Monday, April 04, 2005

1 - Is maths real?

So this is an old discussion and there even was a conference recently at the Royal Society where the guy said he would answer it, and then neatly sidestepped the issue. He did go on to talk about fractals and Jackson Pollock so it was interesting anyway.

Basically there are two sides:

- Mathematics is created by the human species (added to this you could say that it arises from the particular functional structure of our brain) and is used by some human cultures to describe the world around them.

- Mathematics exists in the Universe (i.e is 'real') and human beings were fortunate enough to discover it. Essential to this of course is the concept of absolute reality.

So you probably already guessed that I'm on the first side. This happened quite a while back and for some time my mother solved it for me (and passed me to to the second side) by pointing out that if Mathematics wasn't real you wouldn't have been able to put a man on the moon. That's the kind of common sense and perspective you only get if you're not a scientist.
However, if you consider approximations, you could think that there are any number of ways a being could describe the Universe that would allow him to predict it approximately enough to be able to put a man on the moon. Say colours, for example. Imagine if we had evolved to descrive the Universe and Nature in terms of colours and colour combinations rather that numbers. Quite plausible if you consider certain synesthetics. Would we still have been able to put a man on the moon?

On the second side, as I said before you have to consider that there is an absolute reality where physical laws are irrevocably linked to their mathematical description. And human beings are getting gradually closer to perceiving it.
I'm sure there are more arguments for the second side but I'm waiting for you to provide them.

Also the issue if mathematics is 'built' into our brain or not. What do you think?


At 9:50 am, Anonymous Anonymous said...

maths does seem like a human construct. But that is because of the way we are taught it. I would argue that numbers are real, and maths is a way of manipulating numbers, and is therefore also real.
If you have two oranges, and then you find two more, you have four. the human construct bit is that part where we have a particular way of describing it to each other, and develop particular rules for dealing with equations. These are usually short cuts but are still real.
what do you think?

At 10:16 am, Anonymous Anonymous said...

I think if you look at some oranges and see TWO oranges, then look at some more oranges and see again TWO oranges and then DECIDE to look at all these oranges together and see FOUR oranges, you could consider this is particular to our mind's way of seeing reality.Going back to my colour hypothesis, you could looke at some oranges and instead of seeing two oranges, see orange, red-orange, orange with a tint of green, pinkish orange and so on. Or you could (if you were a synesthetic for us) see a colour that corresponds to the quantity we refer as two (although this is still maths).

One of my workmates just came up with the question of imaginary numbers. What about those? (Specially since we couldn't find a proper definition on the web).

Thanks for your comment, please answer back, you are, of course, welcome to remain anonymous. And I am, of course, dying to know who you are...

At 11:43 am, Anonymous Anonymous said...

Yes you are right if you DECIDED to only look at two oranges then that is alls you would see. You could also have decided to see two single oranges and add that together to get two. So again we find maths.
The only way that there couldn’t be any maths is if there were no numbers at all, and for that to happen there could only be one thing in all reality and this is not the case.
If numbers exist then maths exists.
And numbers do exist.

Maths is there and we have discovered it, but I do think it was there for the finding. For example these people have not discovered it and would be unable to send a man to the moon.
And on this basis I would also say that a world populated entirley by synesthetics would be unable to send a man to the moon.


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