One of my hopes in studying math over the last year had been that it could provide a totalizing precision that would allow me to dispense with other sloppier forms of language altogether. But mathematics deals only with distances and quantities. It doesn't deal with anything more paradoxical like emotions or beauty.
What mathematical language gains in terms of precision, it loses in terms of expressiveness.
The calibrations of limits in turn limits mathematics to observable and empirical reality. Other realities are perhaps better accessed and expressed by other means.
All mathematical equations can be put in ordinary language. But poetry, ethics, dessert recipes, love letters, funeral orations, and discussions of the weather, cannot be translated into math. Even if it's true that mathematics is infinite (numbers never end, as you can always add one more), language is much more infinitely infinite, in that it not only contains mathematics, but all other domains of human thought, and thus is larger than math by a ratio of billions to one.
I had hoped that mathematics would give us a more reliable method of discussion, and that its smallness would be made up for by its precision. It turns out to be a valuable and necessary method of discussing reality, but not sufficient for all of life's porpoises.
7 comments:
There can't be a reliable form of discourse. If there were, there wouldn't be a need for discourse.
It's interesting to think that the strongest telepathic cultures represented in scifi have been "hive minds" -- if we all had inner-head access, I think we'd quickly set ourselves up in an even more rigid hierarchy than we currently live in. . .
M
Kirby,
But mathematics deals only with distances and quantities.
These are probably the among the most ancient of things mathematics deals with, but they are far from the only things. Distances are but one sort of measurement that mathematics describes. Other such measurements from geometry include angles, areas, and volumes. From physics, other measurable quantities include things like force, time, mass, work, etc. These all have quite a few things in common, and some differences, which have led to the mathematical study of things like measure and vectors.
But mathematics studies other things as well. There are concepts of nearness and continuity, which is studied in topology, in general without dealing with numbers at all. There is also the concept of symmetry, which is important in many applications, which is studied in group theory, a branch of modern algebra, but also not necessarily with any reference to number.
Logic is another important branch of mathematics which can do without numbers. There is also the study of order, which doesn't necessarily have to refer to number.
One large theme in modern mathematics is how we can study certain things without having to use numbers.
It doesn't deal with anything more paradoxical like emotions or beauty.
This is true, I suppose, but I think that it's more or less a reflection of the fact that we just don't understand emotions or beauty. It's an exaggeration, but there's a germ of truth in saying that if we can't mathematize something, our understanding is far from complete.
The calibrations of limits in turn limits mathematics to observable and empirical reality. Other realities are perhaps better accessed and expressed by other means.
How many "realities" are there? I don't understand what you're saying here.
All mathematical equations can be put in ordinary language. But poetry, ethics, dessert recipes, love letters, funeral orations, and discussions of the weather, cannot be translated into math.
Ah, but one of Godel's great insights is that anything can be written in mathematics, to a certain extent. If something can be encoded in language, then it can be encoded in mathematics, since each letter (or phoneme, if you only want to deal with spoken language) can be assigned a number. This is the basis of cryptology.
Even if it's true that mathematics is infinite (numbers never end, as you can always add one more), language is much more infinitely infinite, in that it not only contains mathematics, but all other domains of human thought, and thus is larger than math by a ratio of billions to one.
Actually, both whole numbers and sentences in, for example, English, are countably infinite, and so therefore they are the exact same size.
I had hoped that mathematics would give us a more reliable method of discussion, and that its smallness would be made up for by its precision. It turns out to be a valuable and necessary method of discussing reality, but not sufficient for all of life's porpoises.
Why should it be? Porpoises are remarkable things in and of themselves. But mathematics can lead to a better understanding of many aspects of them.
By George, George, I loved this, but it's you who convinced me of math's limited nature when you said that you couldn't turn negative numbers into actual things, in the way I was trying to turn negatives into bad things, and positives into good things.
Now I have to rethink this entirely.
This is a beautiful little post, George.
GM, I think we might actually agree on something. By gum! And what do we agree on? That we can never actually agree on anything.
I like to think that higher physics (which can only be "discussed" in the language of complex mathematics) is really just a "short-hand" (or longhand??) for religious discourse.
When we get down to the nitty-gritty of describing how the universe actually "works" we arrive at a level of riddle (or conundrum) which is not unlike the mysterious pronouncements of the prophets.
Methinks that as we try to conceive of the macro or the micro we cross into a realm of thinking which is quite absurd: We are just talking about angels dancing on pin-heads as the medieval scholars were said to do--nonsense.
There are evident "mysteries" in the universe which it seems safe to say--at this point--we'll never be able to "explicate" satisfactorily. If that's true, then there are natural barriers to human intelligence. Will we be always barred from ultimate insight into the meaning of existence?
It's a question.
As I now watch the Science channel almost every night where they discuss the universe at its macro level, it appears that we won't be able to find a final form for the universe at any time quickly. One model posits infinite universes, of which this is only one. We don't even know if our own universe is curved, or p-shaped, or oval, or what.
Our galaxy has trillions of stars. The closest galaxy is Andromeda, which is 2 million light years hence.
And there are trillions of galaxies with trillions of stars each.
And this could just be one of infinite universes.
I thought your post was very well written. I somewhat agree that math has no direct way to deal with emotions and love,... However, there are underlining concepts that links Art and Math together. The gold's number that describes perfect proportion, pi constant for perfect circles...
Our emotions are effected by reality. Reality is governed by certain laws, and math describes and predict those laws.
Math is not all about counting, and quantity, but about describing reality and eventually predicting outcomes with mathematical expressions.
Thank you so much for your comments. I'm feeling down lately, and they felt glorious.
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