Math Is Fun Forum

Well its difficult to explain exactly what I mean, maths doesn't have a corporeal existence, there is no 1 that exists in reality. I have one glass of water, but if I split it into 2 glasses do I have 2 half glasses or 2 glasses of water, whether it is 1 or a half is entirely context sensitive. If send those 2 glasses of water to different places so other people have no knowledge that this glass of water is actually half a glass of water, would it be half a glass of water or just 1 glass of water. If they split the glass of water in half again are they quarters or halves? The answer is only relevant to the context. Maths is a model or a tool for explaining things. It can be used to explain reality, but it can explain things that don't exist in reality as well.

Things like infinity get a lot more difficult to explain because this is an abstraction that exists in Mathematics which itself is an abstraction. The idea of oneness can be applied to things in reality, but the idea of infinity cannot be correctly applied to things in reality. Even in mathematics it is a nebulous entity.

So going by that reasoning, the number 1 does not exist (nor does maths), neither does infinity, but infinity exists half as much than the number 1 because its an abstraction of an abstraction.

Its sounds very metaphysical but I think the important thing to understand that maths does not exist in the world as corporeal thing, it is entirely manufactured by the mind, there are many things that are not possible in reality but can exist in the mind. Maths is a model with corresponds very closely with reality within strict or perhaps not so strict boundaries, but it is not reality, reality isn't as neat as maths.

You can explain some maths with reality, and some reality with maths but the problem is if you start to think the two are the same thing, if you think reality is maths or maths is reality.

Its down to human perception (And by this I mean what we perceive with our senses) really when we perceive things we perceive them in a way which fits with how we understand things. We expect to see things in a specific way and so we make them fit that way. Look at the stars, do they make patterns? Do you see a plough or a bear or a dipper? You recognise Orion the Hunter. They are just dots, you brain interprets them as a pattern you have learnt to recognise.

In this way if we rely only on our perception then we are limited to it, the trick is to understand the limits of perception, and that there are some things you can't perceive naturally, that don't make sense in your natural understanding, because of the way you are wired, it doesn't mean they don't exist, or you can't accept them.

In the mind we are only limited to what we can imagine, its easy to think in the same way you perceive the world through your senses. But there are things beyond what we can perceive, atoms and molecules so small we can't see them, galaxies so far away we can't see them. And the mind is a playground we can move beyond our perceptions into a bigger world, a world that does exist but we cannot perceive directly, and into those than don't exist as well.

Anyway so I think an understanding of the abstract nature of maths is important, and one thing that is rarely taught to people. Without such understanding simple things are difficult to accept, like 1 and 0.9 recurring being equal, it doesn't make sense or is not correct if you do not apply the correct rules. If you use the rules of reality, of your perception of the world then it doesn't make sense.

And so I agree with you there is no reason to limit maths to reality, just as we don't limit our understanding to only what we can sense.

And so you can see clearly that 0.9 recurring = 1