Hello. I’ve got a quick question for The Straight Dope message board citizens.
I firmly subscribe to the idea that mathematical (and other forms of) expression are metaphors for what is actually happening in this so-called universe. The most famous example of this, I’m told, is light, which can be mathematically shown to travel as waves, and tested to show as such. Light can also be mathematically shown to travel as particles, and tested to show as such.
So my question is this: are there any other examples of mathematics that imply the language is more of a metaphor rather than an absolute truth?
Well, one view of mathematics is that it’s not about the real world: it’s just about purely logical constructs. However, you can use mathematical ideas to create theorioes about the real world. If the theory matches the real world, then it’s a good theory. However, that says nothing about whether it’s good mathematics. Perhaps that’s what “mathematics as metaphor” is about.
The philosophy of mathematics is not really a good fit in GQ, but before it’s sent off to GD, I do have to say that it is physical experimentation that shows that light can be viewed as either particles or waves, not mathematics. The mathematical formulation of quantum mechanics describes light as its own thing, which can be physically interpreted as either particles or waves depending on the situation but isn’t really either. This “example” just does not do what the OP thinks it does.
Worms, your question is based on a number of hidden premises about how the universe works. What you have asked are philosophical questions. There are, for example, many people who would gladly argue that absolute truth is a fiction. Or another way to look at it is, how can you possibly know “what is actually happening in this so-called universe”? Another way to look at your question is to ask if math is a discovery or an invention. There are a zillion ways to look at it.
Perhaps phrased differently: mathematical expressions are the language that much of the poetry of science is written in. These poetic expressions are no less metaphors of reality than poetic expressions in other human languages.
Certainly I recall this being the position of the great humanist, mathematician, and Blake scholar, Jacob Bronowski (which some may remeber from The Ascent of Man)
The significance is to remind ourselves that we are always bound by the limits of our language as we attempt to make sense of the universe and decode reality via analogy and metaphor.
In this case it’s properly stated that mathematical physics is a metaphor. Then again, I don’t know a working physicist who seriously believes that physical constructs are mathematical objects. Einstein himself spoke of “elements of a physical theory” corresponding to “elements of physical reality” in his position on physical realism. For instance, read the famous EPR paper on quantum mechanics.
Ah, I’m sorry for posting this in the wrong forum, and I’m sorry for not being a little more specific- though Giles (and others) was pretty much on the money for what I was aiming at. Basically, it’s along the lines of “the map is not the terroritory”, as quoted from that famous E-Prime guy. Mathematics is a language, that can be tested, to present models of the universe. As such, mathematics isn’t really a language of absolute truths, it’s just a language, and I sort of consider lingual constructs to be metaphors, or models, for what’s actually happening.
By the way, thanks for the info on quantum mechanics and light, Exapno Mapcase. Obviously I need to look in to that more closely.
Okay, I’ll try to rephrase this question in another way: are there any mathematical formulas (and accompanying tests, perhaps) which can be construde to suggest that all of our descriptions of the universe are only models? In the event that you’re trying to understand what exactly I mean by this, I’m heavily influenced by Robert Anton Wilson, E-Prime and Buddhism… specifically the whole lack of knowing what really “is”, and just knowing how things appear to be. A friend had presented the whole light and quantum mechanics thing to me (saying that he was quoting Wilson) as a presentation for how there isn’t really any vantage point in which “real” reality can be viewed.
Sorry for the double post… this thought just came to me and I see there is no edit function for previous posts. Is that because I’m a guest? I should mention I’m not overly good with math… but I guess you could say I’m thinking along the lines of how fractals are just models for chaos theory, though they do show up in nature I’m told. Anyway, I’m looking for observations of the universe that suggest that the observations themselves are just that- observations, and not some kind of an absolute truth.
Look, I’m a great fan of RAW. I also know better than to take him at all seriously on matters of physics and mathematics. Frankly, I get the feeling that he’d laugh his ass off if he knew anyone did take him seriously. His thoughts on the subject are pure metaphor drawn from the awful attempts of the 70s to popularize QM and draw shaky analogies with Eastern mysticism.
If you’re talking about that sort of viewpoint, it’s a worthwhile discussion. You need to understand, though, that you’re not talking about physics or mathematics.
I don’t get what the debate is here. Maths is something of a symbolic language that can be used to describe physical things. Think of a rock. Now think of the word “rock”. Not the same. Yet the latter is a useful representation of the former if you want to convey to someone the concept of rock. You could concoct more elaborate symbolism to describe the real rock more completely, to the point that you could specify every iota of that rock. But your description wouldn’t be the rock, and no one would take it to be.
No, as others have said, it is scientifically shown to travel as waves.
As others have also said, mathematics (and logic) is an epistemology which science (another epistemology) uses to describe the universe, rather like language. Sometimes it is incredibly useful, giving us great confidence that we, these incredible biological computers on this lonely rock, are describing the universe as it is (“truth”) rather than as it is not. Sometimes it has absolutely no relevance to reality whatsoever.
In fact, all of this was summed up in two sentences of beautiful conciseness output by possibly the most impressive biological computer ever to exist:
I have to agree. I read a bunch of his stuff from about age 15 to 17. Looking back, some of what he says is useful as metaphor or for the sake of being weird, but he’s not a scientist or a mathematician or an expert (heh) on any of the topics he sounds like he knows a lot about.
I think this might be a misuse of the word “metaphor” (unless it has other definitions beyond those I’m familiar with.)
To clarify my understanding of what “metaphor” means, here are two different usages:
“The statement ‘All the world is a stage’ is a metaphor.”
“Shakespeare uses a theatrical stage as a metaphor for the world.”
In one case, “metaphor” means a statement comparing two things (by stating them to be the same), and in the other, the “metaphor” is one of the things being compared. But in either case, the two are not actually equivalent, just related in some way. (In this case, for instance, the connection is between the triviality and ephemerality of a theatrical performance on the stage and of life in the world.) I couldn’t use my knowledge of the properties of a stage to deduce properties of the world, e.g. “A stage is made of wood, therefore the world is made of wood.” However, a physicist can use mathematical equations to make predictions about the world. If the theory is correct, then one can expect these predictions to actually occur in the real world based on the fact that they occur in the theory.
I’d say “representation” would be a better word to use. The equations of theoretical physics are a “representation” of the world, in the sense that the objects in the theory correspond to objects in the real world, and the relations between objects in the theory are equivalent to the relations between objects in the real world.
I’m also saying “the equations of theoretical physics” rather than “mathematics” because of course not all math is meant to describe the world (although efforts to describe and predict events in the world have certainly provided an impetus for many developments in mathematics). Mathematical research can be aimed at just understanding math better, (although in many cases developments in pure mathematical research are discovered after the fact to be of use in physics.)
Nobody on the SDMB can edit (except the Moderators/Administrator types, of course) – I think the idea is that with all the debates and such that go on here, there’s too much potential for abuse (e.g. someone saying something inflamatory, waiting for someone to respond, and then changing their original post to make the person who replied look like an idiot.)
Ah, I unfortunately must be brief… though it seems like this thread has already run it’s natural course. I don’t know about you guys, but I sometimes run in to people who consider mathematics and the sciences to be absolute and always 100% accurate, especially at school… where as I consider them at best a model for what is actually going on. Perhaps I did use the term <i>metaphor</i> incorrectly, but what I was looking for was something in math itself that could show such people that it isn’t in fact something to be taken as an absolute truth. However, I think after taking a good look at what everyone here has said, I’ve been approaching this whole thing all wrong anyhow…