Does math exist or did we make it up?
It seems like a stupid question. Modern intuition tells us that it obviously exists – it’s freaking everywhere. But the more I thought about it this week, the less and less sure I was. It got to the point where I grew so unsure about this question that I questioned my own existence, had an existential meltdown, locked myself in my room for three days, and finally decided I would go ahead and read about it.
Fast forward a week and some long lectures from old German guys on Youtube, and I am here – still not really knowing what is going on, but slightly more informed. Now knowing a tiny bit about it, I figured I would try to share it with others, who I assume have never even given the topic a thought.
Let’s start from the beginning!
Origins of Math
Math originated nearly 10,000 years ago in a hunter gatherer society as a means for trade and money. Basic tasks like one item being grouped with another item forming two items were done for survival. Since then, math has grown into a tool used to model some of the universe’s most complex actions.
The question of whether math is invented by humans or discovered in the laws of the universe is one of the greatest philosophical questions to date.
Arguments for Discovery
The human brain has evolved to aid in our survival as a species in the different environments human beings have encountered throughout history. Our brain has evolved to reason about the physical world as well as the social world we live in. The brain did not evolve to reason about abstract objects like numbers. In order for the brain to reason about numbers, the brain must have learned how to handle abstraction or it must have acquired the ability to take abstract objects and present them for thought as if they were concrete. For example, when I say “3 apples” you hopefully picture three apples in your head.
From an evolutionary perspective, the human brain originally began as a simple stimulus-response device, that “recognized” certain forms of input and generated appropriate forms of output, similar to a sunflower that grows in the direction of the sun.
The human brain then acquired the ability to mediate between input stimuli and output responses. [The neocortex]
Types of Mathematicians
There are two types of mathematicians, Platonists – who believe that mathematical truths are discovered because they literally exist and they literally are true, and Nominalists – who believe that math is just what we do when we account for things / the process of labeling things.
Nominalists believe that Math is a concept of the human brain for the following reasons:
- The Human brain does not process directly in the new domain. It pulls back to the familiar domain and utilizes existing processing procedures.
- This means that humans don’t learn something all at once. It’s like a new leaf on a tree. You can’t just get the leaf without first having the trunk, the branch, and finally, the leaf
- Mathematics is abstracted from the world – mathematicians construct abstract, skeletal models of the world.
- Because of human beings process of ‘thinking in metaphors’ ( tree example) and the end result of the metaphor grounding in the everyday world, mathematics carries the sensation of thinking about the real world.
- Since we all share the same world, we all end up with the same mathematics
- The feeling of concreteness that comes along with the mastery of a new abstract domain is neither a precursor of mastery nor is it a consequence; instead, it is part of the process in which the brain acquires that mastery.
However, the Platonists tell a different story.
In 1612, Galileo said “The underlying rules that make the universe tick are inherently mathematical.” Fifty years later, Isaac Newton claimed that he agreed with Galileo’s assertion that the universe was inherently mathematical, and then proceeded to create the equation for the law of universal gravitation, accurate down to the thousandth percentile – all based on an assumption that planets orbited in an elliptical motion.
Do you realize how crazy that last part is?
This guy basically took a shot in the dark at a problem that had stumped scientists since the beginning of time and ended up being not only correct, but so accurate that to this day we have not changed it. Nuts.
Mathematical Platonists believe that we discover mathematical entities and mathematical truths because they literally exist and they literally are true. Ultimately, Platonism boils down to faith. To a Platonist, math is about truth. If you tell a Platonist that math isn’t real, it is like telling them that truth doesn’t exist. Which would, ya know, like break them or something.
The Good Stuff
Perhaps maths relationship with reality is in its ability to describe it. Just like the English word “pencil” has a relationship with reality in that it refers to things we experience as pencils. While mathematics is not able to say anything with exact truth about reality, it does give us useful approximations and so it is worth talking about in that respect. However, if this is the case, it gets a lot more complicated.
Now entering the rabbit hole. Hold on tight, because shit is about to get whack.
If math is a reality of our experience, then where is the reality of your other inner experiences, for example your love?
Well, it depends how you look at it. Are “inner experiences” really that different from “real” experiences? We are not just guests experiencing the universe, we are part of the universe experiencing itself. The mental state that a human is in is simply neuron connections bathed in hormones and endorphins. This is no more or less a ‘real’ experience than eating a salad, or punching your friend in the face.
When we talk about ‘real’ experiences as being different from ‘fantasy,’ that’s a completely different type of conversation. That would not be talking about the internal events of the mind, but rather the connection between that event and another event. When a character on a TV show dies, that human life doesn’t actually end, and that is different from when an actor who plays a character dies, because then a human life has actually ended.
The ‘inner experience’ of grief for the audience could be identical however, because in each case those people experience the loss of a constructed image of a person who existed and now no longer exists.
So the experience is a different event from the prime event, and the experienced event is real whether or not the prime event is real.
So too, math is real and it has real-world consequences, but math is not the same thing as the events that it describes. Math describes physical interactions, but it does not prescribe them. One could say “the math indicates that human brains cannot survive for more than 7 minutes without oxygen” but one could not say “the math dictates that human brains won’t survive for more than 7 minutes without oxygen.” The math describes the physical events, but it does not create them.
Where this gets even more exciting though, is back inside the brain. Humans with limited or no language cannot think like normal people. There was an interview on NPR with a man who was not educated in any language, he had grown up like a wild animal and he was never taught any words. The man referred to the time before language as “the dark time,” and he remembered very little of the experiences that he had during that time. Without words to describe his experiences, he was not able to form memories. Without memories, he could not learn or understand ideas. Language is so essential to human thinking that without language, we don’t understand the world. The same goes with math. For example, we only understand quantum mechanics as math, and we have no other way to talk about it.
The question of does math exist or did we make it up is similar to the paradox of The Ship of Theseus, which is: if you replace the parts of a ship one piece at a time and build a new ship out of the original pieces, then which ship is the original ship at the end? If the one with the original pieces ‘is’ the original ship, then when did the identity of the ship switch?
This parable gets at a very fundamental question; what defines a things essence? The Earth and the humans that are on it were made of elements that were created eons ago in the stars, but no one identifies the Earth or the people on it as those original objects. It seems pointless to do so. But then consider a car. Let’s say it needs a lot of work and 80% of it needs to be replaced and you use second-hand parts from another vehicle to do so. Most people would still say that the original car is still itself.
Ultimately, we are making decisions as to what constitutes a thing unto itself. The question of whether math exists or whether it is made up depends on what you mean by the word “exist.” Some people claim that once you fix a system of axioms, every theorem that follows from those axioms is sitting there waiting to be proven. But isn’t that the same thing as saying that once you fix the alphabet, every possible English word is sitting there waiting to be said? It’s not necessarily wrong, just completely useless.
Eventually, I think the question of whether math exists in the universe or not ultimately boils down to whether or not the universe is logical.
And from everything that humans have observed, it seems that the universe is logical. The universe has an inherent set of logical rules that define how it works. How gravity should act, how birds fly, the shape of a leaf and the branch to which it is connected, and so on.
Math is the logic of quantity. It is our way to quantify the inherent logic that drives the universe, in the form of symbols that we call numbers. Perhaps every physical form in the universe could be emulated with the proper equation.
But while it seems that the universe is logical, what then is illogical? That is a slightly more difficult question to answer. Logically, our muscles, tendons, ligaments and bone structure support the ability to jump a certain height. Taking into consideration the logic of gravity and other forces that might be acting on the body at any given moment, it would be illogical for a human being to jump and then fly away or shoot laser beams from their eyes… those things break the existing logic of the universe and therefore they are illogical.
One could say that whatever rules that define how a universe must “behave” are automatically logical to the inhabitants of said universe, and anything that would break those rules would be illogical. Whether the rules are inherently logical or not is a meaningless question. There could be dimensions in which breathing fire is completely logical, or your mom and dad both being chairs is 100% normal.
In 1977, two voyager spacecrafts were launched to outer space with a message to any life form who could decipher it. The message had no words, just pictures. Pictures are the barebones of mathematics. While Aliens might not draw “1 + 1 = 2”, they can most likely understand that one item with another item becomes two items.
If extraterrestrial life has a similar background as we do and has experienced the same phenomena as we have, then it is possible to communicate with them via mathematics. This is similar to how you can travel to a rural part of the world and not speak the same language, yet conduct trade by doing simple math together.
However, if extraterrestrial life has a different background, different sensory apparatus, or different cognitive structure, it might be impossible to communicate with them via mathematics. If extraterrestrial life does not understand our form of mathematics, it would be like trying to communicate with color to an alien life that can only see in black and white. It simply would not work.
And now I am sitting at my desk, questioning everything I have ever known, and feeling more lost than I was when I started researching this topic.
I hate to end the post like this, but unfortunately I don’t have a satisfying conclusion for you. For that matter, I am not sure anyone has a satisfying conclusion to this problem.
I will however leave it at this – after researching the topic and thinking about it nonstop for a week, I am not sure what is more terrifying – The idea that the universe follows a set of rules in the form of mathematics, indicating that either a higher power put these in place or that the universe is a simulation, or the lonely prospect of mathematics being a construct of the human mind, applicable only to the environment in which we are accustomed, meaning that we are either alone in the universe, or that we will never be able to communicate with other life.
So which is scarier – being alone in the universe or not?
Comment what you think below.
Oh btw, I found a sweet picture of you and I
Most of the ideas in this post are not mine. I tried to pool together the main ideas from some distinguished philosophers and scientists to present in a ‘easier’ to understand way.
Massimo Pigluicci – “On Mathematical Platonism”