Perelman was probably simply following one of the grand traditions in mathematics, illustrated by the story about Laplace below:
Laplace's Mecanique Celeste, an enormous five volume tome on just about everything you ever wanted to know about celestial mechanics, was first translated into the English language by Nathaniel Bowditch. Though others did it before him, Laplace was notorious for leaving length demonstrations to the reader, usually preceded with "C'est visible que..." (It is obvious that...). Bowditch meticulously filled in all the gaps, but before long he grew to dread those words, for he knew that when he saw them, he was in for a lengthy bit of derivation before what Laplace claimed was obvious was, in fact, obvious.
I think I first came across this anecdote in E.T. Bell's Men of Mathematics, but don't recall for sure - I found it on the net here: http://math.bu.edu/people/jeffs/joke.html
I find this comment funny, since most people would be hard pressed to name more than two transcendental numbers (namely pi and e).
This is even funnier when you consider that the set of transcendental numbers is uncountably infinite!
"Not everything that counts can be counted. Not everything that can be counted counts." -- Albert Einstein
Re:Starquake? We need a more... extreme name
on
'Starquake' Cracks Star
·
· Score: 2, Insightful
That's why we have exponential (aka scientific) notation. A trillion is 1 x 10^12, hence a trillion trillion trillion is 1 x 10^36. Of course, 10,000 (1 x 10^4) of those gives 10^40 watts. Your attempted decimal notation representation of the number is off by three orders of magnitude.
"God created the integers, all the rest is the work of man." -- Leopold Kronecker
One of my favorite passages from Surely You're Joking, Mr. Feynman! illustrates what he was up against in those freshman lectures:
I often liked to play tricks on people when I was at MIT. One time, in mechanical drawing class, some joker picked up a French curve (a piece of plastic for drawing smooth curves -- a curly, funny-looking thing) and said, "I wonder if the curves on this thing have some special formula?"
I thought for a moment and said, "Sure they do. The curves are very special curves. Lemme show ya," and I picked up my French curve and began to turn it slowly. "The French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal."
All the guys in the class were holding their French curve up at different angles, holding their pencil up to it at the lowest point and laying it along, and discovering that, sure enough, the tangent is horizontal. They were all excited by this "discovery" -- even though they had already gone through a certain amount of calculus and had already "learned" that the derivative (tangent) of the minimum (lowest point) of any curve is zero (horizontal). They didn't put two and two together. They didn't even know what they "knew."
I don't know what's the matter with people: they don't learn by understanding; they learn by some other way -- by rote, or something. Their knowledge is so fragile! -- RPF
Exactly. The profs were probably trying to design the tests to exhibit the full Gaussian distribution within the scoring range - probably with a target mean of about 40%, and a standard deviation of about 10%. This lets them see where everybody is really at, see who can think and apply what they've been learning beyond mere regurgitation by rote, as well as ID the truly gifted.
I know this is hard to understand for a generation that has been taught that participation is to be valued over achievement, grade inflation is the rule, everybody is way above average, and nobody goes home without a trophy.
"In mathematics the art of proposing a question must be held of higher value than solving it." -- Georg Cantor
"Listen, strange women cryin' over distributin' music is no basis for a system of government. Supreme executive power derives from a mandate from the masses, not from some farcical RIAA ceremony." -- apologies to Dennis
I believe the EEOC only prohibits discrimination based on age, sex, race, national origin, disability, creed or religion (the so-called "protected classes").
Last time I checked, IT cert'ed as well as Yale degreed individuals do not comprise "protected classes" - hence, discrimination in hiring based on these criteria is not illegal per se under EEO law.
"A lot of fellows nowadays have a B.A., M.D., or Ph.D. Unfortunately, they don't have a J.O.B." -- "Fats" Domino
Exactly, except the concept people seem to be groping for here is leadership, not management.
"Let's get rid of management. People don't want to be managed, they want to be led. If you want to manage somebody, manage yourself. Do that well and you'll be ready... to start leading." -- excerpt from an ad placed by United Technologies Corporation in the April 12, 1984 edition of the Wall Street Journal; as noted in the essay Leadership: Management's Better Half by John H. Zenger
"Physical concepts are free creations of the human mind and are not, however it may seem, uniquely determined by the external world. In our endeavor to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and cannot even imagine the possibility or the meaning of such a comparison. But he certainly believes that, as his knowledge increases, his picture of reality will become simpler and simpler and will explain a wider and wider range of his sensuous impressions. He may also believe in the existence of the ideal limit of knowledge and that it is approached by the human mind. He may call this ideal limit the objective truth."
-- The Evolution of Physics, Albert Einstein and Leopold Infeld, Simon and Schuster, 1938
It has been said that Relativity was very much "in the air" in the late nineteen and early twentieth centuries. It should not be surprising that many great minds of the time had occasion to intersect with some of the key ideas.
But the hallmark of true genius is to recognize the patterns and boldly shatter the old paradigms and forge new ones - in the process creating useful, verifiable scientific theories that surpass those that came before them. This is why Einstein gets the credit.
Yeah, how hard could it be for a company with $290 billion in market cap to integrate that weather widget with the "locate me" technology from Virtual Earth?
Yep, it's generally referred to as the latent heat of fusion, although in a refrigeration context it might be more appropriate to discuss the latent heat of vaporization/condensation - the heat required for phase change from liquid to gas or gas to liquid (about 540 cal/g for water).
Also, although quantitatively correct, the choice of units in your illustration strikes me as a bit odd. Without getting into all the baroque details, in the metric system a calorie is generally defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius. This would seem to make the Celsius scale more natural when talking about calories (and would make your example run from 0 degrees C to 80 degrees C).
Analogously in the English system, a British thermal unit (Btu) is generally defined as the amount of heat required to raise the temperature of one Lb. of water by one degree Fahrenheit.
Hillary just better hope Bill doesn't unlock the "hot intern" inappropriate intimate relationship mod...
--
"God gave men both a penis and a brain, but unfortunately not enough blood supply to run both at the same time." -- Robin Williams (on Clinton/Lewinsky affair)
On the contrary, if the standard deviation you are refering to is the square root of the bias-corrected sample variance, then it is undefined, not infinite.
--
"A set is a Many that allows itself to be thought of as a One." -- Georg Cantor
I too, some years back, received one of the TransWorld Services collections letters on behalf of BlockBuster regarding some late fees.
I've been renting movies since the betamax days, and, as neurojab says, the custom on late fees was always to settle up on the next rental, which I always gladly did. Back then, most places would even offer to waive the fees if it was only a day or so late, especially for good repeat customers. In BlockBuster's defense, a lot of these shops were Mom-and-Pops who actually knew who their customers were. When the chains took over, the late fee waviers were, of course, sacrificed on the altar of corporate greed. But at least you still paid the late fees on your next visit - until I got the letter.
Needless to say, upon receipt of the collection letter, being both a gentleman and a scholar, I paid promptly as directed.
I also have not rented from BlockBuster since, and never will again. I'm glad to hear I'm not the only one who thought this was an idiotic way to treat good customers. I try to recruit family, friends, and acquaintances into my BlockBuster boycott whenever the occasion presents itself, hence this somewhat redundant post.
Let's do the math - $12 in late fees (which would have collected on my next visit anyway) and the TVM bonanza on the accelerated A/R (which probably didn't exceed 25 to 50 cents) less the TransWorld fees and other program overhead (probably close to $4-$6 bucks per letter), vs $300-$500 per year (for life) in rentals, candy, popcorn, and yes, late fees from a happy customer... Hmmm, a really sharp trade-off - I'd really like to meet the MBA-marketing genius who came up with this program - he/she must have been the one who slept through the course that talked about the cost of customer acquisition and retention in competetive industries!
I don't mean to quibble on what I peceive to be your narrow point - works created by an employee within their "scope of employment" are deemed "works for hire" with copyright ownership accruing to the employer. I agree, it's the Law. I had more in mind the independent contractor situation in my original, off-the-cuff, post, and probably should have chosen my words more carefully.
That said, the legal interpretation of terms such as "employee" and "scope of employment" can give rise to ambiguous situations where employer's copyright ownership under the "works for hire" doctrine is not as clear-cut as you might think.
Although you might have assumed el womble was implying he created his macro:
... at work, while working a regular job, using his employer's computers...
I don't think that he explicitly listed those conditions. If he created it at home using his computer, then the "works for hire" claim of the employer becomes more tenuous. Of course, the employer could always claim, since the macro was related to accomplishing his employment duties, that it falls within his "scope of employment."
The point here is that the doctrine of "works for hire" in the context of employment and copyright ownership, in the absence of a written agreement, can become somewhat complicated and not as cut and dried as one might think at first glance.
"No one sells or mortgages all the products of his brain to his employer by the mere fact of employment." -- Public Affairs Assoc., Inc. v. Rickover, (D.D.C. 1959)
Slashdot Mirror
"C'est visible que..."
Perelman was probably simply following one of the grand traditions in mathematics, illustrated by the story about Laplace below:
Laplace's Mecanique Celeste, an enormous five volume tome on just about everything you ever wanted to know about celestial mechanics, was first translated into the English language by Nathaniel Bowditch. Though others did it before him, Laplace was notorious for leaving length demonstrations to the reader, usually preceded with "C'est visible que..." (It is obvious that...). Bowditch meticulously filled in all the gaps, but before long he grew to dread those words, for he knew that when he saw them, he was in for a lengthy bit of derivation before what Laplace claimed was obvious was, in fact, obvious.
I think I first came across this anecdote in E.T. Bell's Men of Mathematics, but don't recall for sure - I found it on the net here: http://math.bu.edu/people/jeffs/joke.html
In a perfect world, isn't this how it should work anyway?
What's interesting is M$ is consenting to it???
I find this comment funny, since most people would be hard pressed to name more than two transcendental numbers (namely pi and e).
This is even funnier when you consider that the set of transcendental numbers is uncountably infinite!
"Not everything that counts can be counted. Not everything that can be counted counts." -- Albert Einstein
That's why we have exponential (aka scientific) notation. A trillion is 1 x 10^12, hence a trillion trillion trillion is 1 x 10^36. Of course, 10,000 (1 x 10^4) of those gives 10^40 watts. Your attempted decimal notation representation of the number is off by three orders of magnitude.
"God created the integers, all the rest is the work of man." -- Leopold Kronecker
One of my favorite passages from Surely You're Joking, Mr. Feynman! illustrates what he was up against in those freshman lectures:
I often liked to play tricks on people when I was at MIT. One time, in mechanical drawing class, some joker picked up a French curve (a piece of plastic for drawing smooth curves -- a curly, funny-looking thing) and said, "I wonder if the curves on this thing have some special formula?"
I thought for a moment and said, "Sure they do. The curves are very special curves. Lemme show ya," and I picked up my French curve and began to turn it slowly. "The French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal."
All the guys in the class were holding their French curve up at different angles, holding their pencil up to it at the lowest point and laying it along, and discovering that, sure enough, the tangent is horizontal. They were all excited by this "discovery" -- even though they had already gone through a certain amount of calculus and had already "learned" that the derivative (tangent) of the minimum (lowest point) of any curve is zero (horizontal). They didn't put two and two together. They didn't even know what they "knew."
I don't know what's the matter with people: they don't learn by understanding; they learn by some other way -- by rote, or something. Their knowledge is so fragile! -- RPF
Exactly. The profs were probably trying to design the tests to exhibit the full Gaussian distribution within the scoring range - probably with a target mean of about 40%, and a standard deviation of about 10%. This lets them see where everybody is really at, see who can think and apply what they've been learning beyond mere regurgitation by rote, as well as ID the truly gifted.
I know this is hard to understand for a generation that has been taught that participation is to be valued over achievement, grade inflation is the rule, everybody is way above average, and nobody goes home without a trophy.
"In mathematics the art of proposing a question must be held of higher value than solving it." -- Georg Cantor
Differentiation is an integral part of calculus.
In a sense, it could also be said that:
Differentiation is a part of integral calculus (courtesy of the fundamental theorem of calculus)...
The original Copyright Act of 1790 set the term to 14 years, plus a one time renewal term of an additional 14 years if the author was living.
See this page for more information...
"Listen, strange women cryin' over distributin' music is no basis for a system of government. Supreme executive power derives from a mandate from the masses, not from some farcical RIAA ceremony." -- apologies to Dennis
"... I'd rather have this bottle in front of me, than a frontal lobotomy!" -- T. Bone Stankus
I believe the EEOC only prohibits discrimination based on age, sex, race, national origin, disability, creed or religion (the so-called "protected classes").
Last time I checked, IT cert'ed as well as Yale degreed individuals do not comprise "protected classes" - hence, discrimination in hiring based on these criteria is not illegal per se under EEO law.
"A lot of fellows nowadays have a B.A., M.D., or Ph.D. Unfortunately, they don't have a J.O.B." -- "Fats" Domino
OK, I guess that explains why E. T. Bell never penned Women of Mathematics...
Exactly, except the concept people seem to be groping for here is leadership, not management.
"Let's get rid of management. People don't want to be managed, they want to be led. If you want to manage somebody, manage yourself. Do that well and you'll be ready... to start leading." -- excerpt from an ad placed by United Technologies Corporation in the April 12, 1984 edition of the Wall Street Journal; as noted in the essay Leadership: Management's Better Half by John H. Zenger
I think it was best said by the man himself:
"Physical concepts are free creations of the human mind and are not, however it may seem, uniquely determined by the external world. In our endeavor to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and cannot even imagine the possibility or the meaning of such a comparison. But he certainly believes that, as his knowledge increases, his picture of reality will become simpler and simpler and will explain a wider and wider range of his sensuous impressions. He may also believe in the existence of the ideal limit of knowledge and that it is approached by the human mind. He may call this ideal limit the objective truth."
-- The Evolution of Physics, Albert Einstein and Leopold Infeld, Simon and Schuster, 1938
Funny. If you'd signed this post as Roy G. Biv, I'd have really lost it...
Q: If a centimeter had a terminal illness, what would we call it?
A: An erg.
It has been said that Relativity was very much "in the air" in the late nineteen and early twentieth centuries. It should not be surprising that many great minds of the time had occasion to intersect with some of the key ideas.
But the hallmark of true genius is to recognize the patterns and boldly shatter the old paradigms and forge new ones - in the process creating useful, verifiable scientific theories that surpass those that came before them. This is why Einstein gets the credit.
"God casts the die, not the dice" -- A. Einstein
Or perhaps a simple DotNetNuke skin? ...
Yeah, how hard could it be for a company with $290 billion in market cap to integrate that weather widget with the "locate me" technology from Virtual Earth?
Yep, it's generally referred to as the latent heat of fusion, although in a refrigeration context it might be more appropriate to discuss the latent heat of vaporization/condensation - the heat required for phase change from liquid to gas or gas to liquid (about 540 cal/g for water).
Also, although quantitatively correct, the choice of units in your illustration strikes me as a bit odd. Without getting into all the baroque details, in the metric system a calorie is generally defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius. This would seem to make the Celsius scale more natural when talking about calories (and would make your example run from 0 degrees C to 80 degrees C).
Analogously in the English system, a British thermal unit (Btu) is generally defined as the amount of heat required to raise the temperature of one Lb. of water by one degree Fahrenheit.
Hillary just better hope Bill doesn't unlock the "hot intern" inappropriate intimate relationship mod...
--
"God gave men both a penis and a brain, but unfortunately not enough blood supply to run both at the same time." -- Robin Williams (on Clinton/Lewinsky affair)
On the contrary, if the standard deviation you are refering to is the square root of the bias-corrected sample variance, then it is undefined, not infinite.
--
"A set is a Many that allows itself to be thought of as a One." -- Georg Cantor
Cool, but I'm still holding out for Doc Emmett Brown to come back from the future in that DeLorean with the Mr. Fusion mod.
When you can generate 1.21 gigawatts from a banana peel, who needs hydrogen power?
--
"Last night, Darth Vader came down from planet Vulcan and told me that if I didn't take Lorraine out that he'd melt my brain." -- George McFly
I too, some years back, received one of the TransWorld Services collections letters on behalf of BlockBuster regarding some late fees.
I've been renting movies since the betamax days, and, as neurojab says, the custom on late fees was always to settle up on the next rental, which I always gladly did. Back then, most places would even offer to waive the fees if it was only a day or so late, especially for good repeat customers. In BlockBuster's defense, a lot of these shops were Mom-and-Pops who actually knew who their customers were. When the chains took over, the late fee waviers were, of course, sacrificed on the altar of corporate greed. But at least you still paid the late fees on your next visit - until I got the letter.
Needless to say, upon receipt of the collection letter, being both a gentleman and a scholar, I paid promptly as directed.
I also have not rented from BlockBuster since, and never will again. I'm glad to hear I'm not the only one who thought this was an idiotic way to treat good customers. I try to recruit family, friends, and acquaintances into my BlockBuster boycott whenever the occasion presents itself, hence this somewhat redundant post.
Let's do the math - $12 in late fees (which would have collected on my next visit anyway) and the TVM bonanza on the accelerated A/R (which probably didn't exceed 25 to 50 cents) less the TransWorld fees and other program overhead (probably close to $4-$6 bucks per letter), vs $300-$500 per year (for life) in rentals, candy, popcorn, and yes, late fees from a happy customer... Hmmm, a really sharp trade-off - I'd really like to meet the MBA-marketing genius who came up with this program - he/she must have been the one who slept through the course that talked about the cost of customer acquisition and retention in competetive industries!
I don't mean to quibble on what I peceive to be your narrow point - works created by an employee within their "scope of employment" are deemed "works for hire" with copyright ownership accruing to the employer. I agree, it's the Law. I had more in mind the independent contractor situation in my original, off-the-cuff, post, and probably should have chosen my words more carefully.
... at work, while working a regular job, using his employer's computers...
That said, the legal interpretation of terms such as "employee" and "scope of employment" can give rise to ambiguous situations where employer's copyright ownership under the "works for hire" doctrine is not as clear-cut as you might think.
Although you might have assumed el womble was implying he created his macro:
I don't think that he explicitly listed those conditions. If he created it at home using his computer, then the "works for hire" claim of the employer becomes more tenuous. Of course, the employer could always claim, since the macro was related to accomplishing his employment duties, that it falls within his "scope of employment."
The point here is that the doctrine of "works for hire" in the context of employment and copyright ownership, in the absence of a written agreement, can become somewhat complicated and not as cut and dried as one might think at first glance.
"No one sells or mortgages all the products of his brain to his employer by the mere fact of employment." -- Public Affairs Assoc., Inc. v. Rickover, (D.D.C. 1959)