Fascinating, wonder if this can be generalized to - for any local state that has observably occured, its subset will likely occur some where in the universe.
What's more likely: nearly infinite sentient universes complete with false memories of human experiences emerging from entropic chaos, or that we don't quite understand the nature of entropy?
The Boltzmann theory is one of those thought experiments that should draw into question it's assumptions out of the pure absurdity of its logical conclusions rather than be taken seriously itself.
Isn't this just a simple matter of probability? Given an event, however unprobable it is, it can happen given infinite time? From a purely mathematical standpoint, this is correct.
Just because something has a nonzero probability doesn't mean it will ever occur.
Entropy is just dS = dQ/T. It's simply a thermodynamic property that measures where system energy is. All of these grand notions extrapolated from thermodynamics are crazy.
Thermodynamics is/was just a first approach at studying macroscale systems because we didn't yet grasp the underlying quantum behavior. It's incredibly useful when applied to chemical and physical problems, but you can't use it to make wild claims like this.
Its certainly possible that the universe will end in a crunch or a rip, and all this speculation will be for naught. But thermodynaics is still a perfectly valid way of looking at these things, and hasn't been changed much by the addition of quantum mechanics except that we now talk about probability distributions within phase space instead of points. Its basically the same stuff, with the same consequences.
Entropy is much more than just dS = dQ/T. I mean, that equation is mostly valid the same way that Newton's laws are mostly valid, but you won't be able to get any sort of feel for it approaching the subject that way. Imagine a mathmatical space with six dimensions for every particle, three for position and three for momentum. The state of the universe is a single point moving in this space according to pre-defined rules. Now, we don't know which point or microstate corresponds to our universe, because we can only make crude measurements of statistical aggregates of particles like temperature and pressure and so forth. So by making these measurements we can narrow which universe we're in to a set of these microstates, a 6N-k dimensional region of the 6N dimensional space that we'll call a macrostate. The entropy of an observed macrostate is proportional to the log of the number of microstates that a macrostate contains, S = k log W. In a sense, Entropy is a measure of our ignorance of which universe we're in, which is ultimately why Maxwell's demon doesn't work.
Please note, the above does contain simplifying assumptions which don't change the main point. For the full story, go get a physics minor at a good university or start reading Wikipedia[1] and asking your physics major friends questions until you can re-derive the laws of thermodynamics yourself.
If your assumption is infinite time and complete entropy, yes it's correct. It's also why some level of common sense (e.g. Occam's razor) should be applied before such silliness is seriously proposed. I don't think Boltzmann assumes infinite time and entropy, just enough for the completely random emergence of sentient life that thinks (perhaps falsely) that it lives in a universe populated by similar beings who created iPads from dirt and water.
Does it seem more reasonable that there is infinite time and every possible state of matter and history exists at some point, or that we simply haven't figured out the balancing forces of entropy and order?
Infinity is an interesting thought experiment, but it so thoroughly ridiculous that it should cause us to question our assumptions, not believe in absurdity conclusions based on faith in mathematics and unproven postulates that got us there.
We might as well believe the Bible is true. Not only is it less absurd, but given the infinite theory, there must exist a universe where it is true, and this could be it (unless it is truly contradictory and impossible even with infinite states of the universe, which we have no reason to believe.)
The absurdity heuristic is not a good way to decide what is true. People once thought that the idea of humans being descended from monkeys was absurd. Or that the earth going round the sun, rather than vice versa, was absurd.
Occam's razor is more sensible than the absurdity heuristic, but it applies to the fundamental building blocks of a theory, not to the outputs it predicts. So it would cut against a hypothetical unknown set of "balancing forces of entropy and order", since that's an entity not required by our current best known theories.
If a theory implies an absurd outcome, I think it is a reasonable heuristic to question the theory and it's assumptions. I am not saying absurd implications indicate the theory is flawed, only that they should cause one to suspect so and perhaps find a theory that explains reality with less broadly absurd implications.
The Bible as historical non-fiction is most certainly absurd, no implications about that. Not saying so out of sensitivity to those who believe otherwise does reason a disservice, just as not calling out Bolzmann because I don't want to offend him. If this makes anyone unwelcome, they should avoid places where their fragile ego might be challenged by rational conclusions. In a place like hacker news, I see no reason to let sensistivity toward faith restrict my speech any more than sensitivity toward programming language choice. Invite me for dinner and I will respect your religious and any other beliefs. Have a scientific debate in a web forum with me, and I will speak without concern for challenging you. It's not a personal attack to say the Bible is absurd - it's the truth.
By the same standard, "SOPA sucks. Just like PHP/Java." is appropriate. "PHP/Java sucks" may be appropriate when discussing programming languages, but dragging it into a thread about SOPA does not help.
I'm not sure I understand your point. "SOPA sucks. Just like PHP/Java" is a useless statement, since the only thing the two have in common is "sucking."
The Bible is an alternative theory of the origin and purpose of existence, and is directly analogous to the matter of this thread.
Occam's razor says that we should give more credence to the simpler theory, not the more commonsensical one, and I assure you that statistical mechanics is elegant in its simplicity. I hope you don't also go around telling biologists that its absurd that we're descended from Apes, or astronomers that its absurd that the Earth goes around the sun? How about atomic thoery (which Boltzman was an important proponent of)? Unlike the Bible Botzman was working from quantitative theories backed up by scientific experiments. You might say that being a famous scientist is almost the same as being someone who has said things that were regarded as utterly absurd, but which were true.
> Occam's razor says that we should give more credence to the simpler theory, not the more commonsensical one
Yes, and I find Occam's razor itself to be common sense, which is what my point was. If a theory seems to reflect more closely observable reality, I would bias my investigations toward that theory over one the projects something non-sensical.
> I hope you don't also go around telling biologists that its absurd that we're descended from Apes, or astronomers that its absurd that the Earth goes around the sun...
Evolution and Earth's orbit are explanations for observable reality. They do not lead us to conclude outlandish things that are conveniently not observable.
I am not saying Boltzmann was necessarily wrong, only that common sense should direct us to look for what we are missing, and for theories that direct us toward more sensible scenarios. Sure Boltzmann, could be right. I find the Bible more compelling, and Bolzmann's theory doesn't seem to preclude them both being correct.
> If a theory seems to reflect more closely observable reality, I would bias my investigations toward that theory over one the projects something non-sensical.
I don't understand your basis for saying one theory matches observable reality more closely than the other. I mean, have you observed the heat death of the universe? And how can you say that what is being projected is non-sensical, except to the extent that people reliably find arguments involving infinity hard to make sense out of?
It might be that theory of evolution and the heliocentric theory purport to explain the world we observe, but the much more sensible seeming theories that they replaced also purported to explain the world.
As for the Bible being more compelling, well, I'm not surprised since many other people who prize gut feelings over abstract reasoning feel the same way.
Error in Boltzman brains theory is that he assumes that universe with brains randomly fluctuated into existance into its current form , and concludes that this form is more complex than just brain and therefore brains without environments are more common (maybe iPhones or Bible are even more common then), and assumes that brain can exist without environment.
also second law of thermodynamics states that resulting entropy would never be decreased. and doesnt tells us about entrophy dynamics in intermediate steps.
iPhones or Bibles probably are more common. And an isolated brain without an environment really is much more likely than a brain and body and environment, at least if we're talking about random fluctuations rather than structures created as a consequence of the the availability of useful energy in the environment.
If you think about it in terms of the Canonical Ensemble the regions of states that correspond to "a brain and body" are obviously a small subset of the regions that correspond to "a brain". The incompressability of phase space means that this translates directly to the world being less likely to wander into those smaller regions via random fluctuations in direct proportion to their size.
In the end, the second law of thermodynamics is only a (very strong) statistical likelihood. If you mix some salt water and fresh water, then wait long enough you'll eventually find all the salt in one side of the glass (in time proportional to 2^N where N is the number of salt ions). Its not something written into the fabric of the universe directly, but a consequence of more fundamental laws and if you take Statistical Mechanics in college you'll get to re-derive it and see why it works that way. In fact, I'd really recommend taking a Stat Mech class to anyone considering it, it was probably the most interesting class I took in college.
This is simply not possible (maybe in star trek), because self-aware brain requires certain kind of environment to exist into. so if there is brain there is organized environment. probability that boltzman brain exist is 0%. probability that self-aware brain in an orginized environment exists : 100%
probability that Bible exists in a some unimaginable place far far away: unknown.
Anyway what is the point of this (Boltzman brain paradox)? (or point that was supposed to be?)
Brains, per se, don't require any sort of environment. If your head was somehow teleported into interstellar space it would take tens of milliseconds for the nerve impulses indicating that everything was not all right to be acquired and processed, and your consciousness would probably last for seconds beyond that.
The horror of the Boltzman Brain idea is that the vast majority of the conscious beings that will ever exist will be created in environments that cannot support them, and will promptly go insane and/or die.
Still this paradox is too detached from reality, maybe for its time it was smart. How can we know what is the chance of universe create brain and how many brains there will be per universe? How can we know that universe fluctuation is less likely than brain fluctuation? without this numbers we know nothing.
Universe filled with many brains fluctuation can be more simple than brain fluctuation. Fluctuations may also happen in environment that doesn't even have atoms that are needed for brain , but will have atoms that are needed for universe. Maybe this atoms needed for brain can only be created by universe fluctuation.
If we assume all this unknowns and create our imaginary universe yes there can be more brains in it than universes.
Yes, and such strange happenstance that all the human brains we've found so far have been in humans. We must be incredibly lucky to have picked this universe at odds of 1 in infinity where no human brains are suffering bodiless in space.
"10^{10^{26}} is 1 followed by 10^26 (100 septillion) zeroes. Although listed in years for convenience, the numbers beyond this point are so vast that they would be the same in whichever conventional units one could list them in, be they nanoseconds or star lifespans."
All you people who've been saving your OMGs for something a bit more ridiculous than an inane celebrity reaction, now could be the time to use one...
There are numbers and notation schemes there that make Ackermann look pretty insignificant. I'm particularly fond of Conway Chained Arrow Notation for ridiculously large numbers.
Graham's number is VASTLY less than TREE(3), so you lose, actually. Graham's number is around A(64)(4), i.e., the result of iterating the number of Knuth arrows 64 times starting with 4 Knuth arrows, while A(A(187196))(1) is an extremely weak lower bound on...
The maximum length of a sequence of labeled trees, with 3 labels, such that the Nth tree has at most N nodes and no tree can be embedded in any later tree... this being the definition of TREE(3).
Take however many symbols it takes you to describe your large number. Call the symbol count N. Then my counterpoint is the Nth busy beaver number. That's a big number.
Yep!! The point is, if you say 'Take however many symbols it takes you to describe your large number', that's not well-defined and is fundamentally ambiguous due to the nature of language.
I wonder what this list would have looked like if put together 10, 20, 50, 100 or a 1000 years ago. I also wonder what people a 1000 years from now would think of this one.
Probably something like "Based on the antiquity models of Physics, the ancients thought the following" and then the school children will all have a good laugh.
>by 500,000 years from now on the Earth will have likely been impacted by a meteorite of roughly 1 km in diameter
Nah. Let's be optimistic. Within a few decades we will have developed the ability to deflect all dangerous asteroids.
Also, the idea in the article that we will allow the historically priceless Californian coast to disappear 100,000 centuries from now is preposterous. Our ability to alter geography has increased by orders of magnitude in the last century alone thanks to the development of earth moving machinery.
Ditto permitting the Sun to destroy the solar system, etc.
You're assuming that a future society will have the same interest as we do in conserving physical artifacts. A physical structure like a coastline takes up a lot of space and matter compared to the amount useful information it holds. If we're going to be efficient about it, you could map California down to the nearest micrometer and save the data to some form of very high density storage.
"At 15:30:08 UTC on Sun, 04 December 292,277,026,596 AD, the Unix time stamp will exceed the largest value that can be held in a signed 64-bit integer.[84]"
i like that they give a precise time and date, given that the Gregorian calendar is basically meaningless on such scales. (also neither the earth nor the sun will still be around in any recognizable form....)
I find it interesting how several of the events limit what anyone living then can observe about the past. It's almost as if the past itself is vanishing.
It's a nice concept, although I'd more interested if it were written by someone who knew what they were talking (enough not to be proposing things like which blatantly violate conversation of energy, i.e. "antimatter power plants"), and who didn't structure their predictions in the form of a narrative exposition of Malthusianism.
> 600 million : As weathering of Earth's surfaces increases with the Sun's luminosity, carbon dioxide levels in its atmosphere decrease. By this time, they will fall to the point at which C3 photosynthesis is no longer possible. All plants which utilize C3 photosynthesis (~99 percent of species) will die.
Interesting. We should save up our fossil fuels and burn them all at once in 600 million years to save the trees!
But in all likelihood, a lot of new fossil fuels will have formed by then.
aint that funny how we paint future in such a dark colors (since sun will die in 5 billion years) and assume we all gonna die with it at the end, but yet we don't put humans evolution taken into consideration. "in 600 million years plants will die" -- seriously now? look when we have been 1,000 or even 100 years ago. think when we will be in next 1,000, given nuclear war will not push us back to the stone age. otherwise, in 600 million years we as humans will be able to scan entire universe and find perfect new home and teleport ourselves all plants and everything out there. think this is sci-fi? go back in time to 1900 and tell someone in 100 years you will have a palm size device of grapefruit weight that can gather information literally from air, play sounds, show motion picture, and you can interact with it by touching its colorful screen.
We've done things that seem like magic to some hunter-gatherer; that doesn't imply everything that seems like magic to us will come true. (does anyone have a catchy name for this fallacy?)
The boundary between things we know to be possible and impossible is in fact stronger now, because (for most of the events in this timeline) we're now basing this knowledge on the laws of physics.
Sidebar: future events that derive solely from thermodynamics don't really have a get-out-of-jail card; deflecting some of the others would require us to meaningfully harness much larger amounts of energy at the scholar system scale, bootstrapping that sort of thing would require multiple jumps of a few orders of magnitude which might be solvable as an engineering problem, but is economically dicey when we're already squandering the fossil fuel dividend on our current, unsustainable needs. That is to say, please solve politics or economics before dreaming of magitech.
Sure. Quite possibly we'll just see refinements at the edges of what we have access to (because at most scales, physics is already very accurate) rather than outright revolutions.
If I learned anything at college, it is highly likely that things will unravel in a completely different way than it is anticipated by anyone and predicted by any system.
The pi symbol is an icon denoting that the event was determined by mathematical principles. It's not part of the "years from now" value. See the legend above the TOC.
Our entire perspective on existence is based on where we popped up on the cosmological timeline. If we'd come along earlier, we may not have been able to perceive the expansion of the universe, and the apparent disconnect between the hard limit of the speed of light, and the size of the universe. If we'd come along later, we may have figured that we were completely alone in a static sphere, with no observable matter outside our galaxy.
I also find it fascinating that if we had come along a few thousand years earlier or later, our entire history would have been completely different. How effective would we have been as travelers if the north start didn't exist for us as guidepost in the northern hemisphere? So much of our existence is based on lucky chance.
“You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!”
What's really spooky is thinking about the things which we would have been able to observe if we had been around much earlier. Perhaps seeming constants have changed over the history of the universe, or other universes which drifted away from us along now-imperceptible dimensions. (I'm guessing you saw the same Brian Greene TED talk I did.)
Lawrence Krauss's longer talk in Toronto†[1] has a better explanation of the "privileged time" idea (and doesn't invoke string theory except to poke a bit of fun at it).
† Krauss has given more-or-less the same talk elsewhere, but the version recorded by TVO (the Ontario provincial public broadcaster) is probably the best recording. [Edit: I misremembered the location of the talk. Most of the physics talks on Big Ideas are from the Perimeter Institute; Krauss's wasn't.]
