Re: [math-fun] coldest place on earth
Gene in correct, I am using "temperature" in a generalized sense that applies to statistical systems. To connect this with physics, consider Fredkin's "billiard ball" computer; it works only if every mass, angle, velocity, etc. are _perfect_. Even the slightest error starts blowing up incredibly fast to render the system useless as a real computer. Billiard ball computers are subject to the same virial and equipartition theorems as any other physical system. There are lots of degrees of freedom in these systems, but if we want to make a computer, we have to focus on certain of these degrees of freedom and erect a barrier between those degrees of freedom that we care about and all the rest. This barrier _isolates_ and _insulates_ the degress of freedom that are doing computation from the degrees of freedom that aren't. But even simple _insulation_ isn't enough; we need an active _refrigerator_, which rejects energy (and bits!) that we don't want from the computational degrees of freedom. As do all refrigerators, this takes _work_, and produces _waste heat_, which is exactly that waste energy and those corrupting bits that we want to keep out of our computation. A usable billiard ball computer would require little "Maxwell's Demons" on virtually every ball which are capable of doing _course corrections_ to the ball so that the collisions are "true". These Maxwell's Demons would require energy to run and eliminate excess energy and excess bits (low-order bits from the velocity components) to keep the billiard computer actually computing. So how come real computers work at all? It is because _essentially every gate is a little refrigerator_ which keeps the data bits in and the error bits out. Every logic gate _normalizes_ the logic level by bringing it into the acceptable range, and by _squaring_ it up so that it is nice and clean. To the extent that the logic levels are already correct and the pulse is square, then the logic gate doesn't have to work very hard and produces little waste heat. However, if it has to bring a logic level up from 60% to 100% and filter a lot of high(er) frequencies out of the pulse, this gate will generate lots of waste energy and waste bits. These little refrigerators/logic gates have to abide by all of the standard theorems of heat engines & refrigerators, _so long as they are suitably interpreted_. Bennett tells us that a perfectly reversible computer requires no additional energy to run. What I'm saying is that running a Bennett computer in the real world requires a substantial amount of "refrigeration" in order to keep the computational degrees of freedom "cold" enough to operate without error. This refrigeration rejects waste heat and waste bits. At 01:22 PM 12/10/2013, Eugene Salamin wrote:
You seem to be using the term "temperature" in a different sense from "that which is measured with a thermometer". All computers that I'm aware of generate heat, and in fact heat removal is the major obstacle to faster CPU frequency. In your sense, the coldest place on Earth is a petroglyph, a stone carving.
-- Gene
________________________________ From: Henry Baker <hbaker1@pipeline.com> To: Eugene Salamin <gene_salamin@yahoo.com>; math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, December 10, 2013 12:53 PM Subject: Re: [math-fun] coldest place on earth
If you generalize "temperature" as in statistical thermodynamics, then you should be able to do better.
"temperature" is essentially the change in energy content w.r.t. change information content.
Modern computer memory systems are quite good at storing huge amounts of information with very little energy, so they should have a very low "temperature".
In this case the "shielding" is the height of the barriers.
Basically, computers couldn't possibly work unless the "effective temperature" (in statistical thermodynamics terms) of the information stored in their circuits is exceedingly low. Otherwise, they'd constantly be making mistakes & be useless as a digital computer.
At 11:38 AM 12/10/2013, Eugene Salamin wrote:
This is the coldest place on Earth under natural conditions. The coldest place on Earth was in a physics experiment at a temperature of 50 nK. This was touted as the coldest place in the universe.
While a computer logic gate may act as a refrigerator with respect to information theoretic entropy, it acts as a heat source in regard to thermodynamic entropy. A reversible computer can run without an energy source, but which way does it run? You need some entropy increase to drive it in the desired direction. -- Gene
________________________________ From: Henry Baker <hbaker1@pipeline.com> To: Eugene Salamin <gene_salamin@yahoo.com>; math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, December 10, 2013 4:50 PM Subject: Re: [math-fun] coldest place on earth
Gene in correct, I am using "temperature" in a generalized sense that applies to statistical systems.
To connect this with physics, consider Fredkin's "billiard ball" computer; it works only if every mass, angle, velocity, etc. are _perfect_. Even the slightest error starts blowing up incredibly fast to render the system useless as a real computer.
Billiard ball computers are subject to the same virial and equipartition theorems as any other physical system. There are lots of degrees of freedom in these systems, but if we want to make a computer, we have to focus on certain of these degrees of freedom and erect a barrier between those degrees of freedom that we care about and all the rest. This barrier _isolates_ and _insulates_ the degress of freedom that are doing computation from the degrees of freedom that aren't.
But even simple _insulation_ isn't enough; we need an active _refrigerator_, which rejects energy (and bits!) that we don't want from the computational degrees of freedom. As do all refrigerators, this takes _work_, and produces _waste heat_, which is exactly that waste energy and those corrupting bits that we want to keep out of our computation.
A usable billiard ball computer would require little "Maxwell's Demons" on virtually every ball which are capable of doing _course corrections_ to the ball so that the collisions are "true". These Maxwell's Demons would require energy to run and eliminate excess energy and excess bits (low-order bits from the velocity components) to keep the billiard computer actually computing.
So how come real computers work at all? It is because _essentially every gate is a little refrigerator_ which keeps the data bits in and the error bits out. Every logic gate _normalizes_ the logic level by bringing it into the acceptable range, and by _squaring_ it up so that it is nice and clean. To the extent that the logic levels are already correct and the pulse is square, then the logic gate doesn't have to work very hard and produces little waste heat. However, if it has to bring a logic level up from 60% to 100% and filter a lot of high(er) frequencies out of the pulse, this gate will generate lots of waste energy and waste bits.
These little refrigerators/logic gates have to abide by all of the standard theorems of heat engines & refrigerators, _so long as they are suitably interpreted_.
Bennett tells us that a perfectly reversible computer requires no additional energy to run.
What I'm saying is that running a Bennett computer in the real world requires a substantial amount of "refrigeration" in order to keep the computational degrees of freedom "cold" enough to operate without error. This refrigeration rejects waste heat and waste bits.
At 01:22 PM 12/10/2013, Eugene Salamin wrote:
You seem to be using the term "temperature" in a different sense from "that which is measured with a thermometer". All computers that I'm aware of generate heat, and in fact heat removal is the major obstacle to faster CPU frequency. In your sense, the coldest place on Earth is a petroglyph, a stone carving.
-- Gene
________________________________ From: Henry Baker <hbaker1@pipeline.com> To: Eugene Salamin <gene_salamin@yahoo.com>; math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, December 10, 2013 12:53 PM Subject: Re: [math-fun] coldest place on earth
If you generalize "temperature" as in statistical thermodynamics, then you should be able to do better.
"temperature" is essentially the change in energy content w.r.t. change information content.
Modern computer memory systems are quite good at storing huge amounts of information with very little energy, so they should have a very low "temperature".
In this case the "shielding" is the height of the barriers.
Basically, computers couldn't possibly work unless the "effective temperature" (in statistical thermodynamics terms) of the information stored in their circuits is exceedingly low. Otherwise, they'd constantly be making mistakes & be useless as a digital computer.
At 11:38 AM 12/10/2013, Eugene Salamin wrote:
This is the coldest place on Earth under natural conditions. The coldest place on Earth was in a physics experiment at a temperature of 50 nK. This was touted as the coldest place in the universe.
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