Questioning Reality - Is Math Real?
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!
I think the closer words would be LANGUAGE -math is a language of nature or science, some scientist says. The reason why we communicate right now is because we are using English language, same as we communicate to nature by using mathematics. :)
Well you can think of mathematics as a thought experiment to derive a maximally consistent logical structure from nothing but a agreed-upon set of axioms.
Our current knowledge of mathematics is based on a axiom set called ZFC which is predominantly a bunch of set theoretic axioms, including ones guaranteeing that you can construct natural numbers by counting elements.
So you see even the most complex mathematics can be -depending on your stance- very real or very abstract because fundamentally it requires little more than the ability to count objects, all the complicated details can be derived and built up from there.
hmmm good point, food for thought...
I love reading the comments when you post topics like this, because you can have one comment that is astute, rigorous, and based on sound logic and empirical knowledge, literally adjacent to another comment that reads like Deepak Chopra after a massive bong-rip.
The rational comments are fun, but the quantum-woo is even better.
On the substance, I'm fairly certain that I have absolutely no ability to decide if math is a "real" thing or an illusion.
I'm not going to be the one to say with any level of certainty that I understand math better than realists likes Godel or Quine, or formalists like Hilbert or Tarski.
The only thing I'm certain about is that people who claim to be certain about the answer to this may not be giving a fair hearing to the theories on both sides.
I know right! I do appreciate a good bit of woo-woo now and again myself, quantum woo-woo annoys me though, because it usually involves a misinterpretation of a half-truth.
Wait till you see my next musing; I'm really chucking a rabid cat into a whole load of jittery, incontinent pigeons! :-)
Cg
The answer to both is the same. Incredibly useful illusions are the main things we base our choices on, according to Khaneman and Tversky, who won the nobel prize for econ with their work on the predictive role of the illusions we maintain, its the loss of your status quo (real or not to others) that effects your tolerance for risk.
Maths was created to understand the unknown things in the universe and is still the best tool we have to actually quantify the mysteries of the universe and that makes it the most important tool for linking the imaginary concept with the real mystery.
Math is nothing more than a method of describing our physical world. We made it up. Sometimes our made up math leads to artifacts that cannot exist in the read world. For example the number i that is the square root of -1. It is not real, and cannot be real and we flat out call it an imaginary number, but it works as a crutch to get our math past some roadblocks.
Just because math is a human creation does not mean it is arbitrary or illogical, it just means that humans have spent a long time perfecting it. It is sort of like a language. As time goes on, it evolves from simple grunts to an elaborate language used to convey extremely complex ideas. Languages are human creation. Math is merely another language.
Why does it matter? Well for one thing realizing that math is something we created to describe the world, means that math does not necessarily define the world. Just because we could potentially model alternate dimensions and travelling backwards in time mathematically doesn't mean it is actually a reality. It could just be an artifact of making the math work, just like the square root of -1 is imaginary.
Math is imaginary-fairy and all in your head :P
There are no mathematical properties, only physical :P
Albert Einstein asked the same thing,
Incredibly useful illusion? I think so! The same way that an advice gives us purposeless-humans direction. Mathematics, on the other hand, guides us humans into the right path of development. It gives us the confidence to trust on our decisions.
amazing cryptogee-musings post thank you very much