Do you think everything can be described mathematically?

Do you think everything can be described mathematically?

Ophiolite said:

My initial reaction was no, but on reflection I became less convinced. It would appear to depend upon how rigorously one requires that variables and their range of values be defined. If you have an example of something that you think cannot be described mathematically, I'll take a stab at it.

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In the end, I'm leaning toward yes, so I don't have an example. I'll give you some clarification, though. You can't know the position and momentum of an electron simultaneously - an uncertainty principle. But you can describe both it's position and momentum mathematically. In my mind that qualifies as a yes, but it also hints at some of the interesting nuances.

Sabertooth said:

A great many things, but not everything. (You still must feed your loved ones [or they'll get cranky...])

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Love is an interesting example. Physicalists, and their position on things like the mind/body problem, would say love actually can be described mathematically - in terms of brain chemistry, and then into the mathematical description of those chemicals and how they react.

That raises the next question. If love were described that way, would we comprehend it? So while it seems likely all things could be described mathematically, can all things be comprehended in their mathematical form?

I was musing on this because of some of my education. I never really got chemistry. I could go through the motions, pass the tests, get the grades ... but I never really got it until, oddly enough, my son was taking chemistry. My grades in chemistry were better than his, but he understood it better than me. It was he who taught me something that finally triggered an understanding. I get chemistry now.

The same was true about certain aspects of electricity & magnetism. I can do the math, but I never really got it until very, very (embarrassingly) recently.

Sabertooth said:

Before even considering love, there are lesser subjective preferences, too, like music, art, flavors, etc.

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Yes, of course.

Ophiolite said:

I think they can be comprehended mathematically, but only if one has the the requisite mathematical competence.

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Not really. My engineering job involves incredibly complex machinery. 20-some years ago I cowrote a piece of technical software that modeled the first principles of those machines. People have since used it to model machines in ways that amaze even me. But because I was one of the authors, people assume I understand those machines better than I do. I wrote the software because the opposite is true. The software means I don't have to understand those machines, at least not to the lowest levels. And I don't believe anyone understands them at that fundamental level.

Still, they are being mathematically described.

I think that indicates two C's ... three would have been more aesthetically pleasing, but I only came up with two: capacity and correspondence.

The above example relates to my lack of capacity. I may understand pieces of the machine - the fundamental principles - but I don't have the capacity to understand the whole machine.

Correspondence relates to how one knows one has found a basic, fundamental principle. It's a topic not much covered in science discussions, but it fascinates me. Modern science is very reductionist. All my engineering work builds up from accepted first principles of mechanics. But how do you know you've found the "right" first principle? Many were suggested for mechanics before Newton's became generally accepted.

There is a long and fascinating history of people empirically obtaining equations to describe physical phenomena, but which contain dimensional errors. If one knows the context of these equations and applies them properly (so to speak), they will accurately predict certain phenomena. But they can't predict new phenomena, combine with other equations to build systems, etc. It is the Buckingham Pi concept of "nondimensionality" that allows one to assert one has actually found a robust first principle.

My point: Maybe human concepts such as love don't correspond to scientific first principles. Therefore, if love were described mathematically, it would probably seem to use an odd mish-mash of love and something else - maybe love plus how food tastes, or love minus respect ... who knows.