You said a thing is flat to the degree that it's not curved, and a thing is curved to the degree that it's not flat — Metaphysician Undercover

Theorema egregium.

The "remarkable", and surprising, feature of this theorem is that although the definition of the Gaussian curvature of a surface S in R3 certainly depends on the way in which the surface is located in space, the end result, the Gaussian curvature itself, is determined by the intrinsic metric of the surface without any further reference to the ambient space: it is an intrinsic invariant

(Wiki)

I believe the position apokrisis is arguing is contrary to the principles of Gaussian curvature. But apokrisis refers to Gaussian curvature in an attempt to support the argued position. Apokrisis is claiming that flat and curved are two limits, so that all real shapes are somewhere between, being to some degree flat, and to some degree curved. But clearly, anything flat has zero degrees of curvature, and other shapes have varying degrees of curvature, and no degrees of flat. So it is wrong to assert that the same shape is to some degree flat, and to some degree curved. That's just apokrisis attempting to avoid the earlier contradiction in the statements that space is both curved and flat, at the same time.

To go back to the beginning of this thread after some derailment, the idea of physical necessity such that given exactly the same causal conditions, exactly the same result must always reliably follow, no matter how well attested we might think it to be by science, does not equate to logical necessity.

We do not, and cannot, know if such a physical necessity rules, simply because of the vanishingly small sample of the universe, both temporally and spatially, that we have observed, and will be able to observe.

If such a physical necessity does rule, which is questionable given quantum indeterminacy, then it would follow logically that given exactly the same causal conditions, then exactly the same effects must follow.

But in this case the logical necessity would only obtain in the context of a closed situation entirely subject to the aforesaid physical necessity, and there would still be no universal logical necessity to the same effect.

Even if there were nowhere anywhere free form this strict physical determinacy, it would still be logically (if not physically) possible that there might have been. And of course, in any case, we don't, and can't know the truth about any of this.

is Logical Necessity caused by some physical force or entity? Or is it a fundamental principle of Reality? Is it a law of Physics, or a law of Meta-Physics? Are natural Laws (physical regularities) necessary (absolute) or contingent (fortuitous)? If they could be otherwise, what was the prior Cause (the "must") of their necessity for the emergence & evolution of the physical world? — Gnomon

Your question prompted me to review a couple of Robert Lawrence Kuhn's interviews with science educators about this question, Martin Rees and Paul Davies. Their answer, in essence, is that science doesn't know what natural laws are. Davies speculates that science might one day arrive at a super-theory from which the undetermined constants might be explained, but that meanwhile there are simply a small number of undetermined constants - like the force of gravity - that are as they are, but without any further apparent explanation (I think this is related to the 'naturalness problem'). But at this time, we don't know if such constants have a further explanation, if there's a meta-theory that explains them - and I think it's important to understand the sense in which this is not a scientific but a metaphysical question (so - metaphysics is not dead after all.)

One of the articles I refer to is a review by Neil Ormerod, a philosophical theologian, of Lawrence Krauss' book A Universe from Nothing. He speaks of the 'anxiety over contingency' that supposedly underlies many books such as Krauss's (Krauss being a kind of ancillary member of the New Atheist clique). The 'contigency' he's referring to is the requirement to validate hypotheses and mathematical models against observation. Speaking of the Higgs boson discovery, he says:

The...thing this discovery illustrates is the ever present gap between theory and verification. The standard model was enormously successful in its account of the basic particles and the forces through which they interact. It was mathematically satisfying and elegantly based on notions of physical symmetry. Yet no one would ever have suggested that it must be correct regardless of any process of empirical verification. Such a process of verification lies at the heart of the scientific method. Theories are not self-verifying but always remain hypothetical constructs, subject to the next round of possible verification or falsification from the data.

This leads to a significant tension in the whole scientific project. Its drive is to seek intelligibility or patterns in the empirical data, to express these patterns in theoretical constructs, yet in the end it must deal with a brute fact of existence, which either verifies or falsifies these proposed patterns.

That reality is intelligible is the presupposition of all scientific endeavours: that the intelligibility science proposes is always subject to empirical verification means that science never actually explains existence itself but must submit itself to a reality check against the empirical data. This existential gap between scientific hypotheses and empirical verified judgment points to, in philosophical terms, the contingency of existence. There is no automatic leap from hypothesis to reality that can bypass a "reality check." — Neil Ormerod

One of the things that occurs to me is how often it is assumed that the phenomenal domain, the vast realm which is subject to investigation by the natural sciences, is, in this sense, the domain of contigent facts. Yet the conviction among many is that this is the only reality. ('Cosmos is all there is'.) So I think what's been lost sight of is precisely the intuition of the domain of unconditional, the realm of necessary truths (arguably, the noumenal realm). It can be argued that this is what is real, but that it is not existent, in that it's not phenomenal reality, which is 'what appears'. So the conviction that the realm of contingency is the only real realm is the basis of the fundamental confusion (dare we say ignorance) of technocratic culture.

(I suppose this can easily be construed as theist apologetics, but it doesn't have to be. I'm agnostic about the reality of a Biblical God. But there's a broader metaphysical conception that subsumes many different, specific cultural forms.)

Even if there were nowhere anywhere free form this strict physical determinacy, it would still be logically (if not physically) possible that there might have been. And of course, in any case, we don't, and can't know the truth about any of this. — Janus

It depends on what sense of 'knowing'. This writer says that Kant claims that the noumenal is unknowable - but that both Hegel and Schleiermacher then point out that, even though the noumenal might be unknowable in any objective sense, in another sense, it constitutes our own being, that it constitutes us, as subjects of experience.

Whatever the noumenal reality is, I’m a part of it. Not the "me" who is an object of experience—that’s the phenomenal me. And the naïve “phenomenal me” that comes from immediate introspection is no less phenomenal than what scientists look at when they study my brain. What bearing it has on the “noumenal me” remains an open question.

But still, I am what I am—and so in being me (as opposed to putting myself at the objective pole of conscious observation and then studying me) I am being part of noumenal reality. And there may be a way to leverage that fact into some kind of understanding of noumenal reality. That’s what Hegel tries to do in The Phenomenology of Spirit. — Eric Reitan

n deep humbleness I dare to give a definition: information is matter being in formation. — Haglund

Yes. Although I would say that Matter is generic Information in a particular formation. Energy & Matter are different forms of general Information (E=MC^2). And the "formation" is called a meaningful pattern of information interrelationships. But "Energy" & "Mass" are mathematical concepts, while "Matter" is a conventional linguistic term to denote whatever has Mass & Intertia.

I just noted that Quora tech guru Victor Toth said, "Energy and mass do have consistent definitions."
“Matter” is a somewhat more poetic term, and its meaning often depends on context." :smile:

One of the things that occurs to me is how often it is assumed that the phenomenal domain, the vast realm which is subject to investigation by the natural sciences, is, in this sense, the domain of contingent facts. — Wayfarer

Yes. The Big Bang theory caused cosmologists, such as Einstein, to reconsider their presumption that the physical world was eternal, hence unconditional. So some, including Krauss, began to look beyond the BB -- pre-phenomenal domain -- for a First & Final Cause of our contingent universe. But most of those pre-BB causes -- Many Worlds ; Multiverses ; Inflation -- are still assumed to obey the same physical laws as our Real world. So, the question of the (noumenal??) Lawmaker is still open. :cool:

It depends on what sense of 'knowing'. This writer says that Kant claims that the noumenal is unknowable - but that both Hegel and Schleiermacher then point out that, even though the noumenal might be unknowable in any objective sense, in another sense, it constitutes our own being, that it constitutes us, as subjects of experience. — Wayfarer

So, the idea here would be that of intellectual intuition; that in virtue of being the noumenal we can somehow directly know it's nature. The possibility cannot be ruled out, but even if such direct knowing were possible; there could be no discursive "knowing that we know".

Our whole warrant for such direct "knowing" would be its sense of total illumination and complete lack of doubt; there would always remain the possible of being deluded, though.

But then if we actually experienced a sense of total illumination and complete lack of doubt we likely wouldn't care about that possibility in the least. Only one way to find out if such a state is possible, and sustainable, though, and that would be to experience it in a sustained way. How to achieve that is then the problem.

So, it seems that what you are looking for is that experience of illumination and total certainty that would tell you that causation is logically necessary, despite the mundane logical fact that there is no contradiction in, to cite Anscombe's example, thinking that the kettle might not heat up when it's placed on the fire.

Just to be sure,

physical causation is an a priori intuition

That's not the argument in the Anscombe article, which explicitly rejects Kant's a priori imaginings.

Her writing works at multiple levels, between recondite jokes. Cause, like induction, is best considered as a part of the game of doing physics. What her article does is to break the picture of a necessary relation between cause and determinism, and point out that determinism is not an essential part of physics.

Now that undermines many of the lines of thought in this thread. And I had assumed you had understood this, from previous discussions. But now it seems I was mistaken.

SO again, once the relation between physical cause and logical necessity is seen as a misapprehension, your fly is shown the way out of the trap.

Yet no one would ever have suggested that it must be correct regardless of any process of empirical verification. Such a process of verification lies at the heart of the scientific method. Theories are not self-verifying but always remain hypothetical constructs, subject to the next round of possible verification or falsification from the data. — Neil Ormerod

The standard Model is low energy approximation. I think it's pretty obvious that the basis particles are not basic at all. I asked the question about preons on several physics forums and even a philosophy part of a forum. I asked the question why the model is not more popular. But the questions were deleted and one banned me. It was against the standard. Quarks and leptons ARE fundamental. The preon theory has a different mass mechanism, but still predicts the Higgs particle. But not a Higgs VEV and associated Mexican hat. The weak interaction is not fundamental in the preon model. There's simply to much at stake for the defenders of the status quo. And its runners along. ‍♂️ There were no rational arguments against the model given, except the fact that no preons are observed. Which is a ridiculous argument since the collision energies are simply not high enough yet. But dont tellem that... There was another argument to be honest. The mass paradox, which can easily be solved by assuming the preons to be massless, giving massive triplets! So, only advantages. No matter antimatter asymmetry, explanation of particle families and explanation of mass, and only two basic fields! And an explanation of the muon g2 experiment. No preons used to explain that one.

Yes. The Big Bang theory caused cosmologists, such as Einstein, to reconsider their presumption that the physical world was eternal, hence unconditional. So some, including Krauss, began to look beyond the BB -- pre-phenomenal domain -- for a First & Final Cause of our contingent universe. But most of those pre-BB causes -- Many Worlds ; Multiverses ; Inflation -- are still assumed to obey the same physical laws as our Real world. So, the question of the (noumenal??) Lawmaker is still open — Gnomon

There is the possibility that there inflate two spatially 3d universes into existence around the mouth of a spatially 4d wormhole. If matter is confined to 3d and gravity spreads in full 4d, the two universes, once accelerated to infinity, can cause two new universes (one with lefhanded matter, the other with righthanded antimatter) to inflate from the virtuality into existence again. After which the cycle repeats. Dark energy solved!

It depends on what sense of 'knowing'. This writer says that Kant claims that the noumenal is unknowable - but that both Hegel and Schleiermacher then point out that, even though the noumenal might be unknowable in any objective sense, in another sense, it constitutes our own being, that it constitutes us, as subjects of experience. — Wayfarer

Ironically, Kant's unknowable noumena are the very kind of knowledge that philosophers specialize in : speculation & conjecture into the unknown, and objectively unknowable, mysteries that are not amenable to scientific exploration. That's why only "mad-dogs" & philosophers go out into the sun-less mysteries of the Mind : Consciousness & Subjective Knowing. :smile:

So it is wrong to assert that the same shape is to some degree flat, and to some degree curved. — Metaphysician Undercover

Well, there are different metrics involved, but I can see your point. My first grad course in math in 1962 was differential geometry, and it was a puzzling experience, a topic I never found use for in all the intervening years. My view of this issue these days is very superficial: the difference between an ant crawling across the surface of a large sphere and recognizing another dimension above, and an ant somehow embedded and crawling in the same surface and finding it 2-dimensional. Pretty shallow. :roll:

A 2d torus has negative Gaussian curvature on the inside, positive on the outside, and zero in between. Because its embedding in 3d. But in 4d it has zero curvature, like a 2d cylinder.

Just measure angles of triangles. Or the circumference of a circle and it's radius. If you're on a 2d spherical shell, the ratio is less than 2pi because the radius is larger. The difference between the two is a measure of curvature. If the sum of angles is less than pi than curvature is negative, and masses fly apart, repulsive gravity, dark energy. :cool:

My view of this issue these days is very superficial: the difference between an ant crawling across the surface of a large sphere and recognizing another dimension above, and an ant somehow embedded and crawling in the same surface and finding it 2-dimensional — jgill

In my humble view, the space of an ant walking on a 3d sphere is flat. Ants walking in the shallow domain of a 2s shell will, if they start moving parallel, cross each other's paths.

Apokrisis is claiming that flat and curved are two limits, so that all real shapes are somewhere between, being to some degree flat, and to some degree curved. — Metaphysician Undercover

Or did I say the larger picture sees flatness as poised between the opposing extremes of hyperbolic and hyperspheric curvature? And that is why the value of pi might vary between 2 and infinity, with 3.14… being the special case where the Gaussian world would intersect the Euclidean one? :chin:

the idea of physical necessity such that given exactly the same causal conditions, exactly the same result must always reliably follow, no matter how well attested we might think it to be by science, does not equate to logical necessity. — Janus

But isn’t that what we would say about the running of a computer program?

So it is the other way around. The problem is the need to amend the usual notion of material cause so that it ain’t so robotically determined.

If such a physical necessity does rule, which is questionable given quantum indeterminacy, then it would follow logically that given exactly the same causal conditions, then exactly the same effects must follow. — Janus

Bear in mind that the Cosmos exists to serve the second law and thus its aim is to maximise entropy. So even without the inherent quantum uncertainty, the Cosmos is committed to the production of uncertainty at every turn.

Bear in mind that the Cosmos exists to serve the second law and thus its aim is to maximise entropy — apokrisis

You got it the wrong way round. The cosmos has no aim. A gas doesn't expand in a vacuum because it has an aim, an effect to be caused. You conflate aim with effect. The cosmos doesn't exist to serve the second law. The second law exists to serve the cosmos. To serve us! Living creatures, as part of the cosmos, have aim.

So even without the inherent quantum uncertainty, the Cosmos is committed to the production of uncertainty at every turn.
13mOptions — apokrisis

Again, the cosmos is not committed to anything, let alone production of uncertainty. Unpredictable processes are just part of it. But not because of commitment.

I think it's pretty obvious that the basis particles are not basic at all. I asked the question about preons on several physics forums and even a philosophy part of a forum. — Haglund

There’ve been a string of past members enthusiastic about rishons and preons here. @Prishon, @MatterGauge, @EugeneW, probably many more. In fact they exactly share almost all your enthusiasms. Shame you can’t catch up with them somewhere.
.

Do they agree with me on preons?

Even I sort of agree with you on preons. :grin:

The original preons were considered massive. I asked Harari by email and he was kind enough to answer. Massless preons could do the trick. He wrote me not to follow the "preon path". Dunno. Seems so clear. Like quarks before their discovery. I had a long conversation on physics stack exchange with a defender of the standard but in the end he couldn't offer substantial counters. The best he was left with was asking for the field Lagrangians. Well, yes... eeeh... Anyhow, good to know there is at least one person! :grin:

All elementary particles are composite in some sense even in the Standard Model view. Quarks mix like neutrinos. Photons are effective mixes of Bs and W3s. The electron mixes with the anti-positron. We are back to Chew’s S-matrix bootstrap as far as I can see.

So I don’t think preons are the answer. Or at least understood as a new deeper level of concrete particles - rather than gauge degrees of freedom - would be just to recreate the old atomistic paradox of why there would be any fundamental grain of matter at all.

But there does seem to be now broad acceptance in particle physics that all fundamental particles are composite in the fashion of a soliton or other examples of topological order in condensed matter physics.

All elementary particles are composite in some sense even in the Standard Model view. Quarks mix like neutrinos. Photons are effective mixes of Bs and W3s. The electron mixes with the anti-positron. We are back to Chew’s S-matrix bootstrap as far as I can see. — apokrisis

Yes, different neutrinos mix like different quarks can do. But the effect in quarks is much smaller due to their masses. Neutrinos from different generations mix. Quarks from different generations don't. Don't know what you mean by electrons mixing with anti-positrons. Anti positrons are just electrons. In the preon model there are no W3 pre symmetry breaking gauge fields. So the photon is just the photon. The non broken gauge state has never been observed. It's a fantasy to fit the facts, like the value of the VEV, of which the origin is unknown, which is because it's just posited on purpose. The same, but real mechanism is to be seen in condensed matter. Chew's bootstrap applies partially.

So I don’t think preons are the answer. Or at least understood as a new deeper level of concrete particles - rather than gauge degrees of freedom - would be just to recreate the old atomistic paradox of why there would be any fundamental grain of matter at all. — apokrisis

I think the model has only advantages, like I outlined. It explains quark and lepton generations, mass, matter antimatter asymmetry (namely that there is none), etc. And it explains muon g2.

But the standard rules. I guess it has to wait until:smile: higher energies will reveal it. There is still a lot of space between 10exp-22 and 10exp-35. Although tiny. But in comparison with a particle size, 10exp-35, it's a vast distance. Enough for three to form triplets. :wink:

But there does seem to be now broad acceptance in particle physics that all fundamental particles are composite in the fashion of a soliton or other examples of topological order in condensed matter physics. — apokrisis

No solitons or gauge degrees of freedom involved in the preon model. There is no broad acceptance, that's the point. Everyone fears to say they don't believe in the standard. Their careers... :sad:

The non broken gauge state has never been observed. It's a fantasy to fit the facts, like the value of the VEV, of which the origin is unknown, which is because it's just posited on purpose. — Haglund

If you call the mainstream trend of thought a fantasy, then they are right to treat you like a crackpot.

If you made a well motivated case for why it is a blind alley, that would be a different matter.

And it explains muon g2. — Haglund

OK. How?

Everyone fears to say they don't believe in the standard. Their careers... — Haglund

Sure. They are all roped together like nervous mountaineers on an unclimbed summit. You think the prize belongs to the solo athlete with grit and flair.

But if you are going to sell preons, I would expect to see a better motivation being offered. Gauge and topological order have been working for particle physics for 60 years. You sound as if you are happy to take on K2 in your bare feet and no tent.

Don't know what you mean by electrons mixing with anti-positrons. — Haglund

https://www.quantumdiaries.org/2011/06/19/helicity-chirality-mass-and-the-higgs/

If you call the mainstream trend of thought a fantasy, then they are right to treat you like a crackpot — apokrisis

Yes. But then who's the crackpot? They do use an unobserved mechanism. A fantasy. There does exist such a spontaneous symmetry breaking in condensed matter, and from there Higgs took the idea. But for that he had to introduce some weird unexplained vacuum energy. The preon model also predicts mass of particles from massles constitutes and also a Higgs particle, which is just a state of 6 preons, as are the W and the Z. They couldn't offer true counters, except irrational response.

If you made a well motivated case for why it is a blind alley, that would be a different matter. — apokrisis

I mentioned the advantages. Symmetry between particles and anti particles is one of them.

Sure. They are all roped together like nervous mountaineers on an unclimbed summit. You think the prize belongs to the solo athlete with grit and flair. — apokrisis

I don't want no prize but it should belong to the true theory. There is clinging to the standard (quarks and leptons being elementary).

The muon g2 result is explained by considering the muon a triplet of three massless Weyl particles. Each with charge -1/3.

Coming to think about it... How big is that prize? :grin:

Not sure still what you mean by an anti-positron. If an electron meets an anti positron, doesn't it meet an electron? How is helicity involved here?

The muon g2 result is explained by considering the muon a triplet of three massless Weyl particles. Each with charge -1/3. — Haglund

How does that explain the muon discrepancy? An electron would also have the same structure by your account. So why does the electron conform to Standard Model expectations but the muon hint at other BSM particle contributions?