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Mike Renzulli

Mysticism and Mathematics

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While math is not one of my strong points, I was susprised to find out about math and it's ties to mysticism.

Some research on line has lead me to find out that Greecian mathemetician and philosopher Pythagoras founded his own school which focused on teaching and learning of Mathematics, Music, Philosophy, and Astronomy and their relationship with Religion.

Pythagoras brought this with him back to the Mediterranean region after learning a variety of things (like geometry) from Egyptian priests while living in Egypt some 21 years.

Among Pythagorean students was Plato in which it looks like that his teacher's religious orientation had a profund influence on Plato and I would not be surprised if this is how Plato culminated his theory of The Forms.

This also somewhat explains why some people associated with Intelligent Design have been trying to find the existence of God using mathematical equations.

It would seem that any mysticism associated with math can be halted by an injection of Aristotelian/Randian philosophy in order to bring it back down to earth.

This may not be new for many on these boards but it is surprising to me since I didn't know anything about it until now.

I thought I would post this for those who didn't know about this and express my hope that Objectivists proficient in math consider activities to undermine the mysticism applied to math.

Edited by Mike Renzulli

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There are other philosophic views of mathematics, which you can read about here.

A poll of math professors would likely show that a small minority subscribe to Empiricism or Aristotelian realism. The influence of Plato on the majority is pretty clear.

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Sadly, you are correct. There are more mathematicians who subscribe to the Platonic view than Aristotelian realists.

I have also been able to find a physician named Dr. Travis Norsen who is associated with ARI who points out the same thing that I observed in math too.

Norberg states:

What is needed, in short, is a return to the type of physical explanations that dominated physics prior to the 20th century, and which still dominate in the philosophically more healthy sciences of chemistry and biology -- this time with the full philosophic proof of their propriety. Only this will allow physics to progress beyond its current state of mathematics-obsessed superficiality.

None the less, if Plato's influence extends to the field of math, it will make Aristotelians efforts to bring it back to reality all the more daunting.

I wonder if there is some way to assist Aristotelians in their tasks. Anyone know how?

There are other philosophic views of mathematics, which you can read about here.

A poll of math professors would likely show that a small minority subscribe to Empiricism or Aristotelian realism. The influence of Plato on the majority is pretty clear.

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It would seem that any mysticism associated with math can be halted by an injection of Aristotelian/Randian philosophy in order to bring it back down to earth.

Aristotle made no significant contributions to mathematics. Rand made no contributions to mathematics at all. In fact she was a mathematical ignoramus (i.e. knew next to nothing about math).

On the other hand one of the members of Plato's academy, Eudoxus made invaluable contributions to the theory of ratios and proportions. See book VI of Euclid's Elements. It turns out the Platonic-Pythagorean is the axis along which modern mathematics has best flourished.

You might want to read -Pi in the Sky:Counting, Thinking and Being- by John D. Barrow, especially the last chapter on neo-Platonism and mathematics. Among the leading modern Neo-Platonists is Kurt Goedel who proved his famous Incompleteness Theorems and sunk Hilbert's program of formalizing mathematics and establishing the consistency of the theory of real numbers.

This is a very interesting book which gives a view of several approaches to the nature of Mathematics. Aristotle has almost no role in the development of mathematics.

Ba'al Chatzaf

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While math is not one of my strong points, I was susprised to find out about math and it's ties to mysticism.

Some research on line has lead me to find out that Greecian mathemetician and philosopher Pythagoras founded his own school which focused on teaching and learning of Mathematics, Music, Philosophy, and Astronomy and their relationship with Religion.

Pythagoras brought this with him back to the Mediterranean region after learning a variety of things (like geometry) from Egyptian priests while living in Egypt some 21 years.

Among Pythagorean students was Plato in which it looks like that his teacher's religious orientation had a profund influence on Plato and I would not be surprised if this is how Plato culminated his theory of The Forms.

This also somewhat explains why some people associated with Intelligent Design have been trying to find the existence of God using mathematical equations.

It would seem that any mysticism associated with math can be halted by an injection of Aristotelian/Randian philosophy in order to bring it back down to earth.

This may not be new for many on these boards but it is surprising to me since I didn't know anything about it until now.

I thought I would post this for those who didn't know about this and express my hope that Objectivists proficient in math consider activities to undermine the mysticism applied to math.

What do you mean "mysticism applied to math"? Do you have an example?

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Perhaps what I mean is the mystic influences IN mathematics such as Pythagoras's mathematical cult and Plato's influence in the field.

What do you mean "mysticism applied to math"? Do you have an example?

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There are no mystic influences in mathematics. Anyone can use mathematics, also fools and mystics, but that in no way makes mathematics less valid. A hammer is not a bad instrument because you use it to crush the skull of your neighbor instead of hammering nails. Mathematics is, contrary to what some Objectivists claim, a flourishing enterprise. Problems that were unsolved for centuries have recently be solved, like Fermat's last theorem and the 4-color problem. But also applied mathematics open whole new fields in discrete mathematics, combinatorics, cryptanalysis, complexity theory, numerical analysis etc. The idea that mathematics needs an injection of Aristotelian/Randian philosophy is absurd.

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While math is not one of my strong points, I was susprised to find out about math and it's ties to mysticism.

It is an error to project our sensibilities on the past. You might as well complain that the overwhelming themes in Renaissance art are religious... or, perhaps more relevantly, that Thomas Jefferson owned slaves. "Mystical" beliefs do permeate modern mathematics, such as the rationalist claim that logic is pure but that empiricism is flawed. You can find arguments for an "included middle" between A and non-A. You can find the claim that "pure" mathematic has no relationship to "reality" as, for instance, "imaginary numbers." Mathematics professors are not the only university people who advance anti-capitalist nonsense. The only way to overcome such idiocies is simply to continue to advocate for objectivism (rational-empiricism). Mathematics has no special claim to Truth, so mathematicians have no special guilt for their errors.

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While math is not one of my strong points, I was susprised to find out about math and it's ties to mysticism.

It is an error to project our sensibilities on the past. You might as well complain that the overwhelming themes in Renaissance art are religious... or, perhaps more relevantly, that Thomas Jefferson owned slaves. "Mystical" beliefs do permeate modern mathematics, such as the rationalist claim that logic is pure but that empiricism is flawed. You can find arguments for an "included middle" between A and non-A. You can find the claim that "pure" mathematic has no relationship to "reality" as, for instance, "imaginary numbers." Mathematics professors are not the only university people who advance anti-capitalist nonsense. The only way to overcome such idiocies is simply to continue to advocate for objectivism (rational-empiricism). Mathematics has no special claim to Truth, so mathematicians have no special guilt for their errors.

While you are correct in your first two sentences, I must object to most of the remainder of that paragraph. Mathematics is intimately tied to reality and so is physics. Empirical validation through experiment is still something necessary in physics--that's why they built the Large Hadron Collider, for one example. And as for math, there is very little in it that is not tied to reality in some way. Imaginary numbers are no more imaginary than irrational numbers are irrational. It's simply the name applied to a class of numbers not previously studied by mathematicians, and imaginary and complex numbers have some very real world applications, in engineering among things.

I have to say it odd that a philosophy like Objectivism which advocates the law of identity above all else should find the view that "Logic rules" to be objectionable in any way.

What fuels the mystical trend in mathematics is the apparent relation of mathematics to the fundamental nature of the cosmos. To put it as a question: why is it that physics can be expressed so successfully in mathematical terms?

Jeffrey S.

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What fuels the mystical trend in mathematics is the apparent relation of mathematics to the fundamental nature of the cosmos. To put it as a question: why is it that physics can be expressed so successfully in mathematical terms?

Jeffrey S.

That is one of the Major Question about mathematics. See the best known essay on that very question:

http://www.ipod.org....lity_wigner.pdf

"The Unreasonable Effectiveness of Mathematics in the Natural Sciences" written in 1960 by Eugene Wigner, one of the greatest physicists.

Wigner poses the question very nicely and messages the question, but he really does not answer it definitively. To this day no one really knows why mathematics is so effective in the natural sciences. Much of modern mathematics was developed abstractly with no thought to a particular scientific application, yet such mathematics later on turned out to be "just the thing". The best example I can think of is tensor analysis and curvature of differential manifolds which was invented by Gauss and his student Bernhard Riemann and many other there after. It was developed as a generalization of geometry and to deal with curvature in generalized manifold is a very abstract way. None of the founders of this field had physics in mind and certainly not gravitation, yet Albert Einstein put this kind of mathematics to work in formulating his General Theory of Relativity which is a theory of gravitation, the best such theory we have. Your GPS runs on the principles of this theory. Yet Gauss and Riemann would not have guessed how their creation would eventually be applied. To put a point on it, tensors and curvature was developed in response to questions of gravitation. Also tensor theory is the best way to express the electrodynamics of the Special Theory of Relativity. The electromagnetic field is a special kind of asymmetric four tensor. Maxwell did not have this mathematics when he wrote down the four famous equations for the electromagnetic field. Again, tensor math was NOT developed in order to deal with electromagnetic fields but a special case of it is the best way to model electromagnetic fields.

The Objectivist approach which is to make the concrete physical issues the basis of the mathematics simply does not explain why this abstract mathematics is so effective in dealing with the physics. This is what Wigner discusses in his well known essay.

Ba'al Chatzaf

Edited by BaalChatzaf

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There are three major philosophical approaches or "schools" to nature of mathematics; the Formalist, the Intuitionist/Strict Constructivist and the Platonic/Neo-Platonic. The Formalist approach, best exemplified by David Hilbert one of the great mathematicians of the last 19th, early 20th century held that mathematics is a formalism, a "game" (if you will) played with symbols having no more ontological import than, say, chess. The Intuitionist school exemplified by Leopold Kronecker in the 19th century and L.E.J. Brouwer in the 20th century held that mathematics is a manifestation of the human mind. It is a Kantian or neo-Kantian school. The Platonic/Neo-Platonic school holds that mathematical objects actually exist. Kurt Goedel, he of the famous Incompleteness Theorems held this position. Then there are the majority of mathematicians who just do mathematics and do not bother in a deep way with the underlying philosophical issues.

There are great mathematicians from all of these positions or "schools", who have made very important contributions to mathematics and mathematical logic. For a really good review of the nature of mathematics do read:

"Pi in the Sky:Counting,Thinking,Being" by John D. Barrow, Little Brown and Co., 1992. Barrow covers the philosophical grounds thoroughly without making too many technical demands on the non-mathematical reader. There are hardly any equations in the book. This book is not an "easy read" since it deals with the philosophical questions in a way that is not "dumbed down".

The chapter on counting and counting systems, chapter two, is a tour de force covering the history and anthropology of various counting systems. There are (or were) a remarkable number of societies in what counting past two was just not done. It is not that the people of these societies were/are stupid, it is just that they did not need elaborate counting systems to live in their enviornments. For the more advanced cultures the history and development of numbers and counting systems are gone into in great detail. Naturally the Greek contributions to mathematics from the pre-Socratics to the Alexandrian Hellenic Greeks, is also dealt with in detail.

Since the philosophies of Plato and Kant weigh in heavily and Aristotle is barely mentioned at all, this book will not win a popularity contest among "Suni" or "Shi'ite" Objectivists.

Ba'al Chatzaf

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While math is not one of my strong points, I was susprised to find out about math and it's ties to mysticism.

It is an error to project our sensibilities on the past. You might as well complain that the overwhelming themes in Renaissance art are religious... or, perhaps more relevantly, that Thomas Jefferson owned slaves. "Mystical" beliefs do permeate modern mathematics, such as the rationalist claim that logic is pure but that empiricism is flawed. You can find arguments for an "included middle" between A and non-A. You can find the claim that "pure" mathematic has no relationship to "reality" as, for instance, "imaginary numbers." Mathematics professors are not the only university people who advance anti-capitalist nonsense. The only way to overcome such idiocies is simply to continue to advocate for objectivism (rational-empiricism). Mathematics has no special claim to Truth, so mathematicians have no special guilt for their errors.

While you are correct in your first two sentences, I must object to most of the remainder of that paragraph. Mathematics is intimately tied to reality and so is physics. Empirical validation through experiment is still something necessary in physics--that's why they built the Large Hadron Collider, for one example. And as for math, there is very little in it that is not tied to reality in some way. Imaginary numbers are no more imaginary than irrational numbers are irrational. It's simply the name applied to a class of numbers not previously studied by mathematicians, and imaginary and complex numbers have some very real world applications, in engineering among things.

I have to say it odd that a philosophy like Objectivism which advocates the law of identity above all else should find the view that "Logic rules" to be objectionable in any way.

What fuels the mystical trend in mathematics is the apparent relation of mathematics to the fundamental nature of the cosmos. To put it as a question: why is it that physics can be expressed so successfully in mathematical terms?

Jeffrey S.

Was the physics twisted to conform to the mathematics?

--Brant

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What fuels the mystical trend in mathematics is the apparent relation of mathematics to the fundamental nature of the cosmos. To put it as a question: why is it that physics can be expressed so successfully in mathematical terms?

Jeffrey S.

Why indeed. It seems that there is structure, order and relations all around us (the nature of the cosmos) and mathematics is a language devoted to structure, order and relations so it is not surprising that it is useful in describing "the nature of the cosmos". :)

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Was the physics twisted to conform to the mathematics?

--Brant

Physics is "twisted" to conform to observed facts. Mathematics is a tool for physics, not a determiner of the physics. Also the content of physical theory includes propositions that are not mathematical or apriori true. For example, it is not apriori necessarily true that momentum, energy or angular momentum be conserved in the 3+1 space-time manifold. Such conservation is assumed to produce empirically correct results.

Ba'al Chatzaf

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What fuels the mystical trend in mathematics is the apparent relation of mathematics to the fundamental nature of the cosmos. To put it as a question: why is it that physics can be expressed so successfully in mathematical terms?

Jeffrey S.

Why indeed. It seems that there is structure, order and relations all around us (the nature of the cosmos) and mathematics is a language devoted to structure, order and relations so it is not surprising that it is useful in describing "the nature of the cosmos". :)

That still leaves, unanswered, the question: why is mathematics not derived from specific issues and problems of physics so useful in the solution of specific issues and problems in physics. For example; why should Riemann's theory of manifolds be exactly the right mathematics for describing gravitation?

Ba'al Chatzaf

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That still leaves, unanswered, the question: why is mathematics not derived from specific issues and problems of physics so useful in the solution of specific issues and problems in physics. For example; why should Riemann's theory of manifolds be exactly the right mathematics for describing gravitation?

Your first sentence should have said "some mathematics." Isaac Newton invented calculus to tackle specific issues and problems of physics.

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That still leaves, unanswered, the question: why is mathematics not derived from specific issues and problems of physics so useful in the solution of specific issues and problems in physics. For example; why should Riemann's theory of manifolds be exactly the right mathematics for describing gravitation?

Your first sentence should have said "some mathematics." Isaac Newton invented calculus to tackle specific issues and problems of physics.

Quite so.

Ba'al Chatzaf

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What fuels the mystical trend in mathematics is the apparent relation of mathematics to the fundamental nature of the cosmos. To put it as a question: why is it that physics can be expressed so successfully in mathematical terms?

Jeffrey S.

Why indeed. It seems that there is structure, order and relations all around us (the nature of the cosmos) and mathematics is a language devoted to structure, order and relations so it is not surprising that it is useful in describing "the nature of the cosmos". :)

That still leaves, unanswered, the question: why is mathematics not derived from specific issues and problems of physics so useful in the solution of specific issues and problems in physics. For example; why should Riemann's theory of manifolds be exactly the right mathematics for describing gravitation?

Ba'al Chatzaf

Why should we be surprised when we find some mathematics applicable to physics? As I just said, mathematics is a language devoted to structure, order and relations and are these not involved in the theory of gravitation?

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I agree with this statement, Michael. I suppose my concern expressed by my statement is based on the large amount of contributions philosophers (like Plato and Pythagoras) had on the field who just happened to subscribe to mysticism.

Perhaps a more accurate statement would be that mystics twist mathematics in order to justify the existence of their mystical claims such as the mathematician who claimed to find or was looking for the existence of God in an equation.

It is an error to project our sensibilities on the past. You might as well complain that the overwhelming themes in Renaissance art are religious... or, perhaps more relevantly, that Thomas Jefferson owned slaves. "Mystical" beliefs do permeate modern mathematics, such as the rationalist claim that logic is pure but that empiricism is flawed. You can find arguments for an "included middle" between A and non-A. You can find the claim that "pure" mathematic has no relationship to "reality" as, for instance, "imaginary numbers." Mathematics professors are not the only university people who advance anti-capitalist nonsense. The only way to overcome such idiocies is simply to continue to advocate for objectivism (rational-empiricism). Mathematics has no special claim to Truth, so mathematicians have no special guilt for their errors.

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Perhaps a more accurate statement would be that mystics twist mathematics in order to justify the existence of their mystical claims such as the mathematician who claimed to find or was looking for the existence of God in an equation.

Here's a great little dialogue from Foucault's Pendulum that shows this in action:

"Gentlemen," he said, "I invite you to go and measure that kiosk. You will see that the length of the counter is one hundred and forty-nine centimeters -- in other words, one hundred-billionth of the distance between the earth and the sun. The height at the rear, one hundred and seventy-six centimeters, divided by the width of the window, fifty-six centimeters, is 3.14. The height at the front is nineteen decimeters, equal, in other words, to the number of years of the Greek lunar cycle. The sum of the heights of the two front corners and the two rear corners is one hundred and ninety times two plus one hundred seventy-six times two, which equals seven hundred and thirty-two, the date of the victory at Poitiers. The thickness of the counter is 3.10 centimeters, and the width of the cornice of the window is 8.8 centimeters. Replacing the numbers before the decimals by the corresponding letters of the alphabet, we obtain C for ten and H for eight, or C10H8, which is the formula for naphthalene."

"Fantastic," I said. "You did all these measurements?"

"No," Aglie said. "They were done on another kiosk, by a certain Jean-Pierre Adam. But I would assume that all lottery kiosks have more or less the same dimensions. With numbers you can do anything you like. Suppose I have the sacred number 9 and I want to get the number 1314, date of the execution of Jacques de Molay -- a date dear to anyone who, like me, professes devotion to the Templar tradition of knighthood. What do I do? Multiply nine by one hundred and forty six, the fateful day of the destruction of Carthage. How did I arrive at this? I divided thirteen hundred and fourteen by two, by three, et cetera, until I found a satisfying date. I could also have divided thirteen hundred and fourteen by 6.28, the double of 3.14, and I would have got two hundred and nine. That is the year in which Attalus I, king of Pergamon, joined the anti-Macedonian League. You see?"

“Then you don’t believe in numerologies of any kind,” Diotallevi said, disappointed.

“On the contrary, I believe firmly. I believe the universe is a great symphony of numerical correspondences, I believe that numbers and their symbolisms provide a path to special knowledge.”

Umberto Eco, Foucault's Pendulum, P. 279-280

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... You can find arguments for an "included middle" between A and non-A. You can find the claim that "pure" mathematic has no relationship to "reality" as, for instance, "imaginary numbers." ...

... I must object to most of the remainder of that paragraph. Mathematics is intimately tied to reality and ... Imaginary numbers are no more imaginary than irrational numbers are irrational. ...

Sorry. You misunderstood my point because I failed to make it well. You can find the ERRONEOUS claim that ... and the ERRONEOUS claim that... and so on.

There are mathemticians who claim an included middle. While professional mathematicians at some level may well know better at the secondary even college level, the erroneous dichotomy between rationalism and empiricism leads to the mistaken teaching that logic is more correct than experiment. I had that directly from a a professor in a logic class. Firmly convinced of the Law of Identity, she was not so solid in her faith that the sun would rise in the east again tomorrow.

Imaginary numbers, of course, have real applications, for instance, in the tranmission of AC electricity. But the rational-empirical dichotomy of earlier times led to their being considered unreal, as there was no application for them. I believe (personal belief) that any logically consistent mathematics must have physical application, even if we have not found it yet.

Again, I apologize for not making it clear that I was quoting indirectly, not making a claim of my own.

Edited by Michael E. Marotta

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Perhaps a more accurate statement would be that mystics twist mathematics in order to justify ...

We need to understand the long growth of "mathematics." Fred Flintstone never knew the number ten... or even 5. Most "natural" languages stop counting at THREE. Some go to four. "One, two, many" or "One, two, three, many." That's it. The most ancient Sumerians counted "five" as "two-two-one."

The economics of cities evolved by use of clay tokens into cuneiform inventories. That took about 3000 years. My references are the works of DENISE SCHMANDT-BESSERAT. When numbering blossomed -- and here I am on my own, not citing DSB -- the Babylonians went wild with the power of it. Base-60 comes from 3x4x5, the 3-4-5 giving the simplest integer right triangle, the lowest Pythagorean triple.

Look at the scripts for numbers. They all come from Indian ("Arabic") symbols, even the common Chinese and Japanese numbers show the same forms as Arabic numbers. Yet, for "four" the Chinese symbol is only a closed fist. The Thumb does not tally because it is the counter, the index, for BASE TWELVE. Use your thumb and tick off the three flanges on each of the four fingers and you get 12.

Etymologically, SEVEN is the SABBATH. We all learned it from the same source about 3000 BCE.

All of which is to say, that if mystics found meaning in numbers, the fault lies not with the mathematics.

Step by step, we discovered how to use numbers to describe the world. Mathematics is just another (better) kind of language and to wonder why mathematics describes reality is to wonder why language does. That begs a question: what else could it describe, except reality?

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We need to understand the long growth of "mathematics." Fred Flintstone never knew the number ten... or even 5. Most "natural" languages stop counting at THREE. Some go to four. "One, two, many" or "One, two, three, many." That's it. The most ancient Sumerians counted "five" as "two-two-one."

I thought of an illustration from the Elizabethan era:

<object width="425" height="344"><param name="movie" value="

name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="
type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="344"></embed></object>

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Deleted by MSK. - Spammer

No mathematician is going to dedicate twenty years of his working lifetime to the study of abstract objects unless he believes these objects have some kind of existence. Just about every working theoretical mathematician is a closet Platonist, at least when he is doing his mathematics.

The only people I hear dismissing mathematics as (mere) method are Objectivists.

Ba'al Chatzaf

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Deleted by MSK.

Really? Try reading an honest to goodness treatise on the General Theory of Relativity.

As the late Mr. Rogers might have said: Can you say Ricci Tensor? Sure you can.

Ba'al Chatzaf

NOTE FROM MSK: Bob, this is a spammer. He's history and so are his posts.

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