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Author
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Topic: Information really is matter/energy
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The Pixie
Member
Member # 548
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posted 21. May 2003 08:46
Indeed:
I = Smc^2/m * omega
I = k ln(W) * mc^2/m * omega
I = (k * omega * c^2) ln(W)
But k, omega and c are all constants, so we can substitute a new constant, K
I = K ln(W)
Pixie
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Jerry D. Bauer
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Member # 756
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posted 21. May 2003 14:16
I divided out mass after I had already calculated energy which can be gleaned from the equation. But here’s one that may be better: Let M_0 = our rest mass and M_1 = moving mass. If we then express E as (M_1)(C^2)/M_0 something cool happens. On earth the size of our marbles won’t affect information at all. But if this matter begins to move, we know that the closer our marbles get to the speed of light, the closer our mass should get to infinity. Of course, so will energy since they are related. But what’s interesting here is that should our matter/energy ever approach infinity, then so will our information.
This would change the particulars of the equation to: I = (ln[W])([M_1(C^2)/M_0]Omega. So if you can accept this, I think we have a formula that firmly ties in matter/energy with information. And since I’m the ‘honest to the max’ proverbial Southern country boy, at this point, I would have little choice but to rename this formula ‘the Bauer- van Meurs equation.’ ![[Wink]](wink.gif)
NOTE TO FORUM: This is Chronos. I became a member of ISCID under my real name. When I logged in to check out the back rooms, I forgot about the fact I was looged in as Jerry and posted in Brainstorms. Oh well, might as well just leave it that way.
[ 21. May 2003, 14:21: Message edited by: Jerry D. Bauer ]
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Pim van Meurs
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Member # 541
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posted 21. May 2003 14:37
Chronos: You 'calculate energy' and then divide out the mass, leaving something far less than energy and in fact you are left with a constant.
As Pixie showed and as Shannon has shown many decades earlier the general form of entropy is of the form
S= K ln W
Where K is an arbitrary constant. In your case you have set the constant to be some very large number but to suggest that this links entropy/information to energy ignores that you have removed any relevant component to energy. Can this be 'saved' by making entropy a function of gamma (1/sqrt(1-v^2/c^2) ? Perhaps but why all these ad hoc formulas which have so far not been shown to have any physical or logical relationship.
Nothing in your 'formula' ties energy and information other than perhaps in an ad hoc manner which leaves it unclear why information would go to infinity. But an interesting side effect of gamma now is that information increases merely by increasing the speed.
Sorry but these things just don't make sense from any theoretic foundation.
Have you looked at the Helmholz free energy or the link between energy and information via the second law of thermodynamics?
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Jerry D. Bauer
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Member # 756
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posted 21. May 2003 16:41
“Indeed:
I = Smc^2/m * omega
I = k ln(W) * mc^2/m * omega
I = (k * omega * c^2) ln(W)
But k, omega and c are all constants, so we can substitute a new constant, K
I = K ln(W)”
Jerry: Hmmm…Very good, my man. Did Pixie just relate information and matter by boiling all that mess down into a simplistic formula? Yes, he did. Did he also just tie in information with energy? Yes he did. He has taken information and tied it directly into the math of Ludwig Boltzmann.
Remember that Boltzmann defined his entropy as: Entropy (disorder) is the opposite of information. Now Pixie has shown us this mathematically.
K=Boltzmann’s constant which is expressed as 1.38 x 10^-23 Joules/Kelvin. If I then multiply this times the complexity specificity of my information (s or ln(W) I get information expressed as J/K. If I have 10^45 atoms of hydrogen in a closed system, I can express this information thus: (1.38 X 10^-23)(ln(10^45) = I = 1.43 -21 J/K.
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Pim van Meurs
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Member # 541
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posted 21. May 2003 16:59
Chronos:
Pixie indeed showed that energy (mc^2) dropped out and what remained was the Shannon/Boltzman form. The constant K is totally arbitrary and if information was related to energy then it should not be totally independent of energy. In other words no relationship really because if there was a relationship it would not be a constant. Hope you get what I am trying to say here ![[Smile]](smile.gif)
But as I have said before, check out for instance the work by Schneider who has linked Shannon information/entropy and Boltzman entropy via the second law of thermodynamics.
Relevant links
Molecular Information Theory and the Theory of Molecular Machines
Theory of molecular machines
Good page on entropy,uncertainty and information
Equation 11 gives "a direct, quantitative relationship between the decrease in entropy of a molecular machine and the information that it gains during an operation"
Schneider links information and energy via the SLOT
quote:
There is a minimum amount of heat energy:
Epsilon= K_b T ln(2) (16)
that must be dissipated (negative q) by a molecular machine in order for it to gain R = 1 bit of information
Schneider has done some very interesting work using Shannon information to detect binding sites.
[ 21. May 2003, 17:06: Message edited by: Pim van Meurs ]
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Jerry D. Bauer
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Member # 756
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posted 21. May 2003 21:16
Jerry: I understand what you mean, but I think you’re missing the big picture. There can be a relationship between two quantities when a constant is being used. C^2 is a constant too.
What pixie did were two things. 1) He replaced the constant C^2 with Boltzmann’s constant. 2) Then the mass he is using is the mass of atoms. When the density of that mass decreases, entropy goes up. So he is really doing similar to what I was doing, but much better mathematically put.
“Pixie indeed showed that energy (mc^2) dropped out and what remained was the Shannon/Boltzman form.”
Fine, but he still came out in Joules, he just took a couple of different turns to get there. Joules is a direct measurement of energy. Can you see that he is still showing a direct relationship between information and energy which is the same banana just a different perspective?
”But as I have said before, check out for instance the work by Schneider who has linked Shannon information/entropy and Boltzman entropy via the second law of thermodynamics.”
Jerry: Well, shannon’s math has always calculated entropy in the form of Shannon-Weaver entropy. I assume you’re meaning he has linked shannon’s math to thermodynamic entropy. I did check out Schneider’s work in this area and I will go to the pages you have referenced. The problem with him I’m having initially is that he wants to use Shannon’s Math, and that limits us only to information that is being transferred within a channel. I want to go with a broader definition of information entropy if I can.
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Pim van Meurs
Member
Member # 541
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posted 21. May 2003 22:48
Jerry: Fine, but he still came out in Joules, he just took a couple of different turns to get there.
He came up with a constant which can be given any qualifier Joules, Ergs, m/s but certainly from the formula you presented Joules were not part of the equation [L]^2[T]^-2
Nor was the constant related to Boltzman constant in any non ad hoc manner.
jerry: The problem with him I’m having initially is that he wants to use Shannon’s Math, and that limits us only to information that is being transferred within a channel. I want to go with a broader definition of information entropy if I can.
Not really, all is needed is entropy before and entropy after. Calculating Shannon entropy is relatively straightforward.
You also lost me when you stated
quote:
2) Then the mass he is using is the mass of atoms. When the density of that mass decreases, entropy goes up.
Did he use mass or density? And where did he use the mass? How can the constant increase and still be a constant?
Why all this gymnastics if you in the end want to use Boltzman entropy?
Btw when I said "Schneider who has linked Shannon information/entropy and Boltzman entropy via the second law of thermodynamics" then I exactly meant that Shannon entropy and Boltzman entropy were linked as well as the minimal energy involved in information change.
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Jerry D. Bauer
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Member # 756
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posted 22. May 2003 02:21
“He came up with a constant which can be given any qualifier Joules, Ergs, m/s but certainly from the formula you presented Joules were not part of the equation [L]^2[T]^-2”
I don’t believe that’s correct, is it? First, when you multiplied the terms together I presented: mass x c^2, the figure you come out with will be expressed as Joules.
This page explains this quite simply: E=MC^2 = 0.030 x 300,000,000 x 300,000,000 = 2,700,000,000,000,000 Joules. Now, you might see that I did not come up with that equation but stole it from a school in Canada called the Worsley school:
http://www.geocities.com/thesciencefiles/emc2/emc2.html
As a final point, here are the calculations to obtain Boltzmann’s constant:
“Obtaining Boltzmann Constant (k):
R = 0.0821 (atm.L)/(mol.K) 1 atm.L = 101J
R = 8.31 J/mol.K
NA = 6.02x1023/mol
(R)(NA) = k = 1.38x10-23 J/K”
http://web.fccj.org/~ethall/2046/ch17/prob.htm
So I believe we can safely conclude that Boltzmann’s constant should be expressed as Joules/Kelvin. Of course, we can convert to other units of energy/temp but I don’t see why we would want to since J/K is pretty standard in thermodynamics. And a constant cannot increase. I’m not sure where you got that.
As to mass, gasses in a closed system are composed of atoms that contain mass, are they not? So when these atoms diffuse, isn’t that mass diffusing right along with them? I think it is. Now I did not mean to imply that Pixie used a value for mass in the Boltzmann equation. So perhaps you either misunderstood me or I was not clear.
And most finally, I’m also aware that Shannon-Boltzmann entropy has been around for decades. But I still don’t understand how you believe this is relevant to our discussion. Am I missing something? If so, I have an open mind. Tell me how you believe it is relevant.
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Pim van Meurs
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Member # 541
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posted 22. May 2003 14:43
Jerry: You take energy, divide it by mass. How can energy be part of the equation when you take out its relevant parts? But one can simply do the calculation. Of course one can always give your constant K the required qualifiers but if in the end all you were interested in is the Boltzman equation then why the long and irrelevant approach?
Jerry: And a constant cannot increase. I’m not sure where you got that.
Indeed so your constant has no relationship to energy or it would be able to increase when for instance the mass increases.
Jerry: I’m also aware that Shannon-Boltzmann entropy has been around for decades. But I still don’t understand how you believe this is relevant to our discussion. Am I missing something? If so, I have an open mind. Tell me how you believe it is relevant.
I thought you wanted to calculate information/entropu. Shannon has provided you with an excellent tool that can be and has been succesfully applied to the genome.
Although the concept of information/entropy can be somewhat counterintuitive.
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Jerry D. Bauer
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Member # 756
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posted 22. May 2003 18:03
Pim, you're thinking around this and not through it. I sometimes do this as well, because often the obvious isn't that obvious. But look directly at Einstein's formula: E = MC^2. C^2 is a constant. It is only the mass that changes to provide change in energy.
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Pim van Meurs
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Member # 541
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posted 22. May 2003 19:50
Jerry: I am fully aware of Einstein's formula but you forget two factors
1. m is not a constant
2. m is variable
1. m=gamma m_0 where gamma is a function of velocity v
2. m is not a fixed quantity
Thus while E=mC^2 cannot be replace by E=K where K is a constant, S=m C^2/m obviously can be replaced by a constant but then has no real relevance to energy.
It's really obvious that your formula, ad hoc as it is, has no relevance to energy when you divide out some of the relevant factors that make up energy.
I wish I could put it in simpler terms but you cannot claim relevancy to energy if it does not depend on energy in any form or manner.
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