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The existence of Mathematics, Numbers and Concepts

Alright everyone I hope you are as interested in this topic as I am.

Back in high-school I was working with a very long and boring problem full of pesky equations. Being talented at distracting myself I started pondering: Just what exactly is an equation, what is a number or a "concept"? Is it physical? If not how does it exist? The first word that came to mind was relationship. We explain one system in the universe by comparison to another. Humans developed concepts to make these relationships and patterns more general or constant, as you can take the math for one system and apply it to similar one by carrying that concept in your mind. Equations are just a formal way to describe a system and cram multiple concepts into one place, numbers/ variables are the pieces. Where does immaterial come in? This has been my puzzle. I would say that math, numbers and concepts are composed of energy because on some level they have an effect and without forms of energy there would be nothing to calculate or imagine in the first place! You hear people say that thoughts or concepts are abstract and not of a physical nature and I think most of the time they aren't really thinking about it or have a sloppy definition of physical nature. My hunch is that because a concept can be false or fail to manifest in the world as described/ imagined by its maker we put less value on its reality. For example if I have the concept in my head E=mc, it's a false concept/ it isn't "real" (let's assume Einstein was right) but I would say that the concept E=mc still holds physical form, in my mind. I sort of wrote that in a rush so forgive me for any grammatical errors or conceptual confusion.

Agree? Disagree? Unsure? Discuss discuss discuss!

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Permalink Reply by Jaume on August 7, 2009 at 5:29pm

You won't find, on this planet, two brains which are wired exactly the same. Thus, when we both think "42", we don't necessarily use the same set of neurons (it's extremely likely we don't), and the physico-chemical reactions ("energy") that produce this thought are extremely likely to be very different at the molecular level or lower. Heck, it's even true when you think "42" now, and "42" again next month.

From your perspective, I conclude that 42 never equals 42, since these numbers are defined by their underlying physical nature, or energy, which varies with time and place.

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Permalink Reply by Derek Schrock on August 7, 2009 at 6:04pm

I like your choice of 42.

I would agree that 42 from the perspective of different minds never equals 42 but I think you are putting everything under the term concept and I'm starting to think that that's my fault for being unclear. What you described is how we represent them in our minds. I am saying that there's more to their existence. Numbers (such as 42) and equations exist in nature, apart from our perception of them, in the form of relationships of energy. Even if the energetic environments in which we find two "42's" vary I don't think that that means these numbers change value. I think you are touching on the point that we can define a number by it's environment, again I don't see how this changes it. 42 as a general value, to me, is the conglomerate of all the energetic relationships where 42 exists.

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Permalink Reply by Mike on August 10, 2009 at 1:15pm

What you seem to be talking about is organization of information. Generally, in physics, we think of information as properties of entities (mass, energy, etc). The descriptions of them using math is just that, descriptions. The actual equations don't have any more or less 'realness' than this sentence. Math is a language for describing our physical world. It's not more perfect than English is, but it's specialized to look at things in a way that works for a lot of us doing particular tasks. No one would ask you to run down to the store and bring them chips in math the same way no one would try to make predictions on particle placement using English.