December 2013 - mathfun@mailman.xmission.com

Re: [math-fun] coldest place on earth
by Keith F. Lynch 11 Dec '13

11 Dec '13

Warren D Smith <warren.wds(a)gmail.com> wrote: > The interesting thing about this is that dry ice (froen carbon dioxide) > forms at -78.5C (-109.3F) at Earth atmospheric pressures. > Mars has a carbon dioxide seasonal "ice" cap. > It would now appear that the Earth does too. No. That temperature is when CO2 frost will form with a partial pressure of CO2 of one atmosphere. But of course only about 1/2500th of the air is CO2. So if someone dropped a block of dry ice in that Antarctic valley, it would have sublimated, just like it would in your back yard. Well, okay, maybe more slowly, but it certainly wouldn't have grown, much less appeared spontaneously. Note that the partial pressure of CO2 on Mars is much higher than on Earth, since its atmosphere is 95% CO2. In fact, if you neglected to pump the Mars air out of a room on Mars before filling it with Earth air, it would exceed the OSHA limit for human CO2 exposure. If you teleported Mars's CO2 ice cap to Earth, keeping its temperature unchanged, it would quickly disappear. Eugene Salamin <gene_salamin(a)yahoo.com> wrote: > All of space is filled with the 2.7 K cosmic microwave background.? True. That means an inactive object in space far from any other source of heat will (eventually) be at that temperature. An active object can of course be warmer. > It requires shielding and active refrigeration to cool something to > a lower temperature. No. An active object can also be *colder*. Adiabatic expansion can turn a megakelvin gas cloud from a supernova explosion into a microkelvin gas cloud. Atoms in the same vicinity within such a cloud started with the same speed and direction, so their relative speeds are much lower than in a 2.7 kelvin cloud. Of course the cloud will eventually absorb the microwaves and warm up, but that could take a very long time, as a thin neutral gas is very transparent to microwaves and to almost everything else. Spin temperatures, color temperatures, and information temperatures are metaphorical when taken out of context. As Eugene Salamin pointed out, flipping a magnetic field can result in spin temperatures which are either negative or hotter than infinity, depending on your perspective. But I don't think they can be used to heat or cool your home. Nor can a microwave oven be used to freeze food, even though its radiation has a color temperature of less than one kelvin. Nor can you start a fire with an x-ray machine even though its radiation has a color temperature of millions of kelvins. As for information temperature, would you get more heat by burning a deck of punched cards containing the first million digits of pi or by burning a deck of punched cards containing a million random digits? (This is actually a surprisingly subtle question if you analyze it in enough detail. Can Maxwell's Demon calculate pi? And does it have a Szilard engine to play with?)

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Re: [math-fun] coldest place on earth
by Henry Baker 11 Dec '13

11 Dec '13

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(a)pipeline.com> >>To: Eugene Salamin <gene_salamin(a)yahoo.com>; math-fun <math-fun(a)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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[math-fun] coldest place on earth
by Bill Gosper 10 Dec '13

10 Dec '13

"A team of researchers has presented the coldest ever recorded temperature on Earth: minus 136 degrees Fahrenheit (or, minus 93.2 Celsius)"www.csmonitor.com/Science/2013/1210/How-cold-is-the-coldest-place-on-Earth In depressions in antartica on 10 Aug 2010. The interesting thing about this is that dry ice (froen carbon dioxide) forms at -78.5C (-109.3F) at Earth atmospheric pressures. Mars has a carbon dioxide seasonal "ice" cap. It would now appear that the Earth does too. -- Warren D. Smith This is clearly a measurement error since the tetrahedral bond ∠ is 109.471°. -- Dr. I. J. Matrix "Global warming, my assicle."

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Re: [math-fun] coldest place on earth
by Adam P. Goucher 10 Dec '13

10 Dec '13

> Bill Gosper wrote: > > > -109.3° Fahrenheit > > This is clearly a measurement error since the tetrahedral bond ∠ > is 109.471°. Hehe, that's the most amusing thing I've read today... Sincerely, Adam P. Goucher

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Re: [math-fun] coldest place on earth
by Henry Baker 10 Dec '13

10 Dec '13

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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[math-fun] coldest place on earth
by Warren D Smith 10 Dec '13

10 Dec '13

"A team of researchers has presented the coldest ever recorded temperature on Earth: minus 136 degrees Fahrenheit (or, minus 93.2 Celsius)" www.csmonitor.com/Science/2013/1210/How-cold-is-the-coldest-place-on-Earth In depressions in antartica on 10 Aug 2010. The interesting thing about this is that dry ice (froen carbon dioxide) forms at -78.5C (-109.3F) at Earth atmospheric pressures. Mars has a carbon dioxide seasonal "ice" cap. It would now appear that the Earth does too. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] There must be something wrong with Mathematica's Round function--
by Bill Gosper 08 Dec '13

08 Dec '13

(The first time I pasted in the Subject field, GMail padded it with internal blanks, like an ancient text justfier!) For http://gosper.org/Article.pdf Julian made the "obvious" observation that balanced ternary can represent the reals using 0 and ±any (nonzero) digit you want! On p6 he used ±2 to derive the Fourier series for Sierpinski's gasket. Then on p20, I used ordinary balanced ternary to compute a peculiar, three-valued function that draws the gasket rather directly, as well as appearing in the preceding alternate Fourier derivation. --rwg Date: 2013-12-06 11:13 From: "Adam P. Goucher" <apgoucher(a)gmx.com> To: "Eugene Salamin" <gene_salamin(a)yahoo.com>, "math-fun" < math-fun(a)mailman.xmission.com> Nice. These problems are circumvented by the use of an odd radix, such as ternary (base-3). Balanced ternary has the beautiful property that rounding and truncation are precisely the same operation, and it's very easy to represent and compute negative numbers. I seem to recall that the Russians even had a balanced ternary computer in the mid-20th-century, called Setun or something like that. Sincerely, Adam P. Goucher > ----- Original Message ----- > From: Eugene Salamin > Sent: 12/06/13 07:05 PM > To: math-fun > Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function-- > > Every system of rounding has some arbitrary convention for dealing with 5. I like the convention that was used in numerical tables, in which a least significant digit of 5 that was rounded upward had an overbar over the 5 to signal that the number should be rounded downward in a further rounding. For example, the number 0.12349 in a 4-place table is written as 0.1235 with an overbar over the 5. Then if someone wants a 3-place value, they know to use 0.123 rather than 0.124. > > -- Gene > > > >________________________________ > > From: Dan Asimov <dasimov(a)earthlink.net> > >To: math-fun <math-fun(a)mailman.xmission.com> > >Sent: Friday, December 6, 2013 10:44 AM > >Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function-- > > > > > >OK, that would explain Mathematica's reasoning. > > > >But why? According to what system of rounding? > > > >--Dan > > > > > > > >On 2013-12-06, at 9:36 AM, Adam P. Goucher wrote: > > > >> Half-integers are rounded to the nearest even integer. > >

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Re: [math-fun] There must be something wrong with Mathematica's Round function--
by Adam P. Goucher 06 Dec '13

06 Dec '13

Nice. These problems are circumvented by the use of an odd radix, such as ternary (base-3). Balanced ternary has the beautiful property that rounding and truncation are precisely the same operation, and it's very easy to represent and compute negative numbers. I seem to recall that the Russians even had a balanced ternary computer in the mid-20th-century, called Setun or something like that. Sincerely, Adam P. Goucher > ----- Original Message ----- > From: Eugene Salamin > Sent: 12/06/13 07:05 PM > To: math-fun > Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function-- > > Every system of rounding has some arbitrary convention for dealing with 5. I like the convention that was used in numerical tables, in which a least significant digit of 5 that was rounded upward had an overbar over the 5 to signal that the number should be rounded downward in a further rounding. For example, the number 0.12349 in a 4-place table is written as 0.1235 with an overbar over the 5. Then if someone wants a 3-place value, they know to use 0.123 rather than 0.124. > > -- Gene > > > >________________________________ > > From: Dan Asimov <dasimov(a)earthlink.net> > >To: math-fun <math-fun(a)mailman.xmission.com> > >Sent: Friday, December 6, 2013 10:44 AM > >Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function-- > > > > > >OK, that would explain Mathematica's reasoning. > > > >But why? According to what system of rounding? > > > >--Dan > > > > > > > >On 2013-12-06, at 9:36 AM, Adam P. Goucher wrote: > > > >> Half-integers are rounded to the nearest even integer. > > > > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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Re: [math-fun] There must be something wrong with Mathematica's Round function--
by Adam P. Goucher 06 Dec '13

06 Dec '13

Half-integers are rounded to the nearest even integer. Sincerely, Adam P. Goucher http://cp4space.wordpress.com > ----- Original Message ----- > From: Eugene Salamin > Sent: 12/06/13 05:11 PM > To: math-fun > Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function-- > > Now you've uncovered an actual Mathematica bug. If Round handles 5's consistently, Out[9] should be 10, not 0. > > -- Gene > > > >________________________________ > > From: Bill Gosper <billgosper(a)gmail.com> > >To: math-fun(a)mailman.xmission.com > >Sent: Friday, December 6, 2013 2:10 AM > >Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function-- > > > > > >MBGreen>The question still seems likely to confuse 4th graders. "How to > >use rounding to estimate ..."? What would the kids say if we gave them > >almost the exact same problem immediately afterwards, but added 2 days to > >both the United State and Italy numbers. I'm sure they'd expect the > >estimate of the **difference** to remain the same... > > > >Right. Next time I see him, I'll do this to the poor kid: > >In[9]:= Round[45, 10] - Round[35, 10] > > > >Out[9]= 0 > > > >In[11]:= Round[35, 10] - Round[34, 10] > > > >Out[11]= 10 > > > >Also, where do they say 10 anywhere? Why not > > > >In[18]:= Round[42, 100] - Round[13, 100] > > > > > >Out[18]= 0 > >? > >--rwg > > > >On 2013-12-05 17:49, Bill Gosper wrote: > > > >Oops, logophagy time. Docfiend NeilB points out: > >In[5]:= Round[42, 10] - Round[13, 10] > > > >Out[5]= 30 > > > >is almost certainly the question's intent. > >--rwg > > > >On Tue, Dec 3, 2013 at 11:12 PM, Bill Gosper > ><billgosper(a)gmail.com><billgosper(a)gmail.com>wrote: > > > >It has no effect on this 4th Grade homework problem: > >"Estimate: Workers in Italy receive an average of 42 vacation days per > >year. Workers in the United States receive an average of 13 vacation days > >per year. Explain how to use rounding to estimate how many more vacation > >days workers in Italy receive each year." > >--rwg > >Another nice one: "Write 47,000 in expanded form." > >I suggested forty-seven Ms. > >This is a private school. Everybody says parTISSiple. > >_______________________________________________ > >math-fun mailing list > >math-fun(a)mailman.xmission.com > >http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > > > > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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Re: [math-fun] There must be something wrong with Mathematica's Round function--
by Bill Gosper 06 Dec '13

06 Dec '13

MBGreen>The question still seems likely to confuse 4th graders. "How to use rounding to estimate ..."? What would the kids say if we gave them almost the exact same problem immediately afterwards, but added 2 days to both the United State and Italy numbers. I'm sure they'd expect the estimate of the **difference** to remain the same... Right. Next time I see him, I'll do this to the poor kid: In[9]:= Round[45, 10] - Round[35, 10] Out[9]= 0 In[11]:= Round[35, 10] - Round[34, 10] Out[11]= 10 Also, where do they say 10 anywhere? Why not In[18]:= Round[42, 100] - Round[13, 100] Out[18]= 0 ? --rwg On 2013-12-05 17:49, Bill Gosper wrote: Oops, logophagy time. Docfiend NeilB points out: In[5]:= Round[42, 10] - Round[13, 10] Out[5]= 30 is almost certainly the question's intent. --rwg On Tue, Dec 3, 2013 at 11:12 PM, Bill Gosper <billgosper(a)gmail.com><billgosper(a)gmail.com>wrote: It has no effect on this 4th Grade homework problem: "Estimate: Workers in Italy receive an average of 42 vacation days per year. Workers in the United States receive an average of 13 vacation days per year. Explain how to use rounding to estimate how many more vacation days workers in Italy receive each year." --rwg Another nice one: "Write 47,000 in expanded form." I suggested forty-seven Ms. This is a private school. Everybody says parTISSiple.

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