For a while now, I have been aware of certain points of view surrounding the subject of mathematics. For most of my years if you had asked me if maths was real, I would have instantly answered 'of course!'
Now however I'm not so sure, there seem to be strong arguments on both sides; let's have a little muse together and see if we can't decide one way or the other.
The Case For Material Existence
Plato was a pretty clever man, so much so that I have just mentioned him thousands of years after his death, and there's a good chance you know who he is.
However he didn't have use of a laptop, or in fact algebra, so to him numbers were real things. Actual objects, just like a hat or a coat, the only difference between a number and a tree, was that one was an abstract object, whilst the other wasn't.
So the Platonists (from Platonism), believed that whilst numbers could not interact with anything in the real world, they were outside time and space.
This of course is very quickly disproved, like, how can I be aware of something that does not interact with anything outside of space and time; seeing as I inhabit space and time?
Numbers aren't real, that's obvious, however is mathematics real?
A Force Indicator For The Real
The Nominalists believe that whilst mathematics might not have any physical manifestation in the universe, in the way that physics or biology does. It is inherently useful and succesfully describes our world over and over again.
The Nominalists, simply say that when we say that one plus one is two, what we are saying is one object, plus another object, makes what we call two objects.
Therefore mathematics is simply a language to help us translate what is going on around us, end of debate.
Wait just a minute, I hear a set of voices saying no, in fact mathematics is not a translation of the physical universe.
Sure you can say that 10 objects times 5 objects is 50 objects and you can visualise that. But how do you visualise the square root of minus one, or an ever recurring number like pi?
"Oh, well, that's easy, you just... erm, you ah, right . . ."
A Very Useful Fiction
And so to the last players in this charade, the Fictionalists say that numbers are not in fact real at all. Mathematics is simply a human creation that does not exist outside of the mind.
They say that just because something is particularly useful, does not also make that thing true.
For instance, I remember a time when whacking your TV with your fist when the picture went fuzzy, was an accepted practice.
It generally worked, however that doesn't mean that to punch your television is good for it.
OK, you might have a point there, go on . . .
Well, if mathematics were true then the Platonists would have to be right, which they're not. Therefore mathematics can't be true, we are just whacking a metaphorical TV and it happens to work.
Back To Reality
Where do I stand on this? The fact is that there are objective truths about mathematics, and the deeper into it you go, the more apparent these truths get.
The fact is, whether they called it pi or not, aliens of a similar technological stage as we were when we discovered it, would work out the area of a circle, and so on, using pi.
One molecular weight of Caesium will decay at the same rate whether I choose to believe in it or not. Mathematic properties and values are an inherent part of the universe.
The names we have given for the various values are obviously human. However in the same way an alien would conclude the sun is made up predominantly of helium and hydrogen, so to would they agree with us on the square root of minus one.
Fun Fact: The more abstract mathematics gets, the more useful it is in computing, especially cryptography.
Cryptogee Musings Table Of Contents - #1
WHAT DO YOU THINK, DOES MATH EXIST; OR IS IT JUST AN INCREDIBLY USEFUL ILLUSION? AS EVER, LET ME KNOW BELOW!