high mountains near their borders is that borders are often placed in inaccessible regions where there isn’t likely to be much argument over resources.

Then there are the conclusions which can be drawn about landlocked countries which do rely on the current economic system and the way humans tend to behave under it. Landlocked countries are also more likely to be:

• Neutral
• Poor
• Reliant on natural resources more than manufacturing
• Totalitarian
• Have intolerant attitudes among their population

I explained the reasoning behind these attributes yesterday. They don’t apply across the board. For instance, Switzerland is mountainous and neutral but also rich and relies on financial services fairly heavily, although of course it makes Swiss Army knives and clocks, and presumably a lot of other stuff which my ignorance and cartoonish image of the country has failed to reveal.

It’s also possible to invert and go to opposite extremes with the first list at least. For instance, the largest continent is likely to contain the highest mountain, and in fact it does in terms of height above sea level, and likewise the largest ocean is more likely to include the deepest point, which again is so. Maritime and island countries are likely to have wet weather, have relatively little variation in temperature, particularly if surrounded by a lot of ocean as with Polynesian nations, and be fairly flat. Inverting the list of human characteristics doesn’t work as well, at least with island nations, and here I have Britain in mind in particular. They are likely not to be neutral (true), rich (true), not reliant on natural resources (not true – North Sea oil and gas come to mind, also historically coal and tin), be liberal democracies (this is only marginally true in our case) and have tolerant attitudes. It seems to some extent that in fact the same things are true of Britain at least as much as they apply to landlocked countries. It is the case that we have a moderate climate which is also quite wet, and that we have no high mountains.

The economies of island nations tend to be smaller, isolated from the global economy, dependent on shipping and therefore having relatively high prices for imported goods, but this really applies more to oceanic islands such as those of Polynesia rather than those situated on continental shelves. This island I live on is hardly one of the former. Nor is its western companion. As mentioned yesterday, landlocked states are somewhat protected by violent, ocean-related events such as tsunami and hurricanes,and conversely islands aren’t. Their infrastructure is therefore vulnerable. Again, this is one of the realities of a small, exposed piece of land in the middle of an ocean, though only on a planet with a particular set of meteorological conditions. Vast expanses of ocean are generally amenable to the development of tsunami and hurricanes on this planet, and a glance at Jupiter indicates that the latter are common elsewhere, but there might be globally frozen oceans with volcanic peaks sticking out of them for example, or widespread shallow seas.

The Hairy Ball Theorem mentioned above doesn’t apply to tori. This has an interesting consequence for oceans which could be considered toroidal in the sense that they include a range of latitudes where there are only small islands impeding their flow around the planet, because it means there can and probably will be both a steady current running all the way round and also winds able to build up speed without encountering obstacles. There’s a contemporary and a prehistoric example of this. The Southern Ocean exists today in this form, and the Tethys, which was tropical and subtropical, was in place for around 200 million years and still has traces today, although it’s no longer a continuous ocean.

I’ve previously stated that landlocked countries are likely to include high mountains, but this is somewhat misleading as it ignores continental drift. In fact, both Americas have mountain ranges on the Pacific coast caused by the continents moving in that direction and encountering the Pacific Plate. On the other hand, when two continents collide, the result is a mountain range far from any ocean, as with the Himalayas. The trouble is that it looked like I was thinking of a continent as a kind of spread out mountain, which isn’t how it is.

There are forty-seven island nations. Although the largest is Indonesia, which is bigger than Mongolia, that’s distributed over a large number of islands of varying size and it’s also continental, being in Eurasia and Sahul (the technical name for Australia as a continent as opposed to a country). The “U”K is the seventh largest of these and Great Britain the ninth largest island of any kind. Again deploying the rice pudding principle, the area of island nations is likely to follow something like the 80:20 rule, in that eighty percent of the area of island nations will consist of twenty percent of the nations, or something close to that, and also eighty percent of the area of all islands will consist of twenty percent of the islands. It won’t be exactly that, but it should be close. For these forty-seven nations, that means that the nine largest ought to have four-fifths of the area. These are Indonesia, Madagascar, Japan, the Philippines, Papua, Aotearoa/New Zealand, Iceland, the “U”K and Cuba (Ireland is next on the list). It isn’t practical to do the same for physical islands because there are an indeterminate number. These islands taken together have an area of 4 460 372 square kilometres, which suggests that the remainder will have a total area close to 900 000 km². In fact their area adds up to 4 851 659 km² if I’ve calculated that correctly, which is fairly close. The same principle might be applicable to population and population density. Indonesia is again the most populous of these nations, the “U”K being fourth, and the most densely populated is Singapore, which is of course a city-state. The most sparsely peopled such nation is Iceland, although Kalaallit Nunaat/Greenland is even less densely populated but doesn’t quite count as an independent state.

Island nations are of course very subject to climate change, such as the increased acidity of the oceans causing erosion of coral atolls and reefs, rises in sea level and increased occurrence of hurricanes. Some of them are at risk of disappearing entirely, but others, maybe surprisingly, are increasing in size because of it. They tend to be more politically stable than continental states but are more susceptible to invasion by them. This seems not to be true of Britain although some of our reputation for not having been invaded is due to an economic approach to the truth, since it’s also been said that England has been invaded more than six dozen times since 1066, for example the Glorious Revolution of 1688. These states are also often microstates, which means they can’t take advantage of economies of scale.

There would seem to be four different types of island states, depending on whether they’re based on archipelagos with a number of islands of similar size or consist of one larger island or a single island, and whether they’re continental or oceanic. Ireland and Britain are obviously both predominantly single island states and continental, and being continental makes quite a big difference. One perhaps surprising thing about Pacific islands is their linguistic, and therefore presumably cultural, homogeneity. It might be expected that isolation leads to difference, but in fact it seems not to, even though unique ecosystems do evolve on them.

Then there are maritime states. Technically, France and the “U”K have the most borders, most of which are maritime in both cases, because of their dependencies overseas. This is followed by Russia due to its size. Countries with single land borders tend to be on islands, such as Ireland and us, although Canada is a major exception. The characteristics of maritime states don’t seem to be as thoroughly explored as those of island and landlocked states.

Moving away from the sea and land issue brings one to the four-colour theorem. This is remarkably irrelevant to cartography, but involves the proof in the ’70s that any flat surface map or globe could be coloured with at most four colours. This might be expected to have big consequences for politics but oddly, it hasn’t. It is relevant to the number of frequencies needed to operate mobile ‘phone masts though. It doesn’t work for maps with non-contiguous territories such as Alaska and the Lower 48, or presumably the traditional counties of Wales and England, which have many enclaves and exclaves.

Ultimately, all of these kinds of considerations seem to be to do with applying mathematics to a few well-established facts, so in a way they’re all just bits of science. Two questions therefore arise. One is whether everything can be deduced from facts and principles about which it’s possible to be certain. Another is whether there’s an important distinction between the human-related aspects of these facts and the physical ones. Do we have enough control over ourselves, and do governments have sufficient flexibility, for these facts not to be inevitable? Is there something about human behaviour that just will not alter which leads, for example, to landlocked states being more likely to be totalitarian? Is there disruptive technology or other ideas which can change that?

I’ve used geography here to present this issue, but there are other areas where it applies, so to close I want to return to the issue of rice pudding and income tax. Deep Thought was able to deduce the existence of income tax from first principles. This means that money is inevitable. This is actually part of quite an oppressive ether pervading the H2G2 universe, because we know, for instance, that it’s possible (or rather impossible) to deposit a penny in one’s own era and find that at the end of time the cost of one’s meal at Milliways will have been paid for. This means that usury will always exist, and this makes capitalism as we know it a law of nature. There’s no escaping the flawedness of all lifekind for Douglas Adams. This might be connected to the certainty of death and taxes, but the taxes in question there were not income tax, which didn’t exist at the time. In a way, though, this could be seen as hopeful from a left wing perspective to some extent, because it means money will inevitably be pooled for the common good. The contrary view, of course, is that it’s theft. However, the idea that income tax can be deduced to exist from the Cogito does seem to be more feasible than the idea that rice pudding can, because income tax seems to be about numbers and science, but then so is rice pudding.

In order to exist, rice pudding needs milk and cereal. More specifically, it needs rice. According to the recipe Deep Thought came up with, it also needs demarara sugar and cinnamon. Of all these ingredients, the most likely one to be widespread in a Universe with organic life in it is sugar, although it may be glucose rather than sucrose. Milk is strictly speaking the nutrient secretion of a particular clade of Earth animals, but we are fully aware that EU nomenclature notwithstanding, “milk” needn’t mean milk, and in fact has a long tradition of use in other ways, as with almond milk and latex-containing plant sap. There’s coconut milk and a number of “cow trees”. Galactodendron of Central and South America yields a latex which is high in protein and can be used to make cheese and ice cream. We’re actually fine as far as milk is concerned, as an opaque white nutritious fluid is very common and found from all sorts of sources. It does, however, seem to depend either on the existence of seed-bearing plants or animals who secrete it.

Rice is a bit dicier. Although it happens to be a grass, there are grain-like seeds and fruits from other sources. This is important because although large areas of grassland are common today, in the fairly recent geological past grasses were just another species of plant with no particular dominance which coexisted in more diverse ecosystems, although even then they could presumably be cultivated, and there are non-gramineous cereal-like things like buckwheat and quinoa. Rice, however, is fairly distinctive. Porridge is not the same thing as rice pudding, and on the whole rice pudding is considered sweet.

Hence the dependencies of rice pudding seem to be the existence of seed plants. Although milk can be from an animal source, the animals humans actually exploit for it are grass-eaters, so it kind of depends on the existence of grass in two separate ways. Even three, if the sugar is from sugar cane. It is conceivable that rice pudding might be like gin & tonic, in the sense that according to the epic adventure in time and space it’s just called something like that everywhere but doesn’t refer to the same drink. However, this can’t be quite true because we see a list of ingredients, as specific as “pudding rice”. There’s also the issue of rice pudding being deduced if it only exists on Earth, because although Deep Thought knows that a greater computer will be built one day, it presumably doesn’t know the details or it would be able to predict that its own task would be unsuccessful. Therefore it seems likely that rice pudding does exist elsewhere in the Hitch-Hiker universe. It is also the case that variants of rice pudding exist all over the land surface of this planet, but it’s less clear to me whether it’s been invented independently on more than one occasion.

I’ll close, then, with this. Income tax seems to be a more likely candidate for deduction than rice pudding, but is it? Is it just that the use of maths-like concepts applies more easily to the idea of tax than it does to rice pudding? Is there a stereotypical gender-rôle bias here? What’s it about?

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.