Maths made simple

Mathematics is just too complex isn’t it

For instance, can you work out the answer to the displayed equation

I can’t do it either... So instead of trying to work it out, lets simplify things, and see what happens

Numbers can only ever be Big or Small. And we’ll let them be added and subtracted from each other. But that’s all that’s allowed. Anything else will be too complex

Big + Big = Big
Big + Small = Big
Small - Small = Small
Small - Big = Small

So far, so simple. But what about when we do Small + Small? If Small is 6 and Big is anything over 50, then:

Small + Small = Small

But if Big is anything over 10, then it’s going to be:

Small + Small = Big

Oh dear, we don’t know which one it’s is, we’ll just have to say:

Small + Small = Unknown

Aswell as:

Big - Small = Unknown
Big - Big = Unknown

Normally when you hit an Unknown you’re stuffed. But our algebra is unusual, we can do:

Unknown + Big = Big

And just to finish things off, so you have that warm cozy feeling of working within well defined mathematics:

Unknown + Small = Unknown
Unknown + Unknown = Unknown
Unknown - Big = Unknown
Unknown - Small = Unknown
Unknown - Unknown = Unknown
Big - Unknown = Unknown
Small - Unknown = Small

So there you go. But is it of any use? Let’s try it out on a series of questions previously thought difficult to impossible in modern mathematics

How big is the universe?

Answer: Big

You have 50 apples, you give Ahmed 48 and start eating what’s left. How many apples do you have left?

A Small number

If an elephant, wearing a superman cape jumps off the Eiffel tower while blowing a kazoo, how long will it take before it hits the ground?

A Small amount of time

Exactly what kind of noise will it make when it hits?

A Big noise

Small - Unknown + Small + Big - Unknown + Small + Big = What?

... Can you work it out?

We considered adding in negative numbers, but it might get too complex

Can we do any better?

That was great, we simplified things alot. But can we simplify them any more? The first question we tried to answer looked something like this

And my answer to it, at least, was: “I don’t know.” That’s actually quite a good response. I’ve used it a lot over the years, and whenever I do, people walk away with no further questions left to ask

So let’s formalize that into mathematics:

Any equation = I don’t know
Any equation + I don’t know = I really don’t know

It’s like saying: “Where were you on the night Jim Robinson stubbed his toe?” “I don’t know.” “You don’t know? What do you mean ‘you don’t know’? Tell me, where were you, what were you doing, and what colour pyjamas were you wearing?” “Look, I really don’t know

It’s cute, it’s simple, and it works... Or does it? If we were writing in a different language, we would replace ‘I don’t know’ with something that looks like jibberish, and it would still mean the same thing. So lets replace ‘I don’t know’ with 0. And ‘really’ with 1 +

So now:

I don’t know = 0
I really don’t know = 1 + 0
I really really don’t know = 1 + 1 + 0

And what about ‘I really really really don’t know’? Maybe we could call that 3

I’m reliably informed, that from ‘I don’t know’ and ‘I really don’t know’ we can re-create the whole of mathematics

Scary isn’t it

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