A phase space, or configuration space, doesn't have to imply anything about time being presumed simply to conceive of that space. It's just a spatial representation of all the different possible states that a system could be in. — Pfhorrest

But before you can conceive of a phase space, you have to conceive of a theory that gives rise to that phase space. The phase space is just a slice of the theory; you need to lay out the theory first. And as you do, time will already be there, even if you haven't specifically identified it as such. So first you build the stage and place the backdrop and the decorations, and gather actors and give them their parts, and set the play in motion. And then you can point to one of the actors and say: that is time. The play will not make sense without this central character, but neither will the character make sense outside the context of the play. The character of time emerges from the narrative of a physical theory, which in turn needs this character for its coherence. There is a mutual dependence here that makes straightforward reduction ("A is nothing other than B") impossible.

It's the same with time and clocks (@A Seagull): you can't conceive of a clock without already operating with a notion of time, but neither can you conceive of time without representing it using a clock, a physical process of a certain kind. The two notions are mutually dependent but not reducible to each other.

You (@Pfhorrest) make time specifically a thermodynamic actor, but of course time is present in other physical theories as well. It is just that continuum and statistical thermodynamics happen to be the only theories that we have in which time has a preferred direction. At thermodynamic equilibrium time disappears in the description of the macrostate, but it will still have a part to play at other scales and in other theoretical frameworks. It just won't have an overall preferred direction. ("Join the club!" says space. Space also has preferred directions, but only at some scales in some theoretical frameworks, e.g. in Earth-bound sciences.)

Time is what a clock measures. — A Seagull

Great. Now define clock and measurement without referring to time.

The dimension across which that gradient occurs is a dimension of the phase-space. The gradient gives directionality to a span across that phase-space. Without that directionality, a span of the phase-space wouldn't be recognizable as time, so the existence of that gradient in the phase-space is what constitutes the existence of time as we mean it. — Pfhorrest

Let's not put the cart before the horse. "Span across phase-space..." - which phase space? The phase space of classical thermodynamics, apparently. You need to start with the framework of thermodynamics, which, as the name suggests, involves time. That is the important bit. That the positive direction of the time is conventionally chosen as the direction in which entropy increases is almost an afterthought. The essence of this definition is that time is implicitly defined by classical thermodynamics. Which is OK as far as it goes, but we need not define time so narrowly and specifically; we can generalize this definition by stating that time is implicitly defined by dynamical laws of nature.

By "entropic anisometry" I assume you mean entropy gradient in the forward time direction, aka the 2nd law of thermodynamics? You realize that's circular, right? You can reduce the direction of time to entropy gradient (maybe), but you need to have time before you can talk about its direction. The 2nd law already assumes it.

oh but it is about the language, if children were taught from the beginning of their lives that humans are humans and not that there are sub-categories of humans like "black" "white" etc then they would not have a conceptual framework in their brain structures that would allow them to prefer one sub-category over the other
racism would be gone in a matter of a generation or maybe 2 depending on the extent of rate of adoption of this amongst parents — dazed

You are overthinking it. We should just raise everyone in the world as non-racist. There, problem solved.

This may sound like a joke, but that's because your proposal is a joke. Even if such a language change could accomplish anything (of course not), how the hell is this supposed to work? If you have no idea and are just daydreaming, then why set your sights so low? Why not daydream about everyone living happily ever after? If that could be achieved, then we wouldn't have to worry about such petty concerns as racism.

(Of course, daydreaming about reforming language in order to cure racism is only marginally more asinine than daydreaming about a world social revolution as a cure for all ills.)

I suspect the hypothesis is bullshit. — Benkei

These are ivory tower bullshit — StreetlightX

You are taking ernestm way too seriously if you think that his take on the Sapir/Whorf hypothesis has much to do with "ivory tower" anything.

If I pick A + B then there's a 99% chance that I win $1,000 and a 1% chance that I win $1,001,000. — Michael

At the time when you are making your decision the money either already is or is not in the box. Your decision cannot change this fact (unless you entertain some strange ideas of backward causality). So if the money is in the box, then the choice is between $1,001,000 and $1,000,000. If the money is not in the box, then the choice is between $1,000 and nothing. Either way, you get more by two-boxing.

Of course, if everyone reasoned that way, then the predictor would have had a lousy track record, contrary to the stated assumption.

I don't understand how it's a paradox. — Michael

Yeah, that's how most people react to it. The paradox is that half of those people who think that the answer is obvious do not agree with the other half :)

Vacuum energy has to be positive, according to the quantum field theory, and its presence is supposed to explain the experimentally observed Casimir effect. However, it may be counterbalanced by the negative potential energy of gravity.

I never like these predictor-type puzzles. If you have a predictor you can ask it to predict if its next statement will be a lie. If it says yes then then it told the truth, making the statement a lie. You get a contradiction.

Therefore there is no such predictor. The very concept of a predictor is contradictory, hence anything follows. All such puzzles are vacuous. I get that they're popular, but I don't see the appeal. — fishfry

The predictor may be limited to predicting that one thing and nothing else, so you can't defeat it that way. Also, the predictor doesn't have to be infallible, it only needs to be better than chance. Let's say the predictor is known to be right 55% of the time - not all that implausible. With a large enough leverage, the statistical argument still says that you should one-box, while the causal argument says that you should two-box.

But I take your larger point that in general, with such puzzles one should not automatically assume that the described scenario is possible, even if it sounds pretty coherent.

The expansion of space deals with the problem of waste heat, but I couldn't find anything about generating new energy. — Echarmion

If the energy of space itself (vacuum energy) is positive, then expansion produces more energy, in the sense that a volume that expands with the universe (comoving volume) will encompass more and more space, and thus possess more and more energy over time.

Yeah, I don't know. Simple metrics like these don't say all that much. Here's an example: consider a finite volume of gas within a larger volume of the same gas. Let's say the gas is not at thermodynamic equilibrium, so that its entropy is less than the maximum entropy. Now expand the boundary of the smaller volume. Both the current entropy and the maximum entropy inside the boundary will have grown proportionally. Naturally, this purely formal move has not produced any new dynamics. Don't take me wrong, I am not saying that this example reflects the situation in an expanding universe - I am just saying that gross numbers for entropy and energy (calculated how?) aren't enough to conclude anything.

Anyway, here is a classic review paper; it is better than two decades old, but AFAIK it is mostly up to date with what we know in its outlines: A dying universe: the long-term fate and evolution of astrophysical objects (FC Adams, G Laughlin - Reviews of Modern Physics, 1997). It goes into various possibilities for the long-term evolution of the universe, from something like the classical heat death to spontaneous tunneling into a true vacuum state that can annihilate and radically transform the universe in an instant. Scenarios of continuous, indefinite entropy production are also considered. However, such scenarios don't imply the continued existence of the world as we know it; the future in that case may hold nothing more life-affirming than a continual production and evaporation of black holes or clumps of cold dark matter.

Not a cosmology expert by any means, but as far as I know, expansion of the universe is every bit part of the heat death scenario (how could it not be?) Whether energy is being created in the course of the expansion depends on how you do the calculation (there isn't a unique procedure for this in GR). But energy is not everything; for interesting stuff to happen you need entropy gradient.

Presumably, that depends mainly on your interpretation of the equations, i.e. on metaphysical speculation. If it's many worlds, maybe you are an infinite number of persons at once. — Echarmion

Not infinite, the number of superposition states in a finite system would be finite. And assuming that we are in a superposition state at any time (or at all times, as per Everett), then there had better be a coherent account of how it is that we feel as if we were always in a pure state, i.e. all the classical observables always seem to have definite values. A number of such accounts, more or less detailed, have been proposed using somewhat different assumptions regarding conscious observers and with different interpretations of QM.

Note that one does not necessarily need to have a fully worked out theory of consciousness to answer these questions, nor is there necessarily a need for any mysticism. Some explanations posit nothing more than a system with memory, like a photographic plate for instance, one that can keep a record of measured eigenvalues.

The OP question is not as stupid as it sounds. I would reformulate it as "What does it feel like to be in a quantum superposition state?" There is some discussion of this and related questions in the literature on the foundations of quantum mechanics.

On this forum I have come across quotations from classic works that are sourced from that site; unless there is reason to doubt their reliability, I see no problem with that.

Use the one in this thread: https://thephilosophyforum.com/discussion/5738/ignore-list-browser-extension/p1

After watching Nuri Bilge Ceylan's Climates this melancholy little piece is stuck in my head!

Having gone through a journey of discovery, I find I have firmly landed as a hard determinist. But I am having a heck of a time finding any writing that addressed how we should live our mental lives as a hard determinist. I have a lot of ideas on the topic but was hoping not to have to try to reinvent the wheel. My moderate search over the last few months has only turned up a few paragraphs that directly address this problem. I'm hoping to find a writing on how to view justice, personal motivation, and the like, for a hard determinist. Anybody know of such a how-to writing?? — Brook Norton

Compatibilism and related approaches (e.g. some strains of libertarianism) deal with these questions as axiological issues that are largely decoupled from physics. I know that you said that you reject compatibilism, but that is owing to your peculiar definition of free will that reduces it to physics. We do not need to get sidetracked by terminological disputes. If you want answers to the questions that you ask in the OP, then don't change the subject - think about those questions. What do they have to do with physics? On the face of it - nothing. You jump from one to the other too hastily; I don't think you quite thought it through.

If "free will" means you can weigh the pros and cons and then decide how to act, then I'm a compatibilist. But if "free will" means you could have done otherwise, then I'm a hard determinist. I think the later definition is the more meaningful as I believe it is what most people intuit when they speak casually of free will. — Brook Norton

It's not as simple as that. Experimental philosophers and social psychologists have done quite a bit of research over the last couple of decades to try to find out what it is that folk actually believe about free will. It's a mixed bag: neither consistently compatibilist, nor consistently incompatibilist, but some of both.

That's a nice piece.

The Sapir-Whorf hypothesis basically says that people will only call something as they know it to be called. — Anthony Kennedy

That's not Sapir-Whorf hypothesis, that's an obvious fact.

Depending on where people come from, there are many practices that are practiced there, but not allowed elsewhere. But should they be? Say it were illegal in place A to eat a strawberry before they have done their chores. In place B, strawberries can be eaten at any time. Say that person B from place B visits place A and eats a strawberry. Should person B be held to the same law as person A even though they both have a different idea as what is right? — Anthony Kennedy

Your example is too ambiguous. You need to decide whether you want to talk about legal practice, or moral relativism, or multiculturalism - all different questions with different answers.

Is Euclid's line the same thing as the set of real numbers? We take as an unspoken axiom that it is; but if we remember that this is just an assumption, we can resolve our confusion over where the extra points go. — fishfry

@aletheist will be along shortly, I am sure, invoking the ghost of Charles Sanders Peirce and insisting that Euclid's line is not a collection of points at all. He would have a point, at least to the extent that it isn't a given that a line is identical with a particular collection of points.

This is really funny. I’m listening to the birds, the sounds of nature. Who does that? — Becky

There was a blackbird who used to sing right outside my window some time ago (I spotted him a few times). That was very cool. Birds are quieter now, but still present.

Speaking of which, I've recently been listening to all things avian in Messiaen, who loved birds.

Well, "the number line" in its usual sense is just a visual metaphor for the real numbers (it will do for the rationals as well, though see above about "holes"). So in that sense, no, the number line is not missing anything. You have to work harder to motivate things like infinitesimals and hyperreals. And then you have to work even harder just to reproduce all the things that we can already do with real numbers, like addition and multiplication.

One way to make it kosher is to consider it a generalized function. I never worked with those either.

https://en.wikipedia.org/wiki/Generalized_function — jgill

Sure, I shouldn't be surprised that these nasties have long since been tamed, just like infinitesimals and infinities were earlier.

The inept and corrupt populists do what they typically do in such situations: pander to their base.

The Dirac Delta function (0 everywhere except at x=0, there infinite) can be thought of in terms of infinitesimals — jgill

It's funny how ubiquitous the delta function still is in physical and engineering mathematics, and yet it is completely non-kosher from the point of view of standard analysis. It was so useful that it survived Weierstrass's reforms, which did away with non-rigorous infinitesimals of the early calculus.

The situation with surreals vs. reals is a little different than that with reals vs. rationals. Though it may seem as if rationals completely fill their number line, being as you can fit arbitrarily many points between any two points (i.e. they are densely ordered), rationals are actually full of holes, in a sense. You can construct a sequence of rational numbers that definitely converges to... something. But that something is not a rational number. There are lots and lots of such holes between rationals - in a way, the rational number line almost entirely consists of holes. And that is where real numbers come into the picture: they fill those holes.

With real numbers the situation is different: they are complete. Any converging sequence of real numbers most definitely converges to a real number. There are no holes to fill - at least not in that sense. You have to work a little harder to find what those smug bastards are lacking: you have to violate the Archimedean property.

At cosmological scales time translation symmetry breaks down and, as a consequence, so does energy conservation. — InPitzotl

It breaks down in the sense that in a dynamic, curved and possibly infinite spacetime there is no uniquely correct way of calculating and keeping track of the total energy. Physicists don't seem to be much bothered by that though, because energy is mostly useful as a budget in local transactions.

True story. Back in the 60s - that's the 1960s, not the 1860s - I was an under-grad Physics major. Thermodynamics was not on the undergrad curriculum. — EricH

Wha...? What was on the curriculum?

At the end, during the Q&A period I asked how it was that the universe had such a low entropy value. The professor's response??

"When God created the universe he created the Second Law of Thermodynamics" — EricH

Well, that's a crap answer and not even a good joke. The past hypothesis, as the (supposedly) low initial entropy of the universe is known (after David Albert), is an interesting and contentious issue.

The double slit and various related experiments do come close to suggesting the universe likes paradox. But probably we just don't understand what's going on. — Marchesk

No, it doesn't, and yes, we do. This is a typical situation where informal or sloppy language can result in an apparent paradox. IOW is right.

Lancet just published a large observational study of chloroquine-based treatmenets of COVID patients. It found that all treatments that are widely used in hospitals increase the overall mortality. Moreover, it appears that the already known heart complications are not the whole story - the drugs may actually worsen COVID symptoms.

In more cheerful news: a (non-peer-reviewed, preclinical) Canadian study shows potential for medical cannabis to treat COVID-19.

Why didn't influenza stick around? Did it kill too many people back in 1918/19? — Marchesk

The Spanish Flu most likely was never eradicated, in the sense of going completely extinct - more likely, it mutated into less dangerous forms and may still be circulating. Of course, Covid-19 is very different from a flu virus, so direct comparisons are not apt. Nevertheless, the possibility exists that over time it will similarly evolve into something less lethal, as pathogens in general tend to do.

As mentioned earlier, this strategy was successful with the Ebola epidemic in 2014. — Andrew M

Ebola wasn't eradicated though, it is endemic and is certain to reemerge from time to time (in fact there were confirmed cases in April).

Those symbols are just Unicode characters that you can copy/paste from anywhere (e.g. the first Google hit for "set symbols"). But this site also supports Latex.

It makes sense because most masks were not manufactured for the purpose of blocking viruses or very small droplets of virus-carrying moisture. They were designed to reduce inhalation of hazardous dusts and pollution (smoke, for instance). — Bitter Crank

Oh so that's what surgical masks are for? To make those notoriously smoke-filled, asbestos-lined hospitals more safe for medical personnel? Who would've thunk.

There has been largely consistent randomized controlled trial (RCT) evidence in health care workers that wearing surgical masks and N95 respirators can reduce the risks of respiratory illnesses [including severe acute respiratory syndrome (SARS)] by 40–60%, after accounting for key confounders such as other protective equipment or hygiene measures.8,11 However, uncertainty remains as to whether surgical masks are inferior to N95 respirators in preventing infection. A recent meta-analysis shows that, compared with surgical mask use, use of N95 respirators is associated with a >50% reduced risk of overall clinical respiratory illness but has no apparent superiority in preventing viral infection,11 which is supported by a more recent large-scale RCT in an outpatient setting.8 Despite the potential superiority of N95 respirators over surgical masks, the evidence in health care workers defies a common claim that surgical masks are ineffective for prevention because some coronaviruses (e.g. SARS-CoV-2) may be airborne in specific scenarios (e.g. during aerosol generating procedures) and/or can infect people through the mucous membranes of the eyes.

Trial evidence in the general population is, however, more limited, because it is practically challenging to carry out and there is high risk of non-compliance and cross-contamination.15–17 Nonetheless, several case-control studies conducted in the general population in Hong Kong and Beijing during the 2003 SARS-CoV-1 outbreak found that frequent use of facemasks (predominantly surgical masks in both studies) in public spaces was associated with a >60% lower odds of contracting SARS compared with infrequent use, after accounting for key confounders.18,19 Although the effectiveness could be overestimated in observational studies (as seen in studies among health care workers11) the lack of conclusive evidence does not substantiate claims that surgical masks are ineffective for the public, but calls for further research, particularly on the reason behind the failure of transferring the effectiveness observed in health care workers to the general population, and the strategies needed to boost the effectiveness. — COVID-19 epidemic: disentangling the re-emerging controversy about medical facemasks from an epidemiological perspective (Int J Epidemiol. 2020)

The great thing about 'virtue signaling' is that people identify the signaler as virtuous, without the signaler having to actually go to the considerable inconvenience of being virtuous. — Bitter Crank

On the flip side, "covidiot" shaming is also a thing now.

I'll go with the quotational approach - that's the opposite of disquotational, as in the disquotational theory of truth.

The answer to this question is "The answer to this question."

The scientific consensus seems to be that unless one is wearing an N95 mask, and wearing it properly, one is probably not limiting the distribution of corona virus much. — Bitter Crank

There is no such scientific consensus. The evidence is mixed, but the consensus, if anything, is that masks are somewhat effective, some more than others. Don't fall victim to all-or-nothing thinking: even a 20% reduction of the probability of transmission is better than nothing.

Let 'All sets that do not contain themselves as members' be

a = {x}
b = {y}
c = {z}
d = ... and these sets go on for as long as is necessary, e, f, g, h,... — EnPassant

Why are they all singletons?

Yes, but X is a set of sets so X = {{a}, {b}, {c},...} but {a, b, c, ...} might be correct too as long as the logic of what I'm saying holds up. — EnPassant

I don't see what logic could imply that {{a}, {b}, {c},...} is the same as {a, b, c, ...}

You keep making the same mistake over and over again:

The paradox asks if {X} is a member of X — EnPassant

No!

The paradox asks if X is a member of X.

X ≠ {X}

{X} is a set with one member: X

Set X = {{x}, {y}, {z}}

If X is included

X = {{x}, {y}, {z}, {{x}, {y}, {z}}} — EnPassant

No, that's not how it works.

X = {{x}, {y}, {z}}

X' = {{x}, {y}, {z}, {{x}, {y}, {z}}}

X ≠ X'

X ∈ X'

X' ∉ X'

How much of what has been written about philosophy is indubitable? — A Seagull

What would be the point of writing down what is indubitable, except as a jumping off point (like Descartes' cogito)?