Saturday, 5 August 2017

#210 To infinity and beyond

If an uneducated person were to look up at the sky, they'd have no way of knowing how far away the stars were. They wouldn't know how big they were. They wouldn't know how old they were. They'd be able to see the stars but they wouldn't know what they were made of, or if there was anything behind them that they couldn't see.

We know more than that.

Do we know any better?

At school, we're taught about the Big Bang and the speed of light. We can look at Wikipedia, or the lyrics to the intro of an American sitcom and learn that the Universe is 14 billion years old. We can learn about black holes, atoms, quasars and how God travels slower through a speech synthesiser.

There is much that we can learn.

Now and then... and most of the rest of the time, I watch Youtube videos and this week I've been watching some about the concept of infinity. Having stopped studying mathematics thirteen years ago, I was surprised to learn that mathematicians developed notation for different types of infinities, some larger than others.

How in Pythagoras' name does that work?

Well, at first it might seem bonkers but many mathematicians will tell you that it's been proven, so I'll try to think of an example. Say you've got an infinite number of carrots but each carrot has some leaves coming out of it on the top. You know, those green leaves that hang down when Bugs Bunny eats a carrot? Hmm... so you start counting the carrots and each time you count one, you chalk up a little notch on a blackboard.

Next, you want to start counting the leaves and chalking up additional notches on the blackboard for those too but you decide that you're only going to do that after you've finished counting all the carrots. Now, in reality, you'd never finish counting the carrots but in theory, we can at least imagine that however many notches you've chalked up when you start on the leaves must be a bigger number than when you were counting the carrots, even if there were an infinite number of carrots.

The branch of mathematics that deals with these types of numbers is called set theory and if the above example doesn't make sense, or doesn't seem like a proper explanation of set theory, it's most likely because I don't understand it properly.

Could it also be because set theory is codswallop?

I mean really. A bigger number than infinity? Think about it.

Which is what mathematicians have done and to be fair, they're allowed to do that. It's their job. The fact that nobody would ever be able to count an infinite number of numbers is a perfectly valid criticism in the real world, which makes it a perfectly invalid criticism of mathematical theory because maths often involves numbers and numbers aren't real things.

Are they?

Just because a load of mathematicians have imagined that they can imagine the imaginary and then they've imagined that they really did imagine the imaginary, doesn't mean they're wrong.

Does it?

Hahaha :) I love blogging.


Fizzfan said...

Dan I've always been fascinated by planets and space and science, even though I have a head like a sieve when it comes to retaining any of it. When I was young I used to watch James Burke shows and more recently the very lovely Brian Cox.
While I'm watching and listening I'm really enthralled and really seem to understand it. Five minutes later though I have to accept I'm incapable of retaining facts and figures and it's all still a complete mystery to me. I just like listening to it, although only by certain presenters.
You're right though. How can anyone define infinity in numbers. The word defies being able to do it. Surely it's just an imaginary limitless blob. (Not sure that would hold much sway as a description in the higher echelons of academia though)
It's a bit like predicting the future. Someone can say practically anything. It could definitely be true, but there's absolutely no way of actually knowing. I guess that's the point, it's unprovable and without boundaries.

Dan Copping said...

Yeah I agree Fizz. Hmm, I find Brian Cox a bit of a drip but he's done wonders I'm sure for the popularity of the genre. Is he a hot?

I should have said in the blog post that these types of infinities are really concepts rather than numbers and so when people talk about 'counting' them, like you say, it's not really possible in the traditional sense.

Fizzfan said...

LOL. Yeah he does fall a bit short of a complete PHWORGH but compared to most sciency types he's ' 'infinitely' hotter!
Am devastated you think he's a drip! Still laughing....