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. :)
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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.
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hmmm good point, food for thought...
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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.
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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
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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.
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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.
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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.
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Math is imaginary-fairy and all in your head :P
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There are no mathematical properties, only physical :P
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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.
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amazing cryptogee-musings post thank you very much
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Really good thought on the subject
However, I have to disagree with most of it.
There are many things that are outside of space and time that we interact with all of the time. Time and space are constructs. And some of the more higher level constructs at that.
π is actually a rational number. But, the way we have defined mathematics has really big problems and holes in it. A basic premise of modern mathematics is that you can always add 1 to a number. And thus, we add infinity and asymptotic to the mix. Further, we cannot divide by zero.
All of these will change when man learns to tune mathematics.
Like, 1,1,2,3,5,8,13,... approximates the golden ratio. Why does it approximate? Why don't we set the math and the numbers to be defined by the golden ratio? Then math would be a better tool for describing the world we are in.
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By that very definition the things you talk about cannot be outside space and time if we're interacting with them. Perhaps many people believe they are doing so, however since they can only prove it to themselves it doesn't really warrant discussion.
That's the point, because we can't. In the late 19th century, an American mathematician claimed to have solved the old Greek problem of squaring a circle. Problem was, pi had to have a value of 3.2 for it to work, he even got as far as getting a bill passed, before having it rejected by the Senate.
You can't change numbers that approximate to other numbers, because they have very real statistical implications with each other. The values of these things aren't arbitrary, they are very real in that sense, hence not only their usefulness, but their objectively constant behaviour.
Still though, it's interesting to ponder such abstract things.
Cg
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Thanks information
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compounding interest seems like black magic to me
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As an engineer I can say mathematic is real but numbers mathematical operations are human made just like the time... Human being realise day and night and then try to measure somehow a way... And then discover time... But time has already existed but there was no measurement system for it... And again Isaac Newton discover gravity... But again the gravity has been already existed... Anyway I think so at least... Nice subject to talk about...
Have a nice day my friend....
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I wish I was good at maths... sigh... feel like I'm missing out on so much
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this very important subject for us.thank you my daer cryptogee.math is very important aritcl.
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What a great set of directional reflections on a question among the deepest of natural philosophy!
I strongly believe in the reality of numbers, including imaginary and complex numbers, and of mathematics as a whole. I believe the human mind approximates these things rather than inventing them. Here I will try to score 2 points against what I believe.
The counting of objects before and after arithmètic operations are performed on them, though often offered as evidence for integers, is more likely in practice to involve almost integers due to irregularities of replication in the purportedly plural objects being counted.
In their discovery and exploration of circular and n-spherical proportions, aliens — and indeed alternate humans — might well focus on a value other than π. They might prefer what some people denote by the Greek letter τ = 6.283185…, or the 2iπ common factor in the periodic incrementation of complex logarithms.
Did I score 2 points in favor of the Fictionalist position? Slightly less than 2, maybe, or slightly more? Closer to 3? Precisely e points, perhaps?
If so, my rejoinder to my total score and any point within it is this — the fiction involved is still a conceptual approximation to something real.
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It's real. It exist. We are using it. I like Math. You have the formula, you get the answer. Unlike other subjects that you need to give reasons. Why is it like this. Like that. 😂😂😂
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Excellent thinking cap peice, I would surmise since numbers like letters are symbols, and numbers are a symbol system of measurement,
I see numbers as a a way for consciousness to make since of things as a common symbol language that must change as we expand our understanding of how we measure an expanding view of nature... take the number 9,
As you know it cannot be add or subtracted from anything but it looks like it can be . ..so maybe number's are the way our minds set limitations through mathmatics...seeking to discover insights into the natural world, yet maybe we will come to the equation that math and the world it tries to measure is the same..a very concrete centralized dream...
Cool post
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Can you go from pure mathematics to real world mathematical applications?
The answer is, no. You can not start with math only and then apply to real-world scenarios. It is, however, possible to use mathematics in the real world (even in the fictional world, as in the Harry Potter and movie stories), but the path and direction of the applications are different and need to be clarified.The reason you can not go from pure mathematics to real-world math applications is in the nature,the definition (in a sense) of a number.
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I learned a lot about mathematics. I've made algebra. And I did not know the rest. Thanks for the nice post.
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First of all, this is a nice piece and has given me food for thoughts. I think i agree wth both notions that mathematics is both real and abstract. If i have a black pen and another blue one, one would conclude that i have 2pens even though clearly they aren't exact the same.... This is just the practical aspect and as you said it's just human values. Like the platonists , i also agree that mathematics is an illusion and if aliens actually existed (I'm not so sure they do) they'd have their methods of calculations that might look totally different from ours but in conclusion, mathematics has been really helpful.
Nice one, good stuff cryptogee
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This is thought provoking. Thanks. I've often thought about numbers. They are arbitrary to some degree. For example, where is the line between 1 and 2? 1.5? On a ruler, where do you draw the line? Doesn't it become infinitely harder as you change scales and have to decide which atoms to draw between? Is that half way? I find this same problem with all things that are on a continuum. Like time. Or beauty or kindness.
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Everything is Light energy and has no meaning. WE give it meaning.
It is all relative not absolute. A Quantum particle itself has the property of Infinity itself, yet within our eyes it might look tiny and measurable. Our entire brain is designed to navigate through this reality here but not more. Mathematics might follow completely different synchronicities elsewhere in the Universe and make complete sense to them accordingly their reality experience.
Everything in the Universe is constantly shifting and flowing. Mathematics as we experience it here simply follows the flow of energy patterns in this part of the Universe, while elsewhere in the Universe the energy pattern flow entirely differently, and thus translate into different numeric harmonies..:)
Thank you for your thought-provoking input! I enjoyed it :)
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@cryptogee the best way to play...and u hv choosen the best playground. 'Mathematics'.... A playgrou d of numbers which give quantative value of certain things and make their existence possible.
Mathematics - is real and the numbers make everything countable. Even if we say there 'n' number of language...instead we can say there r 5 number of subject. Without mathematics identifying the numbers is not possible . we can call it a numeral language for sure that quanify something 👍
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From my point of view
Math does exist beacause without we cannot solve our problems and get there accurate solution
Now a days math is very important in every part and field of our lives..
You wrote a good post
And good references tOo
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Nice post! Definitely thought provoking.
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Great post
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Well I always told my teacher that math was a lie but she did not seem to agree with me......
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My view on this is, mathematics exist. According to Rene Descartes: je pense, donc je suis translated as I think, therefore i am.
From time to time we doubt but one cannot deny the fact some things, seemingly abstract in nature do exist. Being from the field of computer science, mathematics play a huge role in my day to day endeavours,
Go back a few years and many would have doubted the possibility of technology bringing a more secure way of keeping accounting transactions in check. More secure than the cheques and old school vaults. Now we even got cryptos, so is cryptocurrenct real?
Although one would argue that the problem with accounting is man made, so providing a man made solution falls under an entirely abstract conclusion.
Well, if we are able to believe that cars are real because they are built with the things we can physically touch and feel. Then we should be able to believe that mathematics is real because our computers, our smart phones have operating systems that run on man made notations like the zeros, the ones and other syntactic codes
Codes that make up softwares that affect our lives in one way or the other. Mathematics is real
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