Maxwell's Daemon exists (?), Godel's Theorem disproven (?)
- From: Straydog <asd@xxxxxxxxx>
- Date: Sat, 27 Oct 2007 21:08:12 -0400
Better to set your typeface to constant-proportional spacing for the crude graphics at the end.
Maxwell's Daemon exists (?) and Godel's Theorem disproven?
Below are two sets of horizontal lines of slash marks ("///////")
Below the first is quote on Godel's Theorem. Below the second is quote
on Maxwell's Daemon. Below that is horizontal line of checks ("######"), and my outline of my (tentative) claim that the daemon exists and the theorem maybe not so solid. If you know all this, then scroll down to
the line of checks....
G”del's incompleteness theorems
From Wikipedia, the free encyclopedia
In mathematical logic, G”del's incompleteness theorems, proved by Kurt G”del in 1931, are two
theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of
The theorems are also of considerable importance to the philosophy of mathematics. They are
widely regarded as showing that Hilbert's program to find a complete and consistent set of axioms
for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem.
Authors such as J. R. Lucas have argued that the theorems have implications in wider areas of
philosophy and even cognitive science, but these claims are less generally accepted.
First incompleteness theorem
G”del's first incompleteness theorem, perhaps the single most celebrated result in mathematical
logic, states that:
For any consistent formal, computably enumerable theory that proves basic arithmetical truths, an
arithmetical statement that is true, but not provable in the theory, can be constructed.1 That is,
any effectively generated theory capable of expressing elementary arithmetic cannot be both
consistent and complete.
- - - -
Maxwell's thought experiment
The Second Law of Thermodynamics forbids (due to statistical improbability) two bodies of equal
temperature, brought in contact with each other and isolated from the rest of the Universe, from
evolving to a state in which one of the two has a significantly higher temperature than the other.
The second law is also expressed as the assertion that in an isolated system, entropy never
decreases. Maxwell described his thought experiment in this way:
- - - - - - - Maxwell's thought experiment has troubled physicists since he first published it.
Is Maxwell correct?
Could such a demon, as he describes it, actually violate the second law?
Several physicists have presented calculations that show that the second law of thermodynamics
will not actually be violated, if a more complete analysis is made of the whole system including the
demon. The essence of the physical argument is to show by calculation that any demon must
"generate" more entropy segregating the molecules than it could ever eliminate by the method
described. That is, it would take more effort to gauge the speed of the molecules and allow them
to selectively pass through the opening between A and B than the amount of energy saved by the
difference of temperature caused by this.
One of the most famous responses to this question was suggested in 1929 by Le˘ Szil rd and later
by L‚on Brillouin. Szil rd pointed out that a real-life Maxwell's demon would need to have some
means of measuring molecular speed, and that the act of acquiring information would require an
expenditure of energy. The second law states that the total entropy of an isolated system must
increase. Since the demon and the gas are interacting, we must consider the total entropy of the
gas and the demon combined. The expenditure of energy by the demon will cause an increase in
the entropy of the demon, which will be larger than the lowering of the entropy of the gas. For
example, if the demon is checking molecular positions using a flashlight, the flashlight battery is a
low-entropy device, a chemical reaction waiting to happen. As its energy is used up emitting
photons (whose entropy must now be counted as well), the battery's chemical reaction will
proceed and its entropy will increase, more than offsetting the decrease in the entropy of the gas.
Szil rd's insight was expanded upon in 1982 by Charles H. Bennett. In 1960, Rolf Landauer
realized that certain measurements need not increase thermodynamic entropy as long as they were
thermodynamically reversible. Due to the connection between thermodynamic entropy and
information entropy, this also meant that the recorded measurement must not be erased. In other
words, to determine what side of the gate a molecule must be on, the demon must store
information about the state of the molecule. Bennett showed that, however well prepared,
eventually the demon will run out of information storage space and must begin to erase the
information it has previously gathered. Erasing information is a thermodynamically irreversible
process that increases the entropy of a system.
Note that if the whole universe consisted of the demon and the container, and energy were needed
to operate the gate, the only source of energy is letting heat flow from B to A. Now, the quantum
of B to A heat flow is a single particle going from B to A. This restores entropy, because on
average the single particles going from B to A are more energetic than the ones going from A to
The above argument can take another form if the door is modeled as a potential energy barrier. In
order to raise the potential, work must be done, and that potential energy cliff should be higher
than the kinetic energy of the particle going from A to B. Thus, the quantum of heat flow going
from B to A should be more energetic than the incoming particle.
Put simply, no matter how it is done, both the act of the demon watching molecules and the act of
opening and closing the trapdoor is by definition work and requires the expenditure of energy.
These explanations, however, are inadequate as the concept of the demon is not stated and may
work as described below.
Furthermore, John Earman and John Norton have argued that Szilard and Landauer's explanations
for why Maxwell's Demon begin by assuming that the second law of thermodynamics cannot be
violated, thus rendering their proofs that Maxwell's Demon cannot violate the Second Law
Real-life versions of Maxwellian demons occur, but all such "real demons" have their
entropy-lowering effects duly balanced by increase of entropy elsewhere.
Single-atom traps used by particle physicists allow an experimenter to control the state of
individual quanta in a way similar to Maxwell's demon.
Molecular-sized mechanisms are no longer found only in biology; they are also the subject of the
emerging field of nanotechnology.
A large-scale, commercially-available pneumatic device, called a Ranque-Hilsch vortex tube
separates hot and cold air. It sorts molecules by exploiting the conservation of angular
momentum: hotter molecules are spun to the outside of the tube while cooler molecules spin in a
tighter whirl within the tube. Gas from the two different temperature whirls may be vented on
opposite ends of the tube. Although this creates a temperature difference, the energy to do so is
supplied by the pressure driving the gas through the tube.
If hypothetical mirror matter exists, demons can be envisaged which can act like perpetuum
mobiles of the second kind: extract heat energy from only one reservoir, use it to do work and be
isolated from the rest of ordinary world. Yet the Second Law is not violated because the demons
pay their entropy cost in the hidden (mirror) sector of the world by emitting mirror photons.
Experimental work based on Maxwell's Demon
In the 1 February 2007 issue of Nature, David Leigh, a professor at the University of Edinburgh,
announced the creation of a nano-device based on this thought experiment. This device is able to
drive a chemical system out of equilibrium, but it must be powered by an external source (light in
this case) and therefore does not violate thermodynamics.
Previously, other researchers created a ring-shaped molecule which could be placed on an axle
connecting two sites (called A and B). Particles from either site would bump into the ring and
move it from end to end. If a large collection of these devices were placed in a system, half of the
devices had the ring at site A and half at B at any given moment in time.
Leigh made a minor change to the axle so that if a light is shone on the device, the center of the
axle will thicken, thus restricting the motion of the ring. It only keeps the ring from moving,
however, if it is at site A. Over time, therefore, the rings will be bumped from site B to site A and
get stuck there, creating an imbalance in the system. In his experiments, Leigh was able to take a
pot of "billions of these devices" from 50:50 equilibrium to a 70:30 imbalance within a few
Adams and the demon as historical metaphor
Historian Henry Brooks Adams in his manuscript The Rule of Phase Applied to History attempted
to use Maxwell's demon as a historical metaphor, though he misunderstood and misapplied the
original principle. Adams interpreted history as a process moving towards "equilibrium", but he
saw militaristic nations (he felt Germany pre-eminent in this class) as tending to reverse this
process, a Maxwell's Demon of history. Adams made many attempts to respond to the criticism of
his formulation from his scientific colleagues, but the work remained incomplete at Adams' death
in 1918. It was only published posthumously. 
Maxwell's demon in popular culture
In literature, Maxwell's Demon appears in Thomas Pynchon's novel, The Crying of Lot 49 and
George Gamow's Mr. Tompkins. Also, it is mentioned in the Novel Homo Faber by Swiss author
Max Frisch, as well as in one of the short stories of The Cyberiad by Stanislaw Lem: "The Sixth
Sally, or How Trurl and Klaupacius Created a Demon of the Second Kind to Defeat the Pirate
Pugg". In Greg Egan's hard science fiction novel Permutation City, Maxwell's Demon is the name
of a program used by the character Maria to keep track of individual "molecules" in the cellular
automaton known as the Autoverse. Finally, Maxwell's Demon appears, and fills his typical role,
in the climax of the book Master of the Five Magics by Lyndon Hardy. Maxwell's Demon was
also mentioned in Christopher Stasheff's books from the series A Wizard in Rhyme. Wherein he
let Maxwell's Demon (Max for short) Help out the main character.
In the way of short stories, A homage to Maxwell has been written by Isaac Asimov and Larry
Niven. Additionally, Larry Niven's Warlock in The Magic Goes Away uses such a demon to cool
his home in a vignette titled "Unfinished Story" as published in "Playgrounds of the Mind". The
Demon also contributes to the thesis of Ken Kesey's collection of stories, The Demon Box.
References to Maxwell's Demon has also been referenced to in manga and video games, as well as
cartoons. Oh My Goddess! by Kosuke Fujishima depicts the Demon as a spirit capable of
generating what amounts to a miniature ramjet. Maxwell's Demon is a villain in the fictional
cartoon show 'Captain Baseball Bat Boy', featured in the video game Max Payne 2: The Fall of
Max Payne. During the game, a character is quizzed on his knowledge of the show to save his life.
The question being "Who was the original creator of Maxwell's Demon?", the character cited both
the Captain Baseball bat-boy character who created the demon, as well as the show's writer, but
was killed for not answering "James Clerk Maxwell". In August 08, 2005 strip of the webcomic
Mac Hall, a hallucinated Maxwell's Demon is found in the air conditioner. Some Windows
releases came with a very simple game called "Maxwell's Maniac", in which you play the part of
Maxwell's Demon by moving a sliding door to try to coax red molecules to one side of a chamber
and blue molecules to the other.
In music and film, Maxwell Demon was the name of Brian Eno's first band, which was the
inspiration for the name of a fictional character in the movie Velvet Goldmine, and Maxwell's
Demon is the name of a 1968 film by the American experimental filmmaker Hollis Frampton.
Maxwell's Demon is mentioned in the song 'A Metaphysical Drama', by Vintersorg and also is also
the name of a London alt-pop band.
^ Maxwell (1871), reprinted in Leff & Rex (1990) at p.4
^ Sanderson, Kathrine (2007-01-31). A demon of a device. Nature.com. Retrieved on
^ Cater (1947), pp640-647, see also the paper by Daub (1970) reprinted in Leff & Rex (1990),
^ Adams (1919), p.267
Physical entropy and information entropy
External links and bibliography
University of Edinburgh's recent findings on soon-to-be-possible Maxwell's Demon
Sciencenews.org article about Maxwell's Demon
Adams, H. (1919). The Degradation of the Democractic Dogma. New York: Kessinger. ISBN
1-4179-1598-6. Bennet, C.H. (1987) "Demons, Engines and the Second Law", Scientific American, November,
Cater, H.D (ed.) (1947). Henry Adams and his Friends. Boston. Daub, E.E. (1967). "Atomism and Thermodynamics". Isis 58: 293-303. Earman, J. and Norton, J. (1998). "Exorcist XIV: The Wrath of Maxwell's Demon. Part I. From
Maxwell to Szilard". Studies In History and Philosophy of Science Part B: Studies In History and
Philosophy of Modern Physics 29: 435-471. Earman, J. and Norton, J. (1999). "Exorcist XIV: The Wrath of Maxwell's Demon. Part II. From
Szilard to Landauer and Beyond". Studies In History and Philosophy of Science Part B: Studies
In History and Philosophy of Modern Physics 30: 1-40. Feynmann, R.P. et al. (1996). Feynman Lectures on Computation. Addison-Wesley. ISBN
0-14-028451-6. , pp148-150
Jordy, W.H. (1952). Henry Adams: Scientific Historian. New Haven. ISBN 0-685-26683-4. Leff, H.S. & Rex, A.F. (eds) (1990). Maxwell's Demon: Entropy, Information, Computing.
Bristol: Adam-Hilger. ISBN 0-7503-0057-4. , may be out of print but contains several papers not
in 2003 edition.
- (2003). Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing. Institute
of Physics. ISBN 0-7503-0759-5. , Contents - an anthology and comprehensive bibliography of
academic papers pertaining to Maxwell's demon and related topics. Chapter 1 provides a historical
overview of the demon's origin and solutions to the paradox.
Maxwell, J.C. (1871). Theory of Heat. , reprinted (2001) New York: Dover, ISBN
Norton, J. (2005). "Eaters of the lotus: Landauer's principle and the return of Maxwell's demon".
Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of
Modern Physics 36: 375-411.
Categories: Philosophy of thermal and statistical physics | Thought experiments | Fundamental
physics concepts | Nanotechnology
- - - - - - - - -- - - - - - -
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The basic idea is to replace all of the randomly positioned and randomly moving particles in the two boxes in contact with each other but connected by a hole with a different abstract symbol for the particles: the "$" (these are, otherwise, the representations of money).
Thus: in starting positions we have this::
| | |
| $ $ | $ $ |
| $ $ $$$ |
|$ $$$ $$$$ |
| | |
In ending position, we have this:
| | $ $ $ $ |
| | $ $ $ $ |
| $ $ $ $ | | $ $ $ $ |
| | $ $ $ $ |
Is it not obvious, then, that the box on the left is "the poor" and the box on the right is "the rich"? And, the age-old observation: "the rich get richer and the poor get poorer" really is real?
And, is it not obvious that this particle ensemble phenomenon really does happen in real life? And, has been going on for all of recorded time? Then, the daemon (perhaps quite a few of them, but not a very very very great number of them) does exist! And, being that PhDs are smart, and
the rich don't have PhDs (therefore: not smart?), then the daemon has limited intelligence, right? Then, Godel's theorem has to be violated since the daemon easily manages to accumulate $s on the right--obviously from an incomplete knowledge but very effective process--, coming from the left, and way way before Maxwell figured out his thought experiment.
Now: homework assignment-- to think of all sub-mechanisms and processes that help the daemon work.
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