Comments

  • Light velocity paradox
    ↪TheMadFool
    What you call "relative velocity" does not apply in Special Relativity. You need to understand how velocity addition works in Minkowski spacetime. These are the very basics of the theory, and until you understand them you cannot talk about any "paradoxes." Don't be lazy, do your homework instead of expecting people to spoon-feed this to you.
  • Thinking about things
    ↪Daniel C
    In the broadest sense, a "thing" can be any subject of a sentence, anything to which we refer. The more specific senses depend on the context of the discussion. Sometimes we may be talking about all tangible, bounded things; sometimes - objects of some value (she has many nice things), etc. There is no deeper, truer meaning to thingness than this - same as with any word, really. The general context defines the rules of the game, if we do not set them out explicitly.
  • Objective Morality & Human Nature
    Furthermore, It is objective because it is rooted in our human nature as intelligent social creatures. Mankind forms and lives in societies - and these societies require morality as spoken of above. — iam1me

    I think you should make explicit your definition of Objective Morality. You treat this as something self-evident, but it is not - unless you are simply coining that phrase for your own special use. But it is then all the more important to state ahead of time what you mean by it and disclaim any pretension to generality - otherwise you have to contend with the existing usage and its controversies.
  • Objective Morality & Human Nature
    Based upon all this I would argue there is, in fact, Objective Morality — iam1me

    Based on what, exactly? It is not clear on what grounds you match the words Objective Morality with the platitudes with which you conclude your post. You begin by outlining a naturalistic theory of the emergence of moral attitudes in the human society. I'll grant, for the sake of an argument, that it is a plausible theory. I'll also grant that the imperative of unselfish cooperation is an attitude that, according to this theory, can be expected to be promoted in the human species in the course of its natural evolution. But what does any of this have to do with Objective Morality?
  • From the abstract to the concrete.
    ↪Intermittent
    Can you give us an example of what you are looking for?
  • What do you think about this proof of free will?
    ↪Echarmion
    It's what comes from a thoughtless application of formalisms. The premise "Whatever should be done can be done" is only plausible in the context in which choices exist (whatever we take choices to mean). The corollary of this statement is "Whatever should not be done can be done." Taken together, these two statements express the idea that a moral should only makes sense when you have a choice between what should and what should not be done. If you have no choice, then moral considerations are irrelevant.

    If you plug in the corollary "Whatever should not be done can be done" into the argument alongside the second premise and thoughtlessly crank the handle, then you can end up with this absurdity: determinism supposedly implies that you always do what should be done and what should not be done, all at the same time. Of course, if you remember that choice (supposedly) does not exist under determinism, then you will not get yourself in trouble like that. But this is why it makes no sense to extend the argument past the second premise.
  • What do you think about this proof of free will?
    How does it implies the existence of anything? Premise 2 simply says that for any x, if x should be done, then x can be done. It doesn't even imply that there is something that should be done, nor that there is something that can be done. It is simply a universally quantified conditional sentence, without existential implications. — Nicholas Ferreira

    If the domain of quantification is empty (there are no choices), that entails determinism and denies MFT, shortcircuiting the argument.

    Anyway, this is a crap paper. It looks like a parody of analytic moral philosophy: sterile and trivial logic exercise.
  • What do you think about this proof of free will?
    I got it from "Proof of Free Will", by Michael Huemer. — Nicholas Ferreira

    It should be mentioned that Huemer's argument is supposed to be a proof by contradiction against "determinism," which he defines as the contradictory of the "minimal free will thesis (MFT)", which "holds that at least some of the time, someone has more than one course of action that he can perform."

    Anyway, the argument falls apart much earlier than intended. The premise "Whatever should be done can be done" implies the existence of a choice (as becomes immediately apparent when one begins to unpack its meaning). But this of course already contradicts determinism (as Huemer defines it). Huemer admits a similar objection of question-begging and tries to defuse it, but the fact remains that his argument is trivial and most of it is junk (everything that follows the second premise).
  • 3 orbiting black holes can break temporal symmetry
    But fewer people would care about the paper if it didn't suggest (with plausible deniability in that typical academic way) that it has something to say about time irreversibility of physical/natural trajectories as opposed to time irreversibility of numerical algorithms representing them. — fdrake

    In the conclusion the authors also try to present their work as being relevant to astronomy, but it should be noted that the problem that they actually consider is a very, very special case of the three-body problem, which is notoriously difficult to treat in any general way. They consider three equal masses in free fall with no initial velocities (which also makes this a planar problem, unlike the more general case, which is 3D).

    One fact is here taken for granted, and I wonder whether this is a necessary outcome in this setup, or whether this is an additional assumption: after some time the system ejects one body that flies off into the infinite distance, leaving behind a binary system. This is a dramatic transition in the system's dynamics, which helps understand the criterion of "irreversibility" that they use:

    The main idea of our experiment is the following. Each triple system has a certain escape time, which is the time it takes for the triple to break up into a permanent and unbound binary-single configuration. Given a numerical accuracy, , there is also a tracking time, which is the time that the numerical solution is still close to the physical trajectory that is connected to the initial condition. If the tracking time is shorter than the escape time, then the numerical solution has diverged from the physical solution, and as a consequence, it has become time irreversible.

    Since such an escape happens more-or-less stochastically, if your simulation doesn't track its onset closely, then from that point on it will quickly diverge from reality, and the error will only increase over time.
  • 3 orbiting black holes can break temporal symmetry
    Explain what you mean by "which is, in a technical sense, reversible". Please provide a reference. — jgill

    I won't hunt for a reference, but as I understand it, a reversible system would pass a reversibility test: Allow the system to evolve for some time T, then reverse the time direction of all dynamical properties (flip the direction of all velocities, moments, etc.) and allow the system to evolve further for the same amount of time T. A reversible system would end up in the same state from which it started, but with all of its dynamical properties in reverse.

    "In mathematics, a dynamical system is time-reversible if the forward evolution is one-to-one" — jgill

    Well, your wiki reference gives rather more succinct definitions, though they may require some unpacking.
  • Simple proof there is no infinity
    ↪fishfry
    Right, I was being sloppy, I must have had in mind computable numbers. Thanks.
  • 3 orbiting black holes can break temporal symmetry
    There could be a thread on the concept of time-reversibility. There seems to be a slight conflation here between forward and backward dynamics. — jgill

    A while ago we had a thread on Norton Dome - a simple Newtonian setup that (arguably) gives rise to indeterministic (and therefore irreversible) behavior. Classical mechanics allows for some edge cases where such things can happen. This is distinct from chaotic behavior (which is, in a technical sense, reversible) and also from the second law of law of thermodynamics, which is decidedly irreversible.
  • 3 orbiting black holes can break temporal symmetry
    ↪Pfhorrest
    It has to do with your worry about energy conservation due to Heisenberg uncertainty. Not much with "this" if by "this" you mean the OP.
  • Simple proof there is no infinity
    ↪Borraz
    It is indeed true that between two real numbers there is always another real number. The same is true about rational numbers. This property is called dense ordering, and its proof is very simple - much simpler than Cantor's diagonal argument, which proves something else entirely.

    However, the hypothesized property of pi to which you were referring - that it contains every finite sequence of digits - does not follow from this elementary property of real numbers. This would actually be a weaker version of absolute normality - the property of containing every finite sequence of digits in every base with "equal frequency" (scare quotes because this is more complicated than it sounds). While it is has been shown that "almost all" numbers are absolutely normal, it is surprisingly difficult to prove this property about a specific number. As far as I know, this has not been proven about any known number, including pi, although experimentally it has been confirmed for its calculated digits.
  • 3 orbiting black holes can break temporal symmetry
    ↪Pfhorrest
    You know about time-energy uncertainty, right? It is less straightforward than the other Heisenberg uncertainties, but it is a feature of quantum mechanics. However, the uncertainty only manifests on the quantum scale; on the classical scale it averages out.
  • Simple proof there is no infinity
    Infinity is something else. Somewhere, in the number pi, are all the phrases you have uttered during your life and, moreover, in the same order in which they were uttered. A little further on, there are all the books that disappeared because of the burning of the Library of Alexandria. In another place, there are all the speeches that Demosthenes gave and that he never wrote, but with the letters inverted, as in a mirror. Yes, the conception of what is infinite is too vast for me to grasp well in finite examples. — Borraz

    This property has been conjectured for pi and certain other constants, but it has not been proven. In any case, knowing that a certain sequence is buried somewhere in that infinite stream is not as helpful as it might seem, because on average, the index that points to the beginning of the sequence that you are looking for would be so large that it would contain more information than the sequence itself. Think Borges's The Library of Babel. Anyway, this is indeed fun to think about, and the above mentioned conjecture has kept number theorists busy.
  • What did you mean by "believe"?
    Not this stupid shit again
  • 3 orbiting black holes can break temporal symmetry
    ↪Pfhorrest
    Classically, the three-body problem is time-reversible, and this result doesn't prove otherwise. Indeed, qualitatively this result doesn't prove anything new: the three body problem is already known to be chaotic in the technical sense, i.e. for a certain class of initial initial conditions, any disturbance, no matter how small, results in an unbounded divergence over time.

    The direct result of this work pertains to numerical simulations of a class of three-body problems. The claimed physical relevance comes from making numerical errors (which act as perturbations) smaller than the Planck length.
  • 3 orbiting black holes can break temporal symmetry
    ↪jorndoe
    Thanks, this is interesting!

    Here is the full paper: Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length

    I'm not clear about this. I've always assumed (and I could be very mistaken) that "time reversibility" is just a quirk arising when describing a physical process using mathematics. The two are not the same.

    "And they have shown that the problem is not with the simulations after all."

    Well, they're doing computer simulations in an environment of exceptional chaotic behavior. So I don't know what to think about reversing the actions.     — jgill

    Physics enters the picture when they show that in some fraction of initial configurations the sensitivity to initial positions is so high that a displacement of a magnitude less than the Planck length can result in divergent solutions. They interpret this result as the system being "fundamentally unpredictable" when it starts from one of those configurations.

    Mathematically, if we don't take into account the Planck length limitation, the system is still only chaotic at most, and therefore fully time-reversible.

    By the way, the choice of supermassive black holes is only for astronomical verisimilitude, because in their solution they still use the Newtonian approximation, as in the classic n-body problem.

    As a concrete application of our result, we consider three black holes, each of a million solar masses, and initially separated from each other by roughly one parsec. Such a configuration is not uncommon among supermassive black holes in the concordance model of cosmology and hierarchical galaxy formation... [W]e estimate that the closest approach between any two black holes is on average between 10-2.5 and 10-2 parsec, during which the Newtonian approximation still holds. A parsec equals 1051 Planck lengths. Hence... we estimate that up to 5 percent of triples with zero angular momentum are irreversible up to the Planck length, thus rendering them fundamentally unpredictable. — Boekholt et al.
  • If max speed of light (C) is constant does that mean distance measurements are consistent?
    Treated separately by who? Stephen Hawkings nor my Physics Professor ever said that there were not absolute points in space. — christian2017

    I can readily believe that they never said that, because they wouldn't even know what that means. You can't even explain what you mean, so I suspect that you don't know what you mean either.

    I'm currently reading Einstein's book called "Relativity". It will probably take me 2 years to read that book. — christian2017

    It's a popular book aimed at non-physicists, so you shouldn't have so much trouble with it. But I think you (and Jeff from Youtube) should start from the basics: non-relativistic classical physics. For instance, the question of what it would be like for someone to move at a constant speed - whether they would feel any different than if they were staying put - was considered by Galileo back in the 17th century. Einstein only refined that treatment, but to understand what Einstein did and why, you first need to understand Galilean relativity.
  • Notes From The Underground- Dostoyevsky
    Also in the paragraphs where he accuses the Jews for their demonic power of hatred towards the Russians in particular and Humanity in general? Do you enjoy these paragraphs? Also in the poems in which he manifests a doglike submission to the divine presence of the Tsar? — David Mo

    I don't recall reading either of these, although I am aware of such sentiments by reputation. It is odd though that you should expend so much energy digging up the worst. What is your interest in Dostoevsky ?

    Can aesthetic pleasure silence moral outrage? — David Mo

    I don't know if I would call the experience of reading Dostoevsky an esthetic pleasure. He was not a fine stylist in the usual sense (for that try someone like Turgenev). There is a wicked pleasure to be had in his caustic humor, but when Dostoevsky is in his more serious mood, reading him is about as pleasurable as a hallucinatory fever.
  • Currently Reading
    I found Blindness by José Saramago to be the most terrifying thing I have ever read.
    Its perfect logic sticks to everything I wonder about.     — Valentinus

    I tried reading it a while ago, but... ugh.
  • Notes From The Underground- Dostoyevsky
    The problem is different for me: How can a rational man enjoy the writings of a fanatical believer in God and the Czar, such as Dostoevsky? Can aesthetic pleasure be separated from ideological fanaticism? — David Mo

    I haven't read Notes From The Underground, but I have read some of his other works (C&P, Karamazovs, Idiot, and a few others), so I can comment on those. Dostoyevsky the writer transcends Dostoyevsky the thinker. You (and I) may not much care for his politics, his religion, his philosophy, but that does not detract from the power of his best works. Reading a Dostoyevsky novel is a life experience; you don't walk away from it unaffected.

    The same can be said about Tolstoy - and about any great artist. That is what makes them great: we value them not (or not only) for their ideas, but for their art.
  • The Diagonal or Staircase Paradox
    Because the OP does not specify an axiomatic system but describes the problem essentially in Euclidean geometry. — boethius

    Well, no, it doesn't, because there isn't any problem so long as we stay with Euclidean geometry (as
    ↪tim wood
    rightly noted). The apparent problem only arises when we introduce the notion of a limit, and perhaps other implicit assumptions.

    Note the outer corner points seem to generate a line as n increases, but is the eventual line entirely composed of a countable set of points? How can this be? — jgill

    maybe we're interested in investigating the corners and want to deal with what happens when, trying to take the limit of shrinkifying the stair lengths, essentially every point becomes non-differentiable (that the object is "only corners", or at least all the rational points are defined as corners or some kind of scheme like this; may or may not be of interest to people here). — boethius

    "Almost none" of the limit points on the diagonal (let's just call it that for brevity) is a corner point, for the simple reason that there is only a countable number of them. Also, keep in mind that the diagonal (which we interpret as the limit point of the sequence of curves) is not itself part of the sequence and does not have the same properties. Every member of the sequence is piecewise-differentiable, while the diagonal is, of course, everywhere differential.
  • Coronavirus
    This is exactly what I explain in the sentence you reference. If in some time frame of interest (such as "until now"), the data fits an exponential growth curve, scientists will say "it is growing exponentially". — boethius

    There is always some time frame in which data fits an exponential growth curve! Or logarithmic. Or linear. Or better yet polynomial - it can be made to fit any curve over any time scale. But no scientist in their right mind would propose an exponential growth model just because you can fit an exponential curve to two consecutive points. This is not how scientific modeling works.
  • Coronavirus
    Does this satisfy your doubts that the scientific community describes things as growing exponentially if, in some time frame their interested in, the phenomena does grow exponentially? — boethius

    Yeah, the scientific community describes things as growing exponentially for as long as they grow exponentially. You may insist on exponential growth if you think you have a good handle on the causal mechanism, and can account both for the function and for the changing exponent, without having to make retrospective adjustments after each new measurement. What you don't do is say: "Oh it's still exponential, because we can still express it as a percentage increase." Because that is just cargo cult science.
  • Coronavirus
    ↪fdrake
    It's great, isn't it? If you keep readjusting your model as you go along, you can do pretty much anything. You can make your model linear, or logarithmic, or... why even settle on one function? You can make up a new one for each iteration.
  • Coronavirus
    Apparently, it was originally China's idea. — Baden

    Any bets on whether Trump will start calling chloroquine The Chinese Cure?
  • Coronavirus
    is fatal only among the already very compromised — Hanover

    Yeah, those sick old people had it coming - good riddance!

    (I hear this "point" surprisingly often from people who argue that the threat has been blown out of proportion.)

    Italy had 475 deaths yesterday. With population of 60.5 million and annual mortality rate of 10.2 per 1000, that's 25% increase of mortality rate (even if we allow that, say, 10% of those who died from coronavirus would have died from other causes within the same period).
  • The Diagonal or Staircase Paradox
    ↪boethius
    OK, I didn't notice that you said continuously differentiable in a later post, so sorry about that. But the staircase function is worse than not continuously differentiable - it is not differentiable at all in some points. In any case, no one has actually tried to show that not being continuously differentiable is even a sufficient criterion for the non-convergence of the length difference, and in fact it is easy to construct counterexamples. So all this arguing is kind of a waste of time.

    As for solving any of them. You'll need to do so relative an axiomatic system. If it's Euclidean geometry — boethius

    I am not sure why you keep talking about Euclidean geometry, which, as you admit, doesn't even have the notion of a limit. You may as well be talking about group theory. Yes, I think it's pretty obvious that we are talking in the context where limits and such are defined; real analysis will do for the purpose.

    For any continuous function like whose arclength for a <= x <= b is greater than b-a, its scaled down versions will still have the same ratio of arclength to b-a. So just about any continuous function at all that's not a constant. — Daz

    No, if the arc length decreases any faster than in the examples that have been considered so far, it will converge to the length of the diagonal, as we intuitively expect. This is easy to do with any function whose distance from the diagonal can be scaled. For example, take the half-circle function and scale the peaks down by a factor of n - it will converge like a champ.

    But yes, it is evident that whether the length error is constant, converging to zero or growing without bound is pretty precarious. You have to work to make sure that you get the "intuitive" result, because a lot of the times you will get something else entirely.

    You can obtain the result of the other "paradox" by drawing a symmetrical sawtooth graph on [0,1] that collapses as n increases, and whose length increases without bound. I leave this as an exercise for those interested. — jgill

    Yep, if your sawtooth graph doesn't have this property out of the box, you can easily make it so by multiplying it by some uniformly increasing function of n.


    The reason this looks very counterintuitive to me is because if we put aside analysis and just look at what we get in the limit, every point on the staircase converges towards a matching point on the straight line - which of course has the length of the straight line. So what gives? Well, the formal answer is that the limit towards which the sequence is converging is not an element of the sequence: the limit points do not themselves lie on any staircase curve. This is not so unusual; for example, most converging rational number sequences do not converge to rational numbers.

    Still, it just looks... wrong :)
  • The Diagonal or Staircase Paradox
    My main purpose, as mentioned, was just to explain the definition of "discontinuous" and that normal calculus concepts may not apply. — boethius

    Er, your terminology is all over the place. A continuous function has left and right limits converging to each of its points. The staircase function is, strictly speaking, discontinuous as it is pictured in the OP, but that is just an artefact of the coordiate system. If you tilt the X-Y axes, it will become continuous.

    A differentiable (or smooth) function has the first derivative at each point; the half-circle function is differentiable (again, modulo axis orientation).

    An infinitely differentiable function has all derivatives; the sine function is infinitely differentiable.

    There are also piecewise- versions of all these (piecewise-continuous, etc.).

    You are right, it's a sufficient condition for the failure of the arc-length functional to respect the limiting procedure, not a necessary one. I believe the staircase could be approximated by some differentiable curve (replace the discontinuities with regions of sufficiently high growth, I believe polynomials would work) and cause the same issues. — fdrake

    Yes, that's just what I did with the half-circle curve, and I think the sine curve (with proper scaling) would work as well.

    Do you know a sufficient and necessary condition that characterises this sort of pathology? Other than stating "the arc-length map of the limit of the approximating series of functions is not necessarily the limit of the arc-length map of the approximating series of functions". — fdrake

    Interesting question, but beyond my modest pay grade, I am afraid :)
  • The Diagonal or Staircase Paradox
    ↪boethius
    The half-circle wave is smooth though, i.e. the tangent (first derivative) exists everywhere. I used it for simplicity, but if we want an honest to goodness infinitely differentiable curve, we can use the sine function as in John's other example - just scale it by an additional factor of to make it behave. (I think this will work...)
  • The Diagonal or Staircase Paradox
    ↪fishfry
    It's in the second half of
    ↪jgill
    .

    There must be some neat identity for elliptical functions at work here, because otherwise I wouldn't know how to calculate such a limit.


    By the way,
    ↪fdrake
    and
    ↪boethius
    seemed to suggest that the key to the staircase "paradox" is in some pathology of the shape, namely its corners, where the curve is not differentiable. But this is not so. Consider a similar example, where in place of straight lines there are smooth curves. I'll use half-circle arcs for simplicity:

    FyE4o.png

    No corners here, the curve is everywhere differentiable (although the second derivative does jump around at the intersections). As with the staircase, the amplitude of the wave tends to zero as the number of crests increases without bound. But as with the staircase, the length of the curve does not approach the length of the diagonal. We don't even have to do the calculation to see that the length of the curve does not depend on the number of crests (this is because the length of each half-circle is proportional to its diameter, and the total length of all diameters is the length of the diagonal). And so the length of the wavy curve is always .

    What's more, with a simple modification we can make the length of the wavy curve increase without bound, just as in @jgill's example. Just replace half-circles with ellipses whose major axis is perpendicular to the diagonal and scaled by a factor of .
  • Is Bong Joon Ho's Parasite Subversively Conservative?
    I thought back to Parasite after seeing another film with a somewhat similar theme. To be honest, for all its sleek execution and obvious talent, Parasite turned me off by its heavy-handed messaging (in retrospect, the Oscar win wasn't very surprising). The dream sequence at the close of the film is a good illustration of that. At first I thought that the filmmakers were finally going for a little subtlety by ending the film right there at the happy reunion. Let the viewers work it out for themselves and then congratulate themselves on their perspicacity. But no, they had to drive the message home, lest someone might be confused by the ambiguity, and so they cut back to the half-crazed boy sitting in his squalid banjiha.

    The socially conscious film that I would like to recommend as an antidote is Shoplifters (2018) by the Japanese director Hirokazu Kore-eda. And if you like that, see Nobody Knows (2004) and Still Walking (2008), which I think are even better. I hear that Kore-eda's output is uneven, but these three are excellent.

    Also, anything by the Dardenne brothers.
  • Q. on Fallacy of False Dichotomy
    ↪Tkpa007
    Well, if someone says something to the effect of (A or B), and it is not the case that (A or B), then a logical fallacy has been committed. How damaging that is to their overall argument depends on the context. Sometimes, as you say, not very damaging, and the argument can be repaired without much difficulty.
  • Regulating procreation
    the popular myth merely unilateral or blanket statements based on some silly and highly questionable pop cultural myth or axiom accepted or taken for granted on the basis of faith, nonsensical circular reasoning and rote regurgitation outdated 19th century myths and archaisms archaic and highly debatable or questionable or easily disprovable and contradictroy — IvoryBlackBishop
  • Thought as a barrier to understanding
    ↪Antidote
    I'll try not to think about what you just said.
  • Thought as a barrier to understanding
    If thought were the natural outcome or effect, brought on by confusion, then the more you think, the more confused you will get. — Antidote

    That's a nice example of a self-undercutting argument. If the premise is assumed, then everything that follows from it can be dismissed as confused ramblings. No need to go any further.
  • Intuitions About Time
    Think Heraclitus and Parmenides. — Pneumenon

    I was looking for something in the way of critical reflection, but I find only free-floating metaphors here. I've also been thinking about the metaphysics of time lately, but I prefer a more grounded approach.
  • Intuitions About Time
    Take these two:

    1. Reality is fundamentally flux, and permanency is constructed
    2. Reality fundamentally is, and change is an illusion     — Pneumenon

    I don't even know what either of these statements are saying. It seems like they make some substantive claims about reality, but when I try to nail these claims, they just slip out of my hands.
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