Apologies for going AWOL for so long! Half of the reason is that I got Covid last week, and the other half is that I wanted to do sufficient research to reply to universeness before I posted anything. MU's comments are so ridiculous and irritating that it doesn't take particularly long to write a reply to each one, whereas each of @universeness 's comments take about a full day of research to reply to (with a sufficient level of confidence that I know what I'm talking about). And someone I respect a great deal has instilled in me the idea that "that which matters the most should not be at the mercy of that which matters the least", so I am trying to refrain from replying to dumb comments from trolls (and flooding the thread with that) until I first reply to comments from people interested in collaboratively expanding our knowledge.


Thank you for the validation that I wasn't wasting my time with MU! I don't want to derail a worthwhile conversation with swatting trolls, but I agree that it feels like part of that includes pointing things out like "no no, this guy is not Jean-Paul Sartre, he Deepak Chopra" for the sake of lurkers/newcomers.

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. — jgill

Thank you for that! And also for the warning, I suppose! :lol:

I admire the level of patience you have for fools, but at the same time, I am kind of glad that I will probably never attain it myself.


Pleased to make your acquaintance! Less pleased to share your experiences with MU, but I am certainly heartened to know that my experience is not anything new.


I'll get to you later.

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. — universeness

I agree 100%! When I joined this forum, I anticipated making many rants to this effect, but in short (*for now*), I want to express my feelings that this is absolutely the best thing we can do with our free time, and I think this is the main reason that "free time" has been made such a restricted commodity for most humans.

And I'd love to talk about the Fermi paradox sometime! Maybe one of us should start a whole new thread on it. :)

Thank you for sharing the line from that Carl Sagan directly! It's such a good one! Especially with delightful sarcasm of the original source, and Carl's commentary after it.

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!!!!!!!!! — universeness

Absolutely. A good friend of mine went through a bit of an existential crisis semi-recently about the cruelty of the universe, and the apparently always increasing cruelty of humans towards each other and everything else, and I was honoured to be able to help her through it with discussions of both this and of Hegel's cyclical theory of history. Even if we are mostly just making everything worse, that can still drive longer-term positive progress, and moreoever, it's not even possible to make progress at all when you're really brand new at something and have almost nothing to learn from except your mistakes.

I think I don't want to create a new profile here, but the next time I create a new username, I think will choose something different. I do like the virtues of being an eager, inquiring, or musing scholar, but on reflection, I might go with something like ForeverScholar. It's always been important to me to constantly update my understanding wherever possible (I like to say that at every point in my life, I could look back on myself ten years ago and cringe at how mistaken he was in some way, and if I ever stop doing that, it'll mean I've stopped growing). There is literally always more to learn (in both the expansion of knowledge and the correction of errors), and literally always more and deeper layers of internalised biases that we can uncover within our own thinking, and in doing so, see everything a little more clearly. Both of those are deeply important to me, and I've been reminded of that by the stark contrast in this thread between your thirst to expand your knowledge and MU's determination to avoid doing so.

But getting back to your other comment (I didn't mean to mush my replies to them together, but here we are):

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? — universeness

The short version is that both of these things are really just necessary for string theory to work (or rather, to not violate known, observable physical laws), and I don’t think there’s very much that’s particularly profound about them (unless we can prove they are true, of course).

Supersymmetry has a lot of implications, some of which I definitely am not familiar with (especially, as I mentioned, in the context of string theory), but at its core, I think it boils down to this: Supersymmetry is just the proposition that the quantum spin property of any quantum object/string shouldn’t be restricted (to be necessarily integer or half-integer) by any of the other properties of that object/string. Or: There’s no reason that, for every boson, a fermion with every other property otherwise identical to the boson can’t theoretically exist (and vice versa).

I’m sure you’ve learned some things about Spin, but it’s always been kind of hard for me to be certain I understand what it physically means (despite having used it in the majority of my research). It’s kind of like the rotational momentum of an object’s entire quantum field. However, I just learned that Spin is one of those rare things which is actually simpler to describe in string theory than standard quantum mechanics: it’s defined by the frequency of a string’s rotation around its one-dimensional axis. More on this when we get to tachyons again.

The compactified dimensions involve some much more complex maths (as those manifold images persuasively indicate!), but has always been a very simple idea, at its core. String theory needs more than 4 spacetime dimensions to work, but needs to reduce to 4-space at large scales because relativity would make gravity behave very differently to observed results otherwise. So you need to avoid letting any of those extra dimensions get too big (actually, another thing I just learned is that you don’t have to – but if you don’t, then you need to tweak basically everything else in the maths to make it work again https://en.wikipedia.org/wiki/Large_extra_dimensions). So you compactify those dimensions such that it’s not really possible for them to have any effect on the 4-space formulation of our physical laws. In our three spatial dimensions, you can always keep going and going in one of them, and this will take you farther from where you started. Maybe they’re not actually infinite lines – it’s possible that the edges of our universe join up, and that a random straight line will eventually lead back to where you started, but that doesn’t change anything on a local scale. However, what if some of our spatial dimensions span different scales, and if you changed the orientation of that trajectory by 90 degrees, you might only need to travel half the distance to cross the universe that way? It still makes no difference locally, but I like it as a stepping stone to imagining that there’s some other spatial dimension where, if you rotate another 90 degrees, to move into its plane, it only takes you two steps before you end up back where you started? What if it was so short a loop that it could be lapped even by the vibration of our molecules at room temperature? Or even smaller? No matter how far you travel in that dimension (i.e. how many times you lap around it), you’ll feel the exact same forces from the sun’s gravity, from a nearby magnet, or from any passing photon. It can be small enough so that it is negligible to everything in the universe except the mathematical degrees of freedom of a string’s vibrations.

The Calabi-Yau manifolds and their ilk admittedly involve some incredibly complex maths to add many of these compactified dimensions without changing strings’ behaviour in ways that we don’t want; because when you compactify several dimensions, that can cause strings to affect each other in different kinds of ways, depending on the particular compactifications. Calabi-Yau manifolds are a solution that cleverly balances those complications to return conditions on the behaviour of strings within them to be similar to that of regular 4-space.

Have you watched this lecture by Ed Witten? — universeness

I watched some of that Ed Witten lecture, and it does have some very good summaries of the maths that links many things I understand (or partially understand) to many things I don’t, but I feel like I’d need to find the lecture notes and/or a transcript (and even more spare time than I can possibly scrounge, haha) to help me skim past the stuff I want to and help me drill into the stuff I need to. Some of the things I simultaneously do and don’t miss about uni!

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.' — universeness

Yes and no. I mean, yes, you are, but there is some degree to which it is accurate to conflate them. If I understand it, both of these kinds of motion use the same dimensions, but the motion of the string is the change in where, in spacetime, the string is located, and the vibrational velocity is how fast the oscillations of the string itself are moving. For a silly (and hopefully clearer) example, if you stand up with your feet planted on the ground and wiggle your hips from side to side, your motion in spacetime (as defined by the position of your feet, at least) is zero, but you have a nonzero vibrational velocity. If you stop wiggling but take a jump to the left, then you have moved within spacetime, but have zero vibrational velocity.

I’m less confident on the “inter-dimensional” qualifier, but my guess is that it refers to either the velocity of the vibration between modes in different dimensions/directions, or (more likely) the total vector velocity of the vibration itself (and not the potentially smaller portion of velocity that you get from an inner product with any specific spatial dimension).

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 suggests to me that a string that 'vibrates' in multiple dimensions is 'excited' and would produce mass, is this not the case? — universeness

I think these two sentences are just genuinely confusing ones because of how much ground they shortcut to fit into two sentences. There is a lot of missing logic needed to link QM wave-particle duality to string waves necessarily representing "particles", or to link energy and mass in string theory.

As I understand it, yes, any vibrations in any dimensions should do this, but the cases where they do not are kind of at the crux of your other questions.

The place to start is in the definition of a ground state. The ground state of any quantum system is the lowest-energy state, which is necessarily a zero-mode wavefunction, but not necessarily a zero-energy state. In string theory, the string's vibrational modes are different to the modes of QM wavefunctions, but obey similar rules, I think - most relevant is that they are complex functions that can evaluate to complex numbers for the physical attributes they represent.

This means that the lowest-energy state has no vibrations (and yes, zero temperature) but can potentially have an energy level that is positive or even negative. The latter is what emerges in bosonic string theory, and in that context, negative-energy vibrational modes give rise to negative-squared (imaginary number) values for mass. I.e. tachyons.

The rest of the tachyon-related questions kind of follow on from here and are, I think, easier to answer without quotes, haha.

In every source I checked, the theory on this is kind of buried beneath a whole lot of maths that kind of obscures some of the basics. Two things I learned that helped me piece more together are:

1) String theory seems to have an inextricable relationship between the spin and mass of a particle, mostly in just needing the space of spin states to not be purely bosonic (integers) in order to have a stable ground state of mass/energy (which, more specifically, doesn’t result in a mass that is an imaginary number).
2) Tachyons are what you get when a quantum object has an imaginary mass. They are not a problem per se, since they don’t necessarily break causality despite being nonrelativistic, but they are a big problem if everything can decay into a tachyonic state – because an object with imaginary mass actually increases in speed as its energy decreases, and to slow it down to the speed of light (the bare maximum for creating most particles) would require an infinite amount of energy.

So yeah, clearly an absolutely rubbish ground state to emerge from your theory.

If your system can be specified with a meaningful number of strings in high-energy states, you can still get some reasonable results from it, but if every ground state can only be excited by giving it an infinite amount of energy, you're never going to be able to accurately model our actual universe, in which we see no obvious sinks of infinite free energy and no observations of tachyons at any of the countless particule creation and annihilation events we've ever observed.

I'm sure you still have questions about how the zero-mode state can somehow still have nonzero (if non-positive) vibrational states, and I preemptively admit that I am not sure. I think the answer lies in the need for the (complex-number) wavefunctions to sometimes resolve into non-Real expectation values for mass when their phase space is restricted to only integer spin values, which we know is not realistic. Kind of like how tunneling particles don't have any physical velocity while they are tunneling, but if you force their speed to resolve into a number, it comes out as an imaginary number too.

But that's just a guess, which I have not remotely fleshed out mathematically. I hope it makes you feel better to know that the maths involved in this is absolutely beyond my current capacity too.

Based on the things that allowed me to connect the most dots while writing this, I think that if I were to suggest a direction for you to research to better understand quantum theory and string theory is this: the simple harmonic oscillator. It is one of the most foundational concepts in Physics as a whole, but especially so in QM, and I think even moreso in String Theory. Like these theories themselves, the maths for it starts out very simple, but can get incredibly complex (even before you add 9 other dimensions to it).

P.S. I forgot to work it into my response, but I enjoyed the tunnelling and annihilation puns. :D

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. — jgill

Man, that's recent. I feel like speculating that it could be partly to do with separate departments wanting to not share the funding they received for(/from) their postgrads, or the required kinds of maths being more diverse than would be manageable with maths-only courses for each one, etc. but even with any mitigating factors like that, it seems like a very problematic approach. Or at the least, an approach that unnecessarily limits the potential to collaborate.

As I've said, I'm sure there are some ideological biases in maths and science that I haven't noticed, but I'm glad that the only thing I've ever experienced on this front is when physicists semi-jokingly check the room for mathematicians before writing (Δx)² ≈ 0 or sin(θ) ≈ θ for θ<<1.

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. — Metaphysician Undercover

I am happy to hear that. If we have no other common ground, then I'm glad we at least have this.

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. — Metaphysician Undercover

I may not (re-)respond to every one of your arguments, so I'm glad you started with this one. It's a perfect micrcosm of your position.

I actually have studied philosophy. And science. And maths. And I learned several things about these arguments from studying philosophy, but - and this may astound you - I actually learned much more about the history of maths and science from my studies in maths and science.

The whole point is that you think your arguments are not jibberish because you don't understand what you are talking about. You have learned *just* enough to reach the peak of Mt Stupid on the Dunning-Kruger graph, and it absolutely shows.

To repeat myself somwhat, the way in which you have turned sound criticism into jibberish is by applying it to a context where it doesn't make sense, and then pretending that you're the cleverest person in the room because you also don't understand any of the evidence that what you're saying is insanely stupid, and you don't want to.

Arguing with you is like arguing with someone who doesn't believe that the sky is blue. At a certain point, you can really boil the argument down to the "blue-sky" person asking the other to just go outside and LOOK. I asked you to provide a single example of one of these problems you claim are rife within mathematics, and you refused.

Maybe this was motivated by your indomitable and unsubstantiated confidence, but maybe you refused to do so because you actually know you can't.

So I guess I should speak to the contortion you pulled out to defend against that. My earlier quote had the preceding sentence "I think it is both safe and responsible to assume that one of the fundamental barriers to our full understanding of the universe is that mathematics itself may not yet be sophisticated enough. Whatever the gaps are, they are not what you described - if we could label them, we could have fixed them by now.", so I was clearly referring to actual gaps in the capabilities of mathematics. The scope of that conversation changed when you replied with "The problem is that no one wants to fix them.", and cited a historically inaccurate reference to irrational numbers, a misinterpretation of their nature as a problem with maths instead of mathematicians, and a ridiculous statement about circles that seems to be an attempt to apply one of Plato's arguments for the World of Forms as though it makes any sense here. You finish with "But you cannot say that these problems haven't been labeled."

Your reply was broad and unhinged and its scope referred to more than just problems with mathematics itself as I was speaking about. So I accepted the expanded scope, or rather, sought to levy my challenge to not only include the problems I was talking about but also include any kind of the problems you were talking about. When I said "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).", it's pretty clear that the word "such" referred to what you wrote, and was not a reply to what I wrote myself.

Moreover, despite your dishonest framing that I'm spontaneously "changing [my] tune to say that the ones which are labeled, "mathematicians want solved".", I'm directly addressing your statement that "The problem is that no one wants to fix them.", which - pro tip - you can tell I was doing because my challenge was a direct response to the paragraph where you said that.

Hopefully we can now agree on the words we both said, the order which they were said, and the meanings of those words (here, anyway).

So if you like, I'm happy to roll the premise back to that of my original statement - fundamental gaps in mathematics that prevent it from describing reality - or we can even kick it back down to easy mode for you and talk about problems that only apply to mathematics itself. And I challenge you to find any such problem (that is unsolved) where there is any evidence whatsoever to suggest that the global community of maths and science - in the year 2023 - does not want it solved. You claim that the field is rife with these problems. How hard can it be to find just one?

Just to be extra clear, I mean 2023 CE, not BCE.

If you do undertake this challenge, then I must warn you that it will almost certainly involve you (*gasp*) actually learning something. In which case, I am sorry for your loss, or whatever makes you so averse to that.

Ugh, speaking of which, if you do honestly try to meet my challenge (I expect you won't), then I do ask that you stop embarrassing yourself with that foolishness about irrational numbers (which were never a problem for maths, only for mathematicians) or Newton's law prohibiting infinte acceleration (F=ma, you absolute and utter muppet - I already showed you those, four characters, which is all that anyone needs to see to understand that. Except the genuinely mathematically illiterate, I guess. Case in point.).

Ideally, if you could find some kind of claim that I can't completely refute with more than a short sentence or a single equation, that would give me some hope for you. And no, my refutations still count as refutations even in the face of your standard strategy of making some idiotic claim and then putting your fingers in your ears and yell "LALALA, YOU CAN'T PROVE ME WRONG IF I'M NOT LISTENING."

But it's okay with me if that's a dealbreaker for you. Come to think of it, I'll probably be happier if I don't have to read any more of you talking about the "unsolved problem" of irrational numbers existing, which is not actually a problem - because the only real problem was in mathematicians not accepting their existence. And at the same time, you pretend that the acceptance of their existence is part of the problem. And if you had half a clue, you could easily pivot that to an ACTUAL problem that we have, like us having no real conception of the square root of -1, and all we have is the knowledge that it is absolutely necessary for accurate mathematical modelling of reality (for lack of a better word). But I guess that's the whole theme here - you are avoiding any interesting ideas for the sake of arguing about whether the sky is blue.

...

Anyway, I'm slightly compelled to try and quickly cover the rest of the stupid things you said.

Likening my work to GPT-4, or LLMs in general, that's the highest compliment you could give — Metaphysician Undercover

Haha, of course you think that. I've done a bit of work in the AI/ML field and it's common knowledge there that LLMs mimic human writing well but, by their very nature, understand nothing they say. This becomes apparent in anything they write beyond a simple recitation of facts they were shown - they combine concepts in a way that is driven by imitating human speech/writing, and not by conceptual logic, so virtually every single time they say anything remotely complex, they end up saying things that anyone who actually understands them can see are obviously wrong. Just like the things you say!



Anyway, it serves me right for trying to insult your dedication to not understanding anything in a way that assumes you understand something. But I'm glad that you're proud to be someone who basically got a C- on the Turing Test.

The problem was never solved... — Metaphysician Undercover

Yes, it was. I've explained it several times. The failure to understand is yours alone. You could probably understand it if you weren't trying so hard not to.

I see you have yet to produce a good response to this issue... — Metaphysician Undercover

Pretty sure I have. You could probably understand it if you weren't trying so hard not to.

I haven't seen any refutation from you yet... — Metaphysician Undercover

Yes, you have. You could probably understand them if you weren't trying so hard not to. Your refusal to open your eyes does not mean the light does not exist.

Are you aware of the history of the term "sophistic"? Why are you intent on portraying sophistry as "advanced", "accurate". — Metaphysician Undercover

Yes, I am aware. And that is not what I'm doing, as you can tell from the other words that I wrote after the ones you quoted. Both definitions are ascribed to the word today, regardless of the etymology of the word (which, tbh, I think you only guessed correctly because a broken clock is still right twice a day). I was simply trying to be fair to you in identifying one thing you misunderstood not because of your passion for misunderstanding things, but because of the multiple definitions of a word I used.

What the hell is a "truth-adjacent thing?" — Metaphysician Undercover

Something that was true when it was written, was true when you read it, was kind of true when you remembered it, and less so but still kind of true when you applied it, and then you made a conclusion that completely misinterpreted it. You know, like pretty much every argument you make.

Like taking a valid criticism of horse-drawn carriages (e.g. horse dung) and applying it to cars - you've taken a true thing, but removed it from a context where it is true, and by putting it into an invalid context, it is now untrue, even if the original idea was kind of true. I think "truth-adjacent" is a pretty descriptive label to give that (if a tiny bit too charitable, perhaps).

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? — Metaphysician Undercover

My poor metaphysician. True and False are useful concepts, and we can't help but use them, but they are indeed illusions. So yes, I think we should try to "sink ourselves into a world of probabilities, with nothing to ground what is actually the case", because that is the world we live in. That's not what I am actively doing here, but nonetheless, here's some advice that is exceedingly relevant to your misshapen worldview:
"I tore myself away from the safe comfort of certainties through my love for truth - and truth rewarded me."

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. — Metaphysician Undercover

This just makes it even sadder that you acknowledge that the foundations of mathematics are thousands of years old, and you still can't be bothered to actually learn anything about them. At this point, you're just throwing together relevant words and hoping your throw hits some rhetorical bullseye.

So yeah, do tell: explain "the glaring contradiction of discrete units within a continuity". What is the nature of this problem and what are its implications? Oh my goodness, what affront to mathematics are we engaging in every time we cut a pie into slices?

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". — Metaphysician Undercover

Ah, yes, you have clearly studied and understood philosophy better than me. How could I forget the proud tradition of philosophers never bothering to think about what might be, what could be, how might one live, what hidden systems might govern this world that we can identify by imagining what systems govern all possible worlds? A good philosopher - a REAL philosopher - only concerns themself with "self-evident" truths.

Some of the things that make you such a skilled troll would make you an absolutely atrocious philosopher. Just the worst ever. Unless you're one of those people who counts Ayn Rand as a philosopher. Then you'd probably be only the second worst.

Good luck with that endeavour, you can find me in The Lounge sipping some whisky, and from time to time some whiskey. — Metaphysician Undercover

You know, that actually explains a lot about a lot of the things you say.

You are jumping to conclusion. You approach with prejudice, a preconceive bias, that these problems have been "solved". — Metaphysician Undercover

Note that the specific problems I'm talking about are "problems that are now solved". Zero of these conclusions have been jumped to - they have all been methodically reasoned and calculated to - some of them over the course of many centuries. But yeah, it's possible that you are accidentally stumbling onto a slightly meaningful bias I have in assuming that problems that have been solved are problems that have been solved. But as the saying goes, "a fool may occasionally stumble onto a truth now and then by chance alone, but he will generally pick himself up and continue on", and true enough, this is what you have done. Where you stumbled onwards to is the clearly much more problematic position where you assume (quite explicity!) that every single problem that has ever arisen in the field of mathematics is completely unsolved, and every advancement or revolution in the field has been a communal act of self-delusion.

I'm upgrading my judgement of you from "almost anti-intellectual" to "deliberately anti-intellectual".

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". — Metaphysician Undercover

Hahaha, oh, I see! Horse dung is literally the exact same thing as carbon dioxide emissions, and I'm being sophistic and dishonest in claiming that not all criticisms of horse-drawn carriages apply equally to cars and vice versa. Whereas you are noting insightful truths when you say that the category of "solved mathematical problems" has zero overlap with the completely separate category of "solved mathematical problems", or when you claim that the word "sophisticated" means exactly the same thing as "sophistic", and nothing more, regardless of what those knaves who write our dictionaries will tell you.

As I have said: The things that make you such a skilled troll would make you an absolutely atrocious philosopher.

You pretend that distinctions with zero difference matter, and pretend that distinctions with a world of difference don't matter. You show no respect towards logic, and direct all of your attention towards rhetoric. I trust that you have studied enough philosophy to know the gravity of the insult when I say: you, sir, are nothing but a sophist.

Actually, you're worse. They, at least, sought to contort and abuse truth itself for the sake of making a living out of it. But you do it for free. Apparently just for the passion of saying nothing as loudly as possible, to stifle any possible transfer or generation of knowledge, to chase the feeling of being right about everything, caring nothing at all that the price of that is for you to actually be right about virtually nothing.

You care nothing for the subject nor substance of your arguments, you care only for the argument itself. You seem to have read a lot of things and you consciously decide - day after day - to employ that knowledge for only the most pointless goals you can find. I think you have a lot of intellectual potential and I am somewhat disgusted that you choose to waste it all on aimless vanity.

I'm living for this intellectual battle haha

I wish my brain as amazing as some of y'alls!!

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. — jgill

Thanks for your kind words and your willingness to share some of your mathematical insights with those who are not expert in the field, despite the exasperating responses you will inevitably receive from those who have their own (sometimes rather sinister) sometimes eccentric, agenda or those who are just pathological trolls and just get a buzz from trying to 'dis' an expert on their own field of expertise.

I think your points are well made and ring true, to me at least. I personally think that all philosophical musings and statements require scientific contribution, otherwise they face the 'pure woo woo,' or 'total speculation' accusation. If they don't welcome scientific input then, imo, this will always push philosophy and philosophers into a second class league of thinking and thinkers (this is of-course, perhaps from only my own notion of such 'leagues.') at least this puts philosophical musing ahead of a third class notional league of thinkers, which would include theists and theosophists, imo.
This leaves me open to accusations of 'scientism' or 'favouritism,' as I imply that those who prioritise scientific thinking and use of the scientific method, are 'first class thinkers.' I can only accept such criticism with agreement, and a large grin of personal contentment.

I am a member of some more science based sites and I enjoy the different emphasis from the membership of those sites compared to TPF, but those sites tend to not include the social. political (including realpolitik), humanist, religious and psychological aspects of the topic under discussion, that you get here on TPF. So experiencing as wide a range of responders to your own worldview, is I think very demanding but also potentially very valuable in trying to become a wiser person yourself.

I am personally grateful for the presence and contribution of subject specific expertise, such as yourself, (including of-course those who have academic expertise in the philosophy field) on TPF, as it tends to be a presence and contribution that effectively counters the more eccentric and woo woo peddlers, that are also here on TPF and would otherwise, turn this site into something akin to fox/fake news.

Apologies for going AWOL for so long! Half of the reason is that I got Covid last week, and the other half is that I wanted to do sufficient research to reply to universeness before I posted anything. — Jaded Scholar

Yay you're back! Sorry to hear you got that flipping Covid! I have had it twice myself. Fortunately, only after I had been jabbed, so I survived both and no long-covid. Thank you sooooooooo much for the time and effort you took to answer my questions as well as you did.
I need to take the time required to unpack your response and do my own further research before I respond with the depth necessary to be able to progress from the rally points you have set.
There are a lot of LED style (soft lighting) points that I can see, have illuminated some distant pathways in my head, based on the main points you laid out in your response. I will move towards them slowly and carefully and investigate. It will take a while but you have given me enough 'trigger points' for me to be hopefully directed correctly. My responses will trickle towards this thread, slowly but surely. I hope you will indulge them and enjoy them.

Here is my plan of action:

The short version is that both of these things are really just necessary for string theory to work (or rather, to not violate known, observable physical laws), and I don’t think there’s very much that’s particularly profound about them (unless we can prove they are true, of course). — Jaded Scholar

This affords me some conformation of how 'consequentialism,' plays such a large role in the scientific method. 'String theory/Superstring theory/Mtheory have an aesthetic beauty imo, that make many of us sooooo hope that them or such as them, are 'true.' So the 'what do we need to be true, for this idea to work,' becomes a motivation. This is not a criticism of science or scientists, but more a celebration of the robustness and honesty of the method applied. For string theory to be correct, this, and this, and this, etc are the consequentials that MUST follow, based on our current understanding of the workings and structure of the Universe. You have helped to make that fundamental 'scene' and 'big picture,' crystal clear, in my psyche. A good starting point imo.

Supersymmetry is just the proposition that the quantum spin property of any quantum object/string shouldn’t be restricted (to be necessarily integer or half-integer) by any of the other properties of that object/string. Or: There’s no reason that, for every boson, a fermion with every other property otherwise identical to the boson can’t theoretically exist (and vice versa). — Jaded Scholar

So I need to look a little more into the concept of the colloquially named 'spin,' or 'angular momentum,' and understand how that seems to govern the findings that
1. Fermions have antiparticles and bosons don't.
2. The Pauli exclusion principle only applies to fermions.
3. Supersymmetry is a fermion–boson symmetry, postulating that multiplets of fundamental particles contain both fermions and bosons. Thus, for example, since electrons exist there should also be “selectrons”
Understanding how 1,2 and 3 apply to string theory are key, I think. Would you agree?

I just learned that Spin is one of those rare things which is actually simpler to describe in string theory than standard quantum mechanics: it’s defined by the frequency of a string’s rotation around its one-dimensional axis. More on this when we get to tachyons again. — Jaded Scholar

I need to learn more about where my imagery is incorrect when I try to relate strings moving within spacetime and strings creating spacetime. A string as a 1D extension and as a closed loop. In my research so far I have came up against such as Weyl Symmetry and Conformal field theory, so I get quickly swamped, but its great fun, trying to process my understanding and your insights help me direct my efforts in the right directions.

The compactified dimensions involve some much more complex maths (as those manifold images persuasively indicate!), but has always been a very simple idea, at its core. String theory needs more than 4 spacetime dimensions to work, but needs to reduce to 4-space at large scales because relativity would make gravity behave very differently to observed results otherwise. — Jaded Scholar

Yes, the best image I have of that so far is 'wriggle room,' which I have tried to cognise as 'vibrating in three directions is not enough to make the workings and structure of this universe and cause every object that exists in it,' so a string has to vibrate in more than 3 physical dimensions. But I would probably need a maths skill level like that of @jgill to be able to start to understand, exactly why!

I don't like very long posts that folks have to scroll through too much so I will end this post here and break things up into smaller more manageable 'chunks.'

Continuing my 'plan of action:'

So you need to avoid letting any of those extra dimensions get too big (actually, another thing I just learned is that you don’t have to – but if you don’t, then you need to tweak basically everything else in the maths to make it work again https://en.wikipedia.org/wiki/Large_extra_dimensions). — Jaded Scholar

Interesting, and this reminds me of an aspect of Computing Science in the ADITDEM cyclical model for software development. The further back in the analysis, design, implementation, testing, documentation, evaluation, maintenance you find weakness or error, the more 'cascade effect' you will have to deal with. If the weakness or error is found to be at the analysis stage then the entire code may be seriously impacted.

it’s possible that the edges of our universe join up, and that a random straight line will eventually lead back to where you started, but that doesn’t change anything on a local scale. However, what if some of our spatial dimensions span different scales, and if you changed the orientation of that trajectory by 90 degrees, you might only need to travel half the distance to cross the universe that way? It still makes no difference locally, but I like it as a stepping stone to imagining that there’s some other spatial dimension where, if you rotate another 90 degrees, to move into its plane, it only takes you two steps before you end up back where you started? What if it was so short a loop that it could be lapped even by the vibration of our molecules at room temperature? Or even smaller? No matter how far you travel in that dimension (i.e. how many times you lap around it), you’ll feel the exact same forces from the sun’s gravity, from a nearby magnet, or from any passing photon. It can be small enough so that it is negligible to everything in the universe except the mathematical degrees of freedom of a string’s vibrations. — Jaded Scholar

Well, in sci-fi they certainly use such notions as subspace and hyperspace. I have often wondered how these are proposed, when it comes to extension? Sci-fi shows seem to suggest travel through subspace or hyperspace without any alteration to an objects 3D extensions. If when we move, we are actually traversing 10D space, then we can't get from A to B any faster than our current tech permits. So I can't currently imagine a tiny dimension that a 3D extended (macro) object can enter and traverse, and by doing so, travel (tachyon style) faster than light. Something smaller than the planck size can only exist within a black hole, is that not true? So this is another area I need to learn a lot more about.
I have great difficulty trying to imagine a tiny extra wrapped (compactified) dimension as a 'continuum of space.' I can understand using a coordinate to represent a point in that space but that's about it.

The Calabi-Yau manifolds and their ilk admittedly involve some incredibly complex maths to add many of these compactified dimensions without changing strings’ behaviour in ways that we don’t want; because when you compactify several dimensions, that can cause strings to affect each other in different kinds of ways, depending on the particular compactifications. Calabi-Yau manifolds are a solution that cleverly balances those complications to return conditions on the behaviour of strings within them to be similar to that of regular 4-space. — Jaded Scholar

Yeah but is the main problem not that there are ${10^{200,000}}$ possible configurations and we don't know which one is our universe?

Yes and no. I mean, yes, you are, but there is some degree to which it is accurate to conflate them. If I understand it, both of these kinds of motion use the same dimensions, but the motion of the string is the change in where, in spacetime, the string is located, and the vibrational velocity is how fast the oscillations of the string itself are moving. For a silly (and hopefully clearer) example, if you stand up with your feet planted on the ground and wiggle your hips from side to side, your motion in spacetime (as defined by the position of your feet, at least) is zero, but you have a nonzero vibrational velocity. If you stop wiggling but take a jump to the left, then you have moved within spacetime, but have zero vibrational velocity. — Jaded Scholar

That's a very interesting comparison. Are you posing a 1D open string state that may be 'anchored' at one or both ends, but vibrating along its extension, and a 1D open string state that is a 'free' moving object but is not vibrating?

I have had a different imagery of strings. I imagine a spacetime of continuous tiny guitar strings, that have no 'rest state' other than a potential one (the heat death of the universe via entropy).
If you observe a human 'Mexican wave' the waveform is created via each human involved, just standing up and sitting back down again. It's the undulations of the 'point particle' or 'individual humans acting like an aspect of a string,' that causes the waveform. In a similar way, strings vibrate and cause waveforms or field excitations etc. I imagine that an object can move in this underlying structure by being passed from human to human along the wave form. Now I struggle a lot more when I have to appreciate that the moving object being passed along the string vibrations is itself made of string vibrations, so I know my imagery is wrong, so I need to learn a lot more about possible 'string states.' But are you suggesting that a non-vibrating string state is a valid possibility within string theory?
Would that not mean that there is something in the universe that does not move, relative to anything?

The place to start is in the definition of a ground state. The ground state of any quantum system is the lowest-energy state, which is necessarily a zero-mode wavefunction, but not necessarily a zero-energy state. In string theory, the string's vibrational modes are different to the modes of QM wavefunctions, but obey similar rules, I think - most relevant is that they are complex functions that can evaluate to complex numbers for the physical attributes they represent.
This means that the lowest-energy state has no vibrations (and yes, zero temperature) but can potentially have an energy level that is positive or even negative. The latter is what emerges in bosonic string theory, and in that context, negative-energy vibrational modes give rise to negative-squared (imaginary number) values for mass. I.e. tachyons. — Jaded Scholar

I bolded the words that impact my current understanding the most.
As you suggest, a lowest-energy state is not a zero energy state, so my question then becomes (or perhaps what I need to research more is) is there an example in physics of an energy state that involves an object being completely at rest relative to every other object in the universe, including an 'expanding' spacetime? I know such as this:
"Some might think that at absolute zero particles lose all energy and stop moving. This is not correct. In quantum physics there is something called zero point energy, which means that even after all the energy from particles has been removed, the particles still have some energy."
but I don't currently really understand it, other than assuming that the remaining energy being referred to is a potential energy, that exists because something is present rather than 'nothing' (whatever that label refers to within any notion of 'real.') I need to learn a lot more about a posited string state that is not vibrating and is not moving in any way.

In every source I checked, the theory on this is kind of buried beneath a whole lot of maths that kind of obscures some of the basics. Two things I learned that helped me piece more together are:

1) String theory seems to have an inextricable relationship between the spin and mass of a particle, mostly in just needing the space of spin states to not be purely bosonic (integers) in order to have a stable ground state of mass/energy (which, more specifically, doesn’t result in a mass that is an imaginary number).
2) Tachyons are what you get when a quantum object has an imaginary mass. They are not a problem per se, since they don’t necessarily break causality despite being nonrelativistic, but they are a big problem if everything can decay into a tachyonic state – because an object with imaginary mass actually increases in speed as its energy decreases, and to slow it down to the speed of light (the bare maximum for creating most particles) would require an infinite amount of energy.

So yeah, clearly an absolutely rubbish ground state to emerge from your theory. — Jaded Scholar

Yeah, it's never a good sign when any kind of infinity shows up in a theory.

If your system can be specified with a meaningful number of strings in high-energy states, you can still get some reasonable results from it, but if every ground state can only be excited by giving it an infinite amount of energy, you're never going to be able to accurately model our actual universe, in which we see no obvious sinks of infinite free energy and no observations of tachyons at any of the countless particule creation and annihilation events we've ever observed.

I'm sure you still have questions about how the zero-mode state can somehow still have nonzero (if non-positive) vibrational states, and I preemptively admit that I am not sure. I think the answer lies in the need for the (complex-number) wavefunctions to sometimes resolve into non-Real expectation values for mass when their phase space is restricted to only integer spin values, which we know is not realistic. Kind of like how tunneling particles don't have any physical velocity while they are tunneling, but if you force their speed to resolve into a number, it comes out as an imaginary number too.

But that's just a guess, which I have not remotely fleshed out mathematically. I hope it makes you feel better to know that the maths involved in this is absolutely beyond my current capacity too. — Jaded Scholar

It's comforting that you can so easily and correctly predict where your comments will send my thinking, as it reassures me that there is no surprise amongst the experts when lay folks like myself stumble so easily on this stuff. I also hope that you realise that the time and effort you have spent in trying to explain some of the fundamental ideas involved here are very much appreciated by many lay folks who are very interested in truth seeking.

Based on the things that allowed me to connect the most dots while writing this, I think that if I were to suggest a direction for you to research to better understand quantum theory and string theory is this: the simple harmonic oscillator. It is one of the most foundational concepts in Physics as a whole, but especially so in QM, and I think even moreso in String Theory. Like these theories themselves, the maths for it starts out very simple, but can get incredibly complex (even before you add 9 other dimensions to it). — Jaded Scholar

Oh absafragginlootly! I have encountered the 'harmonic oscillator,' so many times in my general research into this stuff. I have watched this a few times. It's a very good beginning imo.

P.S. I forgot to work it into my response, but I enjoyed the tunnelling and annihilation puns. :D — Jaded Scholar

it's important to always leave room for a wee giggle or two! otherwise we might become too prone to despair when dealing with the sophistry that can seem so ossified and so deep rooted in the place of mind where folks like MU decide to anchor and vibrate from.

I think I don't want to create a new profile here, but the next time I create a new username, I think will choose something different. I do like the virtues of being an eager, inquiring, or musing scholar, but on reflection, I might go with something like ForeverScholar. It's always been important to me to constantly update my understanding wherever possible (I like to say that at every point in my life, I could look back on myself ten years ago and cringe at how mistaken he was in some way, and if I ever stop doing that, it'll mean I've stopped growing). There is literally always more to learn (in both the expansion of knowledge and the correction of errors), and literally always more and deeper layers of internalised biases that we can uncover within our own thinking, and in doing so, see everything a little more clearly. Both of those are deeply important to me, and I've been reminded of that by the stark contrast in this thread between your thirst to expand your knowledge and MU's determination to avoid doing so. — Jaded Scholar

Seem's to me that you also have a good plan of action!
Thanks again for all the help you have offered so far! :clap: :clap: :clap: :clap: :flower:

I'm glad that the only thing I've ever experienced on this front is when physicists semi-jokingly check the room for mathematicians before writing (Δx)² ≈ 0 or sin(θ) ≈ θ for θ<<1. — Jaded Scholar

Hey, I use that. The wiggle makes it true. :smile:

Your discussion with Uni is the best thing I have seen on this site.

turn this site into something akin to fox/fake news — universeness

Hey, I love Bret Baier ! :cool:

Just off the top of your head, can you think of instances where complex functions are composed? I appreciate your comments about string theory and spin in that subject, in particular. I'm looking into compositions of contours in C and I have wondered about compositions of strings.

Ugh, speaking of which, if you do honestly try to meet my challenge (I expect you won't), then I do ask that you stop embarrassing yourself with that foolishness about irrational numbers (which were never a problem for maths, only for mathematicians) or Newton's law prohibiting infinte acceleration (F=ma, you absolute and utter muppet - I already showed you those, four characters, which is all that anyone needs to see to understand that. Except the genuinely mathematically illiterate, I guess. Case in point.). — Jaded Scholar

I will happily fulfill your expectations. Your separation of maths from the mathematicians who practise the art, is a premise I cannot accept. Furthermore, ad hominem doesn't interest me, and that seems to be all you have to offer me.
See ya, wouldn't want to be ya.

Huh. You surprise me. I'll resist arguing with anything you just said, and will instead follow your example. :up:

Hey, I use that. The wiggle makes it true. :smile: — jgill

:lol: I love that. I forgot to mention that physicists don't just use that, but sometimes use it in proofs (non-foundational ones, but still). But now that I've gotten a mathematician's blessing, you can't take it back. :joke:

Your discussion with Uni is the best thing I have seen on this site. — jgill

Thank you kindly! It's certainly the most that my physics knowledge has been challenged in a while!

Hey, I love Bret Baier ! :cool: — jgill

I just learned who that is and I hope this is fake news. :joke:

Just off the top of your head, can you think of instances where complex functions are composed? I appreciate your comments about string theory and spin in that subject, in particular. I'm looking into compositions of contours in C and I have wondered about compositions of strings. — jgill

I have to admit that I'm not exactly sure what you mean. Do you mean practical applications outside of theoretical maths/physics? I know they are used in quantum computation and other programming for QM research, but the only non-research application I can think of outside of that is in devices used for troubleshooting electronic circuits - I am not certain, but I think some of those need to use complex functions to model electronic circuits. Let me know if I'm way off base in terms of what you're actually asking. I think you mentioned something close to this earlier that I also sidestepped because I wasn't sure exactly what you meant.

And you probably are, but I wanted to ask if you were aware of Matlab? It's a program/programming language that is basically C, but combined with some Java to build higher-level functionality that makes it way better for programming with matrices, tensors, and other multidimensional features (the name is short for "Matrix Laboratory"). It's what I used in my PhD and gave me my jumping off point into C and other more conventional programming languages.

Sorry to hear you got that flipping Covid! I have had it twice myself. Fortunately, only after I had been jabbed, so I survived both and no long-covid. Thank you sooooooooo much for the time and effort you took to answer my questions as well as you did.
I need to take the time required to unpack your response and do my own further research before I respond with the depth necessary to be able to progress from the rally points you have set. — universeness

Thanks - this is also my second time. I got it the first time juuust before I was due for my booster needle, so at least it was much less intense this time around.

And you're very welcome! Apologies if I take a lot longer to reply fully, but I'm happy that what I've said makes sense and has given you some good directions for research! :)

I'll reply to everything I can in full, but for now, I had two things that I wrote as soon as I read your comments, and wanted to finish now instead of later:

It's comforting that you can so easily and correctly predict where your comments will send my thinking, as it reassures me that there is no surprise amongst the experts when lay folks like myself stumble so easily on this stuff. — universeness

The accuracy of my prediction is not at all because you're a layperson - it's because I noticed your tendency to zero in on the gaps in the logic. You're the sort of person who, for example, reads something like my comment in the Thought Experiments thread where I said something like "This is how the framework of QFT consistently works with special relativity (with one weird potential edge case called the Reeh–Schlieder theorem, which is so mathematically complex that I don't understand it and can't explain it myself), and this is what that means for the question you have raised." and your immediate reaction is "NEVER MIND THAT - I MUST LEARN MORE OF THE REEH–SCHLIEDER THEOREM.". :lol:

Yeah but is the main problem not that there are 10^200,000 possible configurations and we don't know which one is our universe? — universeness

I feel the need to mention again that I am nowhere near an expert on string theory, because I started my reply to this with "I don't think so", then changed it to "yes and no", and basically I think all I can say is that I think I have several fragments of the answer :lol:. Firstly, I'm pretty sure that there's nothing that strictly says that those dimensions need to compactify in the same way in every part of our universe, aside from the consistency of our physical laws strongly indicating that it would need to (to reproduce those laws*). On that note, I'm also pretty sure that the vast, vast majority of those possible configurations lead to string behaviour that doesn't reproduce our kind of universe. That's the real benefit of Calabi-Yau manifolds: they're one of the only variants we have discovered that definitely aren't garbage.

*I want to take a minute to devolve into wild speculation. If I'm right (which I may not be - I need to research that) about it being possible for different compactifications to exist in different parts of the same universe, then that would lead to a lot of potential universes where the physical laws are different in different regions. A perfectly stable hydrogen atom in one region may decay into a puff of light or a micro black hole if it wanders into a region with vastly different, say, scale factors of the four fundamental forces. So a consistent compactification of our spacetime might exist by virtue of the anthropic principle - we could only possibly exist in one of the more stable possibilities. But ... what if our universe is dotted with regions where "normal" matter is mostly unaffected, but things like sfermions rapidly decay or something? That might be a potential answer to the how those particles can be functionally absent from our universe without necessarily breaking supersymmetry? I'm sure that doesn't make it any easier to test or anything, but it could be interesting if it were possible.

If I ever meet a real string theorist, I might ask them whether that idea is horribly misguided or not. :)

Hey, I love Bret Baier ! :cool: — jgill

I just learned who that is and I hope this is fake news. :joke: — Jaded Scholar

My wife and I usually vote moderate conservative these days, and we both enjoy the evening news with Bret. A tilt to the right, but maybe less than CNN's tilt to the left. The Fox commentators is another matter. Hannity and his ilk are way off my radar.

It's a program/programming language that is basically C, but combined with some Java to build higher-l — Jaded Scholar

I meant the complex plane, C. Not a programming language. And I'm actually talking about

${{F}_{n}}(z)=\underset{k=1}{\overset{n}{\mathop{\Re }}}\,{{f}_{k}}(z)={{f}_{1}}\circ {{f}_{2}}\circ \cdots \circ {{f}_{n}}(z)$ , $F(z)=\underset{n\to \infty }{\mathop{\lim }}\,{{F}_{n}}(z)$

And going the other way, as well, in physics (mathematical) research? A contour in C looks like $z(t)=u(t)+iv(t)$ , t = time.

Ah, I see. I don't live in the US, so my superficial impression of Fox is shaped by 1) the overt bias in the Murdoch-owned outlets in my country and 2) the people on the internet who make "Fox News" a core part of their personality. So I will definitely offer you the benefit of the doubt.

I meant the complex plane, C. Not a programming language — jgill

Oh my goodness, I am deeply embarrassed. In my defence, I've never really spoken about the complex plane outside of tex-enabled (or whiteboard-enabled) environments, so I honestly have never represented it or seen it represented as anything except:

Also, I only just learned that this environment is tex-enabled too, so that's nice. Can I ask how you did that? I can't seem to figure it out.

To answer the actual question, it's hard to summon up specific examples, but I think I have seen countless compositions that fit this general form. It's been a while since I've done any serious maths, so apologies if what I can recall is a bit trivial to you or doesn't exactly hit the mark, but my QM maths virtually always involved converting operators (which were not always, but almost always complex functions) into their Taylor series or some other infinite composition. There were other infinite-series transformations that were very handy, but Taylor series were especially useful because, for well-defined operators, each term usually meant something almost physical (like the separation of an object's energy into different kinds of energy relating to their rest mass, their kinetic energy, their kinetic potential energy - apologies for the fuzziness of that example too - and separately dictated their evolutions). The cases where the expansion actually made use of every term up to n=∞ generally didn't have that property, but those were rare and (frustratingly) interesting too. Since QM is not so much a self-consistent theory, but a huge bag of complex tricks, almost every time you want to get something useful out of it, you end up hitting a wall of impossible complexity that you can best get out of by applying some expansion or transformation - the Bogoliubov transformation is another one that comes to mind from how often I made use of it, and it also involved decomposing your operators into an infinite series (usually infinite, anyway) of operators defined in a different reference frame that hopefully simplifies the actual problem.

If this is closer to what you mean (and not entirely trivial), I'll dig up my old research work to look for some more specific functions for you.

The first thing that actually came to mind was an incredibly interesting paper I once read about trying to define quantum operators in an infinite-dimensional version of the complex plane involving not just the square root of -1 but all (integer) roots from -1 to -∞, but alas, I cannot find that right now.

Your separation of maths from the mathematicians who practise the art, is a premise I cannot accept. Furthermore, ad hominem doesn't interest me, and that seems to be all you have to offer me. — Metaphysician Undercover

You complain about getting compared to a muppet and then you insult all mathematicians by calling their science an art. Stealth insults are still insults. You continue to focus on complaining about what science still does not know for sure, and you then assume that this gives you legitimacy, when you offer your own very weak claims and pure speculations about what you claim must be true. You will only ever gain followers who are easily fooled but that will only ever be some of the people, some or all of the time. You have no solutions, and you offer no methodology that is even part of the solutions our species need. You remain part of the problem as you are ossified in your anti-science stance. That is a very unfortunate legacy to burden the more easily mislead members of the next generation with, imo.

*I want to take a minute to devolve into wild speculation. If I'm right (which I may not be - I need to research that) about it being possible for different compactifications to exist in different parts of the same universe, then that would lead to a lot of potential universes where the physical laws are different in different regions. A perfectly stable hydrogen atom in one region may decay into a puff of light or a micro black hole if it wanders into a region with vastly different, say, scale factors of the four fundamental forces. So a consistent compactification of our spacetime might exist by virtue of the anthropic principle - we could only possibly exist in one of the more stable possibilities. But ... what if our universe is dotted with regions where "normal" matter is mostly unaffected, but things like sfermions rapidly decay or something? That might be a potential answer to the how those particles can be functionally absent from our universe without necessarily breaking supersymmetry? I'm sure that doesn't make it any easier to test or anything, but it could be interesting if it were possible. — Jaded Scholar

An interesting idea but would such not mean that the cosmological principle was not true a.k.a a homogenous and isotropic universe would be untrue? That would have very big consequentials, would it not? Such as every constant might be not be a constant within certain regions of space, such as light speed or even the expansion rate and the temperature of the cosmic background radiation?
Is the idea of different laws of physics applying to different regions not part of the basis of the many world theory and the 'bubble' universe as a label for 'conceptually' different universes in a multi-verse or different 'regions' in an alternate use of a label such as 'Cosmos?'

BTW, I plan to spend some of my free time researching under the keywords of 'string/superstring states.' I hope that will gain me some more insight and prompt questions. I often try to email questions to folks who offer their help on sites such as 'ask an astrophysicist' or 'ask a mathematician,' etc. I have had some very useful responses in the past. I have not came across an 'ask a string theorist,' site yet. I have also tried to directly email folks like Ed Witten, Brian Greene and other known popular scientists such as Sean Carroll, Lee Smolin etc. Sean has his monthly 'ask me anything podcasts,' such as the most recent one below, but I have not tried to use that avenue yet. These are over 3 hours long, so good to fall asleep to at night, when the TV is so crap! :blush:

My wife and I usually vote moderate conservative these days, — jgill

:scream: :lol:
I am a leftie democratic socialist Mr Gill, I hope that does not lower your opinion of me too much.

You complain about getting compared to a muppet and then you insult all mathematicians by calling their science an art. Stealth insults are still insults. — universeness

I complained about JS's use of ad hominem, which is abundant throughout the post, everywhere. The muppet comment I could not even grasp so it has no bearing.

Mathematics is commonly classified by philosophers as a form of art. There is no insult here, just a statement of truth.

You continue to focus on complaining about what science still does not know for sure, and you then assume that this gives you legitimacy, when you offer your own very weak claims and pure speculations about what you claim must be true. You will only ever gain followers who are easily fooled but that will only ever be some of the people, some or all of the time. You have no solutions, and you offer no methodology that is even part of the solutions our species need. You remain part of the problem as you are ossified in your anti-science stance. That is a very unfortunate legacy to burden the more easily mislead members of the next generation with, imo. — universeness

Jaded Scholar is an odd sort, first engaging me with

...I think everything you said is generally on the right track.. — Jaded Scholar

Then,

I've given myself permission to be quite rude — Jaded Scholar

and

What you are saying is a collection of truth-adjacent things — Jaded Scholar

And when I pointed out that Jaded Scholar's tune was changed as we proceeded, this seemed to cause some sort of ill-temper. Now Jaded Scholar has become completely "unhinged", a word directed at me above. There is an extensive post as a reply to me, with nothing of substance, merely one insult after the other. There is nothing there for me to reply to without stooping to the JS's schoolyard level. It would be like "you're an asshole", "no I'm not". What's the point? I mean this is the lounge, but it's just not my type of entertainment.

I am not suggesting or recommending that you engage in tit for tat ad hominems, as fun as I personally find that at times on TPF, depending who I am dealing with. I was merely pointing out that in general, I do not find you a good interlocutor or an impressive thinker. I fully accept that you feel the same way about me and perhaps some other members of TPF, would agree with me or with you. So there it is, and on the universe goes, regardless of our little disputes. As far as I am concerned, I will continue to read what you type, when perusing threads and I will consider what you type, and respond if I feel it's important to do so, based on my own worldviews. For me, that's just 'my usual approach,' for discussion forums. So, you are not a good interlocutor imo, and I think your approach and the worldviews you offer, in what I have read from you so far, exacerbate the problematic rather than aid the solutions I think our species need. I expect your response to be 'I don't give a f*** what your opinion is of me,' and I feel the same way, so, we all move on. Who knows MU, there have been many occasions when a person on a forum quickly becomes a perceived enemy, then due to some identification of some unexpected common ground, they become more like a frenemy and then on occasion, almost a friend, and then on another occasion, right back to a full enemy and then sometimes such folks even get married and have children or the very same people might choose to kill each other in a field of battle, a terrorist act, or in a marital home. Individual human psyche is rarely boring when you drill down deep enough.

I am a leftie democratic socialist Mr Gill, I hope that does not lower your opinion of me too much. — universeness

Wife & I are still registered Democrats. You might be surprised at where we would agree on politics. For example, I have always felt there should be free education all the way to professional degrees and PhDs, and there should be free health care for all. I firmly support Medicare and Social Security, along with defined benefit retirement plans. The USAF made me a meteorologist at the U of Chicago, free of charge and fully financially supported, then, later, the GI Bill helped with my terminal degree. :cool:

But our country's immigration catastrophe and a few other issues, like overly liberal law and order policies, pull us to the moderate right at times.

OK. So much for all that. My opinion of you is very, very high, Buddy ! :smile:

I have always felt there should be free education all the way to professional degrees and PhDs, and there should be free health care for all. I firmly support Medicare and Social Security, along with defined benefit retirement plans. — jgill

That's some good and wide common ground we are on sir! I would be proud to stand firm beside you in any fight on any of those issues.

My opinion of you is very, very high, Buddy ! — jgill

Well, I can only hope I never let you down. Thanks for the boost, we all need a little of that sometimes.
I have valued every exchange we have had so far and I really enjoy reading your posts.

Mathematics is commonly classified by philosophers as a form of art — Metaphysician Undercover

You and I have our differences, but here I am more or less in agreement. Mathematics is a practice, a device used by the sciences, etc., but mathematicians would largely agree it is a kind of art, requiring imaginative progress - the canvas upon which I apply my mental brush is the complex plane.

As for failure in mathematics, le mieux est l'ennemi du bien.

Also, I only just learned that this environment is tex-enabled too, so that's nice. Can I ask how you did that? I can't seem to figure it out. — Jaded Scholar

I use MathType, what you see is what you get. Then copy and paste to this forum, changing "<" to "[" and so on. But there is a tutorial here on MathJax I think. Enter the word in the search box.

Thank you for your comments about the use of series in physics. A power series is one kind of infinite composition of complex functions. I got started in the subject with another, continued fractions. Then there are infinite product expansions. Finally, examples I came up with after a colleague pointed the direction, elementary functions

The Bogoliubov transformation is a new one for me. Not quite sure how to decipher it in Wikipedia. Some symbols probably physics related.

When I got my degree fifty years ago, a professor told us that we would never know as much math as we did then. He was correct. As the years flow by we mathematicians get more and more entrenched in our specialty, and don't get off that path very much, allowing progress in math to surge past us. At my age I'm lucky to remember elementary topology or group theory. :worry:

The issue here is not the relationship between you and I, rather it is an issue of how Jaded Scholar and I both relate to some current problems of physics, in specific, the zero point in time. Let me paraphrase our discussion like this.
JS: The zero point in time, i.e. the point at the beginning of time, is a problem for physicists.
MU: Not only is the supposed zero point at the beginning of time problematic, but in any measurement of motion there is an assumed zero point which starts the measured duration, and this is also problematic, as described in Zeno's paradoxes.
JS: There is no current problem with this, because mathematicians have solved that problem.
MU: Mathematicians have only produced a sufficient workaround for the problem, and the same problem has reemerged as the time/frequency uncertainty relation of the Fourier transform.
JS: The time/frequency uncertainty relation is no different from any other uncertainty relation of conjugate variables.
MU: The time/frequency uncertainty relation is the basic uncertainty of the Fourier transform, from which the others are derived.
JS: Ad hominem galore.

Man, I was happy to leave "well enough" alone, but you drag me back in.

I had to rewrite how I first drafted this response, because you have actually produced a pretty accurate summary of these particular talking points. The beef I have is the same re-heated beef that I have been talking about in more and more detail.

The claims you are making about the mathematical implications of Zeno's paradox and the Fourier transform are ridiculous and inaccurate, and it is frustrating that you seemingly refuse to even try to understand why I keep saying this - you just keep saying some version of "I have skimmed what you wrote, I don't understand it, and I don't intend to, but the implication is that you disagree with me, so the only conclusion I'm willing to accept is that you're wrong.".

To more specifically address Zeno's paradox/es: The mathematical implications of these questions were not solved by adding some extra features, but in the exact opposite of what you claim. These problem(s) emerged from Zeno's problematic and ideologically-motivated additions to the axioms of conventional mathematics (around his opinion that we should actively avoid every treating "the many" and "the one" in similar ways, mathematically - he was specifically trying to attack the mathematical operations of multiplication and division for ideological reasons, not academic reasons). And these problems were solved by removing his deliberately problematic axioms. And this was highlighted not just in modernity, but by Zeno's contemporaries too!

This is not to say that his paradox(es) are not still interesting metaphysical questions - they definitely are. And mathematicians still play around with new solutions for them every few decades. But in terms of the actual mathematical "problem": all versions of Zeno's paradox are rooted in the assumption that when you divide a finite number by infinity, each division is also a finite number, not an infinitessimal one, which arose from Zeno's preferred mathematical axioms. It's very clearly solved by abandoning his restrictions on what kind of infinities you can use, and then seeing that when you divide a finite number by infinity, you get an infinite number of infinitessimal numbers, not an infinite number of finite numbers, i.e. x*∞/∞ = x, not x*∞/∞ = ∞.

The INTERESTING part is whether or not there is a mathematical interpretation that literally describes reality, because that question applies to the entirety of mathematics itself, which I have repeatedly said, and you seem to have no interest in. But there is literally no problem with describing the observable dynamics of the situations you are talking about.

MU: Mathematicians have only produced a sufficient workaround for the problem, and the same problem has reemerged as the time/frequency uncertainty relation of the Fourier transform. — Metaphysician Undercover

Good grief, if you are so married to this insane idea, then please, please dig up some tiny shred of logic that actually connects these ideas instead of just baselessly asserting that they are somehow related, and straight-up ignoring every single piece of evidence for why you are wrong.

JS: The time/frequency uncertainty relation is no different from any other uncertainty relation of conjugate variables.
MU: The time/frequency uncertainty relation is the basic uncertainty of the Fourier transform, from which the others are derived. — Metaphysician Undercover

See above. It's one of the earliest integral transforms to be derived, but it's completely ridiculous to claim that the attributes of the general case are derived from the attributes of one narrow specific case, and not vice versa. It's like you've found some unintuitive issue in a grey car, and the manufacturer tells you "yeah, sorry, the exact same issue exists in all of our cars", and your reply is to say "I see! You have somehow taken this uniquely grey-car issue and spread it to all of the other colours of cars!". Even if the first car their assembly line produced was a grey one, you're still being obtuse and ridiculous.

JS: Ad hominem galore. — Metaphysician Undercover

Is it really an "ad hominem" attack when literally all I know about you and all I am referencing are the actual arguments you are making? Sure, it's kind of rude to say "You keep saying dumb things, and responding to arguments that those claims are dumb by simply ignoring those arguments and reiterating the exact same dumb things, so maybe you're kind of dumb?"*, but it's not like I started out by saying "only an idiot would say this". We really worked up to it by me providing clear refutations and directions for you to investigate which of us was really accurate or not, and after you responded to multiple arguments for, like, the third time each by just ignoring any additional information and saying "I see you disagree with me, which means that you are wrong", then I think it's not unreasonable to posit that the actual core of the contention is that you don't care what's true and you just want to argue until you can convince yourself that you've "won".

I am not sure if using insults like calling you a "muppet" or "mathematically illiterate" really count as "ad hominem" arguments, but even if they technically do, I think it is a dishonest framing to call them as such here, because every instance was very explicitly motivated by my frustration at you deliberately refusing to consider any single scrap of information that wasn't already a part of your own position, deliberately refusing to admit to any possible error in any statement you have ever made (no matter how obvious those errors were). Maybe you'd prefer it if I played the game the way you do, just endlessly rewording the same arguments instead of asking why you do nothing except endlessly rewording the same arguments, but if me refusing to do that is what you call an "ad hominem" argument, then I'd much rather do that than the alternative.

*(in other words: You keep saying things that don't make sense - over and over - and keep refusing to try and understand the counter-arguments, instead just relying on repetition ad nauseam and deliberately misconstruing my statements, so it seems like you really don't care for knowledge or logic at all, and you really only care for "winning" arguments or something.)

To more specifically address Zeno's paradox/es: The mathematical implications of these questions were not solved by adding some extra features, but in the exact opposite of what you claim. These problem(s) emerged from Zeno's problematic and ideologically-motivated additions to the axioms of conventional mathematics (around his opinion that we should actively avoid every treating "the many" and "the one" in similar ways, mathematically - he was specifically trying to attack the mathematical operations of multiplication and division for ideological reasons, not academic reasons). And these problems were solved by removing his deliberately problematic axioms. And this was highlighted not just in modernity, but by Zeno's contemporaries too! — Jaded Scholar

Zeno's paradoxes involve problems with the human understanding (misunderstanding) of the relationship between time and space, which creates the appearance of infinity in the human attempts to represent motion.

https://en.wikipedia.org/wiki/Zeno%27s_paradoxes

See above. It's one of the earliest integral transforms to be derived, but it's completely ridiculous to claim that the attributes of the general case are derived from the attributes of one narrow specific case, and not vice versa. — Jaded Scholar

See below.
https://en.wikipedia.org/wiki/Uncertainty_principle

Indeed, the uncertainty principle has its roots in how we apply calculus to write the basic equations of mechanics. — https://en.wikipedia.org/wiki/Uncertainty_principle

https://en.wikipedia.org/wiki/Fourier_transform

Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. — https://en.wikipedia.org/wiki/Fourier_transform

https://math.unm.edu/~crisp/courses/wavelets/fall16/ChrisJasonUncertaintyPple.pdf

1 Introduction
Fourier Analysis is among the largest areas of applied mathematics and can
be found in all areas of engineering and physics. Atomic physicists use the
Fourier transform to characterize and understand molecular structures, optical
physicist use Fourier series to decompose and resconstruct ultrafast photonic
pulses and particle physicsts use the ideas of orthogonal basis and Fourier coefficients to describe the wave functions of particle states.
One of the most well known concepts in modern physics is the Heisenberg
Uncertainty Principle which tells us that we cannot know both the position and
momentum of a subatomic particle within a certain accuracy. To understand
this principle in some detail, we look to the subject of Fourier analysis. We
begin by motivating the idea that such a mathematical relationship exists and
then proceed to derive and describe the uncertainty principle in the formal setting of Fourier analysis. After this, we discuss Fourier analysis as it is used and
understoof by physicists in quantum mechanics for several simple examples. Finally, we will attempt to see the relationship between our formal discussion of
the principle and some of the physical laws that govern the natural world. — https://math.unm.edu/~crisp/courses/wavelets/fall16/ChrisJasonUncertaintyPple.pdf

https://www.math.uga.edu/sites/default/files/uncertainty.pdf

In Harmonic Analysis, the uncertainty principle can be succinctly stated as follows: a nonzero function and its Fourier transform cannot both be sharply localised. That is, if a function is restricted to a narrow region of the physical space, then its Fourier transform must spread (be essentially constant) over a broad region of the frequency space. It then expresses a limitation on the extent to which a signal can be both time-limited and band-limited. — https://www.math.uga.edu/sites/default/files/uncertainty.pdf

https://www.linkedin.com/pulse/uncertainty-principle-derivation-from-fourier-emanuele-pesares

When applying this reasoning to filters, it is not possible to achieve high temporal resolution and frequency resolution at the same time; a common exemplification is the resolution issues of the short-time Fourier transform. Namely, if one uses a wide window, it is possible to achieve good frequency resolution at the cost of temporal resolution, while a narrow window has the opposite characteristics. — https://www.linkedin.com/pulse/uncertainty-principle-derivation-from-fourier-emanuele-pesaresi

https://towardsdatascience.com/how-does-the-uncertainty-principle-limit-time-series-analysis-c94c442ba953

However, the Fourier Transform (FT) comes with a trade-off: it strips away temporal information as the uncertainty principle shows, rendering us unaware of when these frequencies manifest in the series. This is where the uncertainty principle steps in. Instead of pursuing infinite accuracy in either frequency or time, we can harness the uncertainty principle, allowing us to gain insights into both quantities at a reduced resolution, all the while maintaining balance. — https://towardsdatascience.com/how-does-the-uncertainty-principle-limit-time-series-analysis-c94c442ba953

https://mathworld.wolfram.com/FourierSeries.html]

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions. The computation and study of Fourier series is known as harmonic analysis and is extremely useful as a way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually, and then recombined to obtain the solution to the original problem or an approximation to it to whatever accuracy is desired or practical. Examples of successive approximations to common functions using Fourier series are illustrated above.

In particular, since the superposition principle holds for solutions of a linear homogeneous ordinary differential equation, if such an equation can be solved in the case of a single sinusoid, the solution for an arbitrary function is immediately available by expressing the original function as a Fourier series and then plugging in the solution for each sinusoidal component. In some special cases where the Fourier series can be summed in closed form, this technique can even yield analytic solutions.

Any set of functions that form a complete orthogonal system have a corresponding generalized Fourier series analogous to the Fourier series. For example, using orthogonality of the roots of a Bessel function of the first kind gives a so-called Fourier-Bessel series. — https://mathworld.wolfram.com/FourierSeries.html

Notice the use of "analogous" in the last paragraph: "Any set of functions that form a complete orthogonal system have a corresponding generalized Fourier series analogous to the Fourier series." It is not as you say, that the particular is derived from the general. It is a simple procedure of inductive reasoning whereby the general is derived from the particular. The Fourier transform provides a mathematical principle for time/frequency relations, and this is extended to many domains such as position/momentum, which can be expressed in the required, related, terms.

, ,

As I sit on the sidelines I find this conversation fascinating, and I am learning some math as well. I've never worked with formal integral transforms and am surprised at how many there are. I now understand a bit more about the uncertainty principle.

(IMO Zeno should be dead and buried)

Hey, you did some research! That's great! :)
It's a shame you only did so - as the saying goes - like a drunk uses a lightpost: for support instead of illumination. But it gives me hope that you might take that leap one day.

You even stuck to reputable websites for your references too! LinkedIn is kind of hit-and-miss, and I have not previously checked out towardsdatascience.com, but if those ones check out, then I won't be able to find any fault with your sources. :)

However, I am pretty confident that all of those sources are consistent with what I have claimed, and do not support the connection you are trying to defend. Even if you did cherry-pick some pages with wording that kind of fits the point you're trying to make, it still seems like you haven't found any genuine weakness with my claim that the general case of integral transforms isn't somehow intrinsically limited by the features of the specific cases that were derived earliest.

But I will read up on it more thoroughly and get back to you. Among all of the other points that you were wrong about, it's possible that the one you're defending hardest is one that I'm indeed over simplifying or mischaracterising. The way I'd most like to differentiate myself from you is not by being more right, but by being less egocentric. So I'll flesh out the data before getting back to dunking on you and, for my own sake, will honestly confirm whether I'm right or wrong or somewhere in between.

However, I am going to stick to my other stated principles and am now going to do my best to ignore you until after I have time to fully reply to universeness and jgill, because they seem, like me, to be primarily motivated by the desire to learn, instead of your objective of, like, pwning noobs or whatever it is.