“What Is The Universe Expanding Into?”

Steve, I wrote this with you in mind.

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

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

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

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

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

James Muriden, ‘The Handbook Of Astronomy’ 1964.

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

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

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

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

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

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

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

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

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

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

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

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

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

Pyramid Power

A couple of days ago, I eluded to the question of pyramid power as an attempt at a joke, then went on to talk about pyramid schemes. It then occurred to me that I could actually talk about pyramid power itself, and also about pyramids.

Nina Aldin Thune

Whatever else may be true, no-one can deny that the Egyptian pyramids are dead impressive. They’re so old that when they were built, there were still mammoths. The mammoths in question were a few inbred individuals who were rife with birth defects on an island in the Arctic Ocean, but they did exist. Their population was just too low for them to be viable. It’s said that the six million tons of masonry in this single building is greater than the combined mass of building materials in every church in the world. It was the tallest building in the world for forty centuries. It was not, however, built by slaves. Rather, people were expected to volunteer their time to create the thing. Nor did it require mysterious alien or otherwise advanced technology to construct. The ground was levelled by digging a series of interconnected ditches and filling them with water, then chipping away until everything was at the same level. A ramp was then built and gradually steepened and lengthened to put the blocks in place. The planning is impressive, to be sure, but as is often the case it’s a testament to human ingenuity and organisation rather than extraterrestrial intervention or lost high technology.

The Great Pyramid is also said to be at the junction of the lines of longitude and latitude which cross the most land. The line of latitude passing through its apex is said to match the speed of light in kilometres per second, since it’s supposed to be 29.9792458 decimal degrees north of the equator and the speed of light is 299792.4562 kps. Although the idea of decimal degrees might at first sound like shoehorning, it does make sense because the length of the metre was originally defined as a ten millionth of the distance between the North Pole and the Equator. This in fact involves a bit of jiggery pokery because it isn’t actually the position of the apex, although it’s an interesting coincidence. It’s also been said that there is a “pyramid zone” around the planet, which is a narrow range of latitudes within which the older pyramids were built. This always reminds me of the linguistic “click zone” – a narrow range of latitudes within which languages with clicks are spoken. This last has turned out to be completely untrue because for some reason it used to be thought that certain Mesoamerican languages had clicks when they haven’t, so outside Afrika that just leaves the two unusual registers of Chinese and Australian aboriginal languages with them as proper phonemes used as parts of words. Likewise, there are in fact many pyramid-shaped buildings away from this zone, and many of the buildings made out to be pyramids for the purposes of constructing the zone are not really that similar: they’re ziggurats or pagodas. That said, there are many roughly pyramidal buildings from days of yore, probably because it’s such a stable shape. The maximum height of a pyramid of granite on this planet is 13.4 kilometres, whereas a column of granite, i.e. a cuboid or cylinder, is less than five kilometres. It’s also notable that hills and mountains are usually roughly pyramidal or conical. In that sense, pyramid power does exist.

The other famous pyramids are the Mesoamerican ones built by the Mayans and Aztecs.

Attribution: Pedro Marcano

These are a little different although they’re still roughly the same shape, probably for the reasons given above. There seem to be about three dozen surviving Mayan pyramids, which may have evolved from burial mounds, so their function was similar to the Egyptian ones, of which there are 118. This also links them to the Western European barrows. It seems that, left to ourselves, we humans will eventually get around to burying our dead in pyramids with spiritual overtones.These are a little different although they’re still roughly the same shape, probably for the reasons given above. There seem to be about three dozen surviving Mayan pyramids, which may have evolved from burial mounds, so their function was similar to the Egyptian ones, of which there are 118. This also links them to the Western European barrows. It seems that, left to ourselves, we humans will eventually get around to burying our dead in pyramids with spiritual overtones.

Tenochtitlan, the pre-Columbian Mexico City, was also known for its pyramids:

The steps here interest me because they look rather like they could’ve been used as a ramp which was left there, unlike with the Egyptian examples although those do have the remains of their ramps next to them. I seem to recall that the Aztecs built a larger pyramid around the smaller one every fifty-two years because they expected the world to end every time their calendar cycle came to an end. In fact, it more or less did because their final cycle ended in 1519 when the Conquistadores arrived. It’s interesting to observe the number of similarities between the Mesoamerican and Egyptian civilisations, such as the use of hieroglyphic writing in both, their Sun worship and of course their pyramids. I think this indicates some kind of commonality in human life rather than communication, but it has been used to justify the idea of Atlantis (as has the Aztec idea of Aztlan). There are quite a number of oddities about Mesoamerican culture which are very hard to explain naturalistically, but I won’t go into that here.

Getting back to the Great Pyramid, it has been claimed that the structure has encoded prophecies in its height, including the exodus of Moses from Egypt, the birth of Jesus, the outbreak of World War I and the foundation of the modern state of Israel, and downward into the Christian End Times, measured using “pyramid inches”, which was a twenty-fifth of a cubit. These units were actually used in part of the debate about adopting the metric system.

The burial chamber in the Great Pyramid is a third of the way up. This is where the believers in pyramid power put their objects. The basic idea behind pyramid power is that square pyramids can keep razor blades sharp, preserve food, improve health and boost libido, and also act as “thought form incubators”. I don’t know what this last bit means. I used to believe in pyramid power as a child but have grown out of it. In fact I used to own Bill Schul’s famous book ‘The Secret Power Of Pyramids’. Among other things, this contains a series of photographs comparing, for example, grapes kept inside a pyramid and kept in a cuboid box, noting that the former appeared to dry them out whereas in the latter they just went mouldy. They were also said to boost the growth of plants, control pain, purify water and rejuvenate. The whole idea was triggered when someone called Antoine Bovis claimed to have seen a bin full of dead animals in the Great Pyramid who had become trapped inside it and died, but had not decomposed, although it later emerged he’d never even been to Egypt. Now here’s the thing: I do not believe in pyramid power because I can’t see how it would work, so I’m skeptical, but note that that is spelt with a K. It isn’t actually respectable scepticism spelt with a C. There is of course an established scientific system into which the idea of pyramid power doesn’t seem to fit, and I’m confident it doesn’t exist, at least in the sense claimed in Schul’s book, but I’ve never tested this myself. I just take it on faith that it doesn’t happen because I can’t see how it would, but maybe I’m being too dismissive.

I’m prepared to accept that a square pyramid made of magnetised iron might have interesting effects on oxygen and water. Oxygen is magnetic, but at temperatures we’re used to surviving in there is too much arbitrary vibration of molecules due to heat for it to become concentrated near a magnet. Liquid oxygen, on the other hand, behaves very differently because its molecules move around less randomly, and is visibly attracted to a magnet, unlike nitrogen. Magnets repel water slightly, so magnetic pyramids of various orientations would in fact have various effects on it, such that if, for example, they were built of sheets polarised through their thickness, it would increase water vapour concentration around the point where the tomb was placed in the Great Pyramid, which is, however, not made of ferromagnetic material. Likewise, extremely cold air would have its oxygen concentration boosted near the walls of such a pyramid and lowered near the centre. There’s also the question of the angles of the vertices, and in this case the idea is more straightforward and links into general geometrical principles.

The shape of a square pyramids slightly offends my sensibilities because it isn’t a Platonic solid. Platonic polyhedra consist entirely of spaces enclosed by faces which are regular polygons – polygons whose every angle and side are the same. I find it disappointing that neither Mesoamerican nor Egyptian pyramids are tetrahedral, and if they were their vertices would be more acute. Many houses have mouldy corners, particularly ones in the British Isles (Boreonesia?). If these corners were more acute, they’d be damper and they’d attract more mould. In an arid climate, presumably the opposite applies: acute corners are drier than right angled ones. This probably also means that in a tetrahedral greenhouse, plants needing more water would do better in the corners if the air is humid outside it and it isn’t watertight. A tetrahedral loaf would also be crustier than a cuboid one. A tetrahedral bar of soap would dissolve faster and a sugar tetrahedron would sweeten coffee quicker than a sugar cube. Similarly, a vegetable stock tetrahedron would dissolve faster, and if it were in an inverted tetrahedral container which was properly heated, that would cook faster.

Continuing to maintain my doubt, there are a couple of problems with the idea of pyramid power. Firstly, there’s no requirement that the pyramids be made of any particular material. As far as Earth’s magnetic field is concerned, with which they are supposed to be aligned, this seems likely to invalidate any special properties they might have. Secondly, they’re square pyramids, which are less “extreme” than tetrahedra, and therefore likely to have less interesting properties. However, with this I’m attempting to connect the idea of pyramid power with an established scientific paradigm, which is not guaranteed to be true, and which is in fact guaranteed to be false.

All of this reminds me of attitudes to homeopathy. I should state that my position on this is that I neither use nor recommend homeopathy, because I’m not aware of a mechanism whereby it could be said to work, but that’s not the same as believing that it doesn’t. I think the established scientific fact that both sharks and moths can detect scents when probability suggests the compounds concerned are not sufficiently concentrated in the medium concerned for them either to encounter a single molecule or work out which direction they’re coming from is interestingly similar to homeopathy, but the responsible position is to remain agnostic. This is because all the studies I’ve seen from an apparently scientific perspective regarding homeopathy lack good ecological validity and are not undertaken within the environment of a protocol which has been agreed between homeopaths and the scientific researchers. This could for all we know be a special case of Dunning-Kruger. But I’m not knowingly a homeopath and I have my doubts, even given apparent double-blind provings.

In the case of pyramid power, I feel more confident that there’s nothing in it, and as such I would count as a “K” skeptic rather than a “C” sceptic. This is because I haven’t personally encountered any research on the matter which is well-designed, but even so feel the urge to reject it because it doesn’t fit into the current general scientific world view. This could also be compared to astrology, where I have specifically rejected it owing to the opportunity to undertake a research programme using thousands of subjects and personally crunched the numbers statistically to establish that in that situation, there was nothing in it, at least regarding sun signs. Hence my position on pyramid power is that I don’t believe in it, but that may be unfair because I haven’t tested it experimentally. That would be true scepticism.