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Letters to the Editor, February 2003


This a traditional letter column. You are encouraged to write a letter of comment on anything that you find worthy of comment. It will (may) be published in this column along with my reply. As editor I reserve the right to delete material; however I will not alter the undeleted material. E-mail to me that solely references the contents of this site will be assumed to be publishable mail. All other e-mail is assumed to be private. And, of course, anything marked not for publication is not for publication. Oh yes, letters of appreciation for the scholarly resources provided by this site will be handled very discreetly. This page contains the correspondence for February 2003.

Some of it is a little ancient; I'm slowly catching up - very slowly.

Index of contributors

Other Correspondence Pages


From: Toby Trackman
Date: 02/10/2003
Subj: On Not being an Idiot Savant

I read with interst your page on not being an idiot savant. autistic but seem to posses savant abilities. 'see' the answers forming in his his mind. He had a very severe epilectic fit as a child and says these abilities came to him afterwards. Having spoken to many scientific experts they have agreed this might be possible, but I am intirgued in your explanation that anyone can do it. towards maths or is a skill you sat down and learnt? thoughts or ideas you have on the subject and look forward to hearing from you.

The "seeing answers forming in his mind" sounds familiar. When I do a complex calculation I can see the answer forming. There was a theory that savant abilities are compensatory, i.e., brain damage in one area is compensated for by special skills in another area. However there are cases of otherwise normal people being able to rapidly do complex calculations in their head, so the "compensation" theory is a little suspect.

I come in the category of people who are naturally adept at arithmetic but who are not savants. Put it this way: I could, when in practice, multiply five digit numbers in my head; that is a learnable skill. I could not multiply ten digit numbers in my head; that requires a talent I don't have.

My impression is that for most people skill in calculation is something you have to practice with the view of becoming adept in a particular skill. Thus, if you want to multiply five digit numbers in your head, you have to practice multiplying five digit numbers in your head.

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From: Phil LaRouche
Date: 02/21/2003
Subj: Howe and Hummel

Hello, I liked your site I really enjoy true crime stories from the 19th century.My question to you is: Where can I get a copy of the book Howe and Hummel wrote? it is called "In Danger,Or Life in New York:A True History of the Great City's Wiles and Temptations" I can't seem to find it on Amazon or Alibris or Ebay.......do you have any Ideas....Alibris is offering a cheezy xeroxed reprint for $85.00 !!! I'd love to find an original.Any info you could provide about this book would be appreciated.Thanks alot-Phil LaRouche

I didn't have any luck finding a copy for sale, although the New York Public library (NEW YORK PUB LIBR RES LIBR) supposedly has a copy. There is also a book entitled "Howe & Hummel, the magnificent shysters" which does seem to be available.
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From: Anthony R. Lewis
Date: 02/12/2003
Subj: the only state w/out noreascon members

Get out of South Dakota while you can. http://www.theonion.com/onion3904/north_dakota.html

Not to worry. Mayor Neville of Chamberlain is on a diplomatic mission to North Dakota to arrange peace with honour in our time.
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From: Mark Olson
Date: 2/11/2003
Subj: proofs

Arluis' proof is quite elegant! (He's probably forgotten it, himself.)

He may have forgotten this specific instance, but he has, I assure you, refined the technique over time to produce an admirably irrefutable mode of argumentation.
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From: Arthur Varshavsky
Date: 02/13/2003
Subj: Noam Chomsky and Ayn Rand

It turns out the only reference on the link between Noam Chomsky and Ayn Rand on the entire WWW is your posting (http://richardhartersworld.com/cri/2001/noamrand.html) on some newsgroup. Is it any chance you can elaborate on the topic? I am looking for any provable evidence - articles, interviews etc. Did Chomsky at least ever mention her name publicly? What is the title you are providing at the bottom of your posting - "Ayn Rand, A Mind for our Time", by Noam Chomsky?

Any help will be greatly appreciated.

I regret to inform you that the page you found is a joke. It is possible, I suppose, that there might be some connection between Chomsky and Rand, although it seems unlikely given their respective positions in the political spectrum. The title, "Ayn Rand, A Mind for our Time", is a fabrication.

Best of luck in your search for a connection.

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From: Marion McCoskey
Date: 02/17/2003
Subj: Histogram Sort

Since the histogram sort received such a negative reaction from the people in academia and industry who I talked to when I introduced it in 1999, I was surprised to get a bunch of Google hits when I recently searched for the term.

Thanks for you help in getting the posting on NIST.

I am curious about how you heard of the sort, etc.

I have posted some information about the history on my web site at:

http://www.mcky.net/hsrt.htm

In case you are interested.

Thanks again,

Let me give you the bad news up front - as far as I can tell there is nothing novel in your work. It appears that you have rediscovered the "most significant byte first" radix sort, also known as the post office sort. It is a very old sorting algorithm, one predating computers. Nor is the term "histogram sort" original with you - I was using the term and the concept in 1984, and I am quite confident that the concept and quite possibly the term were not original with me.

Although the sort is not original with you, none-the-less it is a good sort (but not universally superior) and you are to be commended for your insight.

... continued on next rock

I wasn't aware that the term histogram sort was in general use. However I was aware that the concept of a "most significant byte first" radix sort was not novel. My claim to novelty is that my sort uses only one buffer. I believe that both Knuth and Sedgewick both state clearly that a radix or count sort require two data buffers.

Knuth does cites a "linked list" technique that uses a buffer that is proportional to the data size. However, my algorithm uses only the histogram and one data buffer. Not only does it just use one buffer, it is slightly faster than the two buffer technique, even though the code is a little more complex. I think that is because of locality of reference.

If this technique has been previously been discovered, I would appreciate a citation. Either way, it's not a big deal.

As I say, I discovered the trick in 1984, using it to sort integers. Since it is a simple device and since it is a special case of a more general algorithm for doing permutations in place, it is one of those things that is certain to have been discovered and rediscovered. Oddly enough, it is quite possible that there are no actual description of the device in the literature or that, if present, it occurs as a casual mention in a larger context. Be that as it may, I don't have any citations immediately at hand.

I don't feel like digging through Knuth at the moment, but if his book says that O(n) auxilliary storage MUST be used for a lsb radix sort then it is wrong. One can use the same device (construct a histogram and from it construct bucket boundaries) to make each sorting pass in place.

You mentioned that you found that the msb radix sort is faster than the lsb radix sort. There are two positive factors working for the msb radix sort - the first, as you note, is locality of reference, and the second is that the average number of passes will be proportional to O(log n) and not m, where n is the number of items and m is the record length. In compensation the lsb radix sort only requires one pass over the data to construct the m histograms whereas each histogram must be constructed separately in the msb radix sort.

As a note, the reason that radix sorts are potentially faster than comparison sorts is that in effect they do comparisons in parallel. Thus a radix sort with 256 (= 2**8) bins potentially requires 1/8 the number of passes as a comparison sort. There is a catch; a radix sort must make m passes where m is the record length and a comparison sort must make log2(n) passes. If the keys are unique m > log2(n) and can be considerably greater.

... continued on next rock

Perhaps I answered your post to quickly. We need to make a distinction between the histogram storage and the data storage, and when we say "in place" are we talking about the histograms being in place, or the data being in place. What I "discovered" was a "data in place" histogram sort.

I believe that what Knuth was saying is that he didn't know of a method to make the radix method sort data "in place". He did know of a method for substituting a linked list for the second data buffer, but that linked list would be proportional to the size of the data. He didn't say anything about the speed of the linked list method. I don't think he even discussed the issue of partitioning the histograms. I would assume all that would be fairly obvious to most competent programmers.

I first assumed that you were familiar with the "data in place" histogram sort, but then, on re-reading your message, I couldn't be sure. If you would clear that up for me I would appreciate it.

I had thought that it was clear that I was talking about "data in place" sorting, but evidently it was not. It occurs to me that the technique that you used is something other than the rather simple method that I used. The algorithm that I used runs much as follows:

Suppose we have a function f on the data set S such that (a) there is an m such that for all x in S f(x) is an integer in the range 0...m-1, and (b) for all x,y in S, x .le. y => f(x) .le. f(y). Informally, f is a order preserving, bin mapping function that maps S into m bins.

We make one pass over the data to construct a histogram h where h[i] is the number of elements of S such that f(x) = i. The histogram array contains the number of elements in each bin.

From the histogram we determine the bin starting indices for the in-place data movement. These are given by the equations

c[0] = 0
c[i] = c[i-1] + h[i-1], i = 1...m-1
(With a minor bit of ingenuity the c array can overwrite the h array if space is a consideration.) The in-place sorting pass then walks through the data in a loop indexed 0...n-1. During the course of the pass c[i] always contains the address where the next element in bin i must go. At each step in the sorting pass the element examined is either already in its correct bin or it belongs in a later bin. In the former case we increment the corresponding c[i]. If it belongs to a later (greater bin number) bin we do a permutation cycle, moving the initial element to its proper bin, moving the displaced element to its proper bin, and so on until we get to the original bin. In each move the corresponding address value in c[] is incremented.

Each element is examined at most twice and moved at most once. At the end of the main loop all elements in bin 0 are at the beginning, all elements in bin 1 follow them, and so on. Rather nicely, this makes for a stable sort.

Does this sound familiar or did you have something quite different?

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From: Mark Olson
Date: 10/24/2002
Subj: Web pages

The piece with the extended analogy of cell biochemistry was a very nice piece of science writing, also.

As you can see I am catching up with old email. I particularly like that piece beause bad analogies (computer code, recipes, blueprints) can lead to serious misunderstandings of how evolution operates.
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From: Towse
Date: 02/08/2003
Subj: Out of the past and into the present ...

I was reading the Late Show archives because Barry Popik over on ADS-L is a bit of a nut about "The Big Apple" and noted that "The Big Apple" had been mentioned on the Late Show. I kept reading the archive and came across mention of a diary from 1948 ... http://www.cbs.com/latenight/lateshow/exclusives/wahoo/

Hey. I recognize that name.

You're famous!

Now that is seriously weird. I suppose that one has to take fame anyway that one can get it. Thanks for the heads up.
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From: Charles Hitchcock
Date: 10/24/2002
Subj: new urban legend / Darwin award?

Your memory is fading -- Back to Rivets was first, and the incompetent concom (based on our experiences with a certain out-of-town concom) was in The Decomposers. I suppose you have an excuse -- as Richard Deadwood you were lead away with a wastebasket over your head and various SCAdians beating on the wastebasket with sticks, which would tend to blur recollections....

As you can see, I've been a bit slow in answering my email. I've modified the Rabid Rivets page to match your account. I do fear, though, that you've been messing around with reality again.
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From: Gong BingXin
Date: 01/29/2003
Subj: uncertainty principle is untenable

THE UNCERTAINTY PRINCIPLE IS UNTENABLE

By re-analysing Heisenberg's Gamma-Ray Microscope experiment and the ideal experiment from which the uncertainty principle is derived, it is actually found that the uncertainty principle can not be obtained from them. It is therefore found to be untenable.

Key words: uncertainty principle; Heisenberg's Gamma-Ray Microscope Experiment; ideal experiment

Ideal Experiment 1

Heisenberg's Gamma-Ray Microscope Experiment

A free electron sits directly beneath the center of the microscope's lens (please see AIP page http://www.aip.org/history/heisenberg/p08b.htm or diagram below) . The circular lens forms a cone of angle 2A from the electron. The electron is then illuminated from the left by gamma rays--high energy light which has the shortest wavelength. These yield the highest resolution, for according to a principle of wave optics, the microscope can resolve (that is, "see" or distinguish) objects to a size of dx, which is related to and to the wavelength L of the gamma ray, by the expression:

dx = L/(2sinA) (1)

However, in quantum mechanics, where a light wave can act like a particle, a gamma ray striking an electron gives it a kick. At the moment the light is diffracted by the electron into the microscope lens, the electron is thrust to the right. To be observed by the microscope, the gamma ray must be scattered into any angle within the cone of angle 2A. In quantum mechanics, the gamma ray carries momentum as if it were a particle. The total momentum p is related to the wavelength by the formula,

p = h / L, where h is Planck's constant. (2)

In the extreme case of diffraction of the gamma ray to the right edge of the lens, the total momentum would be the sum of the electron's momentum P'x in the x direction and the gamma ray's momentum in the x direction:

P' x + (h sinA) / L', where L' is the wavelength of the deflected gamma ray.

In the other extreme, the observed gamma ray recoils backward, just hitting the left edge of the lens. In this case, the total momentum in the x direction is:

P''x - (h sinA) / L''.

The final x momentum in each case must equal the initial x momentum, since momentum is conserved. Therefore, the final x momenta are equal to each other:

P'x + (h sinA) / L' = P''x - (h sinA) / L'' (3)

If A is small, then the wavelengths are approximately the same,

L' ~ L" ~ L. So we have

P''x - P'x = dPx ~ 2h sinA / L (4)

Since dx = L/(2 sinA), we obtain a reciprocal relationship between the minimum uncertainty in the measured position, dx, of the electron along the x axis and the uncertainty in its momentum, dPx, in the x direction:

dPx ~ h / dx or dPx dx ~ h. (5)

For more than minimum uncertainty, the "greater than" sign may added.

Except for the factor of 4pi and an equal sign, this is Heisenberg's uncertainty relation for the simultaneous measurement of the position and momentum of an object.

Re-analysis

To be seen by the microscope, the gamma ray must be scattered into any angle within the cone of angle 2A.

The microscope can resolve (that is, "see" or distinguish) objects to a size of dx, which is related to and to the wavelength L of the gamma ray, by the expression:

dx = L/(2sinA) (1)

This is the resolving limit of the microscope and it is the uncertain quantity of the object's position.

The microscope can not see the object whose size is smaller than its resolving limit, dx. Therefore, to be seen by the microscope, the size of the electron must be larger than or equal to the resolving limit.

But if the size of the electron is larger than or equal to the resolving limit dx, the electron will not be in the range dx. Therefore, dx can not be deemed to be the uncertain quantity of the electron's position which can be seen by the microscope, but deemed to be the uncertain quantity of the electron's position which can not be seen by the microscope. To repeat, dx is uncertainty in the electron's position which can not be seen by the microscope.

To be seen by the microscope, the gamma ray must be scattered into any angle within the cone of angle 2A, so we can measure the momentum of the electron.

dPx is the uncertainty in the electron's momentum which can be seen by microscope.

What relates to dx is the electron where the size is smaller than the resolving limit. When the electron is in the range dx, it can not be seen by the microscope, so its position is uncertain.

What relates to dPx is the electron where the size is larger than or equal to the resolving limit .The electron is not in the range dx, so it can be seen by the microscope and its position is certain.

Therefore, the electron which relates to dx and dPx respectively is not the same. What we can see is the electron where the size is larger than or equal to the resolving limit dx and has a certain position, dx = 0.

Quantum mechanics does not rely on the size of the object, but on Heisenberg's Gamma-Ray Microscope experiment. The use of the microscope must relate to the size of the object. The size of the object which can be seen by the microscope must be larger than or equal to the resolving limit dx of the microscope, thus the uncertain quantity of the electron's position does not exist. The gamma ray which is diffracted by the electron can be scattered into any angle within the cone of angle 2A, where we can measure the momentum of the electron.

What we can see is the electron which has a certain position, dx = 0, so that in no other position can we measure the momentum of the electron. In Quantum mechanics, the momentum of the electron can be measured accurately when we measure the momentum of the electron only, therefore, we have gained dPx = 0.

And,

dPx dx =0. (6)

Ideal experiment 2

Single Slit Diffraction Experiment

Suppose a particle moves in the Y direction originally and then passes a slit with width dx(Please see diagram below) . The uncertain quantity of the particle's position in the X direction is dx, and interference occurs at the back slit . According to Wave Optics , the angle where No.1 min of interference pattern is can be calculated by following formula:

sinA=L/2dx (1)

and L=h/p where h is Planck's constant. (2)

So the uncertainty principle can be obtained

dPx dx ~ h (5)

Re-analysis

According to Newton first law , if an external force in the X direction does not affect the particle, it will move in a uniform straight line, ( Motion State or Static State) , and the motion in the Y direction is unchanged .Therefore , we can learn its position in the slit from its starting point.

The particle can have a certain position in the slit and the uncertain quantity of the position is dx =0. According to Newton first law , if the external force at the X direction does not affect particle, and the original motion in the Y direction is not changed , the momentum of the particle int the X direction will be Px=0 and the uncertain quantity of the momentum will be dPx =0.

This gives:

dPx dx =0. (6)

No experiment negates NEWTON FIRST LAW. Whether in quantum mechanics or classical mechanics, it applies to the microcosmic world and is of the form of the Energy-Momentum conservation laws. If an external force does not affect the particle and it does not remain static or in uniform motion, it has disobeyed the Energy-Momentum conservation laws. Under the above ideal experiment , it is considered that the width of the slit is the uncertain quantity of the particle's position. But there is certainly no reason for us to consider that the particle in the above experiment has an uncertain position, and no reason for us to consider that the slit's width is the uncertain quantity of the particle. Therefore, the uncertainty principle,

dPx dx ~ h (5)

which is derived from the above experiment is unreasonable.

Conclusion

From the above re-analysis , it is realized that the ideal experiment demonstration for the uncertainty principle is untenable. Therefore, the uncertainty principle is untenable. Reference:

  1. Max Jammer. (1974) The philosophy of quantum mechanics (John wiley & sons , Inc New York ) Page 65
  2. Ibid, Page 67
  3. http://www.aip.org/history/heisenberg/p08b.htm
I have not yet had the chance to review your work, although it does have its points of interest. It quite escapes me, though, why you are sending it to me rather than to Phys. Rev. In any event I shall print it on the chance that some reader may find it of interest.
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From: Charles Hitchcock
Date: 01/06/2003
Subj: new urban legend / Darwin award?

http://ars.userfriendly.org/cartoons/?id=20021229

Thankee. Pigs fly south on the wings of metaphor; vehicles go airborne with the aid of JATO.

JATO = Japanese American Treaty Organization?

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From: Don Webb
Date: 02/05/2003
Subj: Jane Austin

Dear Great One,

This is the funniest damn page on the Internet. I always thought I was best at this with my account of the James gang -- Jesse, Frank, William and Henry -- but I bow now in your direction.

I presume that Henry was the one who kept the books for the gang.
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From: Neil deGrasse Tyson
Date: 01/27/2003
Subj: Earth's Age

Just stumbled on your history of Earth's age web page. A succinct, yet thorough accounting. Congratulations on the effort. -NDT

Thank you for the kind words. In response to your letter I reread the page. I was struck by the fact that the topic is a good illustration of how science works. Science does not deal in absolute truth as such. Rather it catches the lineaments of truth within a net of constraints. At first the net is cast wide and all manner of chimera meander in and out of the net. With time the net is drawn tighter, leaving no room for the monsters of imagination, and the shape of truth takes form.
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From: napdrick
Date: 1/31/2002
Subj: that was pretty entertaining

If you have any new ones please e-mail them to me

I don't have a mailing list as such. However I put up a new set of pages every month, on or about the first of the month. Visit my site again when the urge strikes you.
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From: Gabor Horvath
Date: 01/28/2003
Subj: "disproving" what ?

Would you please tell me what "all quantum superpositions" means? Thanks.

Could you please give me some context. The phrase is a little mysterious all by its lonesome naked self.

... continued on next rock

I've read into an article on your site by the title something like that: "Disproving God's existence by quantum superposition" so I wonder what that amazing concept could cover.

Ah, got it. The article is "A new disproof of the existence of God". The idea is that the wavefunction of a particle collapses when the particle is observed. If there were an all-seeing observer then all wave-functions would collapse. We know, however, that they aren't all collapsed (else tunnel diodes wouldn't work). It is a mystery to me where I got quantum superpositions from; however it certainly sounds impressive.

A friend of mine invented the Heisenberg missile defense. The thought behind that was to measure the velocity of an incoming missile with such great precision that the uncertainty of its position was greater than the continental United States. As I recall, there were some engineering difficulties.

... continued on next rock

Thanks a lot for your response.The idea is truly intriguing. I've read a small popularizing book on quantummechanics in my younger years long ago back in Hungary. It was written by Heisenberg himself. Having an engineering degree which is on the rather practical side of applied math I thaught the book was good entertainment. He says that it was possible to "experimentally prove" that the same particle "A" existed two different locations at the same time.

Well...The other little idea I still remember was that an elementary particle can not truly investigated in its genuine condition since the method/device by which it would be inspected exerts some influence which inevitably changes the behaviour of the subject of experiment. I happily agree with that. Now I am an avid student of the Bible for quite a long time understanding that the Creator is the omnipotent ruler of his creation, laws of nature, time, space matter energy included. It is simple: if the wave-function of a particle behaves in a certain way it is surely the result of known or unknown laws (regulators) which are definitely above the matter/energy (particle/wave) phenomenon. At the same time the maker and maintainer of all those laws is the ruler over them. It is definitely very naive to to assume that He is subject of his own creatures.

But that argument is somewhat of a cop-out. The maker and maintainer of those laws cannot maintain the created laws as inviolable laws and also violate them.
I understand, as you write recalling "some engineering difficulties" initializing your friend's idea on the "Heisenberg missile defense", your tremendous sense of humor. I like it and appreciate it.
I'm glad that you like it. I spared no expense in importing it from an unnamed country.
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This page was last updated February 23, 2003.
It was reformatted and moved February 20, 2006

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