“Falling of space” is an analogy anyway. There’s still no explanation of gravity is except we know that it’s some function of mass somehow and that it bends the fabric of space-time. We still haven’t found any gravity-bearing particles.
Not in a rigorous or scientific manner.
And if the math says one thing, and experiments say another, which one gets tossed?
I don’t think the universe is an equation, but I do believe it is a probability distribution. I don’t think the quantum world is real. As Niels Bohr put it, “There is no quantum world. There is only an abstract quantum mechanical description.”
I think there are two serious problem with the universe being real (aside from the way in which I personally define reality.) One is the problem of emergence from the quantum world to the comparitvely well ordered universe in which we live. It is obviously an issue of perception. At what point does order emerge? And why would it? After all, we never really see anything out there in the world; we see only images in our brains. The other problem has to do with the circularity of material essence. That is to say, particles cannot be made of stuff because stuff is made of particles.
Rather than there being something “out there”, it is my opinion that the whole lot is an illusion based on perception. It is possibilities made into actualities — which would make for a weird premise. Even particles themselves aren’t real. They’re just abstractions. “The atoms or the elementary particles are not real; they form a world of potentialities and possibilities rather than one of things or facts.” Werner Heisenberg
That’s not possible. Contradictions do not exist. There would have to be an error in one or the other. It would need to be found and fixed.
Got any examples in mind? :dubious:
To dive a little more into the philosophy, and the question of what we know, versus what we can know, I’m gonna sketch out a few thoughts, so bare with me…
Our math in physics, both theoretical and experimental, is modeled on our observations of the universe. We’ve had the macro/micro discrepancy since Relativity and QM came on the scene. But require rigorous math, and some new math is being explored in String Theory. All amazingly accurate (sometimes to a fault), and like others up-thread have said, the one tool that’s done the most heavy lifting in modern physics.
Even some abstract math and curiosities are starting to point toward interesting things in the way certain phenomena works. The mechanisms behind it. We’re on the verge. I truly believe it’ll be within my lifetime that a Theory of Everything will finally crystalize. But then what?
It still doesn’t explain what this Everything is.
How can math help us understand Life? Consciousness? Sentience? I have no doubt it has, and should continue to do so in some ways, but will we have to fashion new tools of thought. Be prepared to throw away some 20th century thinking. I believe we’re missing something huge. And, I’m not trying to be coy and say it’s God, or something supernatural, I’m saying it might be unfathomable. I hope our evolved minds are vast enough to grasp it. Like the spider spinning its web in the linked article, could our minds be as tiny, compared to what reality actually is; beyond our little web?
The fact that sentience exists might be key to understanding, and we don’t even have a good theory on how that works.
/stream-of-consciousness
You’re right, I chose my words wrong. It doesn’t get tossed, it gets fixed. But assuming the experiment has been done many times by different scientist, and experimental error, what gets fixed, the math or reality?
I just did an experiment. I have some perfectly good, valid and consistent math here, that says that 1+1=1. So, I took one rock in my left hand, and one rock in my right hand, then put them together and got… Hm. Well, I guess that math I was using didn’t actually describe what I thought it described.
I don’t readily have any real example of this kind of thing, because real cases are never so clear cut. But it’s more or less the case when any hypothesis turns out to be wrong.
And, really, if you think that math can’t ever possibly disagree with experiment, then what’s the point of experiments at all? Paying a mathematician to come up with theorems is a lot cheaper than building particle accelerators.
The math. (Assuming you meant without experimental error.) There is much precedence for this. Many scientists have had to review, renew, and reissue their mathematical productions.
The most elegant scientist of all, in my opinion, was Einstein. He often perceived a viewpoint of reality that no one else had ever perceived (or at least, fully expressed). He then produced a deductive proof, relying mainly on only two premises: (1) that physical law is everywhere the same, and (2) that the speed of light is constant in a vacuum. Once his conclusion was reached, it was impossible that observation would fail to bear him out.
That was my point. DSYoungEsq said that math is more important than experiment, but that’s wrong.
Not impossible, only very unlikely. We still tested his predictions. The universe is not guaranteed to be either logical or consistent. We have to convince ourselves that it is through experiment.
Actually, for that specific statement, I agree with DSYoungEsq. 
Just because the math must be revised due to experimental findings doesn’t make the math less important. It just means that someone was sloppy or careless or just plain incompetent with the math.
In fact, the math is much more important than the experiment if the goal is to prove a generality to be true. For example, you can attempt to “prove” that 1+1=2 by repeated experiments with lining up stones and counting them. And after having done this a thousand times, you may convince yourself that you have proved that 1+1 does indeed equal 2. However, what you have NOT proved is the critical thing that math DOES prove. Math will prove that the NEXT time — and in fact EVERY time — you do your experiment, your 1 stone plus your other stone will equal 2 stones. Without math, you are proving only what happened in the past, not what must happen in the future.
Well, I do agree with you in the sense that his premises could be wrong. And if they are, then the conclusions are not reliable. Take for example the premise that physical law is everywhere the same. Einstein himself discovered an exception to this. At the centers of black holes, for example, physical law is unknown, and the mathematical representation is a singularity (an undefined mathematical statement).
Well, then I guess we disagree on what constitutes “more important”.
And with your example, you can’t mathematically prove that that math accurately describes the universe. You can mathematically prove that starting from certain axioms, 1+1 always equals 2, but the only way to determine those axioms is to make educated guessed based on past observations of the universe.
I know there must be a better example than this, but didn’t it take mathematics to establish/prove the heliocentric nature of the solar system? Direct observations put us at the center, and direct observation made some planets wobble about in funny ways (e.g., Mars retrograde). But someone with a calculator came along (they did have those back then, no?) and showed that conclusions from observations were wrong, and by adjusting our thinking we’d have a much better picture of what’s actually happening.
That would be a case of finding a better mathematical description of the universe.
I’ve been under the impression that we’re either constantly refining the mathematical descriptions of our universe, or creating all-out new math to do so.
Physics tries to explain and predict nature. It’s entirely dependent on math and experimentation. But nature will always be nature, and that’s the white rabbit we’re chasing down the proverbial black hole.
We know of areas in our universe where our math breaks down, and experimentation eludes us. Like Zeno’s paradox, we’ll get ever closer to a full explanation, but never quite reach it. We are an observer looking at the white rabbit passing the event horizon.
[bolding mine]
This isn’t really right. Pure mathematics doesn’t depend on what does or doesn’t hold in the real world. Mathematicians define various structures and our assumptions about them in precise, unambiguous ways. Then they apply rigorous logic to determine what new conclusions about these structures follow from these definitions and assumptions. Whether these structures correspond to anything in the real world, or whether these assumptions hold in the real world, is irrelevant to the validity of these mathematical results.
Physicists, however, have found that many mathematical structures are extremely useful in describing the real world. Likewise, mathematicians may decide a certain mathematical structure is particularly interesting to study because of its apparent correspondence to some real-world phenomenon.
At any rate, trying to do physics without math would be highly misguided. (Note that I’m not accusing cmyk of suggesting we do this.) It would amount to taking ideas that are concisely articulated in an unambigous language that we know how to work with, and instead making them substantially wordier, vaguer, and more resistant to systematic manipulation. While the math may be frustrating to those who don’t know how it works, it’s still much easier to learn it than it would be to do away with it.
People often talk of the “math breaking down”, but it doesn’t really mean that mathematics doesn’t work at that point. It’s more accurate to say “The equations of our theory give nonsensical answers, indicating that the theory doesn’t apply in those circumstances.”
Simple example:
According to the classical theory of electromagnetism, the force exerted by a charged particle (say, an electron) on another charged particle is proportionate to 1/r[sup]2[/sup], where r is the distance from the electron. But what is the force of an electron on itself?
According to our theory, it’s 1/0[sup]2[/sup], which is infinity. Thus, the theory predicts that the electron exerts an infinite force on itself, which makes no sense. The problem isn’t that math is wrong in saying that 1/0[sup]2[\sup] is infinity. The problem is that our theory of the 1/r[sup]2[/sup] force is wrong, at least when it comes to describing the force at r = 0. In other words, classical electromagnetism isn’t the right theory for those circumstances.
More Technical Correction: I’m glossing over the fact that it’s not really accurate to say 1/0[sup]2[/sup] = infinity. Rather the limit of 1/r[sup]2[/sup] goes to infinity as r goes to 0 from above.
I need to point out that the people making a distinction between math (theory) and experimentation are incorrect. Experimentation is math. Results of experiments, in physics at least, which is the subject at hand, are numbers or equivalents. (Particle paths from accelerator experiments, or even the more primitive bubble tracks from the old days, may not look like numbers but they essentially reduce to them. Modern astronomy and cosmology are printouts, not pictures.)
In the best case, the results of experiments are numbers that fit the predictions of theory, i.e., the results spit out by equations, which are numbers.
The proper antithesis to math is, once again, words. The crackpot community can only offer words, which is one way to know that they can be safely and immediately ignored. The professional community may use words in discussion of results, and certainly when trying to communicate to the lay audience, but never progresses by creating word theories.
You may argue that math does not explain why. Physicists will tell you it’s not supposed to. Talking about why is a different discipline. The distinction, again, is that all physicists agree about what physics says and whether or not experiments agree with that (within the limits of precision: when those limits are fuzzy, so is agreement).
No two people ever agree about why. Words are always fuzzy. You can and will get every possible interpretation of every subject. That’s what makes GD GD.
Throwing words into a physics thread will get you nowhere, unless they are explicating the math.
If you can’t explicate the math, then you devolve into the OP, who apparently saw that words and imaginary equations weren’t going to cut it, and cut out. Some of the rest of you, despite better sentence structure, have been just as wrong in what you’ve said about physics. Physics is math. Math is theory and experimentation. A theory that gives correct answers can’t be wrong, although it can be partially or woefully incomplete and therefore misleading. (Newtonian mechanics being the most famous example.) But the words that take an incomplete theory and try to apply it philosophically to the world will be incomplete at best themselves. That’s a lose-lose proposition. First the math, then everything else.
Which is pretty much what I was saying there, in lesser words, of course. The sentence you chose to nitpick, in the rest of that post, I was saying that we’re always course correcting our math to better fit our observances of nature.