| Topic: |
Science > Physics |
| User: |
"Roman Arce" |
| Date: |
11 May 2004 07:04:53 AM |
| Object: |
arrow of time |
"if the laws of nature do not distinguish between past and future, why are
eggs seen to break but broken eggs never seen to recombine" from
http://physicsweb.org/article/review/17/5/1.
It's not the first time I read that.
An egg can be in many states, a small percentage of those states would be
called unbroken and arbitrarily called order, the majority of the states
would be called broken and arbitrarily called disorder, starting from a
state with low probability (order) and going to one of less probability
(disorder) will be more likely than the opposite, but that doesn't challenge
the arbitrariness of "order". Using a dice instead of an egg if I call 1
order and 2-6 disorder then the chance of going from 1 to 2-6 is 5/6, now if
you ask what's the opposite probability, the trick is there:
Incorrect "opposite" probability: if I start with a 2 (disorder) the
probabily of going to 1 (order) is 1/6.
Correct "opposite" probability: if I add the probabilities of all disorder
states going to order: (2 to 1)+...+(6 to 1) I have 5 initial states with
1/6 each with a total of 5/6.
The choice of a specific initial state like 2 in the incorrect case was
totally arbitrary and therefore unphysical when in the correct (at least
physically meaningful) case there was no arbitrariness.
Note the arbitrariness of choosing 1 as order instead of any other number in
the same way that unbroken egg is chosen as order, unbroken is just an
arbitrary state and the question could be asked with any states as long as
the "order" states represent a tiny percentage of the possible
configurations.
Please tell me if I'm saying something wrong or something "not even wrong"
:).
.
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| User: "Ulmo" |
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| Title: Re: arrow of time |
12 May 2004 03:01:48 PM |
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(Roman Arce) wrote in message news:<3ec0ba0c.0405110053.6d54520a@posting.google.com>...
"if the laws of nature do not distinguish between past and future, why are
eggs seen to break but broken eggs never seen to recombine" from
http://physicsweb.org/article/review/17/5/1.
It's not the first time I read that.
An egg can be in many states, a small percentage of those states would be
called unbroken and arbitrarily called order, the majority of the states
would be called broken and arbitrarily called disorder, starting from a
state with low probability (order) and going to one of less probability
(disorder) will be more likely than the opposite, but that doesn't challenge
the arbitrariness of "order". Using a dice instead of an egg if I call 1
order and 2-6 disorder then the chance of going from 1 to 2-6 is 5/6, now if
you ask what's the opposite probability, the trick is there:
Incorrect "opposite" probability: if I start with a 2 (disorder) the
probabily of going to 1 (order) is 1/6.
Correct "opposite" probability: if I add the probabilities of all disorder
states going to order: (2 to 1)+...+(6 to 1) I have 5 initial states with
1/6 each with a total of 5/6.
The choice of a specific initial state like 2 in the incorrect case was
totally arbitrary and therefore unphysical when in the correct (at least
physically meaningful) case there was no arbitrariness.
Note the arbitrariness of choosing 1 as order instead of any other number in
the same way that unbroken egg is chosen as order, unbroken is just an
arbitrary state and the question could be asked with any states as long as
the "order" states represent a tiny percentage of the possible
configurations.
Please tell me if I'm saying something wrong or something "not even wrong"
:).
There is no way to define "order" versus "disorder" or "random" versus
"not random" separate from the human psychology, the prejudice or bias
of the observer. If you "see a pattern" you call it "order" and if you
don't "see a pattern", you call it disorder. If you showed a list of
prime numbers to someone who never heard of prime numbers, they would
call it random. However, any possible list of numbers could be
produced by some algorithmn even if we don't know what it is. If you
show someone a series of numbers, and they don't see any pattern, and
they call it "disordered", and then you give them the algorithmn that
produces it, does that mean the series changed from "disordered" to
"ordered" just because of the change in the observer's knowledge.
If you are playing poker and receive a royal flush, you think, "Wow!
That was very unlikely!", but of course a royal flush isn't any less
likely than any other possible combination of the cards. The
difference is, in our society, most combinations of the cards are
called "nothing", and don't correspond to any hand in our game of
poker. If you are dealt a hand we call "nothing", you don't notice
anything unusual. If you are dealt a hand we call a "royal flush", you
notice it, and feel like something very unlikely has happened, even
though both hands are equally likely. We would call a royal flush
"ordered" and the nothing hand "disordered" but that's totally
arbitrary.
People invented the second law of thermodynamics to explain why you
don't see the air rush to the corners of the room you are in, but
there is no need to invent such a thing because you can totally
explain the fact you don't see the air rush to the corners of the room
by the mere fact that it is a tiny percentage of all possible
trajectories of all the molecules in the room that lead to that
configuration, about 1 in 10^10^20. It's the same as the fact that if
you roll a dice, you probably won't roll a 6 because the likelihood is
1 in 6. Therefore, there's no need for any second law of
thermodynamics. Furthermore, there is no objective logical reason to
attach any significance to a set of trajectories of all the air
molecules in the room that lead to a configuration where all the air
is in the corners of the room, versus any other configuration. It's
the same as attaching an arbitary significance to the number 6 when
rolling a dice. The only reason we attach a significance to it is
because we notice all the air rushing to the corners of the room.
Well, so what? You cares if we notice it or not. Some alien
civilization might notice eddies in the air in the room or something
else we would never notice. If your definition of ordered versus
disordered depends on what a given observer would "notice" then it
depends on the observer. Calling the air rushing to the corners of the
room "ordered" is like rolling a dice and calling rolling a six
"ordered" and rolling any other number "disordered".
David
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| User: "Douglas Natelson" |
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| Title: Re: arrow of time |
14 May 2004 04:09:02 AM |
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Ulmo wrote:
There is no way to define "order" versus "disorder" or "random" versus
"not random" separate from the human psychology, the prejudice or bias
of the observer.
While there is some truth to your later statements, I disagree
with this. One can define a correlation function, for example,
that measures the periodicity of the spacings of particles.
Crystals produce diffraction spots; liquids do not. This kind
of structural order is well-defined mathematically, and in fact
is related to the fundamental concepts of symmetry and
symmetry breaking (and phase transitions and so forth).
Those correlations, independent of whether one chooses to
quantify them, are certainly there in crystals and not in
liquids.
<snip>
Calling the air rushing to the corners of the
room "ordered" is like rolling a dice and calling rolling a six
"ordered" and rolling any other number "disordered".
So, don't you think it's surprising that, from the hugely
large number of possible microstates of all the matter in the
universe, the universe apparently started out in a configuration
such that we can easily prepare an empty room for air to
rush into? One of the great mysteries, to many physicists,
is why the universe started off in such a low-entropy state.
--DN
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| User: "Jerzy Karczmarczuk" |
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| Title: Re: arrow of time |
13 May 2004 05:25:04 AM |
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Ulmo wrote:
There is no way to define "order" versus "disorder" or "random" versus
"not random" separate from the human psychology, the prejudice or bias
of the observer. If you "see a pattern" you call it "order" and if you
don't "see a pattern", you call it disorder. If you showed a list of
prime numbers to someone who never heard of prime numbers, they would
call it random. However, any possible list of numbers could be
produced by some algorithmn even if we don't know what it is. If you
show someone a series of numbers, and they don't see any pattern, and
they call it "disordered", and then you give them the algorithmn that
produces it, does that mean the series changed from "disordered" to
"ordered" just because of the change in the observer's knowledge.
This is a metaphysical, not an operational viewpoint. When I launch a
random number generator, I KNOW that the sequence is perfectly determi-
nistic and repeatable, yeat I *call it random*.
Physicists are rarely medieval scholastics. There *ARE* ways of defining
randomness, e.g. the quality of a RN generator through proofs of ergodicity,
statistical tests, etc. There are ways of defining - not always but
frequently - the notion of order as the breakdown of a symmetry.
Sorry for being a bit brutal, but reducing notions which are analysable by
the theory of measure, etc. to human prejudices and psychology doesn't
sound very scientific.
Jerzy Karczmarczuk
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| User: "Thomas Dent" |
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| Title: Re: arrow of time |
14 May 2004 11:25:56 AM |
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Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote
Ulmo wrote:
There is no way to define "order" versus "disorder" or "random" versus
"not random" separate from the human psychology, the prejudice or bias
of the observer. If you "see a pattern" you call it "order" and if you
don't "see a pattern", you call it disorder. If you showed a list of
prime numbers to someone who never heard of prime numbers, they would
call it random. However, any possible list of numbers could be
produced by some algorithmn even if we don't know what it is. If you
show someone a series of numbers, and they don't see any pattern, and
they call it "disordered", and then you give them the algorithmn that
produces it, does that mean the series changed from "disordered" to
"ordered" just because of the change in the observer's knowledge.
This is a metaphysical, not an operational viewpoint. When I launch a
random number generator, I KNOW that the sequence is perfectly determi-
nistic and repeatable, yeat I *call it random*.
Physicists are rarely medieval scholastics. There *ARE* ways of defining
randomness, e.g. the quality of a RN generator through proofs of ergodicity,
statistical tests, etc. There are ways of defining - not always but
frequently - the notion of order as the breakdown of a symmetry.
Sorry for being a bit brutal, but reducing notions which are analysable by
the theory of measure, etc. to human prejudices and psychology doesn't
sound very scientific.
Jerzy Karczmarczuk
To expand on this a little, one can use Shannon's
information-theoretic entropy to give a very precise definition of
"randomness" as it applies to entropy. The more bits of information
needed to completely specify a state, the more "random" it is
considered and the greater its entropy. Now, of course, the number of
possible states grows exponentially with the amount of information
needed, and hence with the entropy, so given a minimal assumption of
ergodicity, you are exponentially more likely to make a transition
into a state of higher entropy.
Of course, you could interpret "random" to mean ergodic, so you get
the apparent paradox that "random" (ergodic) evolution can sometimes
lead to a "less random" (i.e. lower entropy) state! (And yes, this
means that the Second Law is violated - but only very very rarely!)
.
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| User: "Kirk Gregory Czuhai" |
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| Title: Re: arrow of time |
17 May 2004 02:03:56 AM |
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(Thomas Dent) wrote in message news:<cb504c2c.0405140745.29695d48@posting.google.com>...
Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote
Ulmo wrote:
There is no way to define "order" versus "disorder" or "random" versus
"not random" separate from the human psychology, the prejudice or bias
of the observer. If you "see a pattern" you call it "order" and if you
don't "see a pattern", you call it disorder. If you showed a list of
prime numbers to someone who never heard of prime numbers, they would
call it random. However, any possible list of numbers could be
produced by some algorithmn even if we don't know what it is. If you
show someone a series of numbers, and they don't see any pattern, and
they call it "disordered", and then you give them the algorithmn that
produces it, does that mean the series changed from "disordered" to
"ordered" just because of the change in the observer's knowledge.
This is a metaphysical, not an operational viewpoint. When I launch a
random number generator, I KNOW that the sequence is perfectly determi-
nistic and repeatable, yeat I *call it random*.
Physicists are rarely medieval scholastics. There *ARE* ways of defining
randomness, e.g. the quality of a RN generator through proofs of ergodicity,
statistical tests, etc. There are ways of defining - not always but
frequently - the notion of order as the breakdown of a symmetry.
Sorry for being a bit brutal, but reducing notions which are analysable by
the theory of measure, etc. to human prejudices and psychology doesn't
sound very scientific.
Jerzy Karczmarczuk
To expand on this a little, one can use Shannon's
information-theoretic entropy to give a very precise definition of
"randomness" as it applies to entropy. The more bits of information
needed to completely specify a state, the more "random" it is
considered and the greater its entropy. Now, of course, the number of
possible states grows exponentially with the amount of information
needed, and hence with the entropy, so given a minimal assumption of
ergodicity, you are exponentially more likely to make a transition
into a state of higher entropy.
Of course, you could interpret "random" to mean ergodic, so you get
the apparent paradox that "random" (ergodic) evolution can sometimes
lead to a "less random" (i.e. lower entropy) state! (And yes, this
means that the Second Law is violated - but only very very rarely!)
I am pondering the statement, "The more bits of information
needed to completely specify a state, the more "random" it is
considered and the greater its entropy." and wondering if this applies
always to living organisms OR if I may jump ahead to what many have
faith in, God !!!
Would not God have to have infinite entropy or total disorder based on
this definition? Pardon me if this topic is not allowed discussion
here.
Back to the life forms:
Consider two two rabbits that were twin siblings. Suppose one was
starved of vitamin C and eventually died as a consequence. Would you
say that while it lived with scurvey that it was more ordered and had
a lower entropy than its healthier twin that was recieving an adequet
diet? Surely you see, less information was needed to describe the diet
of the rabbit that was gonna die.
peace and love,
(kirk) kirk gregory czuhai
http://www.altelco.net/~churches
http://heavensense.intranets.com
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| User: "Phillip Helbig---remove CLOTHES to reply" |
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| Title: Re: arrow of time |
17 May 2004 05:05:17 AM |
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In article <68c18740.0405161853.753737cf@posting.google.com>,
lovekgc@altelco.net (Kirk Gregory Czuhai) writes:
I am pondering the statement, "The more bits of information
needed to completely specify a state, the more "random" it is
considered and the greater its entropy." and wondering if this applies
always to living organisms OR if I may jump ahead to what many have
faith in, God !!!
It depends on the definitions of "information" and "randomness". In
some sense (the sense alluded to above), the more one can compress
something (say, a text file with a compression program), the less
information it contains, since there is some redundancy (otherwise it
couldn't be compressed). In this sense, something random cannot be
compressed, and thus has a high information content. Intuitively, one
would attribute "complexity" neither to something completely random, nor
to something completely predictable, but somewhere in-between.
There is a reasonably good discussion of this in Murray Gell-Mann's
popular book THE QUARK AND THE JAGUAR.
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| User: "alistair" |
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| Title: Re: arrow of time |
22 May 2004 04:49:33 AM |
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(Phillip Helbig---remove CLOTHES to reply) wrote in message news:<c89oio$c6f$2@online.de>...
Intuitively, one
would attribute "complexity" neither to something completely random,
nor
to something completely predictable, but somewhere in-between
A good example of this is prime numbers, some of which can be
predicted and follow a pattern but primes as a whole cannot be
predicted by one equation
and the greatest mathematicians in history have failed to solve this
problem
-people like Bernard Riemann.
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| User: "Kirk Gregory Czuhai" |
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| Title: Re: arrow of time |
17 May 2004 08:19:20 PM |
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(Phillip Helbig---remove CLOTHES to reply) wrote in message news:<c89oio$c6f$2@online.de>...
In article <68c18740.0405161853.753737cf@posting.google.com>,
lovekgc@altelco.net (Kirk Gregory Czuhai) writes:
I am pondering the statement, "The more bits of information
needed to completely specify a state, the more "random" it is
considered and the greater its entropy." and wondering if this applies
always to living organisms OR if I may jump ahead to what many have
faith in, God !!!
It depends on the definitions of "information" and "randomness". In
some sense (the sense alluded to above), the more one can compress
something (say, a text file with a compression program), the less
information it contains, since there is some redundancy (otherwise it
couldn't be compressed). In this sense, something random cannot be
compressed, and thus has a high information content. Intuitively, one
would attribute "complexity" neither to something completely random, nor
to something completely predictable, but somewhere in-between.
There is a reasonably good discussion of this in Murray Gell-Mann's
popular book THE QUARK AND THE JAGUAR.
Thank you for the explanation. I admit my basic lack of education in
information theory. Seems somehow intuitive (and apparently wrong) to
me that the more information something contained would make something
have more order not less! (neglecting any compression ability). I have
been subjected enough to both classical and quantum mechanical physics
and have seen Murray Gell-Mann's work in other areas to see that we
indeed for many reasons live in a very Complex Universe!
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| User: "George Buyanovsky" |
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| Title: Re: arrow of time |
20 May 2004 03:47:11 PM |
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(Thomas Dent) wrote in message news:<cb504c2c.0405140745.29695d48@posting.google.com>...
Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote
To expand on this a little, one can use Shannon's
information-theoretic entropy to give a very precise definition of
"randomness" as it applies to entropy. The more bits of information
needed to completely specify a state, the more "random" it is
considered and the greater its entropy.
Shannon's entropy is defined for simples 0-order context model; the
higher orders will produce different entropy for each probabilistic
set of outcomes. So entropy is a product of source modeling. More
precise definition of complexity (randomness) has to account the
modeling algorithm as well. If some one proposed the predictive
apparatus (let's assume "Quantum Mechanics"), which is implemented as
a computer program to predict the probabilistic set of outcomes, then
complexity of modeled process can be defined as entropy of
probabilistic set of outcomes multiplied by set size plus amount of
memory necessary for modeling algorithm to accomplish prediction.
Still "amount of memory necessary for modeling algorithm" is weakly
defined since there is significant variation of algorithm
implementations.
Best,
George
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| User: "alistair" |
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| Title: Re: arrow of time |
23 May 2004 03:13:59 AM |
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Jerzy Karczmarczuk
to make a transition
into a state of higher entropy.
evolution can sometimes
lead to a "less random" (i.e. lower entropy) state! (And yes, this
means that the Second Law is violated - but only very very rarely!)
But the second law will not
be violated - the entropy of the surroundings in which the lower
entropy state was created will increase.The total entropy is what
counts.
Entropy cannot be interpreted in terms of isolated systems because
there is no known system that is isolated in the real world, apart,
perhaps from the universe itself.
.
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