Can't stop listening to Arvo Pärt - so good!

Sleeping Beauty, Doomsday, etc. — SophistiCat

Though debates about these frequently seem just as intractable as those around theism. Answers to these problems rely so heavily on your basic epistemological stance that it's hard to make a convincing case to someone who doesn't have the same background. — Echarmion

I don't actually take a strong position on these puzzles. I suspect that there may not be a good answer to them, or what's worse, there may not be a good question...

One of my hobbies (or obsessions) is to debate theists on their Fine Tuning Argument for God — Relativist

I've been "guilty" of this in my younger years, but eventually I lost the appetite for arguing just for the sake of arguing. Apologists are often too quick to accept the desired conclusion, and lacking the motivation they fail to put up a strong argument.

Awhile back, someone on this forum posted a link to this paper: The Fine Tuning Argument. The author (Klaas Landsman) argues that the existence of life is not a good reason to infer either a designer OR a multiverse. — Relativist

Yes, I've come across this paper before. It continues a long series of debates (as can be seen from its references), of which I think the more interesting ones aren't even about God/designer (that one seems to be pretty hopeless). Selection bias, on the other hand, poses challenging epistemological problems in the same line as Sleeping Beauty, Doomsday, etc.

Who says life can't adopt as many different forms as existent universes? Maybe life can exist in many possible universes. The "laws" of physics are based on models of our universe, not every possible universe. — Enrique

Life is "fine-tuned" in the sense that

small changes in the parameters of physics produce catastrophic changes in the evolved universe. In particular the complexity of the evolved universe, and hence its ability to support life, would be undermined by small changes in the universal constants... Thus, parameter sensitivity is the claim that the target in parameter space which is compatible with a complex universe is small in some sense. — RAW Bradford, The inevitability of fine tuning in a complex universe, 2011

But here is the rub: as the paper above argues, this parameter sensitivity of complex structures is a mathematical inevitability. It will be true in any parametric system that is at all capable of producing complex structures (and most systems would not produce complex structures, no matter how you tune them).

Something slow and beautiful to take your mind off coronavirus.

Arvo Pärt: Spiegel im Spiegel

But supposing, contra the above, that we can meaningfully answer the question about the probability of the universe being fit for life, I do get what you are saying.

This seems similar to the "luck" of our improbable existence that is the result of the (presumed) low probability fact that the structure of the universe happens to be life permitting.

Thoughts? — Relativist

There has been a lot of discussion along these lines. John Leslie offered a now well-known firing squad analogy: You face a firing squad of trained marksmen. Shots are fired, but to your immense surprise, you find that they all missed. Are you justified in inferring that the marksmen intended to miss? Leslie argues that a similar scenario in the case of the universe's fundamental constants suggests two alternative explanations: God or multiple universes. Objections have been put forward in terms of gambler's fallacy and observation selection effect, among others. You can find many such debates under the heading of anthropic reasoning (see also SEP entry on fine-tuning). Although I believe that the considerations that I gave above preempt any such debates with respect to the universe as a whole, I still think that they are instructive.

Sure, the denominator of the probability is still finite - but it's so large that it makes it surprising that any actual person is alive. On the other hand, it's imminently reasonable that SOME people exist. This is the tension. It's erroneous to apply this to individuals to "prove" they shouldn't be expected to exist, because we should expect SOME people to exist.

In terms of the FTA, life (or intelligent life) is one sort of existent, but there infinitely many sorts of existent. So IMO the analogy holds.

I'm wondering if this can be described mathematically. — Relativist

Well, I brought up one difficulty with any such mathematical description: in order to be able to talk about probabilities at all, we need to have random variables and their probability distributions. And there had better be good reasons behind the choice of both the variables and the distributions.

Already in the case of the "lottery" of being born we can see many difficulties in this regard. Depending on what we consider to be the chance circumstances and how we treat those chances, we can get wildly different results. For example, we could, like in so many romantic comedies, consider the first time the two future parents met due to some happenstance. What were the chances of them being in the same compartment on the train on that day? We could go on and estimate those chances using some simple probabilistic model of ticket sales, which might give us a small probability, but not inconceivably so. But we could take a completely different route - like, for instance, in your OP, and get a result that differs by many orders of magnitude.

There is an endlessly variety of such probabilistic models at our disposal, each giving a different result, and there doesn't seem to be any particular reason to prefer one over another, if all we want is to estimate the chance of being born in some very general sense. This uncertainty exposes the meaninglessness of such probability talk even in this intuitively suggestive example: there is no "general sense" of the probability of being born. There can only be a sense relative to some chosen model. Generally speaking, the choice of the model is dictated by our interest in the matter: what is under our control, what isn't, what we know, what we don't know, and what we wish to know.

In the case of the universe's fitness for life the situation is that much worse. Nothing is under our control. We know nothing about the reasons for the universe being the way it is, nor whether such reasons even exist. (And if they did exist, that would only push the question further, forcing us to ask about the reasons of the reasons, and so on.) We can't infer distributions from observed frequencies, because we only have this singular instance. If in the previous example we could at least idly pick among many possible probabilistic models, here there aren't even any models to pick. What are the random variables? How are they distributed? It's impossible to answer. So what could the probability of the universe being fit for life even mean?

Not actually true: https://www.gov.uk/government/statistics/annual-flu-reports — I like sushi

You should look at how these figures are actually arrived at and you will see that there is a good deal of uncertainty. Just read any study of flu morbidity/mortality.

Read a couple of novels by George Sand. And staying with female writers named George, now reading George Eliot's Middlemarch.

The deliberate element was what threw me off as how can one do something deliberate if they are not given a second choice? That is, having patience isn't something you can practice because nature forces you to wait, you have no other options. However, it is the reaction and the emotions you feel in moments where great patience is asked of you. — Lecimetiere

But you can also be patient, practice patience - as opposed to losing your cool and acting rashly out of frustration and anxiety. Or lashing out at those who "try your patience." That is an active, effectual kind of virtue. Is this the sort of patience that you think characterizes you?

We could say that John is lucky in some sense, but not in any analyzable sense. Therefore no meaningful conclusions can be drawn from it. This seems similar to the "luck" of our improbable existence that is the result of the (presumed) low probability fact that the structure of the universe happens to be life permitting. — Relativist

The "probability" of John being born as a result of chance circumstances is a rather iffy concept: you have to make a pretty arbitrary choice of random variables and their distributions in order to estimate it. But at a stretch one can perhaps make some sense of it.

With the fundamental physical laws the situation is much worse: what probabilities could possibly mean in this case is anyone's guess. We only know about this one universe; there is no statistics, no generative model. What probabilities could we be talking about?

You could say Finland is prepared. While its neighbors are scrambling, the country is sitting on an enviable stockpile of medical supplies dating to the 1950s. It includes personal protective equipment like face masks, but also oils, grains and agricultural tools.

Finland is now tapping into this supply for the first time since World War II, positioning the country strongly to confront the coronavirus. — The New York Times

@ssu

Either way, if so, why claim to be retreating to syntax? — bongo fury

I am deliberately "retreating to syntax," because that is the most basic function of things: as (grammatical) subjects. We can talk about "such things as unicorns." What, if anything, we mean by such talk is a secondary question, and the answer to that question will vary from case to case.

Trouble is, a unicorn can be the first but not the second. — bongo fury

I had the same syntactic sense in mind in both cases. We can refer to unicorns in thought and in speech.

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.

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.

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.

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?

Can you give us an example of what you are looking for?

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.

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.

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).

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.

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.

Right, I was being sloppy, I must have had in mind computable numbers. Thanks.

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.

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.

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.

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.

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.

Not this stupid shit again

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.

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.

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.

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.

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.

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.

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 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.

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.

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.