Man, you have really gotten into this stuff !! I admire your tenacity and ability to digest material that spooks me. :smile:

a singularity represents a transition point where our theories (or maybe just our current system of mathematics, or both) stop working and, as far as we can tell, no longer describe reality. — Jaded Scholar

The essential singularity of complex analysis would seem strange enough it might provide some clues about how math diverges from reality in a spectacular way and how our ideas of reality could shift. Particularly since the exponential function is fundamental in physics. Just idle thoughts. Good you are around.

Thanks so much, for your encouraging words sir. I am happiest when I can spend time pondering such stuff. It seem to me that it is my best experience of being a human and living the human condition.

Sure, I will always have to accept that the nihilists, the doomsters and the pessimists have a valid case, but experiencing the wonder I sometimes do, like a child, when I think about seeking truths and I get to read the words of mathematicians like yourself or physicists like @Jaded Scholar(whose handle I disapprove of, but whose knowledge I envy,) means that we are not a lost cause of a species.

We are an infant species, when you consider the cosmic calendar scale.
Do you not think that we truly are, as Carl Sagan suggested, in the title of his first episode of the series COSMOS, 'on the shores of the cosmic ocean?'

Do you not think that we truly are, as Carl Sagan suggested, in the title of his first episode of the series COSMOS, 'on the shores of the cosmic ocean?' — universeness

Eloquent.

I've given myself permission to be quite rude in this comment, which I'm hesitant to do in a forum where I'm pretty new, but the points you are holding fast to are so flawed that they're almost actively anti-intellectual. And that's the main reason I'm responding at all.

I've approached you with the assumption that we have different areas of expertise that lead to different interpretations of modern physics. But your last comment has clarified things for me: you obviously just don't understand anything about modern or classical physics and are just parroting random critiques of physics and maths from throughout the ages, which were all valid at the time, but have been turned into jibberish by your comprehensive ignorance of the actual contexts they apply to.

What I'm talking about is better understood through principles of calculus. The "t=0" represents the limit, and the problem is in approaching the limit. — Metaphysician Undercover

This is a sentence that I think could only be written by someone who has never studied calculus. A year 10 calculus student would recognise this as literal nonsense. The "problem" you describe was solved by calculus.

At the very least, you are right in linking it to this nonsense:

There is a point in time, when it changes from being at rest, to being in motion. At this point in time, its rate of acceleration must be infinite. — Metaphysician Undercover

I literally just detailed in my last response that you are describing a problem that existed in pre-Newtonian classical physics which was solved by Newtonian physics. Newton's second law, often symbolised as "F=ma", clearly prohibits infinite acceleration in every case except with infinite force or massless objects. This is not some artificial curb placed upon the results of calculus in this area, but an emergent property.

I believe the uncertainty is based in a time/frequency relation. — Metaphysician Undercover

Yeah, thanks for (again) confirming that you don't know what you're talking about. Within Fourier transforms, there is intrinsic uncertainty within first-order terms between time and frequency for the exact same reason that any other integral transformation has an intrinsic uncertainty between conjugate variables, be it time/frequency, position/momentum, gravitational potential/mass density, voltage/charge, etc. There is nothing remotely unique to time itself in this line of argument.

Exactly, our understanding of anything is incomplete, therefore deficient, lacking, — Metaphysician Undercover

...Some moreso than others.

Set theory in general, presupposes that numbers are objects, Platonic Idealism. — Metaphysician Undercover

Again.
What you are saying is a collection of truth-adjacent things, which you have combined into something that is just not true. And you could easily have avoided asserting something this ridiculous if you were interested enough in what you're talking about to spend 30 seconds looking it up online.

But I do not think that it is sophistication which makes good math, I think the opposite. Good math is based in simple principles with universal applicability. — Metaphysician Undercover

I don't agree with your definition of "sophistication", which seems to be equivalent to "complexity". My meaning of it in this context was more like "advanced"/"accurate"/etc. If two systems were equally universally applicable, and one was more complex and the other less complex, I'd apply the label of "more sophisticated" to to the simpler one. However, on looking up dictionary definitions of the word, your usage of it seems to be a more common interpretation than mine, so saying that you have misunderstood me here is not as reasonable as saying that I have miscommunicated.

I do slightly object to the value label of "good" maths systems being those which are better tools for modelling our specific reality, but then again, that's the whole point of maths, so it's probably not worth quibbling about here.

The problem is that no one wants to fix them. The principles work in most situations, so they do not need fixing. Then for the places where they do not work, keep using them and add some more principles to make them sort of work. Look, thousands of years ago Pythagoras label pi and the diagonal of a square as "irrational". To me, this indicates that there is something fundamentally wrong with the dimensional representation of space. But who cares, the principles work, and when it turns out that real circles in the real world are not actually circular, but ellipses and things like that, we just adapt "the circle" and pi principles to make them work in the real world. — Metaphysician Undercover

This commentary is a completely valid critique of ancient Greek mathematics. I was just looking up the actual label they applied to irrational numbers ("alogos", meaning "inexpressable"), and learned that the first proof of their existence was attributed to Hippasus of Metapontum, who made the discovery while at sea, and was thrown overboard by his fellow Pythagoreans for it. But in keeping with the theme of my rebuttals, both maths itself and our scientific culture have changed a bit since then!

The most lauded contemporary mathematicians and scientists are the ones who completely break, fix, or replace flawed systems! I went on at length previously about the current state of the field not remotely rejecting, but actively embracing things like irrational and imaginary numbers because they are necessary for new kinds of maths and necessary for modelling reality.

Moreover, one of the reasons for modern mathematics no longer being merged with the field of physics is that - as I also mentioned previously - assumptions and value judgements about physicality or "reality" are outside the field of mathematics, which is now primarily directed with finding and fleshing out any and every mathematical system we can think of. This is closest to an actual reason for the abundance of complexity and axioms that you lament: the field is not defined by or limited by an attempt to describe our perceived reality. It seeks to describe all possible mathematical systems. Each of which require axioms to define.

And I don't even know what you're trying to say with your circle argument. I'm just as critical of the "world of forms" as you (if not moreso), but I don't see what there is to fault about the idea - or rather, the empirical observation! - that the macroscopic world of our everyday experience is more complicated than an empty Euclidean plane.

But you cannot say that these problems haven't been labeled. — Metaphysician Undercover

If you feel the need to reply again, then I challenge you to point out one such problem that has been labelled, and is not something that modern mathematicians want solved (or have already solved).

I think mathematics and science are not perfect tools for modelling the real world. And nailing down the exact nature of their problems is both important and difficult. And I think it does a great disservice to these very valuable pursuits if we pretend that the long-solved problems of their forebears are some kind of inescapable black mark upon them. It can be highly useful to learn from the problems of the past, but the most instructive part of that kind of analysis is how they were solved - another reason it's counterproductive to ignore the fact that those solutions exist.

It's like pretending that all criticisms of horse-drawn carriages are equally valid criticisms of cars. You're not accomplishing anything worthwhile when you muddy the debate by saying that cars are good, but all of the horse dung is a real problem. That's the problem with you doubling down on arguments like "Oh, the problems are clear - they just can't get over [method of thinking they got over a millennia ago]."

Of course, I'm probably wasting my time by spelling out the problems with your approach. All of the arguments you have doubled down on by basically just repeating yourself and ignoring my refutations (and any other easily accessible information on them) are a series of data points suggesting that you don't actually care about the truth or falsehood of the arguments you are summoning and, for some reason, are primarily motivated by a desire to disagree, and not remotely motivated by any desire to seek out actual truths.

When I started writing this response, I was intending to liken your responses to that of a LLM like Chat GPT-4 - nominally referencing a rich variety of information sources, but demonstrating no contextual understanding of any of them - but after a more thorough read of your commentary, I'm quite confident of your humanity. LLMs haven't yet got the exact register we see in humans with nothing to say and a determination to say it as loudly as possible.

For me, it's such a pleasant breeze of cool fresh air on a hot and sticky day, to read your posts. — universeness

What a lovely thing to say! Thank you! :D

Sabine's ... is ... not a long article, so it would be great if you could have a look at it and give your opinion on it. — universeness

To be honest, I needed to brush up on many things to answer your previous questions, and that article was one of the things I read for that, haha.

I assumed some string or perhaps superstring states, were responsible for the actual (for want of a better term) 'fabric' of spacetime itself. I thought that's part of the reason why supersymmetric particles were so sought after at the LHC?
String theory/Mtheory was/is a possible t.o.e, is it not, and as such, does it not also suggest that spacetime is quantisable? If QFT is correct, is it not that string states, would be the same as field disturbances, rather than be free travelling particles/strings? Rather than the concept of a single electron (as such), we would have an electron as a string state/field disturbance?

I hope I am not frustrating you too much with my poor grasp of the details involved here. — universeness

I wanted to quote and address that line about your grasp of the details, to note that in my last comment, I almost brought up the caveat of string theory being set up to have relativistic spacetime emerge from it, but left it out because I didn't fully understand that mechanism - and you have immediately honed in on that missing part of the picture. So your grasp of the problem is demonstrably better than you give yourself credit for.

So in the hopes that my poor grasp of the details wasn't leading you astray - I'm a quantum physicist, but have never done any actual work with String Theory - I've read several more articles (from both arXiv and the good folks over at physics.stackexchange.com), and I think I've got the gist.

In string theory, strings exist within a continuous spacetime that has various dimensionalities (usually 11 dimensions, courtesy of M-theory's unification of superstring theories) and other properties that allow strings to generate a reality like ours. However, this spacetime is not the spacetime we experience. Gravitons distort everything's interaction with the underlying spacetime, and produce gravitational dynamics that match the dynamics of relativistic spacetime. In the perturbative interpretation that leads to String Field Theory (the direct analogue of QFT), this leads to a field that does the same job - and that field can indeed be quantised in a version of string theory called "background independent open string field theory" (though I think this version has some large and unresolved problems). And we can even think of that field as our spacetime, which is distinct from the underlying spacetime in which strings are defined.

However, in every version of string theory, this formal spacetime is dependent on the a priori spacetime in which strings are defined. It has never been able to (successfully) build spacetime from scratch.

So you are onto something with your intuition to extend string theory into SFT, and doing so has the potential to resolve the problem of non-emergent spacetime, but as I understand it (I. E. Very vaguely), all current attempts along these lines result in some physical implications that are incompatible with our measurements of our own universe.

Relatedly, I also did not understand the specific need for supersymmetry, which this paper helped me most with: https://arxiv.org/abs/gr-qc/0410049
Horowitz plainly notes one big instantiation of the problems that arise in string theory without supersymmetry is that, in that case, the ground state of every string becomes a tachyon. Admittedly, I don't understand specifically why that's a problem, but it definitely seems like it should be a big problem. A more detailed problem is that supersymmetry is required to construct Minkowski spacetime - the metric where time is the same kind of dimension as space. Otherwise your theory can't obey general relativity.

To get back to your next question:

So is the difference between String theory and LQG, your earlier point that in string theory, all proposed string states exist WITHIN spacetime. Spacetime would thus be a 'container,' for all string/superstring states, so, LQG includes spacetime and string/superstring theory does not? This seems to clash with my own (probably incorrect) interpretations of the Sabine Hossenfelder article. — universeness

I think this comment is accurate, but the language of the second sentence throws me a little. I really don't want to come off like I'm the grammar police (maybe something more like "the physical interpretation social worker"?) when I say that I don't really like the language here that LQG "includes" spacetime and string theory does not. I think it's a more useful interpretation to say that LQG constructs spacetime as an emergent property of its laws, whereas string theory is built upon the assumption of the pre-existence of spacetime, which makes it (almost) impossible to say anything about the fundamental nature of spacetime itself within that framework.

(Sorry, that ended up not being the simple replacement of "includes" that I had in mind when I started that sentence.)


On Sabine's article itself, I admit that it also took me some re-reading to understand the overarching point, but I think it's just that - despite the general disunity within the scientific community between advocates of LQG and String theory - there are several researchers who think we shouldn't necessarily assume that the two cannot be unified. I think the hope is to look at places where String theory and LQG don't disagree with each other, and therefore you can formulate both of them at the same time, and then you have a starting point to figure out what modifications you could make to either theory to achieve compatibility between them in other examples (and eventually, in the general case).

The first example being the AdS/CFT conjecture, a theoretical spacetime configuration which achieves the limiting case where strings do not affect the shape of spacetime, so you can have both strings and LQG without one conflicting with the other - the hard part being that someone still has to figure out how String theory could possibly reduce to LQG in that setting (or vice versa).

The other examples of the black hole firewall problem and supersymmetry/extra dimensions are a different kind of point of potential compatibility - more of an observation that several of the problems and methodologies in String theory have a very comparable counterpart in LQG, and vice versa. So both camps could benefit a lot from a more inclusive attitude towards the other.

Overall, it's not an actual argument that these points of compatibility necessarily imply the potential unification of both theories; it's more of an argument that both theories are very incomplete, and the path towards a true TOE would be better served by scientists not backing one horse or the other at this early stage, and being more open to the possibility that the truth may lie somewhere in between. That's my take on it.


Phew. It was a bit challenging to research all of that, but it was a very fulfilling challenge! I hope the above makes sense, and please don't hesitate to point out any parts that don't - especially because you have demonstrated an excellent radar for asking the right questions about these theories! And I meant to say above, but another point to your credit is that the parts which confused both you and I most were around the emergence of spacetime from String theory, which was mostly so difficult to research because it's a very problematic part of the theory that most people just kind of ignore (in one stackexchange post, someone mentioned asking Brian Greene in a Q&A in 2012, basically, why it was so hard to find papers on the nature of spacetime in string theory and BG said "you aren't missing anything, we just don't know").

The essential singularity of complex analysis would seem strange enough it might provide some clues about how math diverges from reality in a spectacular way and how our ideas of reality could shift. Particularly since the exponential function is fundamental in physics. — jgill

Good commentary! It would be a bit hypocritical of me to not be equally open to unphysical results being either a breakdown of mathematical modelling or just a breakdown in our capacity to interpret how they could be an accurate reflection of reality. Especially since, as you note, they tend to pop up all over the place in physics.

You know, I actually didn't give much thought to my username here! I came up with the Jaded Scholar username about 15 years ago and have been using it in a variety of settings ever since (which I expected to doxx me a little, but apparently my presence here is the only one that I can see in any search engine results). On reflection, I have to say that I am actually much less jaded than I was back then, especially due to all the things I have learned which convinced me that humans really are a lot more ... good (for lack of a more accurate word) than any capitalist, economist, or powerbroker would like us to believe.

We are an infant species, when you consider the cosmic calendar scale.
Do you not think that we truly are, as Carl Sagan suggested, in the title of his first episode of the series COSMOS, 'on the shores of the cosmic ocean?' — universeness

Oh, man, you have just hit on something that has been rattling around my head for a few months now, and I have to rant about it to you. It'd probably be more appropriate to start a new thread for a tangent this tangential, but whatever.

While thinking about the Fermi paradox (another thing I love thinking and ranting about), I recently looked up some estimates on how much longer the universe is likely to continue birthing new stars and the expected elemental proportions of those stars (and thus, the worlds that are born with them). I'll resist the urge to talk about the answers to the Fermi paradox that I find most plausible, but what occurred to me affects almost all such answers. I hadn't previously appreciated that our universe is very, very young. Incredibly so, for the scales of this question.

It's 14 billion years old, and our solar system is 4.5 billion years old, and most solar systems older than that wouldn't have a lot of the elements necessary for our kind of life. In broad terms, there have been about three generations of stars in the history of the universe (and thus, three generations of solar systems) - ours being born in the third generation, which are the only ones which commonly have enough elements for our kind of life. We have those elements because our star and its planets are made from dead stars from gen 1 and 2 (they're actually called Population II and III, the numbering going backwards from us at #1, as per human nature). Note that not all Population II and III stars have died! The 3s probably have, but many 2s still burn!

Anyway, it was very possible for solar systems older than ours to be as high-metallicity (high-carbon) - recent evidence suggests it was possible as early as 12.5b years ago - but I think ours is from right around when it stopped being rare to have the elemental profile needed for human life to emerge.

Conversely, life on earth emerged pretty much as soon as it was possible for life to emerge! Current estimates have pushed that point to about 4bn years ago, not long after the earth's crust formed - I. E. as soon the surface of the earth stopped being molten rock. That part is really impressive, and is important when we note that, as far as we can tell, we are the first civilisation to emerge on Earth. It apparently took 4bn years for life to randomly produce communal, intelligent creatures like us.

I want to mention that we should absolutely assume that life (as ill-defined as that term is) can arise in completely different ways to how it arose on Earth. But also, the fact that DNA-based life emerged on Earth basically as soon as possible, and that this is unlikely to be a coincidence since the elemental availability at the birth of our solar system made it so easy to form amino acids (as they say, "the building blocks of DNA") that we have even observed them in meteorites that predate the formation of the Earth's crust. It's impossible to say how prevalent any other form of life is likely to be, but we can definitely say that our kind of life seems very likely to arise as soon as an environment like ours does.

The point I'm trying to qualify is that I think there are very, very few alternate timelines where a human-like civilisation could have emerged very much earlier than ours did. We don't know how probable it would be to have something like us arise a billion years earlier or so, but we know that anything emerging significantly earlier than that (on Earth or anywhere in the universe) would be much, much less likely. I know my logic is getting a bit tenuous, so to generalise it a bit: We can reasonably expect that other life exists throughout the universe, but I think we can also expect that if we could group the emergence of intelligent civilisation into generations like our stars, then you'd be hard pressed to put ours into anything except the very first generation.

But the point that I'm really getting at is this: current estimates posit that our universe is going to keep forming new generations of stars for about 100 trillion more years.

If that number was 100 billion years, we would have emerged 14% of the way into the lifespan of the universe. But it's 1000 times that. We have emerged 0.014% of the way into that lifespan. 99.986% of it remains, and all of that will be even more likely to produce life than most of the 0.014% of time that's already passed.

Even if the most generous estimates for the Drake equation are somehow still too conservative, and life already teems beyond our greatest estimates - even then, we are still pioneers at the very, very forefront of the existence of life. Not just the existence of life on Earth (though we also are), or the existence of life in our galaxy (though we also are), but forefront of the existence of life anywhere in all of reality.

It's a very big thought.

It makes me feel a little better about human civilisation acting like a bunch of idiot babies, compared to what (I think/hope) we're capable of. On a cosmological scale, we ARE babies. And what's more, we're the very first ones, with no earlier pioneers we can possibly look to for guidance as we figure out our baby steps on our own - and to quote another sentiment that lives rent-free in my head: "I always love it when people say 'baby steps!' to imply they're being tentative, when actually baby steps are a great unbalanced, wholehearted, enthusiastic lurch into the unknown."

It also makes me feel a little more hopeful and future-focussed on what I (and all of us) can contribute to our countless distant relatives in the very, very long future that lies ahead of us.

Of course, I'm probably wasting my time by spelling out the problems with your approach. All of the arguments you have doubled down on by basically just repeating yourself and ignoring my refutations (and any other easily accessible information on them) are a series of data points suggesting that you don't actually care about the truth or falsehood of the arguments you are summoning and, for some reason, are primarily motivated by a desire to disagree, and not remotely motivated by any desire to seek out actual truths. — Jaded Scholar

:clap: What is sooooooo important about your post to @Metaphysician Undercover is not the hope that he will, at last, gain some better understanding of the scientific method but that other readers of your response to him will. Imo, he may well be fully cooked and lost in a miasma of his own creation, but debunking him so effectively, imo, may assist others.
I hope you don't mind this 'heads up,' to @180 Proof. It's just that I would like his opinion on your response to MU.

:up: Over three years ago, I'm guessing, it'd become irrefutably clear to me that MU and I could only ever talk past each other – not merely substantively differ – on most nontrivial philosophical and scientific topics.

:100:

Welcome to TPF!

Thanks for your kind and encouraging words. They help me believe that I can perhaps even 'quantum tunnel,' :joke: through some of the solid barriers that my limited maths and physics skills present me with.
You have given me lots of 'pathways,' I can wander down, in attempting to improve my understanding and pursuit of the greatest activity any human can have the privilege to take part in. That of 'truth seeking.' Most folks are too busy trying to just survive day to day.

The first example being the AdS/CFT conjecture, a theoretical spacetime configuration which achieves the limiting case where strings do not affect the shape of spacetime, so you can have both strings and LQG without one conflicting with the other — Jaded Scholar

However, this spacetime is not the spacetime we experience. Gravitons distort everything's interaction with the underlying spacetime, and produce gravitational dynamics that match the dynamics of relativistic spacetime. — Jaded Scholar

are two example of the paths I am referring to.

I have found the supersymmetry aspect hard to follow, along with the extra 'wrapped' dimensions.
I get the 'wrapped' idea, by thinking about a 3D pipe viewed from above, so that it looks like a 2D shape, with the 3rd dimension wrapped around. So the extra dimensions of string theory are tiny and are wrapped around every coordinate in our 3D existence.
Do you get any further understanding based on the Calabi-yau manifolds?


Have you watched this lecture by Ed Witten? He is the main genius in string theory imo.

I have watched it twice but I think I need to watch it again and again to try to analyse each sentence Ed utters! :lol: :scream:

Relatedly, I also did not understand the specific need for supersymmetry, which this paper helped me most with: https://arxiv.org/abs/gr-qc/0410049
Horowitz plainly notes one big instantiation of the problems that arise in string theory without supersymmetry is that, in that case, the ground state of every string becomes a tachyon. — Jaded Scholar

So, just to clarify the implication here, without supersymmetry, the ground state (or lowest energy state) of every string would have to have a 'faster than light speed' potential (or actual?).
This confuses me more, but I wonder if I am conflating two ideas here? The motion of a string within spacetime and its 'inter-dimensional vibrational velocity.'

Sentences like the following form the beginnings of the basis of my confusion:
"In quantum mechanics waves and particles are dual aspects of the same phenomenon, and so each vibrational mode of a string corresponds to a particle. The vibrational frequency of the mode determines the energy of the particle and hence its mass."
So, this suggest to me that a string that 'vibrates' in multiple dimensions is 'excited' and would produce mass, is this not the case?
Anything with mass cannot travel at light speed, never mind superluminal speed (as in the case of the elusive tachyon).
I know that a 'ground state' is a 'non-excited' state, ( and a state with an absolute zero temperature) so how can such a state vibrate? I must be missing something quite obvious here!
So, does this mean that the inter-dimensional string vibrations, would not create any mass?
I know that the 'tachyon' ground state is part of the 'bosonic string theory,' and I have read such as this, from a discussion on the physics stack exchange (although the maths involved in the actual entry is currently beyond me):
"The zero mode of the set of harmonic oscillators (the string excitation) gives a negative energy for each dimension. So the ground state has a negative energy (if the "classical" center-of-mass momentum is zero) and a negative squared mass. For the coherence of the theory (there are −2 excited states at first level, so it it a representation of ( −2) which must be massless."

I've read several more articles (from both arXiv and the good folks over at physics.stackexchange.com), and I think I've got the gist. — Jaded Scholar

I read many of the exchanges on the physics stack exchange. One of the TPF members @noAxioms is/was a moderator on a physics site, but I can't remember if it was the physics stack exchange.
They certainly offer quick annihilation, to any peddlers of woo woo, on that site. It is a very good site, imo.

Oh, man, you have just hit on something that has been rattling around my head for a few months now, and I have to rant about it to you. It'd probably be more appropriate to start a new thread for a tangent this tangential, but whatever. — Jaded Scholar

:grin: happy moments!

I'll resist the urge to talk about the answers to the Fermi paradox that I find most plausible — Jaded Scholar

I would like to hear them sometimes! For me, I am content with even the thought that 'someone has to be first,' so why not us, as unlikely as that seems in such a vast universe. I love this quote from Carl Sagan's film Contact:

The original source:

It makes me feel a little better about human civilisation acting like a bunch of idiot babies, compared to what (I think/hope) we're capable of. On a cosmological scale, we ARE babies. And what's more, we're the very first ones, with no earlier pioneers we can possibly look to for guidance as we figure out our baby steps on our own — Jaded Scholar

:clap: :clap: This is part of why I say to the doomsters, the nihilists and the pessimists, that despite their very justified complaints about our bloody history, our very poor stewardship of this planet, that we had better reverse or be made extinct, and our current horrifically bad record of disunity and inhumanity towards our own and other species, they must also realise, that we have only been around for the last couple of seconds in the cosmic calendar scale, SO GIVE US A F****** CHANCE!!!!!!!!!
Btw: After 15 years of labelling yourself 'Jaded,' it's time you changed. How about 'Eager scholar', 'Inquiring scholar' or 'Musing scholar?'

@180 Proof (No! I am not again calling you a doomster, a nihilist or a pessimist! I just included you here, to ask you for a little less affection for your 2001 monolith and a little more for your fellow meat bags :grin: )

Oh what the hell, I might as well include @Vera Mont as well ..... you never know ....... it might at least make her chuckle! ..... of course .... she might also throw something sharp and deadly in my general direction! :scream:

Moreover, one of the reasons for modern mathematics no longer being merged with the field of physics is that - as I also mentioned previously - assumptions and value judgements about physicality or "reality" are outside the field of mathematics, which is now primarily directed with finding and fleshing out any and every mathematical system we can think of — Jaded Scholar

Some time back on this forum I mentioned that October of 1958 when I started a postgraduate curriculum for the USAF at the U of Chicago I found that the mathematics department would no longer offer courses to the physics department, the latter offering all physics math courses. The rift went beyond the obvious differences in notation and symbolism (which I find annoying and distracting) and probably had something to do with differing attitudes about proofs. And the foundational stuff about mathematical systems.

I am an old guy, and when I go to one of 26K pages on math on Wikipedia I'm not sure what is being discussed. Even most of modern complex analysis seems foreign.

I enjoyed reading your rebuttal to MU. Amusing and entertaining, unlike so much on the forum that rehashes and compares what classical philosophers had to say.

I've given myself permission to be quite rude in this comment, which I'm hesitant to do in a forum where I'm pretty new, but the points you are holding fast to are so flawed that they're almost actively anti-intellectual. And that's the main reason I'm responding at all. — Jaded Scholar

This is "The Lounge", rudeness is accepted and expected. I understand that it's all good hearted and meant for improvement, self and other, and I hope you do too.

But your last comment has clarified things for me: you obviously just don't understand anything about modern or classical physics and are just parroting random critiques of physics and maths from throughout the ages, which were all valid at the time, but have been turned into jibberish by your comprehensive ignorance of the actual contexts they apply to. — Jaded Scholar

Sound criticism can never be turned into gibberish. It seems you haven't studied philosophy and therefore have no understanding "of the actual contexts they apply to". I have, and do understand the context. Sorry jaded, but it is you whose talk is gibberish in this context.

I literally just detailed in my last response that you are describing a problem that existed in pre-Newtonian classical physics which was solved by Newtonian physics. — Jaded Scholar

The problem was never solved, as is clear from the evidence I cited, the time/frequency uncertainty of the Fourier transform. As I've told others already on this forum, calculus provided a "workaround" for the problem, which was sufficient in the context of the physical problems of the time period, but it was not long before the physicists reached the limits of the applicability of that workaround, and so, the same problem reappeared.

Yeah, thanks for (again) confirming that you don't know what you're talking about. Within Fourier transforms, there is intrinsic uncertainty within first-order terms between time and frequency for the exact same reason that any other integral transformation has an intrinsic uncertainty between conjugate variables, be it time/frequency, position/momentum, gravitational potential/mass density, voltage/charge, etc. There is nothing remotely unique to time itself in this line of argument. — Jaded Scholar

I see you have yet to produce a good response to this issue, only to say that the problem which is derived from a failure in our representation of time is not limited to time. The so-called "discipline" of physics has managed to spread the problem around to all sorts of spatial concepts, producing a more general "uncertainty principle", through its conventional ways of relating space and time.

I don't agree with your definition of "sophistication", which seems to be equivalent to "complexity". My meaning of it in this context was more like "advanced"/"accurate"/etc. — Jaded Scholar

Are you aware of the history of the term "sophistic"? Why are you intent on portraying sophistry as "advanced", "accurate". In reality, sophistication is the oldest form of deception. Add as many slights of the hand as possible, to make things appear to be advanced and accurate, in order to hide the trickery which is really going on underneath. Simply put, "sophisticated" does not imply "advanced" or "accurate", and you definition is a hope filled fantasy, to portray sophistication as advanced and accurate, instead of as an affront to Occam's razor.

What you are saying is a collection of truth-adjacent things, which you have combined into something that is just not true. And you could easily have avoided asserting something this ridiculous if you were interested enough in what you're talking about to spend 30 seconds looking it up online. — Jaded Scholar

Come on Mr. Scholar, what the fuck are you even talking about here? What the hell is a "truth-adjacent thing? (Excuse the rudeness please, but this is The Lounge.) Either it's true or it's false, or would you prefer that we sink ourselves into a world of probabilities, with nothing to ground what is actually the case?

I do slightly object to the value label of "good" maths systems being those which are better tools for modelling our specific reality, but then again, that's the whole point of maths, so it's probably not worth quibbling about here. — Jaded Scholar

Excellent! We almost have agreement on something, except you would overrule my "good" with something "better". What if I overrule your "better" with "The Greatest" (that would be God).

But in keeping with the theme of my rebuttals, both maths itself and our scientific culture have changed a bit since then! — Jaded Scholar

Yes, math has changed "a bit". Unfortunately the fundamentals of circles and angles remain the same, and the glaring contradiction of discrete units within a continuity, just does not want to go away.

Moreover, one of the reasons for modern mathematics no longer being merged with the field of physics is that - as I also mentioned previously - assumptions and value judgements about physicality or "reality" are outside the field of mathematics, which is now primarily directed with finding and fleshing out any and every mathematical system we can think of. This is closest to an actual reason for the abundance of complexity and axioms that you lament: the field is not defined by or limited by an attempt to describe our perceived reality. It seeks to describe all possible mathematical systems. Each of which require axioms to define. — Jaded Scholar

Here we go... Instead of grounding the mathematical principles (axioms) in what is actually the case, truth, as philosophers do with "self-evident" truths, you'd prefer to waste time looking at an infinite number of "possible mathematical systems". Good luck with that endeavour, you can find me in The Lounge sipping some whisky, and from time to time some whiskey.

If you feel the need to reply again, then I challenge you to point out one such problem that has been labelled, and is not something that modern mathematicians want solved (or have already solved). — Jaded Scholar

That's not the issue. You said:

if we could label them, we could have fixed them by now. — Jaded Scholar

Now you're changing your tune to say that the ones which are labeled, "mathematicians want solved". I would urge you to take another step further, if you're truly a scholar who is jaded, and make a critical inspection of all those problems which have been labeled and which you seem to think mathematicians "have already solved". Creating a sophisticated workaround, which is useful in a multitude of situations, but then fails when physics needs a more precise approach to the relation between space and time is not a true solution. And when the mathemagicians use smoke and mirrors in an attempt to demonstrate that the workaround is a true resolution, that is nothing but sophistry.

I think mathematics and science are not perfect tools for modelling the real world. And nailing down the exact nature of their problems is both important and difficult. And I think it does a great disservice to these very valuable pursuits if we pretend that the long-solved problems of their forebears are some kind of inescapable black mark upon them. It can be highly useful to learn from the problems of the past, but the most instructive part of that kind of analysis is how they were solved - another reason it's counterproductive to ignore the fact that those solutions exist. — Jaded Scholar

You are jumping to conclusion. You approach with prejudice, a preconceive bias, that these problems have been "solved". That is what you state "they were solved". But when you approach these problems, Zeno's paradoxes for example, and the irrationality of pi and the square root of 2, with the attitude that these problems have already been solved, you do not look at them as real problems, they are pseudo-problems, because you have presupposed that they are solved.

Instead, you need to approach the problems as they are expressed, exactly as presented at the time, as real problems, and come to understand them as real problems. Then you are in a position to look at the proposed solutions, and judge them as to whether they are real solutions, or just convenient workarounds. You clearly approach from the preconceived idea that the problems have been resolved, and therefore do not understand them as real problems. Newton's law prohibits infinite acceleration, but prohibiting a problem does not resolve the problem.

It's like pretending that all criticisms of horse-drawn carriages are equally valid criticisms of cars. You're not accomplishing anything worthwhile when you muddy the debate by saying that cars are good, but all of the horse dung is a real problem. That's the problem with you doubling down on arguments like "Oh, the problems are clear - they just can't get over [method of thinking they got over a millennia ago]." — Jaded Scholar

This makes no sense. Both cars and carriages have wheels and bearings, so they share the same fundamental problems of friction and inefficiency. Also, cars pollute at least as much as horses do, so the mention of "horse dung" is just a sophistic trick. You might argue that the car is "better" because the very specific issue of "horse dung" is avoided, but the more general problem of "pollution" remains, as the specific "horse dung" is replaced with other forms of the same problem "pollution".

Of course, I'm probably wasting my time by spelling out the problems with your approach. All of the arguments you have doubled down on by basically just repeating yourself and ignoring my refutations (and any other easily accessible information on them) are a series of data points suggesting that you don't actually care about the truth or falsehood of the arguments you are summoning and, for some reason, are primarily motivated by a desire to disagree, and not remotely motivated by any desire to seek out actual truths. — Jaded Scholar

I haven't seen any refutation from you yet, only false premises, and a refusal to accept the truth, through a veiled appeal to possible worlds as somehow more real that actual truth.

When I started writing this response, I was intending to liken your responses to that of a LLM like Chat GPT-4 - nominally referencing a rich variety of information sources, but demonstrating no contextual understanding of any of them - but after a more thorough read of your commentary, I'm quite confident of your humanity. LLMs haven't yet got the exact register we see in humans with nothing to say and a determination to say it as loudly as possible. — Jaded Scholar

Jesus Christ! Likening my work to GPT-4, or LLMs in general, that's the highest compliment you could give anyone. Then you even go one step further, in saying that I actually add a touch of humanity. Thank you very much Jaded Scholar, you live up to your name very well, and welcome to the ideology of skepticism. You are ready to roll.

But when you approach these problems, Zeno's paradoxes for example, and the irrationality of pi and the square root of 2, with the attitude that these problems have already been solved, you do not look at them as real problems — Metaphysician Undercover

Work-arounds were in existence 3,600 years ago and have improved over the eras since. And, yes, 2,600 years ago there was considerable dismay among the ancients. You have confirmed what is seen frequently here that when one turns philosophical on an issue one goes back in time to see what the Greeks had to say, and to join them across the ages in their despair.

I would think intuitionism might appeal to you. But even there the obvious imperfections are swept into a corner and allowed to exist.

Out of curiosity, are you an old guy like me, middle aged, or a "youngster"?

Just filling in space until JS reappears. :cool:

You have confirmed what is seen frequently here that when one turns philosophical on an issue one goes back in time to see what the Greeks had to say, and to join them across the ages in their despair. — jgill

We look back in time to see how the problems which exist today developed over time. And when we look back we see others who have looked back, and we learn from them. I would not call this an act of despair, but rather the propagation of hope. The denial, which appears more common, that the problems exist today, and the relationship between the past manifestations of the same problems, appears more like despair to me.

Out of curiosity, are you an old guy like me, middle aged, or a "youngster"? — jgill

I've seen you state your age, and I'm not that old, but I'm by no means a youngster.

Deleted

But when you approach these problems, Zeno's paradoxes for example, and the irrationality of pi and the square root of 2, with the attitude that these problems have already been solved, you do not look at them as real problems — Metaphysician Undercover

What makes these "problems" unsolved and real? :chin:

The principal problem expressed in Zeno's paradoxes, involves an issue with the way that we relate space and time, and this problem manifests today in the Fourier transform, as the uncertainty relation between time and frequency.*
The irrationality of pi and the square root of two indicates a problem with the way that we represent space with distinct dimensions. Modern physics demonstrates that these dimensions are not sufficient for a true and accurate understanding of spatial activity. So "string theory" for example proposes a number of extra dimensions, and "quantum gravity" may be viewed as an attempt to avoid dimensions altogether.
https://arxiv.org/pdf/1705.05417.pdf
*Added by edit: https://sepwww.stanford.edu/sep/prof/fgdp/c4/paper_html/node2.html

Thanks for the links. Particularly the one concerning a reduction of ST dimensions to two at quantum scales.( I continue to dabble in the complex plane where the world is two dimensional.) :cool:

I continue to dabble in the complex plane where the world is two dimensional — jgill

I don't know if you can accurately say that is "the world". Isn't it more like two distinct perpendicular worlds, the world of real numbers and the world of imaginary numbers?

I don't know if you can accurately say that is "the world". Isn't it more like two distinct perpendicular worlds, the world of real numbers and the world of imaginary numbers? — Metaphysician Undercover

It's a world in which a being embodies the characteristics of two genres, the rational and the imaginative. A bit like mankind.

"Two genres", I like that. The main criticism with this, or difference I would request, is that I would replace "rational" and "imaginative" with "true" and "fantasy".

Now, we have the "true world" on one plane of existence, one genre, and that consists of everything which is, and must necessarily be, as it what is real by the status or the true physical world. Therefore possible expressions concerning the true plane are restricted by the reality of the physical world. On the other plane of existence, the other genre, we have the fantasy world, and the only restrictions here are the mental capacities, of the human mind. So this plane consists of all the things we want and desire of the world, and in a very fundamental way it is free and unrestricted by that plane of truth and reality.

However, the two planes intersect, the two are orthogonal. Therefore, what we apprehend as the true plane of existence, all the realities of the physical world, must have a logical bearing on the imaginary, all the things we want and desire from the world, or what we want the world to be. And in this way the imaginary plane is truly restricted. I caution you though, be extremely wary because the relation is not defined as unidirectional, therefore it might just as well invert itself, and the imaginary world of all the things we want and desire, and how we want the world to be, might reflect back onto the perpendicular "true world" influencing the way that we apprehend and represent the "true world". Then the axioms for our understanding of that plane would become more representative of how we want things to be rather than how we actually perceive things to be.

Here is what I think is a very good way to look at these two planes. They are temporal in nature, the true world is the past, and this world imposes restrictions on the future world of possibilities, which is the imaginary plane. Notice that if we understand this relation as temporal, unidirectionality is enforced by our understanding of time. However, we cannot place this understanding of time on either of the two planes, because that would restrict it according to the axioms of that plane, disallowing its superiority and ability to order both planes relative to each other. Therefore we must put time as outside any planes, or such a spatial form of representation.

Here is what I think is a very good way to look at these two planes — Metaphysician Undercover

An entertaining and fanciful philosophical abstraction of a bit of mathematics. But we are looking at two lines, not planes. The real axis and the imaginary axis - producing the complex plane. :cool:

For me, this feeds in a little to the string theory concept. A string is posited either as linear, (open) (1D) (1 axis), at any moment in time, or a closed (loop) (2D) and vibrating, and it is the vibration that creates the other macro/extended dimension(s) of 3D space. The extra (tiny) dimensions, required in string theory are 'wrapped around' every coordinate in 3D space. Maths allows this in the way it is demonstrated in Computing (I think). In the vast majority of programming languages, you can declare an array data structure. A linear array might be just declared as Numbers[10], so a list of 10 storage locations, with an associated type, such as REAL. So, 10 empty boxes that you can store 10 real numbers in for the purpose of reading/writing/editing the 'real number' content at those 10 locations (normally contiguous locations). A 2D array could just be declared as Numbers[10][10] and 3D as Numbers{10][10][10].
So mathematically, you can create an nth dimensional array, and such an array would exist in reality, but cannot be geometrically displayed in 3D. Apart from in abstractions, such as the calabi-yau manifolds (I think). When you describe a mathematical axis such as 'imaginary,' etc. Is there any geometric consideration involved in such projections? If pushed, would a mathematician be willing to say something such as 'well you could think of the 'imaginary number line,' as in a sense, 'wrapped around' every coordinate in a standard 3D coordinate system, such as (x,y,z), or (x,y,z,t), t being time.
So a coordinate such as (w,x,y,z,t) would indicate that w is a 4th geometric dimension which is a 'tiny/micro extension, ''surrounding?' every (x,y,z,t) macro coordinate in our 3D existence?
Does this have any credence level with you or is my musing here, no more than pure speculation?

I thought this might also be of some use, as an aid to thinking about this:

"Dimensional disaster
In string theory, little loops of vibrating stringiness (in the theory, they are the fundamental object of reality) manifest as the different particles (electrons, quarks, neutrinos, etc.) and as the force-carriers of nature (photons, gluons, gravitons, etc.). The way they do this is through their vibrations. Each string is so tiny that it appears to us as nothing more than a point-like particle, but each string can vibrate with different modes, the same way you can get different notes out of a guitar string.

Each vibration mode is thought to relate to a different kind of particle. So all the strings vibrating one way look like electrons, all the strings vibrating another way look like photons, and so on. What we see as particle collisions are, in the string theory view, a bunch of strings merging together and splitting apart.

But for the math to work, there have to be more than four dimensions in our universe. This is because our usual space-time doesn't give the strings enough "room" to vibrate in all the ways they need to in order to fully express themselves as all the varieties of particles in the world. They're just too constrained.

In other words, the strings don't just wiggle, they wiggle hyperdimensionally.

Current versions of string theory require 10 dimensions total, while an even more hypothetical über-string theory known as M-theory requires 11. But when we look around the universe, we only ever see the usual three spatial dimensions plus the dimension of time. We're pretty sure that if the universe had more than four dimensions, we would've noticed by now.

How can the string theory's requirement for extra dimensions possibly be reconciled with our everyday experiences in the universe?

Curled up and compact
Thankfully, string theorists were able to point to a historical antecedent for this seemingly radical notion.

Back in 1919, shortly after Albert Einstein published his theory of general relativity, the mathematician and physicist Theodor Kaluza was playing around with the equations, just for fun. And he found something especially interesting when he added a fifth dimension to the equations — nothing happened. The equations of relativity don't really care about the number of dimensions; it's something you have to add in to make the theory applicable to our universe.

But then Kaluza added a special twist to that fifth dimension, making it wrap around itself in what he called the "cylinder condition." This requirement made something new pop out: Kaluza recovered the usual equations of general relativity in the usual four dimensions, plus a new equation that replicated the expressions of electromagnetism.

It looked like adding dimensions could potentially unify physics.

In retrospect, this was a bit of a red herring.

Still, a couple of decades later another physicist, Oskar Klein, tried to give Kaluza's idea an interpretation in terms of quantum mechanics. He found that if this fifth dimension existed and was responsible in some way for electromagnetism, that dimension had to be scrunched down, wrapping back around itself (just like in Kaluza’s original idea), but way smaller, down to a bare 10^-35 meters.

The many manifolds of string theory

If an extra dimension (or dimensions) is really that small, we wouldn't have noticed by now. It's so small that we couldn't possibly hope to directly probe it with our high-energy experiments. And if those dimensions are wrapped up on themselves, then every time you move around in four-dimensional space, you're really circumnavigating those extra dimensions billions upon billions of times.

And those are the dimensions where the strings of string theory live.

With further mathematical insight, it was found that the extra six spatial dimensions needed in string theory have to be wrapped up in a particular set of configurations, known as Calabi-Yau manifolds, after two prominent physicists. But there isn't one unique manifold that's allowed by string theory.

There's around 10^200,000.

It turns out that when you need six dimensions to curl up on themselves, and give them almost any possible way to do it, it … adds up.

That's a lot of different ways to wrap those extra dimensions in on themselves. And each possible configuration will affect the ways the strings inside them vibrate. Since the ways that strings vibrate determine how they behave up here in the macroscopic world, each choice of manifold leads to a distinct universe with its own set of physics.

So only one manifold can give rise to the world as we experience it. But which one?

Unfortunately, string theory can't give us an answer, at least not yet. The trouble is that string theory isn't done — we only have various approximation methods that we hope get close to the real thing, but right now we have no idea how right we are. So we have no mathematical technology for following the chain, from specific manifold to specific string vibration to the physics of the universe.

The response from string theorists is something called the Landscape, a multiverse of all possible universes predicted by the various manifolds, with our universe as just one point among many.

And that's where string theory sits today, somewhere on the Landscape."

But we are looking at two lines, not planes. — jgill

Yeah I know, but the imagery of the metaphor works better to talk about "planes of existence" rather than lines of existence. The representation of the real numbers as a line is just an analogy in the first place. The numbers have a corresponding value, and unless something provides real position to the number line, nothing justifies the assigned order. Placing the perpendicular line at zero, the origin, the Cartesian method, provides a grounding for order, negatives one side, positives the other. I believe that the imaginary part of a complex number produces the need for separate rules of ordination. This alters the relationship between the spatial representation (the line) and the numerical value assigned to the number, leaving the values without fixed location on the line.

At the end of my metaphor, it all gets reduced to the temporal dimension being outside any spatial concepts anyway. I believe that is the only true way to deal with the human urge demonstrated by mathematicians, to escape the boundaries of spatial constraints (and this need is demonstrated to be very real in the local/nonlocal problem of quantum physics), yet still maintain some sort of logical order. The order must be based in a temporal representation, which allows the spatial features to emerge. In this way, spatial order which appears to be illogical from our current representations can be provided for with the appropriate temporally based logic.

Unfortunately, string theory can't give us an answer, at least not yet. The trouble is that string theory isn't done — we only have various approximation methods that we hope get close to the real thing, but right now we have no idea how right we are. So we have no mathematical technology for following the chain, from specific manifold to specific string vibration to the physics of the universe. — universeness

Some physicists, like Smolin would say that string theory is done. It cannot give us an answer ever, because it has run into a dead end. The next foray is quantum loop gravity, but this appears to be headed toward a similar dead end.

So mathematically, you can create an nth dimensional array, and such an array would exist in reality, but cannot be geometrically displayed in 3D — universeness

Done all the time: n-dimensional vector spaces. I think the Hilbert space ( a special kind of vector space) in quantum mechanics may be infinite dimensional. Then some kind of linear operators are defined on it.

If pushed, would a mathematician be willing to say something such as 'well you could think of the 'imaginary number line,' as in a sense, 'wrapped around' every coordinate in a standard 3D coordinate system, such as (x,y,z), or (x,y,z,t), t being time — universeness

Sure. There are no limits to how bizarre math can become. This doesn't seem so outlandish.

Some physicists, like Smolin would say that string theory is done — Metaphysician Undercover

:up:

I just heard a pin drop. :yawn:

The wait for someone to point the way to the path of progress!

It seems professionals in science or math become uncomfortable in this environment. My own experience is my first thread about the diagonal paradox, to which there were some negative replies going beyond mere analytical comments to what seemed personal attacks. But, at least in those days science or math topics were not relocated to the Lounge.

At that time there were a couple of grad level math people here, but after a while they experienced the fatigue of constantly arguing with members who were minimally acquainted with the subject, but held strong views against accepted perspectives. When the competent are belittled by the unknowledgeable the former tend to move on to other conversational pastures.

I'm so old I don't really care. When MU pops up with his highly literate arguments about mathematics I indulge and appreciate his perspective if I can. But I also know that if I open my TPF mouth about QT I wander into unknown territory and my thoughts are trivial.

If those who wished to argue science were Gentlemen, like you my friend, or Ladies, some of those who left might have stayed. But this is all conjecture. And philosophy is all about argument.