:rofl: :rofl:
That's gold.

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. — 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. — universeness

That is very relieving to read! I accidentally found your identity while briefly researching more detail on the questions you asked me (which I would not mention if it weren't clear that you aren't trying to hide it), and was already preparing to accept/avoid discussing the "moderate conservative" thing with justifications about what I'm here for and the demographical differences in our Overton windows (apologies for that), and I am very grateful for the knowledge that we are much closer than I first thought in our political positions.

To both you and , I may as well show my own hand too, and say that my own political position is in support of all the policies you have both stated you are, and is probably a bit more to the left of both of yours in terms of the other policies I support. (I struggled to find the least wanky way to summarise that, but that was the best I could do.) A higher-level summary is that I support most of the goals of socialism, oppose most of the goals of capitalism, but think that both of those approaches focus too much on using politics as a means towards economic goals, and I think we are in dire need of an approach that, instead, uses economics as a means towards political goals (I stole this rhetoric from Hannah Arendt, but have developed it further in my own life). I think democracy should be something ingrained in and emerging from our society itself, rather than just a tick-box exercise we partake in for a single day every four years.

Anyway, I hate to be cryptic, but I also don't want to spend too long talking about my expansive political opinions in this particular thread! I just wanted to join the equal ground in declaring them, not write a manifesto.

(IMO Zeno should be dead and buried) — jgill

I am not sure if you only recently edited your comment to say this, or I only just noticed it, but I was very happy to see it.

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? — universeness

I think this is another one of those "yes and no" answers, haha! The cosmological principle could still hold (since it is often stated with a condition of "on average/on large enough scales" etc.) if the anisotropies, however rare, are fairly evenly distributed throughout the universe. And the cosmological principle is a rational assumption you need to make to start investigating the universe, but is still an assumption, so I think it's not a death nail in this weird idea if it implies that the principal holds for almost every observable behaviour, but not quite all of them. :)

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?' — universeness

I don't think so - that it's not the basis, at least - but tbh, there are so many different multiverse formulations that this is probably true for some of them. The breadth of those theories is probably something that you know more of than me, since my experience, if more technical, is much more focussed.

The first multiverse theories (namely, Everett's) were founded wholly on the goal of finding some interpretation of quantum uncertainty that did not result in genuine randomness being a feature of nature. I. E. Reinterpreting quantum randomness not as randomness in the outcomes of physical laws, but in seemingly-randomised measurements actually giving every possible result by bifurcating our universe at every such measurement point, and the true randomness being just in which one of those universes we "observers" happen to be in.

I think that most multiverse theories involving different physical laws/constants have those arise from their breadth of "all possible universes", and include that kind of diversity on that basis. However, I think the last part you refer to - multiverses where the "bubble" universes are spatially or otherwise traversable - probably are defined by this kind of thing. But if that idea were combined with my weird hypothesis, we would probably see indications of inhomogeneity when we look to different sides of the observable universe, which I don't think we do

And I applaud your exploration of directly emailing those physicists! I do like to repeat/repost that thing about most scientists being happy to talk or share articles - especially if you come up against a paywall in seeking their research - but I've never done so myself (probably mostly because I could usually just directly ask people I know, but most of them are in quantum foundations and none of them are string theorists). But it might be worth making use of Sean Carroll's AMAs - I feel like he kind of owes me one anyway since I was obligated to buy his astrophysics textbook twice because Pluto's demotion happened during my undergraduate degree.

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.

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.)

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.

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 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.

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

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.

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.

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

It's a very big thought.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

To get back to your next question:

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

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

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


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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

...Some moreso than others.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

This is pretty vanilla, but one of the thought experiments I appreciate most is Galileo's thought experiment demonstrating that the nature of gravity cannot involve heavier objects falling faster than lighter objects - the prevailing view at the time (late 16th century).

Imagine a heavy ball falling at a rate V_h. Then imagine two smaller balls, which, because they are lighter, fall at a slower rate, V_l. If you connect them with a long rope, do they still fall at the rate V_l? When you shorten that rope, do they still fall at V_l? What if you make that rope shorter and shorter, up to the point where they are touching each other, but still separate objects - do they fall at V_h or V_l? What if they are pressed together, as two halves of the heavy ball? Do they fall slower just by the very act of imagining them to be separate? Clearly, this is ridiculous. The source of some objects falling slower than others cannot be a difference in how gravity affects heavy and light objects, but must be due to some other factor (air resistance). Without this external factor, even a hammer and a feather would fall at the same rate.

And it was beautiful to learn that the astronauts who went to the moon on the Apollo 15 mission actually brought a hammer and a feather with them, to televise them falling at the same rate, vindicating Galileo's hypothetical claim, 300 years later. :')

I haven't done the maths myself, but I actually read about some practical estimates on this exact thing in Bill Bryson's "A Short History of (Nearly) Everything" (my favourite book): I'm not sure what portion of a body generally gets dispersed to become part of another human or any other organism, but for anything short of a hermetically-sealed chamber, the amount is always nonzero. Whether you are buried, cremated, etc., it only takes a few centuries before a substantial portion of the atoms that comprised you have gotten into the atmosphere and circulated through various physical processes, ultimately distributing very far and wide, including into the atomic makeup of every other human that currently lives. At least a few dozen of the atoms in your body were once part of Isaac Newton, a few dozen were part of Socrates, Cleopatra, Ghenghis Khan, and even the long-forgotten hominid who first artifically kindled fire. But, to continue (roughly) plagiarising Bill Bryson, the process does require a few centuries - you are not yet one with, say, Elvis Presley.

I think that is the basis of the thought that is supposed to have started Einstein on his quest for answers, when he tried to imagine himself. 'hitching a ride on a photon.' — universeness

From memory, I think you're exactly right about that.

But if QFT is correct then there is no such an object as a free particle, there are only field excitations/disturbances. Which for me, suggests that we must be constructions of field excitations, yes? — universeness

This is true, but I think in this context, the existence of "you" requires the sustained existence of those excitations, which are generally constricted to follow the rules of special relativity (sorry, but I have avoided talking about the Reeh–Schlieder theorem because I do not entirely understand how well it acts as an analogue for quantum entanglement), unlike the field itself which has much more wiggle room in terms of relativistic causality.

So I'm not 100% certain, but even within QFT, I think the question does reduce to the implication raised above: that if you could be accelerated to the speed of light, time would cease to pass for you at all.

Do you think that if a human travelled at light speed ( I know that human 'mass' currently makes that impossible) then the human would not age? — universeness

According to Special Relativity, this is exactly what would happen, and you are right in noting that massive objects cannot reach the speed of light, but I think it's worth mentioning that it's only "impossible" because it would require an infinite amount of energy to do so - so it's more that the theory implies that it can't happen, but if it somehow could, SR is pretty clear that your local time would pass more and more slowly as you accelerated and would stop entirely at v=c. At that velocity, everything within your timeframe would effectively stop - the entire lifespan of the universe (even if it's infinite) would zoom past you. You're not wrong in saying that you would continue aging, just in a different temporal reference frame, but "continue" is maybe an ambiguous term in a reference frame where time has reached the limit of not passing at all.

However, makes a very interesting observation, noting that not everything that affects you is from within your own timeframe:

There would be no concept of time, and aging requires the existence of time it seems to me. This takes one back to a previous thread on change and time: does a physical change require a passage of time? For our little scamp, the photon, one has to ask if it changes other than position? — jgill

Of course, we do interrupt photons all of the time to take them out of their timeframe and merge them with matter. And I need to get into the weeds to mention that a human travelling at the speed of light would still be human-sized in the direction of travel (if infinitessimally thin when viewed from the side), so if you started your lightspeed journey in a non-empty universe, it's a safe bet that you would lose a few pieces of yourself before the end of time (probably all of them). Which I agree could conceivably qualify as an alternate definition of aging.

Since you both brought up consciousness, I wanted to talk about that too - but also wanted to stress from the beginning that while I have been fascinated by this subject since first-year university, I have not done any actual research in this field, and the views I hold are mostly the result of recreational reading and not actual scientific experience. But now that I been responsible and warned you of the possibility that this might be a Sermon from Mount Stupid:

I think my own views on consciousness have been shaped most by two things:
1. A series of philosophers and physicists that can't seem to analyse the concept without introducing something innately "special", and devolving into ridiculous theories like panpsychism.
2. A single biology paper I read last year about sleep (after that ranty intro about intellectual honesty, I guess I should admit that I read a series of articles on it and just skimmed the paper itself).
https://www.science.org/content/article/if-alive-sleeps-brainless-creatures-shed-light-why-we-slumber

A key quote being:
“I think if it’s alive, it sleeps,” says Paul Shaw, a neuroscientist from Washington University in St. Louis. The earliest life forms were unresponsive until they evolved ways to react to their environment, he suggests, and sleep is a return to the default state. “I think we didn’t evolve sleep, we evolved wakefulness.”

This was one of those revelations to me that I had never come close to realising, but once I heard it, it made perfect sense to me.

Conscious interaction with the world is a more resource-intensive and more adaptive extension of unconscious interaction with the world, observed only in living things, and - if you allow a generously broad definition - is observed in all living things, to an extent. The thing I find beautiful about this interpretation is that I think it fits so well into what life itself is: a complex chemical reaction that is particularly persistent because it is particularly adaptive. In that sense, consciousness is just "the same, but moreso".

So I think the question "what is consciousness?" can only be answered as an extension of the question "what is life?". We have some definitions for that, but they're all incredibly post-hoc, and I have found them to be either so specific as to be meaningless or so vague as to be meaningless (as much as I like it, I do have to admit the the one I gave in the last paragraph does fall into the latter category).

The question "what is life?" is an enormous one that I think does not get as much attention as it deserves - maybe because it's so easy to be shuffled into the category of "I don't know but I know it when I see it", and there's not much attention to be gained by treating it like a mystery just because we can't actually define it well. Whatever the reason, I think it makes complete sense that any complete definition of consciousness will involve little to no extra "specialness" than a complete definition of life - and if I'm right, then it's a sign of pretty slow progress that our culture is supposedly on the brink of creating artificial life forms, yet our discourse is focussed almost entirely on consciousness instead of life.

Of course I may not be right. But of course, being human, I think I probably am.

Thanks - I will check out that debate between Penrose and Guth.

The bit I struggle with, conceptually, is the final 'state' before the 'new Aeon/Big Bang,' begins. — universeness

To be honest, I still do not understand it either. I have read a little more about it, and I'm pretty sure that it would take a lot more work than I'm able to put in (certainly in the short term). I'm a quantum physicist, and while I have a passable understanding of general relativity, the only time where I have ever felt like I fully understood general relativity was during the year where I intensively studied it in my Honours degree. It takes a LOT of work to really get your head around space and time being the same thing, and gain an intuition for what the dynamics are that the field equations are describing (it did for me, anyway), and I feel like that's basically what I'd need to do to understand how that conformal boundary trick works.

Could you also help me understand a little more as to why any loop quantum gravity quanta could not turn out to be just another vibrating string state? — universeness

This one, I actually can!

String theory was really born out of QM particle physics, where the quantisation of universal forces (like gravity) results in them being mediated by messenger particles (the messenger particle for gravity being the graviton, as I'm sure you know). Obviously, in String Theory, these are constructed from strings using more complex laws, but still, these messenger particles and the strings themselves are objects that travel through spacetime (and/or other available degrees of freedom).

But LQG is based on a modification of general relativity, and in GR, gravity is a force both created and enacted by spacetime itself. In a sense, it's not even accurate to describe gravity as a "force" in this setting. LQG attempts to unify GR with QM by quantising spacetime itself. So LQG quanta are not just the mediators of gravity, they are also, in a way, the origin of gravity and the medium in which its effects occur.

So the results they generate should be the same, but the mathematical mechanisms they use to do so are almost mutually exclusive. If one of them really exists, the other won't.

Does this mean you favour the many worlds proposal, supported by such as Sean Carroll and Alan Guth et al. — universeness

I'm sorry, but I don't. I enjoy scientific speculation about what multiverses might exist, but in much the same way that I enjoy other speculation of what's technically possible, within what we know. (One of my favourite speculations is Feynmann's idea that, because a positron effectively behaves the same as a time-reversed electron, it's technically possible that what we perceive as annihilation events are actually time-reversal events, and there is actually only one electron in the entire universe, just flipping between going backwards and forwards through time on a number of events somewhere between 10^80 and infinity - which would explain why all electrons are identical.)

In terms of actual interpretations of quantum mechanics, I'm fairly vanilla, and am most happy with the Copenhagen interpretation. Overall, I'm not really a fan of manyworlds interpretations of QM because they seem to be based on a desire to eliminate the reality of quantum uncertainty (the original german term translates more closely to "indeterminability" than "uncertainty", which I would prefer, but I don't want to be confusing by not using the accepted name). I think it's kind of profound to observe that quantum randomness seems to be a real thing - that the universe doesn't bother figuring out the result of *any* random event until some physical process needs to actually use that result. There have been several interpretations of QM that seek to eliminate this unintuitive feature, the earliest being Einstein's Local Hidden Variable theory, which was experimentally disproven in 1987 when we were first able to confirm the existence of quantum entanglement. But many other theories - like manyworlds, pilot wave theory/other Bohmian interpretations, and certainly several others I can't remember - are still based on this same idea that we need to find some way around the "unnatural" implication that quantum randomness and quantum nonlocality are real (those quote marks apply to Einstein's description, not just me transcribing air-quotes ... in this case). In the case of manyworlds (Everett's original version, and most, but not all, other variants), this is done by simply shifting the causality of the dice-roll: the universe assigns "real" values to every aspect of a quantum object at its creation, and doesn't actually procrastinate on deciding any of them only at the point where they are measured - it actually just creates a new universe for every possible value. The randomness that gets resolved at measurement is not quantum uncertainty - it's simply the uncertainty of which one of the infinite number of universes we are in. This seems to me like a whole lot more complication purely for the sake of not accepting that reality itself is not as "real" as we like to think it is.

I think that being a good scientist has the same fundamental ingredients as being a good philosopher - to be always be open to the possibility that you are wrong about something (or everything), and to not complicate things any more (or any less) than is necessary. So I much prefer interpretations that accept the possible reality of bizarre mathematical implications, and don't spend any mathematical overhead on merging those implications into a kind of reality that is more intuitive to humans (instead of actually challenging those intuitions).

I have heard about Tegmark's 4 levels of multiverses. It seems like a worthwhile classification system for how different kinds of mathematical models nest within each other, but it's never really struck me as anything more significant than that.

I appreciate that Tegmark seems dedicated to anti-dualism (I was about to say "Monism", but after a quick search, I think that term has more baggage than I want to accidentally reference), especially given the human history of dualistic metaphysics always[citation needed] smuggling in some kind of cultural virtue disguised as a law of nature, and given the power of mathematics to describe reality more accurately than literally any non-mathematical approach. But I think he goes a little too far, and in doing so, glosses over too many flaws and incompatibilities within the mathematical models that he just assumes are going to work themselves out at some point (or so I gather).

The power of modern maths is unprecedented, and I am happy to have science popularisers talking about that, but ... less happy to have them included in academia, where I think more people should be realistically considering that some of our gaps could be the result of fundamental problems with mathematics itself.

Similarly, his (and Tononi's) ideas on consciousness seem like they provide interesting opportunities to quantify our observations in a sophistocated way, but if they are useful at all, I think it will be in identifying the specific kinds of mathematics we observe, and allowing us to use that to infer the underlying mechanisms - and nothing like the validation of the metaphysics used to construct those models.

I want to give a disclaimer that your comment irked me. I'm not certain exactly why, therefore I'm not sure if it was for a good reason or a bad one, hence the disclaimer.

I think it's because I think everything you said is generally on the right track, but is either not entirely accurate or not entirely applicable to what *I* said.

For instance:

Consider that every time we make a temporal measurement there is necessarily a t=0, the point at which the measurement starts ... the very same problem which we have in modeling the Big Bang, exists when we model any temporal reality. — Metaphysician Undercover

When I say "t=0" in this case, I'm using it as a shorthand for the much more difficult-to-characterise hypothetical boundary where our mathematical models interpolate the existence of spacetime itself, as we know it, to exist on this side, and to not be able to exist on the other side. This is very different from what you are talking about; the arbitrary assignment of t=0 on a number line to define the subset of a Cartesian plane that we care about. Though I admit that I did not communicate that at all (in fact, I deliberately avoided it).

In Newtonian mechanics it manifests as an infinite acceleration at the precise moment a force is applied, and in wave mechanics it manifests as the uncertainty of the Fourier transform. — Metaphysician Undercover

This claim about Newtonian mechanics does not make sense. It confused me so much that I honestly think you can't be as wrong as I think and you are more likely to be referring to something I'm not getting. One of the biggest benefits of Newtonian mechanics over pre-Newtonian classical mechanics was that the second law eliminated the artefact of infinite acceleration (except for massless particles).

But I am confident that in your next line you really are just misinterpreting the nature of wave mechanics and/or Fourier transformation. The temporal uncertainty you refer to here has nothing to do with time itself, and is a straightforward result of transformation between any given noncommutative dimensions - none of which are *necessarily* time.

So this is the problem with any supposed "point in time", it is a singularity and we cannot understand what exists at a point in time. Accepted conventions place the limit at about the Planck length, but that is dependent on the conventions. — Metaphysician Undercover

I don't want to say that it's not worthwhile to argue about the physical reality/unreality of "a point in time", and reference the suggested limits of its quantisation, but I do think that it's not actually relevant to what I was talking about.

Likewise, as explained above, we do not understand the universe at the present, at every moment of passing time. — Metaphysician Undercover

Again, I agree, but do not think this is actually meaningful here, and comes across as actively un-meaningful. Along the lines of: "Sure, we don't understand the Big Bang, but like, do we really understand ANYTHING, man?".

I would classify that as metaphysical speculation. The issue with this speculation which is derived from mathematicians and physicists, is that it tends to rely heavily on the reality of mathematical ideals and geometrical figures. This is known as Pythagorean, or Platonic, idealism. — Metaphysician Undercover

I am happy to end on this note, because although your specific criticism is several centuries out of date, I agree completely with the general spirit of this objection.

Most modern physics is grounded in the mathematical framework of Complex Theory, which requires having no hierarchy of validity - real and imaginary numbers have no distinction except the planes they define (sadly, though, the label of "imaginary numbers" has still stuck, despite that name being given to them not by their creators, but by critics who wanted to ridicule the idea of unphysical numbers), and the dimensionalities of objects and planes that get discussed most are discussed because they're most interesting and strange. In Physics, we get mathematical results that can be called "unphysical", but I don't recall any such qualification given a single time in my Complex Theory lectures.

But even in Physics, there is no arrogance behind this label - such a finding is not unwelcome, but rather, is often the most exciting thing. Many unphysical results are known to model phenomena that really exist, and we just don't fully understand yet - like quantum tunnelling, where a particle can bypass any otherwise impenetrable barrier if the circumstances allow it to have a speed that is an imaginary number.

So I'm incredibly confident that the problem of Platonic idealism has been solved, as far as it applies to our mathematical and scientific culture.

But humans still have limits to our imagination, even if we have pushed those limits farther than our predecessors.

We can imagine living on a mobius strip or a cyclical universe. But can we imagine what an "imaginary number" would even mean in the world of our every day existence? What does an "imaginary velocity" actually represent? Or what would our perceptions be like if they could undergo a Fourier transformation (or other dimensional transformation) just like our numbers?

There are clearly limits to what we can imagine. And it follows that there are also greater limits to reality than what we can currently imagine. Mathematics provides a powerful bridge between what we can imagine and what is real. But I think we should assume that there are limits on what mathematics we can imagine, and on how well the nature of the universe itself can fit within any framework constructed from our invented mathematics.

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. But I think the general principle that our blind spots are probably rooted in our difficulty understanding things that don't exist in our macroscopic perceptions of the world (and/or the often-accompanying unwillingness to accept such things as potentially "real") - which I take to be part of the spirit behind your objection - is a very, very good guess.

As a retired mathematician, a "mathematical philosopher" resonates more as someone indulging in mathematical foundations - a topic at the heart of the subject, but one many if not most practitioners have little concern over. — jgill

Interesting. That connotation is pretty much what I meant, just with fewer steps - as crucial as mathematics is to literally every area of physics, the only areas where it gets close to centre stage are the foundational ones, generally.

I hope you stick around. Actual scientists are a rarity here, as are math people. The intersections of science and philosophy can be an entertaining circus. :cool: — jgill

Thanks! :)
And I completely agree. I've often enjoyed being able to expand or refine philosophies that touch on my area of expertise, and look forward to finding out how reasonable/full-of-it those ideas are. At any rate, I'm sure it'll be more worthwhile than just privately scoffing at, say, William James, and never finding out if I'm justified in doing so.

What do you think of proposals such as Roger Penrose's CCC, with his supporting evidence of 'Hawking points?' My quals in physics only go as far as year 1, of my BSc(Hons) in Computing Science, (over 30 years ago). Do you assign any significant credence to any of the cyclical or oscillating universe proposals? — universeness

Overall, I've never found cyclical models particularly appealing, for two (somewhat personal) reasons:
1. It feels... almost anthropocentric to focus too much on the idea that what exists before/after our universe is just a kind of continuation of our universe. It feels a bit like we're just recreating the 19th(?) century assumption that our universe is static and eternal (maybe because that saves us from imagining something different?).
2. Almost all cyclical models I've heard about rely on the assumption that each iteration ends with a big crunch or a big rip (sorry, I'm gonna make any interested parties wiki some things rather than spend even longer defining terms). But the experimental measurements of our universe keep indicating that our fate is *probably* exactly in between those, and unlikely to encounter either. It's very possible that that's not the case, but I think it's too coincidental to not be seen as meaningful that as our measurements get better and better, they generally keep telling us "Yeah, we could be on either side of this knife edge, but it still seems like we're exactly in the middle". So while I think we shouldn't assume every other universe is like we think ours is, it seems even more tenuous to assume that every other universe is unlike ours.

That said, I actually wasn't familiar with Penrose's CCC theory. I've read a bit about it, and can't claim to fully understand it yet, but it's probably my favourite cyclical model so far. It doesn't have problem #2 above, and while it doesn't have any supporting evidence yet (I learned that the "Hawking points" evidence has been refuted as something that is explainable by our current universe's cosmology), the fact that it is potentially provable/falsifiable... doesn't necessarily make it more or less likely to be true, but it does make me like it more.

However, some physicists argue that string theory is falsifiable if an experiment shows quantum mechanics fails.

How would you respond to the last sentence, would your response be anything more than 'yeah ..... IF!' — universeness

Haha, thank you for bringing that up - I hadn't heard that argument before. Your guess at my response is pretty accurate! I've given it some thought, and the best comparison I can think of is that we could say "If someone proves that mathematics itself is broken, that would mean that String Theory is too! So technically, it is falsifiable."

Admittedly, that example gives Quantum Mechanics too much credit (and String Theory too little) but the above statement is much closer to this than it is to any serious claim of falsifiability.

I thought you and others might enjoy knowing that most physicists regard String Theorists and other specialists in unprovable/unfalsifiable theories as not really being "physicists", and actually being "mathematical philosophers". ;)

It's a distinction that is not usually made with disrespect (philosophy is a huge part of foundational physics) - but as more of a demarcation of what should be allowed to be called "science".

Hi there! I have a PhD in Physics and therefore cannot resist chiming in on this.

While I concede that Science itself is not free from biases, but this is one area where the formal position is pretty respectable. This position defines the confirmed existence of the "Big Bang Theory" by the multiple stages of rapid expansion that we know the universe experienced in its first few seconds, days, and years. So we can (and do) know that the Big Bang happened immediately after the birth of the universe, but our knowledge can only get asymptomatically close to "t=0". Our current mathematical models extrapolate the existence of a singularity at t=0, but in every case where they come up, a singularity represents a transition point where our theories (or maybe just our current system of mathematics, or both) stop working and, as far as we can tell, no longer describe reality.

Not only do we not know if or how reality might work on the "other side" of any singularity, we don't know if or how reality might work *at* a singularity.

My point is that Science communicators may talk about the exciting, other-worldly implications of the extrapolating our mathematical models, the actual dominant position in the scientific community is that we can't say anything for sure about the universe before t = 10^-32 seconds or something like that.

Not only is it possible that we don't actually understand the birth of the universe, it is an established fact that we do not.

There is no shortage of scientific speculation about how the universe began, and what may have come before it, like:
- the implication of string theory (or maybe it was M-theory specifically) that two universes (or "branes") colliding within the multiverse could create a Big Bang event,
- the possibility of a "Big Crunch" end of the universe resulting in a collapse that would pull a universe back into a singularity which then inflates into a new Big Bang (and could do so over and over, maybe even indefinitely),
- I forget the formal name for it (and some of the other specifics), but the idea that the quantum foam that makes up our spacetime may have a Ground Energy level lower than we think, and the energy level of our spacetime itself may drop, thus resetting all universal constants and changing all current physical laws (which I think is somehow an even more drastic "reset" than the Big Crunch and Bang possibility),
- or the comparatively mundane idea that the difficulty of nailing down the ultimate reason for time-asymmetries that are not also space-asymmetries exists because time has a capacity to be spontaneously reversed, on occasion (I think this one is pretty unpopular, but honestly I'm running out of ideas).

However, while these kinds of theories are potentially consistent what we do know, no one yet knows how to prove or disprove any of them.

So my own conclusion - which I hope does not come across as a cop-out - is that the ultimate origin of our universe is unknown, and is potentially unknowable. And what (if anything) came before may have been some kind of reality that was a lot like ours - but considering that the nature of the universe at t=0 is fundamentally different to what our reality currently is, it seems very reasonable to expect that anything on the other side is likely to have been radically different to our current reality. Maybe even so different that we wouldn't even be able to understand it as anything "real".

There's a quote from J. B. S. Haldane that I like: "Not only is the universe queerer than we suppose - it may be queerer than we can suppose."

As an ex-Christian, I've done a fair bit of research into the history of Christianity and Judaism, but my take on this question is largely informed by Joseph Atwill's book "Caesar's Messiah", which I think is an incredibly compelling and well-researched analysis of the origin of the New Testament.

With that disclosure, my current understanding is that the vast majority of modern anti-semitism traces its origins back to the New Testament itself, which has many denunciations of Judaism, mostly allegorical, but some quite explicit. The reason I mention Joseph Atwill above is that his research has thoroughly convinced me that the New Testament was written by a small network of scholars of Judaism who were loyal to the Flavian family of Roman emperors. This hypothesis is also reinforced by the vastly different ideologies embodied by the contemporary Judaic messianic literature found in the Dead Sea scrolls (which escaped Roman censorship) that were militaristically anti-authoritarian - which makes sense because Judea was actively subjugated by the Roman empire at the time - as opposed to the New Testament, which is incredibly deferential to authority and pacifistic.

The New Testament was created to exploit existing Judaic religious beliefs, turning them into tools to encourage compliance with Roman subjugation and encourage animosity against Judaic sects (especially messianic movements) that were not as pro-Roman as early Christianity.

Therefore the Christian passages describing Judaism as a tree that no longer bears fruit and needs to be uprooted, or as a shepherd who has started leading his flock over a cliff, or the passages blaming Jews for the death of Christ, and exonerating the Romans who - explicitly - were the actual killers in those very passages.

Christianity was invented to quell the anti-imperialism of pre-Rabbinic Judaism. And you can't really supplant an existing belief system without condemning it, and that is exactly what the New Testament did, and still does. This is the reason that virtually all anti-semitic arguments (all that I've seen, anyway) either directly originate from the New Testament, or mirror its passages in some way.