You seem to be missing the points of these statements.

For example, i dont quote a broken algorithm to have you say that it is a broken algorithm. Why would you think that reply would help when i stated that it is not perfect already? The point was, things look perfect until we find something totally unexpected and then we see the flaw.
What follows could be flaw after flaw, and we hope and pray that as we solve them we get to where we really want to go.

We seem to be missing each other's points, because my point was that you picked a bad example. Prime number generators are either provably correct or provably not. If you use something like Monte Carlo as a heuristic -- to make the algorithm faster -- then it will be provably incorrect. There's no need to wonder if the nth chosen number turns out to be composite; you'll know that, for some large enough n, it will produce a false prime. There's nothing unexpected about it.

Things look perfect until we find something unexpected and that could take us down a totally unforeseen path.

This is not, in general, how anyone does research. Particularly in science, nothing looks perfect -- you start with the assumption that you've made errors. I'm sure I've missed your point again, because I have no idea what you're trying to get at.

 

We seem to be missing each other's points, because my point was that you picked a bad example. Prime number generators are either provably correct or provably not. If you use something like Monte Carlo as a heuristic -- to make the algorithm faster -- then it will be provably incorrect. There's no need to wonder if the nth chosen number turns out to be composite; you'll know that, for some large enough n, it will produce a false prime. There's nothing unexpected about it.


This is not, in general, how anyone does research. Particularly in science, nothing looks perfect -- you start with the assumption that you've made errors. I'm sure I've missed your point again, because I have no idea what you're trying to get at.

Hi,

Gosh darn, i cant believe you still cant understand this point. I can only think you have a mental block or something from preconceived notions.

We KNOW there is an error in the proposed prime number generator. Stop talking about that
The key point is that someone new walking into this problem does NOT know, and so for a while it looks like it works. That is an analogy that we can look at to see how we are today in science. The reason for the example is so that we have a complete and solved model to work with in order to apply it to the REAL future, which hasnt gotten here yet

Think about why someone would talk about an inferior prime number generator, knowing it is inferior. It's not so that we can judge the generator itself from a standpoint of knowing it will fail, it is so we can judge the generator first from a standpoint of not knowing that it will fail, then in the future sometime finally discover that it fails when all along it looked so darn good until we found the failure. So it is a process of discovery, which is what we are doing right now with science.

 

Gosh darn, i cant believe you still cant understand this point. I can only think you have a mental block or something from preconceived notions.

I have precisely the same feeling.

We KNOW there is an error in the proposed prime number generator. Stop talking about that
The key point is that someone new walking into this problem does NOT know, and so for a while it looks like it works. That is an analogy that we can look at to see how we are today in science. The reason for the example is so that we have a complete and solved model to work with in order to apply it to the REAL future, which hasnt gotten here yet

Prime number generators are provable; they're not analogous to scientific theories, because we can know how they'll hold up in the future. It's a bad analogy.

Your actual point seems to be along the lines of A scientific theory can appear to be true, but at some point we may find an error; therefore, we cannot assume our theories are true.

Well, duh! Literally zero scientists believe that any scientific theory is perfect. You're arguing a straw man. The notion of "we don't know what we don't know" is intentionally built-in to the scientific method. Furthermore, scientists don't need to wait for some future experiment, they can plainly see errors in their theories today.

My point all along has been that our scientific models -- though approximate and piecewise -- have been demonstrably improving over the history of humanity. We are slowly converging upon the best possible understanding our species can have about the universe. I asked you to provide a rationale for believing otherwise, and you gave me an analogy about prime number generators. If all you can muster is something in the future may make everything we thought we knew about the universe seem as naive as a flat Earth theory, you'll need to come up with something better, as that's exactly what scientists expect and hope for. They even have a name for it: paradigm shift. But you don't get a scientific revolution out of thin air -- they are a consequence of the evolution of science. It's all part of the process.

 

https://www.scientificamerican.com/article/is-the-schroedinger-equation-true/​

Some of the math she’s learning in school, Cunningham suggests, has little to do with the world in which she lives. “I get addition, like, if I take two apples and add three it’s five. But how would you come up with the concept of algebra?” While some geeks mocked Cunningham, others came to her defense, pointing out that she is raising questions that have troubled scientific heavyweights.

When I contemplate quantum mechanics, with all its hedges and qualifications, I keep thinking of poor old Ptolemy. We look back at his geocentric model of the solar system, with its baroque circles within circles within circles, as hopelessly kludgy and ad hoc. But Ptolemy’s geocentric model worked. It accurately predicted the motions of planets and solar and lunar eclipses.

Wigner points out several problems with this assumption. First, theories of physics are limited in their scope. They apply only to specific, highly circumscribed aspects of nature, and they leave lots of stuff out. Second, quantum mechanics and general relativity, the foundational theories of modern physics, are mathematically incompatible.

 

https://www.scientificamerican.com/article/is-the-schroedinger-equation-true/​

Just because a mathematical formula works does not mean it reflects reality

Bingo. Math is NOT scientific reality.

 

Just because a mathematical formula works does not mean it reflects reality

Bingo. Math is NOT scientific reality.

I'm not sure I understand your statement... the phrase uses the word "reflects" ... reality is one thing, and a tool to describe it (or reflect it) is another thing.

 

I'm not sure I understand your statement... the phrase uses the word "reflects" ... reality is one thing, and a too to describe it (or reflect it) is another thing.

Reflects IMO here means the true image of a thing seen in a different way. Like deriving the same result (first equation of motion with Constant Acceleration) using algebra or calculus. There are warehouses full of thick papers filled with mathematical proofs that the physical reality of experiment proved to be wrong.

 

There are warehouses full of thick papers filled with mathematical proofs that the physical reality of experiment proved to be wrong.

Now I'm even more confused. Are you saying that there are mathematicians out there that have proved that our sense of reality as confirmed by our senses is wrong?

 

Now I'm even more confused. Are you saying that there are mathematicians out there that have proved that our sense of reality as confirmed by our senses is wrong?

No, I'm only saying that mathematical proofs were used to show the mathematical equations used in the theories were correct. Physical proof (if it's even possible in some cases) of actual correctness as we see reality is a different matter entirely.

 

I don't mean to change the subject, but rather to expand it a little. I found this article extremely interesting and related to the subject being discussed here:

https://blogs.scientificamerican.com/cross-check/the-weirdness-of-weirdness/​

In a review of Dennett’s recent book From Bacteria to Bach Nagel states: “To say that there is more to reality than physics can account for is not a piece of mysticism: it is an acknowledgement that we are nowhere near a theory of everything, and that science will have to expand to accommodate facts of a kind fundamentally different from those that physics is designed to explain.”

 

I don't mean to change the subject, but rather to expand it a little. I found this article extremely interesting and related to the subject being discussed here:

https://blogs.scientificamerican.com/cross-check/the-weirdness-of-weirdness/​

It's pretty obvious there is a huge gap in the way we currently understand reality. I see a lot of Cargo cult science selling snake-oil.
http://calteches.library.caltech.edu/51/2/CargoCult.pdf

I would also say you don't need a complete understanding to do incredible things. We don't understand how the brain works at its deepest levels but we can mimic very complex functions like driver-less cars without that level of detail.

 

I would also say you don't need a complete understanding to do incredible things.

Agreed. I'm just wondering if we'll ever get there. And by that I mean complete understanding.

 

https://www.scientificamerican.com/article/is-the-schroedinger-equation-true/​

That article was written by someone who doesn't understand science or math.

He closes with this gem:

Mathematical models such as quantum mechanics and general relativity work, extraordinarily well. But they aren’t real in the same sense that neutrons and neurons are real, and we shouldn’t confer upon them the status of “truth” or “laws of nature.”

I wonder what criteria the author uses to claim that neutrons are "real". Has he considered that the neutron is an object in a mathematical model of sub-atomic particles? Has he considered that without the mathematical model we wouldn't have any idea what a neutron is? Has he considered that the mathematical framework used to create that model is the very quantum mechanics that he claims is "not real"?

The author seems to have fumbled upon the notion of the map is not the territory, a dictum well understood by the vast majority of professional scientists. Physicists describe electrons as the irreducible representation of a certain gauge group, because that particular mathematical object, when formulated within a particular and robust model, is consistent with experimental results. But the model only characterizes how the system behaves; it makes absolutely no claim for what an electron actually is, or even if such a thing "exists". Indeed, the word electron (or neutron, or neuron) only has precise meaning within a model. More to the point, any notion of "reality" (e.g., "neutrons are real") must be framed within some background model. Failing to recognize this, the author incoherently wishes to dismiss the model (quantum theory) while keeping the objects of the model (neutrons).

On the bright side, the author's motivation seems clear:

Pondering Hilbert space makes me feel like a lump of dumb, decrepit flesh trapped in a squalid, 3-D prison.

Like the teenage girl he quotes who thinks that arithmetic is fine, but algebra is "not real", the author is frustratingly mystified by the higher levels of abstract reasoning necessary to understand the mathematical objects used in modern physics. I imagine him reading somewhere that quantum states are vectors in a Hilbert space, then going to the Wikipedia article on Hilbert spaces. Upon finding that it is written at a mathematical level that he is unprepared to understand, he then projects his personal limits onto the reality of the physical universe, concluding that quantum mechanics is too obtuse to be "truth".

The author has a severely confused ontology:

The wave function has embedded within it an imaginary number. That’s an appropriate label, because an imaginary number consists of the square root of a negative number, which by definition does not exist.

Astoundingly, he claims that "by definition" an imaginary number does not exist! I don't know what exactly he means by that, but I suppose he imagines that somewhere in Paris there is a box full of all the numbers that actually exist, and the imaginary numbers are not inside it. I don't know if it's funny or sad, but the author uses this non-existence "fact" to poo-poo the Schrodinger equation. His argument seems to be: Sure, the Schrodinger equation may be the most accurate description of the dynamics of the physical universe, but it uses complex numbers, which obviously don't exist, so it must be wrong. This is equivalent to me telling a creditor that, sure, your calculations accurately show that my account is overdrawn, but negative numbers obviously don't exist, therefore I don't owe you any money.

I'm embarrassed for the author. Ironically, it is the author himself -- and not science at large -- that confuses the map with the territory:

Were quantum mechanics and general relativity waiting for us to discover them in the same way that gold, gravity and galaxies were waiting?

I have no idea why Scientific American would publish such a naive and confused article.

 

Agreed. I'm just wondering if we'll ever get there. And by that I mean complete understanding.

Complete (no gaps) understanding seems unlikely. In mathematics, Godel showed us that there can never be a complete self-contained non-trivial theory, that once a formal theory is powerful enough to describe anything meaningful, it automatically becomes insufficient to describe even itself completely. Godel himself took this as joyful news: we'll never run out of mathematical theorems, i.e., wonder is provably inexhaustible. But does formal incompleteness suggest that our semi-formal nature of thinking is doomed to eternal theory building? Perhaps.

In science, we've traditionally taken a top-down perspective: start with observed phenomena and work your way down to the fundamental causes. This approach naturally leads to piece-wise progress and severe specialization, as each specialty drills down into evermore esoteric and fine-grained domains. The implicit hope is that fundamental connections between disparate phenomena will be noticed and tied together, giving us at last a holistic view of everything. But the universe is very complex, and humans may simply not have the capability to hold enough of it in our minds to form the connections. If we don't expect a giraffe to be able to hold the basic tenets of chemistry in its mind, why should we expect that we can hold enough of everything in our minds to understand it all?

There's another approach that has interesting potential. Stephen Wolfram and his team have recently started research that takes a bottom-up perspective, using very simple computational rules to generate structures that represent everything in our universe. The idea is that whatever electrons, black holes, consciousness, etc. are, there seems to be something driving it all. One thing we know about computational structures is that once a system crosses a relatively low threshold of computational capability, enormous complexity can spring forth, no matter how simple the original system is. (As an example, consider the almost trivially simple polynomials that generate fractal patterns of infinite complexity.) If the universe started as some relatively simple but computationally powerful system -- and it certainly appears that this is the case -- we might be able to explain all the emergent complexity we observe with a few simple rules. Unlike in physics, the rules here do not matter -- the important thing is the patterns in the resulting structures. The patterns presumably show us how everything is actually connected. For example, from playing with their graphs, Wolfram's team believes they have found a bottom-up connection between Einstein's field equations (from GR) and Feynman's path integral (from QFTs). This would be a world-shaking surprise if true, yet -- Wolfram claims -- it's only the beginning.

I'm still quite skeptical, though intrigued by the possibilities. More generally, I think consciousness -- long ignored by most scientific fields -- is finally going to enter the scientific discourse, spurred by research in machine learning. There is a sense in which it is embarrassing that we know more about black hole merges and the metabolic pathways of deep sea bacteria than we know about our own consciousness. I'm hopeful (and somewhat confident) that this will be changing in the next 25 years. I'm much less confident that we will ever truly have a complete theory of everything.

 

For example, from playing with their graphs, Wolfram's team believes they have found a bottom-up connection between Einstein's field equations (from GR) and Feynman's path integral (from QFTs). This would be a world-shaking surprise if true, yet -- Wolfram claims -- it's only the beginning.

I'm quite a bit skeptical about Wolfram's work myself: there are a number of issues with Wolfram's theory, summarized here. Basically, Wolfram doesn't offer really any quantitative proofs as to how his systems come to be, or what defines the "unit time step" of the universe, nor the "arbitrary-ness" of his cellular automata rules he uses to achieve his results, and he hasn't really felt the need to clarify these things. Plus, publishing via your own company with no peer-review (like what Wolfram did) is always a red flag, to me anyway.

I strongly suspect it'll be a long while yet before we achieve anything close to an experimentally-realizable, concrete "theory of everything." Might it mean "new physics?" Maybe. Might it be some way to press two theories together? Perhaps. It just needs to predict GR and QM (QFT) "naturally" from the theory as a consequence, rather than attempt to shoehorn them together.

I must say: I've never seen this thread before, but it's certainly been an interesting read. A long, meandering path, to be sure....

 

I'm quite a bit skeptical about Wolfram's work myself: there are a number of issues with Wolfram's theory, summarized here.

Yep, Aaronson's review was the primary reason I didn't bother to read A New Kind of Science. Note, however, that I'm talking about a new Wolfram research project (started April 2020):
https://www.wolframphysics.org/

I don't know enough about the old NKS theory to fairly contrast it with the new approach, but I believe some of the problems in the former have been fixed in the latter. At a fundamental level, instead of cellular automata, the new approach considers the hypergraphs (like ordinary graphs, but edges can have more than two vertices) formed by simple transformations of n-ary relations. Under the assumption that at the ground floor everything is indeed connected, the mathematics of relations (and their causal evolution) seem like a natural and fruitful way to express the instruction set of the universe.

That said, some of the former criticisms still apply, notably, a lack of (obvious) quantitative predictions, disengagement from the traditional peer-reviewed publication process, and a sense that the approach is a severely underdetermined system -- with so few constraints and so many degrees of freedom, anything can be fit into their models.

As for their seeming unwillingness to participate in the traditional (academic) vetting process, I will say that the way they are doing it is far more transparent, bordering on "open source science". I wouldn't be surprised if this aspect rankles the science establishment more than anything else. And though Wolfram himself seems to be something of an egomaniac, it's hard to argue that there aren't serious problems with the insular and job-keeping goals of the academic establishment.

I strongly suspect it'll be a long while yet before we achieve anything close to an experimentally-realizable, concrete "theory of everything." Might it mean "new physics?" Maybe. Might it be some way to press two theories together? Perhaps. It just needs to predict GR and QM (QFT) "naturally" from the theory as a consequence, rather than attempt to shoehorn them together.

I share you suspicion, and harbor deep doubt that we are even capable of remotely approaching such a thing. Nonetheless, I applaud our attempts to do so. Eric Weinstein recently proposed a theory of everything, called Geometric Unity, that purports to derive the equations of GR and QFTs from an essentially blank canvas. I don't understand the math well enough to have a sense of its validity, but very basically he imagines the universe as a fiber bundle with a metric-less 4D manifold as the base space, and a 10-dimensional space induced by a gauge group as the fiber. It's purely a mathematical theory, a way to show that the mathematical objects of GR and QFTs are compatible, but his hope is that it will inspire physicists to explore the implications and confirm or falsify the theory.

It's interesting that both Eric and Wolfram use a self-organizing principle as the basis of their theories, even though both are vastly different approaches. I find merit in this. We almost certainly can't know why or what caused something to appear out of nothing, but we may be able to deduce the smallest amount of something that leads to the universe. Eric calls it the "fire that lights itself", Wolfram calls it the "machine code of the universe". I can't help but feel that there is something to this, and that our best science to come will be born from similar thinking. Perhaps this explains why overarching top-down descriptions (like string theory) and piece-wise unification (like loop quantum gravity) seem to be dead ends.

Incidentally, Eric is also very critical of the academic industrialization of science. The next scientific revolution may well be one of process.

 

with so few constraints and so many degrees of freedom, anything can be fit into their models.

Exactly. It's what my physics research mentor would call "tinkering." "Tinkering" has its place, but usually better fit to experimental systems, rather than theoretical/mathematical ones.

As for their seeming unwillingness to participate in the traditional (academic) vetting process, I will say that the way they are doing it is far more transparent, bordering on "open source science". I wouldn't be surprised if this aspect rankles the science establishment more than anything else. And though Wolfram himself seems to be something of an egomaniac, it's hard to argue that there aren't serious problems with the insular and job-keeping goals of the academic establishment.

Once again, exactly. There is a fine balance between peer-review for validity and consistency and peer-review for "establishment." Science is not a democracy: the majority doesn't get to determine what is "true" and what is not (it's our job, as scientists, to seek that out, not declare it arbitrarily by "I have a degree, therefore I'm right"). Once you start relying on saying "consensus says" or "a majority of scientists agree" is the moment you've given up science. Science is the process of hypothesizing, testing, and revising, ad infinitum, after all - the honest scientist will say "this is my hypothesis, here's my proof, but here's how it can be disproved." This is the problem I have with "academic establishment."

Now on the flip-side, the transparency of the near-"open source science" is nice - anyone can access it or even contribute to it, if their ideas are consistent with the original model's and don't break any laws of physics - but in avoiding the traditional vetting process, it runs a major risk of inconsistency (with itself and with proven laws of physics) and providing properly rigorous explanations or reasonings. Without others able to review it for problems, or the ability to be tested, it runs the risk of swiftly turning into pseudo-science or a "scientific cult," for lack of a better phrase (as an example: all the people on YouTube claiming to have magnetic monopoles or infinite energy sources that usually involve something spinning with magnets and...sketchy measurement apparati).

I don't understand the math well enough to have a sense of its validity, but very basically he imagines the universe as a fiber bundle with a metric-less 4D manifold as the base space, and a 10-dimensional space induced by a gauge group as the fiber. It's purely a mathematical theory, a way to show that the mathematical objects of GR and QFTs are compatible, but his hope is that it will inspire physicists to explore the implications and confirm or falsify the theory.

That sounds suspiciously like string theory with a twist. At least he's hoping for someone to try to figure out a way to (experimentally?) confirm or falsify his theory; that's been the biggest sticking point of string theory since its inception. As an engineer and a physicist both, though I'm primarily a "theoretical" physicist (I do research in the areas of condensed matter physics and parity-time symmetry, but in systems that can be verified experimentally), the idea of a theory that is purely mathematical in nature makes me kind of uneasy.

It's interesting that both Eric and Wolfram use a self-organizing principle as the basis of their theories, even though both are vastly different approaches.

I'm actually not too surprised by this. Weisstein is the creator of Wolfram MathWorld, after all, so it's possible he got inspiration for his idea from Wolfram himself, combined with his own background.

Incidentally, Eric is also very critical of the academic industrialization of science. The next scientific revolution may well be one of process.

It definitely will be interesting to see how the sciences change. The "academic industrialization of science," as you put it quite appropriately, is somewhat recent, it seems. Long gone are the days of the private researchers (like Faraday, who had no formal education and taught himself almost everything working as a book binder's apprentice; or Ramanujan, who had, until he moved to London, absolutely NO education). Heck - even Einstein may not have been able to be published today, considering he was working as a patent officer when he first proposed his Special Theory of Relativity. If you don't have some kind of university or institution backing you, it's probably pretty hard to get anyone to pay attention to your research, much less get it published.

 

As a side note, it's interesting to see how this thread went from a general discussion of the aestheticism of equations to the general philosophy of science, particularly with modern theories or attempts of "theories of everything."

Edit: this video was just uploaded an hour ago; it seems appropriate for this thread:

 

"Tinkering" has its place, but usually better fit to experimental systems, rather than theoretical/mathematical ones.

The great advantage of "mathematical tinkering" is that it's dirt cheap (at least in terms of direct costs). And it can be fruitful: one can argue that mathematical tinkering was precisely what led Murray Gell-Mann to formulate the quark/gluon model. But I wholeheartedly agree that experiments are a necessary part of science. Theoretical physics without experimental corroboration is not science, it's math.

Now on the flip-side, the transparency of the near-"open source science" is nice - anyone can access it or even contribute to it, if their ideas are consistent with the original model's and don't break any laws of physics - but in avoiding the traditional vetting process, it runs a major risk of inconsistency (with itself and with proven laws of physics) and providing properly rigorous explanations or reasonings. Without others able to review it for problems, or the ability to be tested, it runs the risk of swiftly turning into pseudo-science or a "scientific cult," for lack of a better phrase (as an example: all the people on YouTube claiming to have magnetic monopoles or infinite energy sources that usually involve something spinning with magnets and...sketchy measurement apparati).

Agreed, and this is something the new paradigm -- whatever its manifestation -- will have to address. Any system is only as robust as its weakest part. But it's becoming evident that the status quo is sub-optimal. The culture of publish or perish, which values number of citations over quality research, has led us to the present replication crisis in essentially every scientific field. Given the collaborative success of open source software, I'm hopeful something similar can happen in science.

I'm actually not too surprised by this. Weisstein is the creator of Wolfram MathWorld, after all, so it's possible he got inspiration for his idea from Wolfram himself, combined with his own background.

Different guy, though similar name. Eric Weinstein created Geometric Unity, and though he's met Stephen Wolfram, I don't think anyone would consider them friends.

 

Different guy, though similar name. Eric Weinstein created Geometric Unity, and though he's met Stephen Wolfram, I don't think anyone would consider them friends.

Ah, it appears my extraordinary reading skills have struck again, lol. Didn't even notice a spelling difference. Good to know! That's really confusing, especially considering BOTH Weinstein and Weisstein are mathematicians.