Hmph.

I don’t particularly like Horizon at the moment. I don’t know if it’s because I already know a lot of what they’re talking about, or if it’s because they’re just not very good. Maybe it’s both – with my knowledge I can tell when they’re just stirring shit up to add some drama, and I often feel that the producers are aiming more to entertain and shock than to inform.

Several days ago I watched the episode called “To Infinity and Beyond1”. Unsurprisingly, it’s about infinity, an interesting topic.

It started off exploring the mathematical concept of infinity, which fascinates me and which I may write about in the future. There was a bit of shit stirring (“numbers are not infinite” – ha!), but mostly it was clear and followed a sensible approach to the subject. Nothing was explained in much depth, but the concepts examined weren’t particularly difficult to understand, so I don’t think that was a problem.

The episode also visited the Infinite Monkey Theorem – *I think* it was part of the beginning, mathematical section2. Read the Wikipedia article – I did a few years ago – and you should get a good understanding. All it says is that a truly random letter generator (to make it seem more fun, a monkey typing at a keyboard) run for an infinite time will eventually end up generating the complete works of Shakespeare3

The programme then moved onto physics. Infinity as a mathematical concept is a sure thing, but that doesn’t mean it exists in the real world. For example, there are straight lines in maths, but you can look as hard as you like and you’ll never see a perfectly straight line in the reality. That’s something that’s very important to understand about maths: although it is manifested throughout the universe, it *does not in any way depend* on the universe to be either true or false. Maths would be true in any universe4 because it exists only in our minds.

Unfortunately, I think that the physics part of the programme was downright confusing. Is the universe infinite in size? I think it’s far from certain either way, and I would tend to think that it isn’t5. Some of the talking head scientists said that inflation necessitates a universe of infinite size6, and then proceeded to say that therefore there must be an infinite versions of you in the universe! I think this is a perfect example of where some explanation is needed. I don’t see how either of these things follow from the premise of inflation7, so I’m not willing to accept this uncritically.

I watched 3 other episodes of Horizon this afternoon8; all interesting in the own way but perhaps not worth writing about. We’ll see.

**An aside**, not just to this particular episode, but rather to Horizon in general, I get pissed off by the blind assertions. I know that the producers only have an hour to explore the subject, but it’s not useful to give people such a superficial glimpse of “science”. You need to know the reasons and evidence behind these assertions to gain an understanding, else you’ll just have arbitrary ideas floating around in the audience’s minds. The majority of people have learned nothing, and at worst they will have become suspicious of science because all they have heard will appear arbitrary. Without an understanding of the evidence, their memory can alter, leading to a feeling that science is contradictory and unreliable.

For example9, after watching this programme I was talking to someone who had watched it a few days before. He clearly10 hadn’t understood it fully; and was insisting that if you accept the existence of infinity in one case, therefore you must accept it in all cases! I’d said that I accepted infinity in maths and I accepted the infinite monkey theorem, but I don’t necessarily believe that the universe is infinite in size. Without proper explanation of reasons and evidence, things can easily be misinterpreted, and that’s the sort of confusion that Horizon leads to.

I think Horizon should focus more on explanations, at the expense of variety in the series.

**Anyway**, I enjoy feeling a little hungry, so 1½ hours ago, instead of making my tea, I decided to write a little post on my blog. Now that I’m finished, I’m going to warm up some of the curry which I made last weekend and attempt to cook some pilau rice to go with it. Then I’ll eat it. I’m already salivating11.

- It’s currently available on BBC iPlayer. [↩]
- As it should be. [↩]
- It’s not a real monkey, and it doesn’t mean that it would ever be possible to do this in our universe, even though it is mathematically sound. [↩]
- Whereas the laws of physics could be different. [↩]
- I do quite like the analogy of the Earth, which does have an absolute size but you can set off in one direction and never reach an edge. Something similar could be true with the universe. [↩]
- I’ve not read that Wikipedia article, but it seems like this is not a sure conclusion. [↩]
- Admittedly, I know very little of inflation. [↩]
- I was atching up with the episodes that I had missed, before they went off iPlayer. [↩]
- Some nice anecdotal evidence coming up… [↩]
- Clear to me, that is. [↩]
- Fuck, this was just meant to be a short post that took 30 minutes to write. [↩]

I guess I came to the same conclusion to you (except this thought is going back a few years). Infinity exists as a theory but is very unlikely to exist in reality.

I’m not quite sure if I agree with you that numbers go on forever though. If existence is finite then numbers are finite.

What? How are the numbers related to existence?

How can you count if one doesn’t exist?

You can’t.

But a number doesn’t need to be counted. Pi ‘exists’ even though we’ll never be able to count every digit of it.

God exists even though we may never be able to see him.

I’m not following you WiBu.

If it can’t be counted or recognised it doesn’t really exist. Sure, it exists in theory, but it doesn’t necessarily exist. My God comment was an attempt to highlight that your statement that a number doesn’t need to be counted to exist was based upon blind belief.

I guess it calls into question what defines something as existing. Is the idea of something a valid enough reason to say something exists? Is the idea that numbers could infinitely go on for ever valid enough reason to say they actually do? I see an idea as a theory, the theory exists, but until it actually exists and is able to be perceived/counted, it’s just a theory, just an idea.

Did the number 3 exist before it was counted and understood? It seems in retrospect that it did, since it was counted and understood, but that does not necessarily mean that

nexists.I’d argue that Pi was just a theory too, it probably doesn’t exist in it’s true theoretical sense (theoretically it is infinite), just like straight lines.

I’m not sure if I made sense there, but hopefully it did. I think it might just be us having different view points of what we’re talking about.

(There’s probably huge holes in what I’ve written, please do pick apart.)

Hi WiBu, I’ve got an infected sinus so my head has been destorying any ability to think for several days. It still hurts but I’ll try and think about this the best I can…

When I’m talking about numbers existing, I don’t mean that they necessarily have any presence in the physical universe, but I think you get that.

No, not if we’re talking about something existing in the real world. But maths is

entirelyjust a conceptual thing.I think maths is just a big idea; that’s where I think we have different viewpoints. I think that all maths is, is just a load of ideas. There’s no point where ideas in maths go from being just ideas to being something that ‘exists’.

In maths, you start with a few axioms with seem to make sense, and maths is just stuff with follows logically from those axioms.

What does “actually” mean here? There’s nothing that we can judge the infinity-ness of numbers against to check if it is true, other than our assumptions.

I’d take this as proof that there are an infinite number of numbers: because addition is valid for any two numbers, for any n, there is a number (n+1) which is greater than and different from n. Ultimately that’s still an assumption that n+1 has a result, but not a hard one to make. The alternative is that there is a greatest number.

For me, talking about numbers existing “in theory” doesn’t really mean anything. There are hypotheses that have not yet been proven, but I think it’s impossible to imagine a number which isn’t a number. Yes that’s a tautology but that’s kind of my point. Maybe. I don’t know.

I would tend to be of the opinion that maths is discovered rather than invented, but honestly I’ve hardly thought about it. Hmm actually I’m not sure, and it’s definitely something that’s relevant here.

Our particular study of maths (our axioms etc) is probably invented, but surely it’s an eternal fact that the sum of the squares of the lengths of the 2 shorter sides on a right-angled triangle equal the square of the length of the hypotenuse.