Objects, Concepts, Time, Language, and Mathematics
Today I wanted to make a post that is going to be quite a bit different from my usual posts, but this has been on my mind and so I really wanted to write it out. It's probably gonna get kinda deep. So get ready. Specifically I want to talk about the dichotomy of objects and concepts.
Now before I get started I want to preface this by saying that I am in no way any kind of authority on these topics and could potentially be completely wrong about it all. And wether you think I am right or think I am wrong or anywhere in between I would love to have a discussion and hear all of your thoughts and insights.
A few years ago while climbing mountains in the eastern Sierra Nevada myself and my friend and fellow mountaineer "Alpine Mike" had a fun debate on this topic after he told me that he had written a paper in college all about how numbers are actually physical objects. I disagreed and although his arguments were quite interesting and thought provoking I was not really convinced. But it did inspire me to dig deeper and ponder the topic further on later occasions. And then very recently my interest in the topic was reignited while I was listening to the recent Lex Fridman podcast with Sara Walker and Lee Cronin.
It was a really long podcast but I listened to it all and I found it both very interesting and also a bit frustrating. Which is how I usually feel as an "uneducated" person when I'm listening to academics speak as I often find that their "education" both enables them to have lots of really interesting information, but can also get them stuck in a box, so to say, where they are unable to properly question what they've been taught. For example in the podcast Sara states that "information is physical in time but not in space". I find her statement to be quite confusing, yet she repeats this theme multiple times throughout the podcast, I believe, simply because it's what she was taught. Honestly, I could go through the entire podcast and find a bunch of things said by both Sara and Lee that I could nit pick on, but that is not the point of this post. And for the most part I found the podcast to be really quite good and I definitely enjoyed listening to it. Anyways, I'll return to the podcast in a minute, but first let me actually get to the point.
I believe that things exist in two forms. Object and concept. Objects are the things that make up everything in the known physical universe. Conceptual things are the tools that our consciousness uses to make sense of those physical objects, but I believe that they do not physically exist themselves. Now right off the bat there is often the argument that these concepts do physically exist as electronic signals in our brain. But what I would argue is that the brain physically exists and the electric signals physically exist. Those are both objects. But the ideas created in our head by these electronic signals do not physically exist. They are concepts. Now to help explain this point further I'm going to talk about three areas where the physical and the conceptual often get conflated.
I'm going to start with what is probably the most interesting topic as it's probably where I personally have the most questions. Time. I like to entertain two separate theories about what time is and the crux of them is wether time is physical or conceptual. It must be one or the other. If time is physical then it is essentially a fourth dimension of physical reality that we have yet to really understand and all change of physical things is just due to the movement through it. A concept of physical time would mean that everything that ever happened or ever will happen all exists simultaneously in a physical form and our current conscious experience is actually just us moving through that physical matter. Now I find this theory super interesting because it opens up all kinds of other interesting possibilities like time travel and infinite dimensions. But unfortunately time being a physical thing is not provable in any way that I am aware of. So for now I stick with my other theory, the theory that time is a concept. A concept created for measurement of physical things. Just like inches, or miles, or pounds, or joules. Except that time measures change. So if there was no change there would be no time. But since the nature of the universe is that change is constant and inevitable, so is time. Makes sense, right? Now to sum this theory up I'd just say, you can hold a clock in your hand because it's a physical object, but you can't hold time in your hand because it's not.
Now to make the argument on what is probably a more concrete and easier to understand example, let's talk about language. Every single word in every language is conceptual. There is nothing in physical reality that makes a dog a "dog". Sure the dog exists in physical reality, but the word "dog" is actually just a concept to describe that physical thing. A word that people just arbitrarily decided on. It could just as easily been the word "kgfkhtf" that we decided represented the concept we currently call "dog". So while we do use words to describe and understand physical reality, the concepts related to those words only exist in our minds and could be arbitrarily changed at any time because the words themselves have no real connection to the physical reality beyond what we arbitrarily (and ultimately only temporarily) ascribe to them. So you can show me a dog, you can tell me it's called a dog, but you can't tell me why it should be called a dog beyond the fact that it's what other people call it. So, now that I'm actually writing this I feel like it may not be as easy to understand as I alluded to at the beginning of this paragraph... but to try to simplify and summarize... objects exist in physical reality but the language we use to describe and understand these objects only exists conceptually inside our minds. You can hold a dictionary in your hand because it's physical, you can't hold language in your hand because it's not.
So now to drive the point home with what is likely my favorite subject in this line of thought. The one Mike initially got me really thinking about on that mountain climbing trip years ago. Mathematics. Or even more simply, numbers and numerical systems. Similar to language, numbers are a concept that we use as a tool to describe and understand actual physical things. Except that numbers are specifically for describing and understanding amounts. Also similar to language, the current mathematical system is largely arbitrary and not some physical attribute of the universe as I think many people believe. Why do we use a base 10 numerical system instead of a base 9 or a base 12? Only reason I can think of is that humans started counting on our fingers and we have 10 fingers. lol. Who decided on the "order of operations" and why? Because it sure doesn't make sense to me. Honestly the more you think about it the more you realize how arbitrary it is. Now to quickly go back to the podcast, at one point Lee tells Sara that mathematics doesn't exist (I'm assuming he meant physically exist because obviously math does conceptually exist) and this prompted Sara to go on the defense and to assert that abstractions like math are actually physical objects. Which is essentially what Alpine Mike was saying about numbers as well as other concepts in our debates on the mountain. Sara goes on to say that "the physics of abstractions just isn't understood yet", which in my opinion makes her claim speculative at best. For a theoretical physicist to say that they just don't understand the physics yet is to admit that it's mostly a bunch of imagination and there may not actually even be any physics to understand and it may be as I have been saying all along in this post that these concepts likely do not actually exist physically. Can I hold a "2" or a "5" in my hand? I can hold a physical symbol that represents the concept of an amount. Like a "2" or a "5" written on a piece of paper. And I can hold a number of physical objects. Where I can apply the concept to the objects. "2" of this or "5" of that. But I can not actually hold a number. Imagine trying to hold a "-7". lol. It would seem absurd to think that was possible. Right?
So to conclude, I believe that numbers, and math, and language, as well as all other concepts... only exist in our minds. Which obviously then raises the question of "what is consciousness?" which would lead us down a whole other super interesting rabbit hole of metaphysics and meaning, souls and god, free will and determinism... but I am not gonna even try to attempt to get into any of that right now in this post.
So what do you think? Are numbers physical objects? Is time a physical object? Am I totally crazy? lol. I'd really love to hear what you all think about these fascinating ideas.