Horizon: To Infinity and Beyond

On the 11 February 2010 I watched a new Horizon programme I’d recorded.

And on the 27 March 2012 I watched it again - long enough afterwards to be unsure about whether I’d seen it before! My additional thoughts are at the end of this page.

A lot of scientists and mathematicians getting in a lot of intellectual tangles, it seemed to me, about infinity. There also seemed to be some confusion about the meaning of the word ’universe’ - can the universe be infinite?

In what I’ve written elsewhere in this diary, I’ve basically tried to get my head around the cosmos (what is that?) without straying beyond the limits of the intuitive, and I don’t think I’ve done too bad a job. Not too bad for me, anyway - and all I’m really trying to do is make my own beliefs as coherent as I can! My speculative model of a multiverse seems to make reasonable sense.

My feeling after watching the programme is that mathematicians are wandering way beyond their own area of competence - but then I’m a simple soul. To me, maths is a toolkit for analysing, modelling and predicting the behaviour of things in the real world, and - given that these things now include things as tiny and mysterious as quarks - I’d have thought that there was enough real stuff to keep the mathematicians busy forever. But no: there seem to be a lot of these guys using all their time to speculate about the nature of infinity. Maths seem to have become an end in itself. Number Theory? What is that?

Where I get seriously uncomfortable is when the maths guys start putting that little figure-eight lying on its side into their equations - in other words, treating it as a real number. Surely infinity is just a word to express the idea that there are quantities beyond counting, not because the counting doesn’t go on working but because there’s nothing that vast to be counted...?

Back to the word universe. Since The Big Bang Theory became mainstream as an explanation of the origin of our universe, the word has by definition been used to label something demonstrably finite: the matter and energy sent rushing out into space by the Big Bang. I emphasise: into space. Surely space is just a huge - infinite if you like, because if it stops there must be something beyond it - emptiness in which matter and energy exist and interact. Our universe, on the other hand is the product of the - or one - Big Bang. Since it started as a singularity in which all energy was concentrated (we believe that matter and energy are interchangeable but cannot be created or destroyed, and that no matter existed until some time after the Big Bang) that must be a finite quantity. So asking whether the universe is infinite, as some of these guys do in the programme, is nonsense. Are they confusing the universe and space? I thought so when listening to them.

I’ve said elsewhere that I’m comfortable with the idea that our universe may not be the only one - there could be many scattered across space, each created by its own Big Bang. How the separate singularities required for this model came into being, I can’t imagine - but then I can’t imagine how our singularity came into being. And since, by definition, our own cosmic explosion must have obliterated all physical evidence of what preceded it, I have to live with that. Some things are just unknowable...

Unless, of course, universes are coming into being all the time, and we can develop a hyper-Hubble able to show us not only the entirety of our universe but also the far reaches of space where others exist and may be being born. Of course, if this is true, the term ?universe? is a misnomer since it implies ?everything?, and out visible universe is not everything at all! (Excuse the shorthand: I know that what we see even in the further reaches of our own universe is something that was happening aeons ago, thanks to the fixed and finite speed at which light - a term nowadays used to cover all eletcromagnetic radiation - travels.)

So: infinite universe? No. We know our universe is not infinite, and as long as we define it as the product of one Big Bang it must stay finite.

Infinite space? Sure. How can you imagine anything else. Even the charming primary-school kids in the programme seemed to grasp that.

So we definitely have one finite universe that will continue to grow, occupying more and more of infinite space. And there may be others, elsewhere in that infinite space, doing exactly the same thing. And one or more of those might one day start to interact with ours. And might that create something that lacks the stability of our current universe and starts to collapse in on itself, ultimately creating a new singularity, a new Big Bang and another much bigger universe?

One thing is for sure: we’ll never know!

But, going back to the programme, the idea of an infinite number of universes in which everything possible happens again and again, even (on the basis of the monkeys/typewriters/Shakespeare theorem) to the extent that there is or once was or one day will be other Earths with other Britains and other Paul Marsdens doing exactly what I’m doing...well, does it really matter?

Shouldn’t these expensively educated members of an intellectual élite be doing something a little more useful with their talents, their skills and their time? Or are they driven by the primitive compulsion I discuss on the page about religion and science - the one that made our ancestors interpret their own limited experience as evidence of a supernatural dimension full of gods and spirits - to theorise about what they can’t explain, and for the same reason: because it’s just too scary to say ’I don’t know’?

On lighter note, I was amused by various mathematicians’ claims to have ’invented’ numbers. Surely all possible numbers exist: they are implicit in the way we count and calculate. Even Pi, which is not a real number in the sense that it never resolves to a finite number of decimal places (which isn’t to say it might not in a system with a different base - I’ll leave that to the professionals), exists as the ratio of the circumference of a circle to its diameter and (I think) as the fraction 22 divided by 7. So someone claiming to have invented the googol and the googolplex, which are real numbers (a googol can be written as 1 followed by 100 zeroes, and a goolgolplex as 1 followed by 1 googol zeroes), is a bit presumptuous! Like all others, these numbers were already in existence. All these guys have done is to label them. By the way, I was relieved to find (from Wikipedia) that the spellings are different from those of Google, the search engine I use every day, and Googleplex, which is what they call their headquarters. And even more relieved that the googol was named in 1938, long before anyone even thought of the Internet! This gives the search engine’s choice of name a certain style, though...

I was also entertained by the idea that you would have had to start before the Big Bang to have finished writing out the value of a googolplex in decimal notation by now (or was that another, even more absurdly large, number?). We’re used to billions (1,000,000,000,000) and trillions (1,000,000,000,000,000,000) in the news about various nations’ deficits these days, but if I remember rightly a googolplex is larger than the number of subatomic particles in the known universe - or something equally useless...

27 March 2012

Having just watched the Horizon programme again, I’m greatly reassured. It’s clear that there is no real agreement among scientists of mathematicians about what, if anything, infinity actually is. Which, I think, strengthens my argument on another page against Jim Al-Khalili’s assertion that the result of dividing any number by zero (an operation which my computer still refuses to attempt) must be infinity (my computer doesn’t even have an infinity key). This ’rule’ may be a convenient assumption made by mathematicians to facilitate their more difficult calculations - calculations that may in fact have endless practical applications, without which we might not have lots of very useful bits of technology (as have the subtle differences between Newton’s and Einstein’s equations for gravitational effects) - but that doesn’t alter the fact that, in the real world (or even the real universe) neither zero nor inifinity are really numbers. Zero is simply shorthand for nothing at all, and infinity is clearly very ill-defined.

Numbers are finite, so the very label ’infinity’ says that this much-debated concept cannot be defined mathematically and cannot therefore be a number.

In arithmetic (the only branch of maths of which I have any real understanding), zero is simply shorthand for sweet bugger all. It is used in the writing of numbers - both the familiar base-10 notation we use and the binary representation on which all our digital computers rely - as a place marker in the columns that contain nothing. And, in arithmetic, the very idea of division by zero, which is actually a process for finding out how many of one quantity is contained in another quantity, is meaningless: 3 divided by zero means ’How many lots of bugger all are there in three?’, which is meaningless. I have to say that my computer seems to have a lot more commonsense than many mathematicians.

There was also a lot of loose talk in the programme about the possibility of the universe being infinite. I’ve already noted above that the universe, the product of a single Big Bang generated from just one singularity that has been expanding for a mere 13.7 billion years, must be finite. Space, on the other hand, must be infinitely big because it is just an endless expanse of nothing, into which the universe will presumably be able to expand forever - unless some dark force slows or stops it.

Simpleminded? Maybe - or is it just that the scientists and mathematicians in the Horizon programme make everything unnecessarily complicated?

To avoid confusion (!), spacetime, that strangely bendy entity proposed by Einstein (in his theories of relativity, remember), is not the same thing as space...