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[math-fun] Letter insertions
by Steve Witham 12 Jul '07

12 Jul '07

"Insert letters to form words" is a nice highway passtime with license plates. Similar lateral feeling. Different section of the brain than those used for "what does this acronym stand for" and "what is this vanity plate about." Maybe that would make a cool FMRI study. Trivial Pursuit, too, when you really don't know, but get the right answer out of the blue. Once I did $ grep inel /usr/dict/words and got this scary poem: inelastic inelegant ineligible ineluctable machinelike sentinel trichinella --Steve p.s. what the hec are hectorems? > > .*H.*R.*E.*M.*S.* > >Dan A: HREMS -> harems, theorems, and ? >Mike S: hectorems. > >From: Bill Gosper <rwmgosper(a)yahoo.com> > >scHwaRtzEneggerisMS? higHeR mathEMaticS! > >hypergeometrics, hectorems, hordeolums, >hypernatremias. > >Some reasons to kick yourself: >theremins, thermochemist(ry), threadworms, threesomes, >chrysanthemums,

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Re: [math-fun] Letter insertions
by Eugene Salamin 12 Jul '07

12 Jul '07

----- Original Message ---- From: Steve Witham <sw(a)tiac.net> To: math-fun(a)mailman.xmission.com Sent: Thursday, July 12, 2007 9:40:56 AM Subject: [math-fun] Letter insertions "Insert letters to form words" is a nice highway passtime with license plates. Similar lateral feeling. Different section of the brain than those used for "what does this acronym stand for" and "what is this vanity plate about." Maybe that would make a cool FMRI study. Trivial Pursuit, too, when you really don't know, but get the right answer out of the blue. Once I did $ grep inel /usr/dict/words and got this scary poem: inelastic inelegant ineligible ineluctable machinelike sentinel trichinella --Steve p.s. what the hec are hectorems? > > .*H.*R.*E.*M.*S.* > >Dan A: HREMS -> harems, theorems, and ? >Mike S: hectorems. > >From: Bill Gosper <rwmgosper(a)yahoo.com> > >scHwaRtzEneggerisMS? higHeR mathEMaticS! > >hypergeometrics, hectorems, hordeolums, >hypernatremias. > >Some reasons to kick yourself: >theremins, thermochemist(ry), threadworms, threesomes, >chrysanthemums, 1 hectorem = 100 rems. A rem is a unit of ionizing radiation dose, equal to the absorption of 1 Joule of energy per kilogram of tissue, and corrected for the biological effectiveness of the type of radiation. Is it just coincidence that this is associated with inel = Idaho National Engineering Laboratory (now called Idaho National Laboratory), a nuclear reactor R&D facility? Gene ____________________________________________________________________________________ Fussy? Opinionated? Impossible to please? Perfect. Join Yahoo!'s user panel and lay it on us. http://surveylink.yahoo.com/gmrs/yahoo_panel_invite.asp?a=7

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Re: [math-fun] Stairway to Heaven?
by Eugene Salamin 11 Jul '07

11 Jul '07

----- Original Message ---- From: Steve Witham <sw(a)tiac.net> To: math-fun(a)mailman.xmission.com Sent: Wednesday, July 11, 2007 10:32:57 AM Subject: [math-fun] Stairway to Heaven? I wrote to the webmaster of the HIPAS site http://www.hipas.alaska.edu/hipasweb/hipas.htm and they have improved the description of their transmitters: The Heater system consists of 8 transmitters capable of conducting amplitude modulation of 100 Hz - 20 kHz and phase modulation of 0 -20 kHz. Each transmitter can transmit up to 150kW at 2.85 or 4.53 MHz on CW mode. The HAARP transmitter is also in the HF band (3 - 30mHz), so neither is anywhere close to 17 Hz! I think a 17 Hz transmitter and antenna need to be quite different from HF far-cousins. In fact I'm having a hard time imagining a 17 Hz directional antenna in Alaska since the wavelength is 18,000 kM. CO2 is only .04% of the atmosphere by volume. Maybe the laser can be tuned to heat CO2. And then, maybe a heated column of CO2 can be a major absorber of 17 Hz radio waves even with an omnidirectionnal transmitter? I only watch EE from the sidelines. --Steve _______________________________________________ The Navy once had Project ELF that transmitted at 76 Hz to deep submarines. Perhaps some of that equipment could be recycled for this new purpose. The 17 Hz is the cyclotron resonance frequency, qB/(2 pi m), for singly charged CO2 molecules in a field of 50 µT. However, as the molecules are pushed to higher altitude (which is a pretty dubious assumption), the field becomes smaller and the resonance frequency drops. It would be nice if someone who has confidence in this project would post some quantitative performance calculations. Gene ____________________________________________________________________________________ Fussy? Opinionated? Impossible to please? Perfect. Join Yahoo!'s user panel and lay it on us. http://surveylink.yahoo.com/gmrs/yahoo_panel_invite.asp?a=7

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[math-fun] Stairway to Heaven?
by Steve Witham 11 Jul '07

11 Jul '07

I wrote to the webmaster of the HIPAS site http://www.hipas.alaska.edu/hipasweb/hipas.htm and they have improved the description of their transmitters: The Heater system consists of 8 transmitters capable of conducting amplitude modulation of 100 Hz - 20 kHz and phase modulation of 0 -20 kHz. Each transmitter can transmit up to 150kW at 2.85 or 4.53 MHz on CW mode. The HAARP transmitter is also in the HF band (3 - 30mHz), so neither is anywhere close to 17 Hz! I think a 17 Hz transmitter and antenna need to be quite different from HF far-cousins. In fact I'm having a hard time imagining a 17 Hz directional antenna in Alaska since the wavelength is 18,000 kM. CO2 is only .04% of the atmosphere by volume. Maybe the laser can be tuned to heat CO2. And then, maybe a heated column of CO2 can be a major absorber of 17 Hz radio waves even with an omnidirectionnal transmitter? I only watch EE from the sidelines. --Steve

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Re: [math-fun] Superduperghost
by Bill Gosper 11 Jul '07

11 Jul '07

Dan A: HREMS -> harems, theorems, and ? Mike S: hectorems. scHwaRtzEneggerisMS? higHeR mathEMaticS! > (The grep search would be something like > > .*H.*R.*E.*M.*S.* > > but no fair doing one!) I did one anyway. Merriam-Webster finds 258, excluding hypergeometrics, hectorems, hordeolums, hypernatremias. Some reasons to kick yourself: theremins, thermochemist(ry), threadworms, threesomes, chrysanthemums, de|enthronements, disheartenments, enshrinements, hemorrhoidectomies|mise|mizes, horsemanship, hysterectomies||. More math: three-dimensional, Khwarezmians! Reasons for medics to kick themselves: thyroidectomies|mise|mizes, nephrectomies||, thromboembolism, choleresteremias, hemispherectomies, hyperglycemias. Mensa specials: whoremaster|monger, Christadelphianisms, harlequinisms, headforemost, headstreams, mithraeums (an anagram of rheumatism), phrasemakers|mongers, shrewmouse. Interesting illegals: white sumpremacist,northern|southern hemisphere, charlie mccarthys, hebrewisms HUH?: schnurkeramiks --rwg ____________________________________________________________________________________ Pinpoint customers who are looking for what you sell. http://searchmarketing.yahoo.com/

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[math-fun] Stairway to Heaven?
by Steve Witham 10 Jul '07

10 Jul '07

>From: Eugene Salamin <gene_salamin(a)yahoo.com> > >A stairway to heaven? > >May 31st 2007 | ACAPULCO > >From The Economist print edition > >If implemented, this would be another taxpayer sponsored boondoggle. > >1. Even if this concept works, why will it launch into space CO2 >rather than N2 or O2? There exists far more of these in the >atmosphere. My reading was that the 17 Hz frequency is what selects CO2 ions rather than another ion. >2. Atmospheric CO2 is part of the biosphere. If we throw away >atmospheric CO2, the atmosphere will re-equilibrate by taking away >carbon from life. There will be fewer plants and animals. >Conversely, burning fossil fuels returns to the biosphere carbon >that has been locked up for a hundred million years. The whole global-warming-by-manmade-CO2 hypothesis is that the current concentration of CO2 in the atmosphere is unnaturally high and caused by the rate of burning of fossil fuels, and that the natural correction mechanisms either can't reabsorb it at the current production rate, or will do so by processes catastrophic to us. It's true that this method throws away carbon. To call it "sequestration" stretches the term. I can't tell whether throwing out carbon is a bad or good thing. You might say that fossil fuel is spare carbon. But then, what else are we going to build all those diamond cities and buckycable elevators out of? >3. This expenditure is entirely unnecessary. There already exists >a facility called HAARP that can transmit 3.6 MW of RF power from >the Arctic into the ionosphere. http://www.haarp.alaska.edu/ I believe what doesn't exist is the specific combination of radio transmitters (at 17 Hz) and lasers. The article mentions starting with another existing facility: >The site of the conveyor Dr Wong is proposing to build is the >Arctic. More specifically, he is suggesting it be over one of his >workplaces, the High Power Auroral Stimulation facility near >Fairbanks in Alaska that he set up 20 years ago to stimulate and >study artificial auroras. http://www.hipas.alaska.edu/hipasweb/hipas.htm That page says HIPAS has "8 - 150 kW transmitters," which possibly means 1.2 MW (but it continues, "capable of modulation at an amplitude of 100 Hz - 20 kHz and Phase of 0 -20 kHz," which is so incoherent it leaves the whole sentence in doubt). This map shows both HIPAS and HAARP: http://www.hipas.alaska.edu/hipasweb/alaska_map.htm The article says that ...his lasers and radio transmitters, even if powered by fossil-fuel generated electricity, should cause far less CO2 to be put into the atmosphere than they ship out of it. but it doesn't say what percentage of the world's power production would be needed to make a dent in the CO2 concentration any decade soon. --Steve

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[math-fun] Superduperghost
by Dan Asimov 10 Jul '07

10 Jul '07

My new bride, Karen, and I -- stuck in a ferry queue at the start of our honeymoon -- passed the time playing Superduperghost. This is like the word game Ghost, but each time a person adds a letter to the previous string, the new letter can go anywhere in that string. (So a turn consists of reciting the entire new string.) After Karen recited "HREMS" it was my turn, and I couldn't think of anything but HAREMS, which would be a loss for me, of course, so I gave up. But later I searched a word list and found two more common words (both which would've ended on me anyway). Without using any kind of software, I challenge y'all to find the shorter of these two (Scrabble-eligible) words, which happens to have only 8 letters. (The grep search would be something like .*H.*R.*E.*M.*S.* but no fair doing one!) --Dan

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Re: [math-fun] CO2 sequestration in outer space, take two...
by Eugene Salamin 09 Jul '07

09 Jul '07

----- Original Message ---- From: Henry Baker <hbaker1(a)pipeline.com> To: math-fun <math-fun(a)mailman.xmission.com> Sent: Monday, July 9, 2007 3:27:22 PM Subject: [math-fun] CO2 sequestration in outer space, take two... Obviously, our discussion on math-fun last year must have generated some thinking. I was wrong about utilizing space tethered smokestacks, but Dr. Wong was right on. ----- Economist.com Global warming A stairway to heaven? May 31st 2007 | ACAPULCO >From The Economist print edition Earth has a natural transport system standing ready to get rid of carbon dioxide. Here is how it might be turned on MOST solutions to the problem of global warming are tediously, almost oppressively, quotidian. Switch the lights off. Stop using fossil fuels to make electricity. Run an efficient car. Don't fly. A few grandiose projects have also been suggested, such as giant parasols in space or adding iron to the ocean to encourage planktonic algae to grow and soak up carbon dioxide. On the whole, though, those big ideas are either mad or could have dangerously unpredictable consequences. That does not mean that lateral thinking about the problem has no place. And the idea proposed by Alfred Wong of the University of California, Los Angeles, at last week's meeting of the American Geophysical Union, in Acapulco, is about as lateral as they come. Dr Wong reckons the problem is not so much that CO2 is being thrown away, but that it is not being thrown far enough. According to his calculations, a little helping hand would turn the Earth's magnetic field into a conveyor belt that would vent the gas into outer space, whence it would never return. The site of the conveyor Dr Wong is proposing to build is the Arctic. More specifically, he is suggesting it be over one of his workplaces, the High Power Auroral Stimulation facility near Fairbanks in Alaska that he set up 20 years ago to stimulate and study artificial auroras. The Arctic sky is special because it is one of the two places (the other being the Antarctic) where the magnetic shield of the Earth opens up to outer space. Auroras, such as the one pictured above, pleasingly testify to a stream of particles from the sun that gets through and hits the atmosphere. These particles bring with them many gigawatts of power that Dr Wong wants to harness to reduce the concentration of greenhouse gases in the atmosphere. Going up in the world His idea starts with the fact that CO2 molecules like to team up with loose electrons, to form CO2 ions. A few percent of the CO2 molecules in the air manage to find such electrons. As a result they become negatively charged. The second piece of luck is that all over the Earth there is a constant vertical electrical field. The surface and the atmosphere form a giant battery, as the lightning discharges of thunderstorms demonstrate. This field tends to make negatively charged ions, such as those of CO2, drift upward. At first this happens slowly, because collisions with other molecules keep throwing the drifting ions off course. But after a few days they arrive at an altitude, about 125km up, which is so rarefied that an ion can move freely about. This is when the last stage of their one-way trip into space begins: sailing along the magnetic field of the Earth. High in the polar regions, the lines of magnetic force point almost straight upwards. When a charged particle is in a magnetic field, it tends to travel along that field's lines of force, spiralling as it goes. In the case of a CO2 ion at an altitude of 125km, it spirals round 17 times a second. However, as it travels upwards, it experiences a weakening field. It must then make fewer turns per second, in obedience to a law of physics called the conservation of magnetic moment (this is similar to the law of conservation of angular momentum that slows a spinning ice dancer down as he spreads his arms). And because it cannot just shed its energy of movement, it is forced to travel faster and faster in the direction of the field. The eventual result is that it is ejected into space. That, at least, is the theory. And although CO2 is too rare even in today's atmosphere for the phenomenon to be detected by existing satellites, an equivalent ejection of oxygen, a far more abundant gas, can be detected from space. So it seems more than likely that Dr Wong's analysis of what is going on in nature is right. The question is, can CO2 molecules be given an artificial leg-up into space, so that they leave the atmosphere in sufficient numbers to make a difference to climate change? Dr Wong thinks they can. The leg-up he proposes comes in two stages. First, he has to ionise more CO2. There are many ways this might be done, but for a first experiment Dr Wong proposes zapping dust in the atmosphere with powerful lasers, to release electrons that can then combine with CO2. Having created the ions, he will then nudge those that have drifted upwards to the appropriate height with radio waves of exactly 17 cycles a second, which will give them a nice stock of energy at the beginning of their spiralling phase. Once they are there, Dr Wong expects the incoming stream of charged particles that cause auroras to deliver the bonus that will make the whole thing work, by dumping some of their energy into the spiralling as well. This should happen through a process called stochastic resonance: the spiralling molecules get preferential treatment, so to speak, because they stand out in what is otherwise an environment of random movements. So far, Dr Wong has only rough calculations of the energy needs of his scheme, but these suggest that his lasers and radio transmitters, even if powered by fossil-fuel generated electricity, should cause far less CO2 to be put into the atmosphere than they ship out of it. The key to this efficiency is the free energy arriving by stochastic resonance. If the particles do their bit, he thinks that a few dozen megawatts of additional electrical power is all that will be needed to make a dent in the amount of CO2. Exactly how big that dent would be, he is not yet sure. But he is pretty sure it would be big enough to help. Copyright © 2007 The Economist Newspaper and The Economist Group. All rights reserved. _______________________________________________ If implemented, this would be another taxpayer sponsored boondoggle. 1. Even if this concept works, why will it launch into space CO2 rather than N2 or O2? There exists far more of these in the atmosphere. 2. Atmospheric CO2 is part of the biosphere. If we throw away atmospheric CO2, the atmosphere will re-equilibrate by taking away carbon from life. There will be fewer plants and animals. Conversely, burning fossil fuels returns to the biosphere carbon that has been locked up for a hundred million years. 3. This expenditure is entirely unnecessary. There already exists a facility called HAARP that can transmit 3.6 MW of RF power from the Arctic into the ionosphere. http://www.haarp.alaska.edu/ Gene ____________________________________________________________________________________ Fussy? Opinionated? Impossible to please? Perfect. Join Yahoo!'s user panel and lay it on us. http://surveylink.yahoo.com/gmrs/yahoo_panel_invite.asp?a=7

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[math-fun] CO2 sequestration in outer space, take two...
by Henry Baker 09 Jul '07

09 Jul '07

Obviously, our discussion on math-fun last year must have generated some thinking. I was wrong about utilizing space tethered smokestacks, but Dr. Wong was right on. ----- Economist.com Global warming A stairway to heaven? May 31st 2007 | ACAPULCO >From The Economist print edition Earth has a natural transport system standing ready to get rid of carbon dioxide. Here is how it might be turned on MOST solutions to the problem of global warming are tediously, almost oppressively, quotidian. Switch the lights off. Stop using fossil fuels to make electricity. Run an efficient car. Don't fly. A few grandiose projects have also been suggested, such as giant parasols in space or adding iron to the ocean to encourage planktonic algae to grow and soak up carbon dioxide. On the whole, though, those big ideas are either mad or could have dangerously unpredictable consequences. That does not mean that lateral thinking about the problem has no place. And the idea proposed by Alfred Wong of the University of California, Los Angeles, at last week's meeting of the American Geophysical Union, in Acapulco, is about as lateral as they come. Dr Wong reckons the problem is not so much that CO2 is being thrown away, but that it is not being thrown far enough. According to his calculations, a little helping hand would turn the Earth's magnetic field into a conveyor belt that would vent the gas into outer space, whence it would never return. The site of the conveyor Dr Wong is proposing to build is the Arctic. More specifically, he is suggesting it be over one of his workplaces, the High Power Auroral Stimulation facility near Fairbanks in Alaska that he set up 20 years ago to stimulate and study artificial auroras. The Arctic sky is special because it is one of the two places (the other being the Antarctic) where the magnetic shield of the Earth opens up to outer space. Auroras, such as the one pictured above, pleasingly testify to a stream of particles from the sun that gets through and hits the atmosphere. These particles bring with them many gigawatts of power that Dr Wong wants to harness to reduce the concentration of greenhouse gases in the atmosphere. Going up in the world His idea starts with the fact that CO2 molecules like to team up with loose electrons, to form CO2 ions. A few percent of the CO2 molecules in the air manage to find such electrons. As a result they become negatively charged. The second piece of luck is that all over the Earth there is a constant vertical electrical field. The surface and the atmosphere form a giant battery, as the lightning discharges of thunderstorms demonstrate. This field tends to make negatively charged ions, such as those of CO2, drift upward. At first this happens slowly, because collisions with other molecules keep throwing the drifting ions off course. But after a few days they arrive at an altitude, about 125km up, which is so rarefied that an ion can move freely about. This is when the last stage of their one-way trip into space begins: sailing along the magnetic field of the Earth. High in the polar regions, the lines of magnetic force point almost straight upwards. When a charged particle is in a magnetic field, it tends to travel along that field's lines of force, spiralling as it goes. In the case of a CO2 ion at an altitude of 125km, it spirals round 17 times a second. However, as it travels upwards, it experiences a weakening field. It must then make fewer turns per second, in obedience to a law of physics called the conservation of magnetic moment (this is similar to the law of conservation of angular momentum that slows a spinning ice dancer down as he spreads his arms). And because it cannot just shed its energy of movement, it is forced to travel faster and faster in the direction of the field. The eventual result is that it is ejected into space. That, at least, is the theory. And although CO2 is too rare even in today's atmosphere for the phenomenon to be detected by existing satellites, an equivalent ejection of oxygen, a far more abundant gas, can be detected from space. So it seems more than likely that Dr Wong's analysis of what is going on in nature is right. The question is, can CO2 molecules be given an artificial leg-up into space, so that they leave the atmosphere in sufficient numbers to make a difference to climate change? Dr Wong thinks they can. The leg-up he proposes comes in two stages. First, he has to ionise more CO2. There are many ways this might be done, but for a first experiment Dr Wong proposes zapping dust in the atmosphere with powerful lasers, to release electrons that can then combine with CO2. Having created the ions, he will then nudge those that have drifted upwards to the appropriate height with radio waves of exactly 17 cycles a second, which will give them a nice stock of energy at the beginning of their spiralling phase. Once they are there, Dr Wong expects the incoming stream of charged particles that cause auroras to deliver the bonus that will make the whole thing work, by dumping some of their energy into the spiralling as well. This should happen through a process called stochastic resonance: the spiralling molecules get preferential treatment, so to speak, because they stand out in what is otherwise an environment of random movements. So far, Dr Wong has only rough calculations of the energy needs of his scheme, but these suggest that his lasers and radio transmitters, even if powered by fossil-fuel generated electricity, should cause far less CO2 to be put into the atmosphere than they ship out of it. The key to this efficiency is the free energy arriving by stochastic resonance. If the particles do their bit, he thinks that a few dozen megawatts of additional electrical power is all that will be needed to make a dent in the amount of CO2. Exactly how big that dent would be, he is not yet sure. But he is pretty sure it would be big enough to help. Copyright Â© 2007 The Economist Newspaper and The Economist Group. All rights reserved.

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[math-fun] Open problem #6 now solved
by Christian Boyer 09 Jul '07

09 Jul '07

In 2005, I published 10 open problems on magic squares in my paper of The Mathematical Intelligencer. One of them (open problem #6) was: Construct a magic square of cubes of prime numbers I am please to announce that this very difficult problem is now solved by a joint work of Jaroslaw Wroblewski (Poland) and Hugo Pfoertner (Germany). Their square is a 42x42 square, and use 1764 consecutive prime numbers: from 11 to 15137. Magic sum = 33151363766492. It remains now 8 unsolved problems on 10. And my €100 prize + bottle of Champagne are still to win! (open problem #2). Christian.

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