It's easy to come up with strange coincidences regarding the numbers 9 and 11. See, for example,
http://www.unexplained-mysteries.com/forum/index.php?showtopic=56447
How seriously you take such pecularities depends on your philosophical point of view. A typical scientist would respond that such coincidences are fairly likely by the fact that one can, with p/q the probability of an event, write (1-p/q)n, meaning that if n is large enough the probability is fairly high of "bizarre" classically independent coincidences.
But you might also think about Schroedinger's notorious cat, whose live-dead iffy state has yet to be accounted for by Einsteinian classical thinking, as I argue in this longish article:
http://www.angelfire.com/ult/znewz1/qball.html
Elsewhere I give a mathematical explanation of why any integer can be quickly tested to determine whether 9 or 11 is an aliquot divisor.
http://www.angelfire.com/az3/nfold/iJk.html
Here are some fun facts about divisibility by 9 or 11.
# If integers k and j both divide by 9, then the integer formed by stringing k and j together also divides by 9. One can string together as many integers divisible by 9 as one wishes to obtain that result.
Example:
27, 36, 45, 81 all divide by 9
In that case, 27364581 divides by 9 (and equals 3040509)
# If k divides by 9, then all the permutations of k's digit string form integers that divide by 9.
Example:
819/9 = 91
891/9 = 99
198/9 = 22
189/9 =21
918/9 = 102
981/9 = 109
# If an integer does not divide by 9, it is easy to form a new integer that does so by a simple addition of a digit.
This follows from the method of checking for factorability by 9. To wit, we add all the numerals, to see if they add to 9. If the sum exceeds 9, then those numerals are again added and this process is repeated as many times as necessary to obtain a single digit.
Example a.:
72936. 7 + 2 + 9 + 3 + 6 = 27. 2 + 7 = 9
Example b.:
Number chosen by random number generator:
37969. 3 + 7 + 9 + 6 + 9 = 34. 3 + 4 = 7
Hence, all we need do is include a 2 somewhere in the digit string.
372969/9 = 4144
Mystify your friends. Have them pick any string of digits (say 4) and then you silently calculate (it looks better if you don't use a calculator) to see whether the number divides by 9. If so, announce, "This number divides by 9." If not, announce the digit needed to make an integer divisible by 9 (2 in the case above) and then have your friend place that digit anywhere in the integer. Then announce, "This number divides by 9."
In the case of 11, doing tricks isn't quite so easy, but possible.
We check if a number divides by 11 by adding alternate digits as positive and negative. If the sum is zero, the number divides by 11. If the sum exceeds 9, we add the numerals with alternating signs, so that a sum 11 or 77 or the like, will zero out.
Let's check 5863.
We sum 5 - 8 + 6 - 3 = 0
So we can't scramble 5863 any way and have it divide by 11.
However, we can scramble the positively signed numbers or the negatively signed numbers how we please and find that the number divides by 11.
6358 = 11*578
We can also string numbers divisible by 11 together and the resulting integer is also divisible by 11.
253 = 11*23, 143 = 11*13
143253 = 11*13023
Now let's test this pseudorandom number:
70517. The sum of digits is 18 (making it divisible by 9).
We need to get a -18. So any digit string that sums to -18 will do. The easiest way to do that in this case is to replicate the integer and append it since each positive numeral is paired to its negative.
7051770517/11 = 641070047
Now let's do a pseudorandom 4-digit number:
4556. 4 - 5 + 5 - 6 = - 2. Hence 45562 must divide by 11 (obtaining 4142).
Sometimes another trick works.
5894. 5 - 8 + 9 - 4 = 2. So we need a -2, which, in this case can be had by appending 02, ensuring that 2 is found in the negative sum.
Check: 589402/11 = 53582
Let's play with 157311.
Positive digits are 1,7,1
Negative digits are 5, 3, 1
Positive permutations are
117, 711, 171
Negative permutations are
531, 513, 315, 351, 153, 135
So integers divisible by 11 are, for example:
137115 = 11*12465
711315 = 11*64665
Sizzlin' symmetry
There's just something about symmetry...
To form a number divisible by both 9 and 11, we play around thus:
Take a number, say 18279, divisible by 9. Note that it has an odd number of digits, meaning that its copy can be appended such that the resulting number 1827918279 yields a pattern pairing each positive digit with its negative, meaning we'll obtain a 0. Hence 1827918279/11 = 166174389 and that integer divided by 9 equals 20312031. Note that 18279/9 = 2031,
We can also write 1827997281/11 = 166181571 and that number divided by 9 equals 203110809.
Suppose the string contains an even number of digits. In that case, we can write say 18271827 and find it divisible by 9 (equaling 2030203). But it won't divide by 11 in that the positives pair with positive clones and so for negatives. This is resolved by using a 0 for the midpoint.
Thence 182701827/11 = 16609257. And, by the rules given above, 182701827 is divisible by 9, that number being 20300203.
Ah, wonderful symmetry.
Monday, June 14, 2010
Monday, March 15, 2010
Blinded by the algorithm
This post is a bit lame, as I have not yet been able to locate a copy of Richard Dawkins' "Blind Watchmaker."
I've been reading Francis Crick's autobiographical "This Mad Pursuit," written when he was about 70. He was very enthusiastic for Dawkins' argument against intelligent design, which he summarized thus:
The probability of obtaining a single string of binary digits is extraordinarily remote for even 40 digits (2^40). However, the probability of obtaining a string through "cumulative probability" is quite high. Dawkins had a program select a random digit string and then match it against a template string. By a series of approximations the template was matched after some 40 steps. This is really a variation of the game of Twenty Questions.
Crick, who trained as a physicist, doesn't seem to have noticed the difference in issues here. If one is talking about the origin of life, we must go with the 2^40 analogy. If one is talking about some evolutionary algorithm, then we can be convinced that complex results can occur with application of simple iterative rules.
(Interestingl;y, one study has recently determined that speciation events are not normally distributed, but appear to be exponentially distributed, like radioactivity half lives.)
One can only suppose that Crick, so anxious to uphold his lifelong vision of atheism, leaped on Dawkins' argument without sufficicient criticality. On the other hand, one must accept that his analytic powers may have been waning.
I've been reading Francis Crick's autobiographical "This Mad Pursuit," written when he was about 70. He was very enthusiastic for Dawkins' argument against intelligent design, which he summarized thus:
The probability of obtaining a single string of binary digits is extraordinarily remote for even 40 digits (2^40). However, the probability of obtaining a string through "cumulative probability" is quite high. Dawkins had a program select a random digit string and then match it against a template string. By a series of approximations the template was matched after some 40 steps. This is really a variation of the game of Twenty Questions.
Crick, who trained as a physicist, doesn't seem to have noticed the difference in issues here. If one is talking about the origin of life, we must go with the 2^40 analogy. If one is talking about some evolutionary algorithm, then we can be convinced that complex results can occur with application of simple iterative rules.
(Interestingl;y, one study has recently determined that speciation events are not normally distributed, but appear to be exponentially distributed, like radioactivity half lives.)
One can only suppose that Crick, so anxious to uphold his lifelong vision of atheism, leaped on Dawkins' argument without sufficicient criticality. On the other hand, one must accept that his analytic powers may have been waning.
Friday, October 16, 2009
A fun zero
There is an infinite family of infinite series that represent any complex number z. For details, go to
http://www.angelfire.com/az3/nfold/1funzero.html
http://www.angelfire.com/az3/nfold/1funzero.html
Friday, August 7, 2009
Crash course in entropy
One way to think of entropy gain in a building collapse is thermodynamically, whereby the maximum Boltzmann entropy is reached when one cannot easily distinguish the rubble from the environment. In terms of Shannon entropy, the maximum is reached when one cannot distinguish the signal, or the information consistent with building structure, from the noise, or the ambient information of the environment. The entropy gain means that application of information is required if the building is to be restored.
But we can apply Shannon information somewhat differently to the issue of building collapse, specifically the fire-driven collapse of steel structures. The National Institutes of Standards and Technology concedes that the collapse of a steel-frame building with fire as the main cause is an exceptionally rare event. In fact --excluding the case of the twin towers -- the only one known instance is the collapse of World Trade Center Building 7 at 5:20 p.m. on 9/11.
So we could review records of steel building damage by fire and ask these questions: what percentage of the building was destroyed?; what was the highest point remaining in the post-fire structure?; what degree of symmetry was evident in the collapse? This last question would match the collapse against some symmetrical grid and assign values. We should be able to come up with a method that works satisfactorily for a number of cases.
Here a high-information outlier isn't a building unscathed by its fire, but a building with either near-total collapse or with near-symmetrical collapse (the two cases intersect).
Now the NIST might respond that the information gain reflects a unique building design for Building 7, which proved to be an Achilles heel once fire broke out. The building used an outlier design, in other words.
However, the twin towers also collapsed that day. The NIST deftly suggested that a combination of jet impact and fire led to the collapses. A close reading of the agency's reports, however, shows that its simulations put the blame largely on fire. And, the agency brought up the unique design used in the twin towers. This unique design was the Achilles heel that supposedly permitted the utter collapses. So, in the NIST scenario, the design of the towers would represent another outlier.
The design "flaws" and hence the Achilles heels were completely different in the cases of Building 7 and the twin towers.
The existence of two strikingly different Achilles heels side by side in New York of course represents something highly anomolous. Either the killers were magically aided by one of the most bizarre flukes in history or the gain in information represents a non-random influence.
But we can apply Shannon information somewhat differently to the issue of building collapse, specifically the fire-driven collapse of steel structures. The National Institutes of Standards and Technology concedes that the collapse of a steel-frame building with fire as the main cause is an exceptionally rare event. In fact --excluding the case of the twin towers -- the only one known instance is the collapse of World Trade Center Building 7 at 5:20 p.m. on 9/11.
So we could review records of steel building damage by fire and ask these questions: what percentage of the building was destroyed?; what was the highest point remaining in the post-fire structure?; what degree of symmetry was evident in the collapse? This last question would match the collapse against some symmetrical grid and assign values. We should be able to come up with a method that works satisfactorily for a number of cases.
We then compile our cases, using the statistics gathered, and generate one (or several, if we like) normal curves. Now we know that the highest information is under the outliers and the least within the central 68 percent of the curve. Entropy increase here implies that, statistically, we will tend to move from outlier events to central events.
Here a high-information outlier isn't a building unscathed by its fire, but a building with either near-total collapse or with near-symmetrical collapse (the two cases intersect).
Now the NIST might respond that the information gain reflects a unique building design for Building 7, which proved to be an Achilles heel once fire broke out. The building used an outlier design, in other words.
However, the twin towers also collapsed that day. The NIST deftly suggested that a combination of jet impact and fire led to the collapses. A close reading of the agency's reports, however, shows that its simulations put the blame largely on fire. And, the agency brought up the unique design used in the twin towers. This unique design was the Achilles heel that supposedly permitted the utter collapses. So, in the NIST scenario, the design of the towers would represent another outlier.
The design "flaws" and hence the Achilles heels were completely different in the cases of Building 7 and the twin towers.
The existence of two strikingly different Achilles heels side by side in New York of course represents something highly anomolous. Either the killers were magically aided by one of the most bizarre flukes in history or the gain in information represents a non-random influence.
Thursday, August 6, 2009
Colliderscope
Gail Collins mixes some sci-fi with politics in her New York Times column today. Even though jokingly, she makes sure to refute my suspicion that black holes in the Large Hadron Collider had made the Times' squelch list.
Check the post below and her column at http://nytimes.com
It must be a wormhole. That explains how we journalists are bypassing the embargoes.
Check the post below and her column at http://nytimes.com
It must be a wormhole. That explains how we journalists are bypassing the embargoes.
Monday, August 3, 2009
Paint it black
So suppose Hawking is right that the Large Hadron Collider will have a one in a hundred chance of producing mini-black holes? His theory, buttressed by many physicists, is that such entities would vaporize so fast they could do no harm.
But I'd like to know, are they sure these little buggers aren't quantum entities subject to the Heisenberg uncertainty principle? Because if they are quantum entities, wouldn't that imply that every once in a great while something improbable happens? The hole violates energy conservation just long enough to translate from virtual to real, in which case it I presume could then gobble the planet in short order.
The fact that statistically energy conservation can't be violated does no good if one little beastie acts wildly but in accord with quantum rules. Remember, all solid state circuits are based on this improbable energy violation, whereby a "particle" slips through an energy barrier or potential well. So occasional energy violation would be expected if the mini-holes are quantum particles.
If hundreds of thousands of such particles are produced, is there a signficant chance that one will balloon into a doomsday particle within the next, say, 20 years?
Anybody have an answer for me?
Aug. 4, 2009--Today's New York Times had a feature on the CERN collider saying that the engineers were having a tough time getting the machine to crank up the highest energies. They're still tinkering with it. Scientists would be happy even if it doesn't go at full tilt since the energy levels would still be far higher than those the Fermilab's Tevatron can produce.
Nowhere in Dennis Overbye's otherwise respectable story were black holes mentioned. So I suppose we must infer that we shouldn't worry because the collider won't reach black hole energy levels anytime soon. Funny how many things are on the uncool-to-discuss list. Now even the scientific topic of black holes has made the list, it seems.
But I'd like to know, are they sure these little buggers aren't quantum entities subject to the Heisenberg uncertainty principle? Because if they are quantum entities, wouldn't that imply that every once in a great while something improbable happens? The hole violates energy conservation just long enough to translate from virtual to real, in which case it I presume could then gobble the planet in short order.
The fact that statistically energy conservation can't be violated does no good if one little beastie acts wildly but in accord with quantum rules. Remember, all solid state circuits are based on this improbable energy violation, whereby a "particle" slips through an energy barrier or potential well. So occasional energy violation would be expected if the mini-holes are quantum particles.
If hundreds of thousands of such particles are produced, is there a signficant chance that one will balloon into a doomsday particle within the next, say, 20 years?
Anybody have an answer for me?
Aug. 4, 2009--Today's New York Times had a feature on the CERN collider saying that the engineers were having a tough time getting the machine to crank up the highest energies. They're still tinkering with it. Scientists would be happy even if it doesn't go at full tilt since the energy levels would still be far higher than those the Fermilab's Tevatron can produce.
Nowhere in Dennis Overbye's otherwise respectable story were black holes mentioned. So I suppose we must infer that we shouldn't worry because the collider won't reach black hole energy levels anytime soon. Funny how many things are on the uncool-to-discuss list. Now even the scientific topic of black holes has made the list, it seems.
Saturday, July 25, 2009
Weather warfare?
Several days ago the History Channel aired a That's Impossible segment about weather warfare. The show discussed the possibility that extremely low frequency radio transmissions could be used to alter regional weather.
The idea was that the ELF waves can heat up the ionosphere, causing it to bubble upward and pushing aside the jetstream, yielding marked changes in regional weather. Other possibilities were that such tinkering could redirect hurricanes toward or away from coastlines or that the powerful waves, that can penetrate deep sea depths, could cause human brains to malfunction. And one oil-search technologist was interviewed who claimed that ELF waves, used to probe for oil deposits, can trigger earthquakes in quake-prone zones, and that he had been with a crew that had inadvertently done just that.
Of course there's lots of misinformation and goofy speculation out there on TV and the internet; when I heard that the fantastic ELF effects derived from Nikola Tesla's research I was even more wary. Tesla's name is affiliated with all sorts of nonsense. Nevetheless, I did some checking.
A man named Nick Begich of Anchorage wrote Angels Don't Play This HAARP, an expose book about the HAARP project, a federal operation that beams ELF waves into the ionosphere. I found a summary of his book via Google Scholar which describes how he used Pentagon documents and patent filings to uncover that ELF transmissions might not only be used for long-range submarine communication or exploration of the auroras, but also could possibly be used to focus on a specific part of the ionosphere to generate a plume that affects the jetstream. As for the point that ELF (between 3 and 30 Herz) might cause people to become confused or depressed and to suffer headaches, there is already bona fide research that shows that certain wavelengths (with sufficient amplitude) can indeed have such consequences.
An ELF pulse might be used to jam communications worldwide, while itself being very hard to jam, it has been reported. Such a pulse could be used as a substitute for the method of setting off a high-altitude thermonuclear bomb to jam telecommunications, reports say. The feasibility of this is hinted at by the so-called "Russian woodpecker" ELF transmissions, which disrupted global ham radio with a persistent annoying pulsing noise during the latter Soviet era. The "woodpecker" has been said to have been part of an over-the-horizon missile warning system. (One "crazy" theories is that the woodpecker was used to force a longterm drought over the Western United States as part of a failed economic warfare scheme during the Soviet Union's last years. Another wild theory is that there was an attempt to cause free-floating anxiety in the American population, though I would wonder whether sufficient amplitudes were available.)
I glanced through a Navy document about its ELF transmitters (not the Alaska operation) and noticed that the Navy's research showed that no significant biological effects resulted from its transmissions, but one was left to wonder why the Navy felt it so important to check for biological consequences.
It should be noted that Dr. Begich is the son of a noted Alaska politician, now deceased, and that he has served as head of the Alaska teachers union. (I don't know what field his doctorate represents.)
Geoengineering may be a taboo topic ethically, but it is not so far-fetched. For example, one of a number of ideas for combating global warming is the so-called Geritol solution, whereby iron ore is dumped in the Pacific to stimulate plankton growth, which then sucks the greenhouse gas carbon dioxide out of the atmosphere. One test-run of this idea is known to have been wildly successful, according to a 1995 Science News article.
The idea was that the ELF waves can heat up the ionosphere, causing it to bubble upward and pushing aside the jetstream, yielding marked changes in regional weather. Other possibilities were that such tinkering could redirect hurricanes toward or away from coastlines or that the powerful waves, that can penetrate deep sea depths, could cause human brains to malfunction. And one oil-search technologist was interviewed who claimed that ELF waves, used to probe for oil deposits, can trigger earthquakes in quake-prone zones, and that he had been with a crew that had inadvertently done just that.
Of course there's lots of misinformation and goofy speculation out there on TV and the internet; when I heard that the fantastic ELF effects derived from Nikola Tesla's research I was even more wary. Tesla's name is affiliated with all sorts of nonsense. Nevetheless, I did some checking.
A man named Nick Begich of Anchorage wrote Angels Don't Play This HAARP, an expose book about the HAARP project, a federal operation that beams ELF waves into the ionosphere. I found a summary of his book via Google Scholar which describes how he used Pentagon documents and patent filings to uncover that ELF transmissions might not only be used for long-range submarine communication or exploration of the auroras, but also could possibly be used to focus on a specific part of the ionosphere to generate a plume that affects the jetstream. As for the point that ELF (between 3 and 30 Herz) might cause people to become confused or depressed and to suffer headaches, there is already bona fide research that shows that certain wavelengths (with sufficient amplitude) can indeed have such consequences.
An ELF pulse might be used to jam communications worldwide, while itself being very hard to jam, it has been reported. Such a pulse could be used as a substitute for the method of setting off a high-altitude thermonuclear bomb to jam telecommunications, reports say. The feasibility of this is hinted at by the so-called "Russian woodpecker" ELF transmissions, which disrupted global ham radio with a persistent annoying pulsing noise during the latter Soviet era. The "woodpecker" has been said to have been part of an over-the-horizon missile warning system. (One "crazy" theories is that the woodpecker was used to force a longterm drought over the Western United States as part of a failed economic warfare scheme during the Soviet Union's last years. Another wild theory is that there was an attempt to cause free-floating anxiety in the American population, though I would wonder whether sufficient amplitudes were available.)
I glanced through a Navy document about its ELF transmitters (not the Alaska operation) and noticed that the Navy's research showed that no significant biological effects resulted from its transmissions, but one was left to wonder why the Navy felt it so important to check for biological consequences.
It should be noted that Dr. Begich is the son of a noted Alaska politician, now deceased, and that he has served as head of the Alaska teachers union. (I don't know what field his doctorate represents.)
Geoengineering may be a taboo topic ethically, but it is not so far-fetched. For example, one of a number of ideas for combating global warming is the so-called Geritol solution, whereby iron ore is dumped in the Pacific to stimulate plankton growth, which then sucks the greenhouse gas carbon dioxide out of the atmosphere. One test-run of this idea is known to have been wildly successful, according to a 1995 Science News article.
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