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.
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.
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 and asking your physics major friends questions until you can re-derive the laws of thermodynamics yourself.
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.)
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.
(I'm an atheist.)
The Bible is an alternative theory of the origin and purpose of existence, and is directly analogous to the matter of this thread.
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.
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.
"Common sense" might be a tool to produce such a theory but it is not a theory by itself.
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.
Anyway what is the point of this (Boltzman brain paradox)? (or point that was supposed to be?)
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.
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.
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.
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.
Here are the results of current attempts to track the objects that can potentially impact the Earth:
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.
Ha, as if it needs our permission.
Remember that we have 100s of millions of years in which to develop the required technology.
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.
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.
"7 May 2012 at 16:45 - Andy Murdoch creates a post on twitter referencing this page. Universe invites celebration by all."
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 cannot predict the results of a shuffled deck of cards.
Similarly, our current universe is impossibly improbable.
Therefore, God did 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.]