If time is the cosmological concept that keeps everything from happening at once, I figure gravity is the cosmological concept that keeps everybody from just wandering around aimlessly.
Math will never be anything but an analog to the universe. Not the universe itself. Unless you think the universe is one big equation? I love math as much as the next guy, but there is more to exploring the nature of reality than just always trying to pin equations to the phenomenon. Sometime the philosophy has to come first. We can’t be so arrogant to rely strictly on one tool and hope it provides all the answers. Sometime progress in science comes from new perspectives and new ways of thinking about reality, as absurd as they may appear at first blush.
Philosophy is very important.
Well, I would say that in this context, “math” is simply rigorous philosophy. It’s not that there’s anything fundamentally “perfect” about math when it comes to explaining the universe; it’s that mathematical exercise alone represents the rigor and specificity necessary to construct accurate models of natural phenomena.
Not seen my life, have you? 
English (or French, German, Mandarin, etc.) are languages of man. Math is a primal language of the universe. I am not a mathematician, but I did stay at a Holiday Inn Express while taking a course in Quantum Mechanics. Though taught out of our school’s philosophy department, there was a substantial math component. I had to spend about four hours a week in the Professor’s office hours throughout the course (and a heck of a lot more time on my own in the math lab and at home – told you I wasn’t a mathematician) learning linear algebra and other necessary concepts. About halfway through the course a light clicked, and I could suddenly see that the already impressively surreal concepts and explanations of what was going on at the subatomic level paled in comparison to the mathematical description – to the much more precise descriptions and definitions of what was actually happening.
Philosophy is very important, but it is not the right language to approach understanding of certain topics.
I’d be careful about describing math as a rigorous philosophy. Philosophy is about asking the right questions and exploring the logic behind those questions. Math is about Answers and holding those answers up to the light of the physical phenomena we encounter.
So the question is, is the math we are using now adequate to explain what we are observing. The obvious answer is no, at least not yet. So, what’s missing? Math might not be able to answer that until we know what questions to ask next.
I agree with you on a lot of points. Math is the language of the universe. But like language, we can’t think of the “words” standing in for the real thing. My only point being, that math is just as important as the other tools of human thought and abstract thinking we have at our disposal. Let’s not be too quick to dismiss them, simply because it’s not hard science,* or even science at all.
*hard science being one of my absolute passions.
Alternative thinking is very useful, but since our current understanding of how the universe works can be expressed precisely with mathematics, any new descriptions need to use mathematics to be that precise or better.
No, mathematics is also a language of man. It’s a very precise language and so is very useful for precisely describing the universe.
There’s no special relationship between mathematics and the universe. If it seems otherwise, it’s because you’re only familiar with the mathematics that scientists have selected to describe the universe. There are other parts of mathematics that are not useful to scientists, because they don’t describe the universe.
Yet.
Almost all modern physics makes use of math that no one every thought be would physically meaningful. String theory is full of that type of math. (That’s why it’s often called a 21st century theory that slipped into the 20th century. They’re still working out the math.)
Literally no one knows which pieces of math will become physically important in the future, but everyone is sure that they exist.
As for philosophy, well, as a professional writer I am enamored of words yet totally aware of their limitations. Philosophy has consistently failed in giving meaning to relativity and QM, despite a huge literature. No philosopher appears to understand the math sufficiently to make comments as subtle as the physicists’ findings. For example, QM and relativity do not agree about the nature of Time. There are hundreds of books and articles (and websites) talking about Time. Yet Time remains a mystery. Philosophy will not answer that question. If an answer appears it will emerge from new math.
We’re talking about a subject that in its modern form has been around for over 100 years. In all that time every piece of understanding has emerged from math rather than words. I don’t see how anyone can expect that to suddenly reverse.
Interesting. May I suggest that units and certain math descriptors are human based/subjective, while the, er, logical underpinnings and frameworks are universal? That no matter where you go, prime numbers will be prime numbers, the ratio of the radius to the circumference of a circle will always be irrational, and that state vectors of a two-paths experiment will always work out the way they do. Advanced math is likely (assuming a more advanced alien culture) to astound, baffle, and solve/explain phenomena we find mystifying, but it will be comprehensible.
Only the part of mathematics that describes the universe is universal. The hard part is determining which mathematics actually describes the universe. For example, the ratio of the circumference of a circle to its diameter is pi in Euclidean space. That statement is true, but not necessarily applicable to the real world.
Because in general, Euclidean space is not an accurate description of the shape of the universe. It’s approximately true in many places and so Euclidean mathematics is useful, depending on the precision we need. But experiments show us that to find we actual ratio, we’d need to do an integral of the space-time metric along the circle (which is itself tricky to define), because Euclidean geometry is not an accurate description of actual space.
This is what I mean by mathematics not being the inherent to the universe. Mathematics is a tool we use to describe it. In fact, it’s the best tool we have. But it’s only a tool, and we still need to gather evidence to determine which and how the math applies to the universe.
Egg Shen: Can see things no one else can see. Do things no one else can do.
Jack Burton: Real things?
Egg Shen: As real as Lo Pan!
Jack Burton: Hey, what more can a guy ask for?
I thought of a wonderful haiku, that cogently describes the relationship of gravity to space-time in the current physics models, but it is too large to fit in this post. Instead, here is a link to The Unreasonable Effectiveness of Mathematics in the Natural Sciences. For those of you who are interested in mathematics as the language of physics but have not yet encountered this paper.
Right – our defining pi in terms of Euclidean space is subjective, but yet doesn’t pi function in a boatload of applications (sine waves, e to the two pies for a dollar equaling -1, etc.)? And as above there is plenty of math with no known (or even predicted) physical relation, and there is plenty of math that can be extended beyond what we’re doing now, but that doesn’t mean that underlying the physical world isn’t a set of constants and laws that are accurately described with math – no matter where you are in the universe (save some esoteric fiddling in which constants change).
This doesn’t discount straight-out philosophy, of course – math has little to say about ethics (though game theory and utils do encroach). But as far as metaphysics is concerned, I think math has the upper hand in describing the universe and getting at the heart of quantum mechanics and gravity.
If a tree falls in a forest, does that demonstrate the existence of gravity?
If the sound of one hand clapping is the same as breaking wind, does that demonstrate the existence of levity?
I think we’re agreeing now, but emphasizing different things. Mathematics is our best way to describe the universe, but it’s a mistake to presume that the universe necessarily follows any mathematical system. In other words, experiment comes first, then we find the math that matches the data, rather than the universe being mathematical and we try to discover the details.
I disagree that mathematics is equivalent to understanding. Definitely, math is a good aid to understanding, and probably the best aid to understanding there is. But math alone doesn’t constitute understanding. For example, if you have an equation that predicts how a particle will behave, the math lets you understand what it will do, but not necessarily why it will do it.
And words will tell you why? Can you give examples?
This is not true historically. Many discoveries have emerged out of theory - antimatter, neutrinos, the whole quantum nature of particles that started this discussion - that were only later confirmed by experiment. In modern physics experiment and theory leapfrog one another constantly.
You misunderstand me. When I say “experiment comes first”, I mean it is of primary importance, not that it is temporally before.
Again, as pointed out before, even this is not correct. Math sometimes involves discussion of concepts not yet seen in the real world, and only later do we find the real world situations that are explained by the math we’ve worked out.
Mathematics is not seen in the world and cannot explain it. Math is used to describe and predict the world.
ETA: When I started typing, all I saw was Strinka’s last post from this afternoon. This may lead to a bit of confusion, so I thought to add the detail.
Mathematics, in and of itself, is not understanding. My computer does all sorts of math but does not understand (or so I believe).
However, it is the understanding of mathematics that is tautologically equivalent to understanding a concept. I think we can put all sorts of words to the two-paths experiment, and lots of words to describe what’s going on with the collapse of a wave function, or why Bohm’s statistical analysis of EPR entanglement (man I hope I got those names and concepts right, but I’m sure someone will correct me if I’m wrong) and we’ll approach a comfortable level of understanding.
However, since all the wackiness that’s going on doesn’t comport with intuitiveness or human experience, true understanding of the processes can be achieved only through comprehending and following the math. As insights into the subatomic world progress, human language becomes less and less useful to the underlying pursuit of knowledge.
The math has turned intuitive processes on their heads. Upthread it was suggested that the math follows experience… but in some domains (I’m sure this isn’t the only one), mathematical theories are created, which in turn lead to absurd results, which in turn have been empirically verified.
And the really crazy thing is, the micro/macro line is elusive such that when starting with a collection of wee bits one can never say when there are enough particles around to start talking with macroscopic language. I think I’m at the end of my abilities (not that I have any), but I think that’s part of the weirdness of the cat paragraph’s context (or implications thereof).