Welcome to Gaia! ::

The Physics and Mathematics Guild

Back to Guilds

 

Tags: physics, mathematics, science, universe 

Reply The Hangout
On complicated theories

Quick Reply

Enter both words below, separated by a space:

Can't read the text? Click here

Submit

Layra-chan
Crew

PostPosted: Mon Jun 22, 2009 9:38 am


In the Sci&Tech, there is a creature of mild interest who goes by the name of Kaz-Balan. She asks why scientists believe in the general theory of relativity instead of the simpler theory of Newton and the Aetherists. While not a particularly intelligent question, it does have some pedagogical merit, so I attempted to answer her.
Here's a slightly less context-dependent assortment of my thoughts on why physical theories end up being complicated:

There are, from what I can tell, four main points to consider:
1: Accuracy: The important of being right
2: Integrity: One thing versus many things
3: Intuition: Simple but not easy to understand
4: Language: Intrinsic versus linguistic complexity

1: The first point is the most relevant to science. The goal of science is not to be pretty, but to be accurate. Art can be pretty all it wants, but science has the rather dirty job of trying to predict the universe and to do so requires accuracy more than it requires beauty.
There are many ideas that are simple and wrong. "Blue is the only color" is simple but demonstrably wrong. We can easily show that there are colors other than blue. So the statement "blue is the only color" is useless scientifically, even though it is a very simple statement and is indeed simpler than acknowledging that there are other colors.
Would it be better to say "Blue is the only color", or to go through the rather long list of colors that actually exist? Is it better to have an idea that is simple and wrong, or an idea that is complicated and right?
We used to think that planetary orbits were all perfect circles, but now we know that they're more like ellipses. Circles are simpler than almost-ellipses, but that's not what orbits are shaped like. So we don't care about circular orbits anymore.
Blue as the only color is simple. But it's wrong. Circular orbits are simple. But they're wrong. And so we discard these ideas for ones that are harder to explain but aren't wrong.

2: Suppose you see a square shadow on the sidewalk. Later on, in the same place you see a rectangular shadow. And later still you come back to the spot and find a hexagonal shadow. So you have something that is sometimes a square, sometimes a rectangle, and sometimes a hexagon.
Alternatively, you could look up and see that the object casting the shadows is a cube. A cube is a three-dimensional object, inevitably more complicated than a two-dimensional object like a square or a rectangle. On the other hand, a square, a rectangle and a hexagon (and the other shapes that the shadow of a cube can take on) together are more complicated than a single cube. So which is simpler, many simple objects, or one slightly complicated object?
Another example is a Newtonian description of the Universe versus an Einsteinian one. Newton's description has space, time, forces, fields, mass, and many kinds of energy. Einstein's has just spacetime and energy, and there is only one kind of energy in Einstein's universe. Which description is simpler?

3: Something being simple does not mean that it is easy to understand. The number 1 is simple, but I would not say that the concept of 1 is easy to fully understand. Our notion of 1 is very dependent on rather silly things, empirical observations, hand-picked lists of acceptable examples. We can say 1 cat, but it is harder to say 1 milk, or 1 air. Can you explain why? Why are all 1s the same, except for 1 milk or 1 air?
Truth should be simple, but philosophers have been struggling to define truth since the beginning of philosophy. Things that are simple are often difficult to understand because we do not perceive a world of simple things. We perceive a world of complicated things, and we perceive a world far away from the things that are fundamental. The world we perceive is built upon many, many layers of interactions of fundamental things, so in order to get to the things that are fundamental, we have to go through all of these layers. Thus even if the fundamental things are simple, we have to say a lot to describe them in terms of what we perceive.

4: A lot of mathematics and physics looks pretty ridiculous linguistically. Jargon, jargon, jargon everywhere. It might as well all be in another language, mainly because it is. Natural language isn't terribly good at describing things precisely; it's not built for that. Natural language is built for communicating the terribly imprecise world we experience.
So mathematicians and physicists make up words to describe things precisely, and describe things in terms of these made-up words. And if you don't know these words, it's just like trying to read a different language. Of course it's going to be difficult for you. That doesn't mean that it's difficult, just that you don't speak the language.
It's like going up to a non-Greek speaking child, giving them a text in Greek and blaming the Greeks when the child doesn't understand what the text says. "Why must the Greeks make everything so complicated?" you moan, flipping through your Greek-to-English dictionary, never minding the Greek child half your age flipping through their English-to-Greek dictionary and cursing the British for spreading their multiply-bastardized language.

To recap, there are four things to keep in mind:
1: Accurate but complicated theories are more useful than simple but incorrect theories
2: A single complicated but comprehensive thing is simpler than many individually simple things
3: Simple and especially fundamental things appear more difficult to understand because we don't experience fundamental things
4: Mathematics and physics are written in a different language out of necessity, but that doesn't make it more complicated, just different.
PostPosted: Mon Jul 13, 2009 7:34 pm


Regarding your original topic, GTR is in some senses much simpler than Newtonian gravitation. There are many reasons why gravity should be a metric theory, but other than observational ones, there's something quite attractive to having gravity as another aspect of inertia--that's certainly a plus from an Ockhamian viewpoint.

While you're quite correct that the empirical adequacy is the ultimate criterion in science, there's still a place for beauty and simplicity in physics. Making gravity a metric theory is a part of that (although there are certainly lots of empirical reasons as well), and from there, anyone who cares to compare GTR with Newton-Cartan theory (metrization of Newtonian gravity for Galilean spacetime) would quickly see that GTR is much simpler, more compact, and more beautiful than Newton's.

VorpalNeko
Captain


Layra-chan
Crew

PostPosted: Tue Jul 14, 2009 10:29 pm


The difficulty with that comparison comes from mainly point four, in that the metrical description of GTR certainly appears more complicated than GMm/R² and the usual forms of Newton's laws. Sure, if you translate Newton-Cartan gravity into a metrical form, you get something obviously more complicated than GTR, but Newtonian gravity doesn't seem to necessitate such a translation, and hence appears simpler due to language.
PostPosted: Wed Jul 15, 2009 12:56 am


I suppose that would depend on what you mean by "necessitate". That we don't need to do so in order to get results, certainly. But Newton's theory 'requires' such a transformation in the same sense that electric and magnetic forces 'require' an electromagnetic field or that electromagnetism and weak force 'require' an electroweak formulation.

Such a reformulation is admittedly inferior in terms of practical utility, but it is superior from in terms of what is fundamental (and thus also explanatory power), and also simpler in the sense of Ockham's razor, since it trades two primitives (inertia, gravity) for just one.

I don't have any better reason than that, but unification of different phenomena seems to be a value shared by many physicists, and is pretty objective. Although I also find something very attractive in the possibility of axiomatizing physics as a kind of geometry.

VorpalNeko
Captain


Layra-chan
Crew

PostPosted: Thu Jul 16, 2009 12:16 am


You must admit that the language barrier (and, perhaps, the math and abstraction barrier) is a pretty strong one, however. Physically and mathematically simple differ quite a bit from linguistically/pedagogically simple. You can teach Newtonian gravity in terms of Newton's formula to high-school kids. GTR? Not so much.
PostPosted: Thu Jul 16, 2009 5:20 am


Yes, of course. I guess what I'm really saying is that there are two separate notions of "simple" going on there
  • , but there is a subtle connection between them. There is the sense sense of fundamental entities or primitives, i.e.:
    Layra-chan
    Another example is a Newtonian description of the Universe versus an Einsteinian one. Newton's description has space, time, forces, fields, mass, and many kinds of energy. Einstein's has just spacetime and energy, and there is only one kind of energy in Einstein's universe. Which description is simpler?

    and there is also the sense closer to the ordinary vernacular that we're focusing on now.

    My point, poorly expressed as it might have been, is that although the two are disconnected on the purely logical level, there's actually something interesting going on: if you take a theory and unify some of its fundamental entities, say by constructing a language that destroys such distinctions, simplifying them in the first sense, one tends to find that the more empirically adequate theories become simpler in the second sense as well.

    So, for example, Newton's theory expressed in a way that unifies gravity and inertia is more complicated than Einstein's, and the latter is more empirically adequate. Unifying electrical and magnetic forces gives at least two alternatives for an underlying fundamental: aether or just that the signature contribution of space is exactly opposite that of time. The latter is simpler and is more empirically adequate (when one considers effects other than classical electromagnetism).

    Now, I'm not exactly sure what's going on. It could be coincidental, or there could be some sleight of hand due to some psychological bias, but in any case, there seems to me a very real trend in which the laws of physics tend to become simpler in the second sense, despite the opposite trend that our ability to apply them worsens. It's just prepended by the requirement of simplicity in the first (Okhamian) sense: one follows the other as if on a leash.


  • Actually, more like three: the vernacular case can make the distinction about simple-to-state and simple-to-use, which are not always hand in hand.

  • VorpalNeko
    Captain


    Layra-chan
    Crew

    PostPosted: Sat Jul 18, 2009 10:25 pm


    I fully agree with you on that point; theories are getting simpler in terms of the number of fundamental concepts needed per phenomenon, and the language in which these theories are cast are getting "simpler" alongside them, at least internally.
    Externally is different. The need to construct new languages (or perhaps I should say paradigms? Branches of mathematics? Wikipedia pages?) makes the teaching aspect difficult, even if the theories in the abstract are simpler. Each language is progressively simpler, but each word carries more and more meaning, with more background knowledge necessary to comprehend it in terms of the colloquial. It doesn't help that the languages typically give their definitions in terms of previous theories, so that newcomers must chase the chain of definitions and concepts all the way back before reaching English.
    We end up with a physics-to-English translation dictionary with only a few entries, but each entry is cast in terms of different set of auxiliary translation dictionaries, each containing themselves but a few entries, which are defined in terms of the contents of yet more translation dictionaries. This is the natural structure of knowledge but from the bottom of the pyramid one does not see the single block at the top, but rather the myriad blocks at the base. I have a metaphor problem.
    PostPosted: Thu Jul 23, 2009 11:46 pm


    Yes. You're absolutely right. I now understand what I was seeing through a glass darkly: the distinction between he sum of the scientific laws of a theory with the theory itself. (That's where I was going toward in reference to our ability to apply them earlier, but I didn't think on it clearly at all, and outright conflated them in my first post.)

    Because even with a fixed language, if we look at even the starkest shift in physics from the classical to the quantum, there's really not much additional complication in the core laws themselves--even the reverse, from a certain point of view, e.g., Feynman's path formulation no longer explicitly picks out a specific path. But there's indeed a lot of baggage--both in terms of physical and especially mathematical concepts--in getting from them to even a trivial application. It's as if we found out that instead of playing chess, we're going to play checkers from now on, but on a board that's a million-fold times larger, making strategies much more difficult even as the rules themselves get simpler.

    I was trying for a stronger form of your intrinsic/extrinsic distinction by taking a more narrow view about what's "intrinsic"--something does get simpler, and not just different. A bit too narrow for the word 'theory' to apply, though, because we do need to get actual predictions at some point.

    VorpalNeko
    Captain


    StandingOnTheMoon

    PostPosted: Thu Oct 22, 2009 7:51 pm


    Layra-chan
    In the Sci&Tech, there is a creature of mild interest who goes by the name of Kaz-Balan.


    That doesn't seem very respectful. Did she do something to piss you off?
    PostPosted: Fri Oct 23, 2009 11:19 am


    She's pretentious, she's self-righteous and she's willfully ignorant. The first two character traits are unfortunate but forgivable, but the fact that despite my giving her enough evidence and explanation to write a book each on General Relativity and on the scientific paradigms of Popper and Kuhn, she still insists on spewing thoughtless fantasy into otherwise decent threads.

    She doesn't understand the concept of matching theory to data, either in terms of confirmation or counter-evidence. She doesn't understand the concept of theoretical elegance as opposed to intuitionistic familiarity. And since she has neither the mathematical or physical background for any evidence or reasoning to be meaningful to her (nor any desire to gain such background or any respect for those with such backgrounds) it's impossible to convince her that she's wrong.

    And then there's the fact that she keeps advocating skepticism and skeptical inquiry but never bothers to apply it to her own pet notions. She tells people to keep an open mind, by which she means don't apply any sort of rigorous scrutiny, just make stuff up. She's like an ID proponent proclaiming "teach the controversy" without actually making sure that ID can actually stand on its own.

    As far as I can tell she's absolutely worthless as an intellect. Fortunately I don't see her in the Sci&Tech much anymore.

    Layra-chan
    Crew


    StandingOnTheMoon

    PostPosted: Sat Oct 24, 2009 9:28 pm


    Well, OK then!!!

    You seem to possess a certain amount of passion over this. Keep in mind you didn't actually waste your time, as I'm sure threads you've posted to in an attempt to educate this person surely educated others.
    Reply
    The Hangout

     
    Manage Your Items
    Other Stuff
    Get GCash
    Offers
    Get Items
    More Items
    Where Everyone Hangs Out
    Other Community Areas
    Virtual Spaces
    Fun Stuff
    Gaia's Games
    Mini-Games
    Play with GCash
    Play with Platinum