Since the info above was informative, here are a few other statistics that interest me and help put minority issues into perspective. They're at best tangentially related to TFA, though.
There are perhaps 100,000 furries in the US, or around 1 in 3000 people. [Furries at a glance: the majority are young white men; they're pretty much evenly split between hetero and homosexual, with many at varying degrees of bisexuality; very few own fursuits; to be clear, furries primarily have an interest in anthropomorphic characters, so "it's not about sex" (though as always it can be).]
Around 25% of all people in Swaziland have HIV/AIDS. The number jumps to over 50% for women 25-29. [Yes, this is unbelievably tragic.] Around 0.4% of the US population has HIV/AIDS, though around 20% of men who have sex with men do (accounting for around half of all cases; receptive anal sex spreads it more quickly than any other common sex practice; interestingly, fellatio is almost entirely safe in this regard; condoms reduce transmission rates by only ~80%, depending on specifics).
Sorry for the self reply.... I forgot to add that I'm not an expert in these issues by any means. Non-standard human sex/gender are just minor interests of mine.
It's worth noting that conditions apart from standard XX female and XY male do occur in humans:
Turner syndrome: usually, single X chromosome, no second X or Y. Creates females who are almost always infertile with varying physical problems. Incidence is around 1 in 2000 to 1 in 5000 (phenotypic) females. Triple X syndrome: XXX chromosomes. Makes females with essentially no physical differences from XX females (including reproductively). Incidence: 1 in 1000 females. Klinefelter's Syndrome: XXY chromosomes. Produces sometimes-infertile males, sometimes with developmental problems. 1 in between 500 and 1000 males affected. XYY Syndrome: XYY chromosomes. Almost no physical differences with XY males (slightly taller). 1 in 1000 males. XX Male Syndrome: XX chromosomes. Produces always-infertile males who usually appear to be XY males. 4 or 5 in 100,000 people. Swyer Syndrome: XY chromosomes. Produces females without developed gonads, though a developed uterus may be able to carry another person's embryo.
The above is only a partial list. There are quite a few related conditions that fall under the general heading of "Intersex" (sometimes you see the acronym LGBTI; that's the I). They vary widely from producing (some type of) hermaphrodites to causing a large number of non-standard sex characteristics. From the article,
According to Fausto-Sterling's definition of intersex, on the other hand, 1.7 percent of human births are intersex.
and
Between 0.1% and 0.2% of live births are ambiguous enough to become the subject of specialist medical attention, including surgery to disguise their sexual ambiguity.
To give a very approximate comparison (these numbers vary a lot by region, time period, and definition), around 1% of the population is bisexual, and around 5% is gay. It's perhaps even more difficult to get an accurate transgender incidence number; I've seen between 0.2% and 0.003%. Those who get sex reassignment surgery are in the minority. (There's a lot more to gender than the type of gonads you have, and female-to-male surgery isn't terribly effective.)
It would also be nice if they could also ignore gay marriage, contraception, abortion both pro or con, and also just about every other distracting hot button issue out there.
Forgive the presumption, but are you a white heterosexual male? Perhaps if any of those "hot button" issues touched you personally you'd feel differently. I, for instance, would like to get married someday, so gay marriage is an important issue to me. I'm actually fine with Obama ignoring it right now, though. I suspect he'll come out in support of it sometime in his second term when he'll take less political flack. I certainly don't want Santorum winning so he can reinstitute DADT or otherwise set gay rights in the US back a decade or so. More than that, Santorum is just not that smart, and I don't want an(other) idiot for a president.
Only one: that we live in a logical and consistent universe. In other words, that if we reproduce the conditions under which a phenomenon was observed, then the phenomenon itself will be reproduced.
Three things:
1. Defining "logic" is extremely difficult; that problem should not be swept under the rug. There are a great many different systems of logic with different axioms and different styles of reasoning. The law of the excluded middle has been controversial in the past (that is, "either X is true or not X is true"). Mathematicians are often uncomfortable with the axiom of choice (one can make an arbitrary choice from each of infinitely many buckets simultaneously) and sometimes try to avoid it or use a weakened form like dependent choice. Aside from which axioms to include in your system of logic, there are formal systems that are fundamentally different from the "intuitive" first order predicate logic most people probably use naturally, like infinitary logic which allows infinitely long proofs. It might seem like splitting hairs to the uninitiated, but there are worlds of fundamental questions to explore in this vein.
2. "Science" is often (ironically) romanticized. The truth is that modern humans have cobbled together a set of effective heuristics and rules which we now call science. I imagine the same basic process gave us religion, though those heuristics and rules aren't as good at predicting how reality will behave. In any case, God did not come down and hand humanity the scientific method (which is actually a rather vague phrase), or mathematical models, or the logical systems those models are based on. We've created them. Perhaps something better will come along and several thousand years from now today's "science" will be tomorrow's "religion". [OT: I sometimes dislike sci-fi for making aliens not nearly alien enough. Who's to say aliens haven't discovered a better set of rules than "hypothesize, experiment, revise, repeat", or a better logical system than what we use? Maybe they have halt checkers that aren't paradoxical since they don't meet the requirements of Rice's theorem.]
3. Preface: I might be reading too far in to what you've written here. You seem to have a classical, deterministic view of the universe. Quantum mechanics was particularly revolutionary because it fundamentally altered this view of the world. If you repeat an experiment under the same conditions, you do not in general get the same result--only the probabilities involved can be predicted. This of course raises fundamental questions about the nature of knowledge, but that's been hashed over to death (and as far as I can tell there's little practical point in discussing the matter).
I thought "mathematical parrot reveals his genius with posthumous paper" was referring to some human who spent his life repeating other people's mathematical ideas but then was validated by some original paper found and published only after his death.
Your complaints seem directed at WinForms. I much prefer WPF--for instance, finding all the functions on a button can be done manually by going to the XAML file, finding the button's UI code, seeing which events go to which functions, and finding those functions in the code-behind file. WPF's separation between business logic and the interface is very appealing to me, as are a bunch of the features WPF offers, like recursive templates.
My evaluation of WPF and C#.NET along the points outlined by the OP:
(A) Check; strong IDE.
(B) Unclear. Being locked in to a particular mindset is too vague for me to quantify and evaluate.
(C) Check, probably. Certainly you can make your own custom interface elements with whatever graphics you feel like. I'm unfamiliar with WPF/.NET 3D capabilities, though they almost certainly would suit the OP's needs.
(D) Not check. C#.NET is largely Windows-only, and WPF is not part of Mono, the "cross platform, open source.NET development framework".
(E) Unsure. Licensing isn't my area. Probably no problem.
While I don't quite agree with you about the quality of his exposition, I also don't see the point of discussing it further since it's such a minor issue. I will if you wish, though.
I'm not sure where "[Nash was] not in any way predictable out-of-house" came from. I'm no Nash expert, but his mental disturbances didn't start until 1959, several years after these letters were written. From the letters, the impression I got was that his ideas simply weren't advanced enough to merit him further time, rather than him being unsuitable for being in-or-out-of-house with the NSA.
No. His "machine" (the letters don't imply it was ever built) certainly wasn't the only one of its kind. If anything, the letters might give him some vague claim on the beginnings of computability and/or computational complexity theory, though his "exponential conjecture" isn't really developed enough to earn him much credit for either, IMO.
Is it ironic that around this time the UK was injecting Turing with hormones?
It's certainly coincidental. There are some rumors that Nash was bisexual (inasmuch as he had some sort of maybe-sexual relationship with some men, or was attracted to some men), though he allowed his wife to deny it in a 60 Minutes interview. There's some discussion of the issue in the book A Beautiful Mind was based on.
While it's a bit off topic, I hope for a day where society doesn't care about a person's sexuality, and where I stop keeping a mental list of the non-heterosexual celebrities I know of. Until that day comes, thank you Anderson Cooper, Ellen Degeneres, Wanda Sykes, Alan Turing,....
I agree that just because they were handwritten doesn't necessarily indicate a lack of thoughtfulness. He probably wanted to avoid having a secretary type them up to keep them secret. That they're sloppily handwritten does indicate a lack of thoughtfulness, though not necessarily about the key ideas: mostly, his presentation could have been better. Beyond the stylistic issues I mentioned above, there is for instance this sentence:
"Recently a conversation with Prof. Huffman here indicated that he has recently been working on a machine with similar objectives."
A more thoughtful presentation might replace the second "recently" with "lately" or similar. His description of his exponential conjecture could also have used a second draft. As an example, he says "n is the maximum span of the 'memory' of the process" when in fact he (probably accidentally) put n+1 x_k's in his function, so the 'memory' would be n+1, not n.
(Just so I don't give the wrong idea, I found the letters fascinating. That I found flaws in them is not terribly important.)
I think we actually agree. By "insecure", I meant he was not secure in his reputation with the NSA. He seemed quite confident about the correctness and worth of the ideas he presented. I suppose he may or may not have literally felt fear about getting ignored. Perhaps it's not standard, but to me the phrase "X was afraid of Y" is an idiom that doesn't necessarily imply X feels fear. For instance, take "I'm afraid you'll have to leave" or "He's afraid the door will be locked and he'll have to go around back in the cold."
To be clear, I understand your "translation" of his "1950's politeness". It's so obvious that I didn't feel the need to explicitly agree with you. I only bring it up now since you repeated your translation in different words as if I didn't understand the first version (or the original text).
I don't know why you keep obliquely insulting me ("Your first mistake was..." [you never got to my second mistake, by the way; did you have one?]; "Wow. You really don't understand how academic politeness works?"). It's distracting.
Yup, and in fact I did think of that when I wrote the post above. My main complaint was his sloppy writing style. He could certainly have done a more professional job of writing his letters by hand. Using the ones we have as drafts and copying their corrected contents carefully to new paper would have made a big difference, for instance. Of course these are minor points; I was just pleasantly surprised the NSA gave him the attention he seems to have deserved in spite of his stylistic flaws.
I wonder if he could type--or, more generally, if academics and particularly mathematicians generally had that skill in the mid 50's.
(I don't think TeX would have been much more helpful than a standard word processor to him since there were so few equations, and typesetting them would be extremely simple. I'd use some other program like OmniGraffle to generate the diagrams.)
What about the "crank or circle-squarer" bit? He was afraid of getting put in a crank file. See this article for a fascinating discussion of mathematical cranks, among them angle trisectors and circle-squarers:
"Many mathematics departments do not bother with crank work, throwing it out or putting it in a file labeled 'nuts' or 'crackpots.'"
That he was at all afraid of that outcome implies his insecurity, regardless of his work in game theory (which is of course distinct from cryptography) or his own opinion of it. By the way, Nash hadn't won any major awards by 1955 (as far as I can tell). His Nobel came in the 90's, for instance. He used MIT math department stationary, probably for convenience and also as proof that he was at least somewhat respectable. Conversely, he wasn't not respectable either; his mental problems didn't develop until around 1959. He was just afraid of getting ignored.
Actually I was surprised by how much interest the NSA showed. Here was a young (~27) assistant professor of math writing to the government largely out of the blue. Nash himself was relatively insecure in his reputation, at least to this audience:
"I hope my handwriting, etc. do not give the impression I am just a crank or circle-squarer. My position here is Assist. Prof. of math. My best known work is in game theory (reprint sent separately)."
Even though he's insecure, he still chose to hand-write his letters sloppily with relatively poor penmanship and words crossed out. Still, the NSA dutifully corresponded with him and analyzed his machine, concluding
"[it] has many of the desirable features of a good auto-key system; but it affords only limited security, and requires a comparatively large amount of equipment. The principle would not be used alone in its present form and suitable modification or extension is considered unlikely, unless it could be used in conjunction with other good auto-key principles."
The letters certainly don't give me the impression of someone who is serious about making a working cypher machine. He's pretty clearly just dabbling in cryptography because it's a nice mental game for him to play. That doesn't necessarily mean his ideas should be ignored, and (somewhat surprisingly) the NSA didn't ignore them.
To be fair, IE10 includes spell checking (and auto correct), though only preview versions have been released. The final version of IE9 was released in March of last year. I'm curious, what other "must-have features" are absent from IE10 (or IE9, for that matter)?
I'm used to people disliking IE for how it was years ago and not giving it a fair chance today--and of course Microsoft hate is popular here (TFS opens with the "grandiose bluster" of an "aging juggernaut"--thanks so much for excellent and fair reporting of facts, slashdot). I apologize if you're not one of them.
You described the plot of Office Space and Superman III. It's a practice apparently known as "salami slicing" or "penny shaving". In real life I imagine the rounding mostly evens out. You'd have eg. $0.99 going to $1, though on multiple-item purchases the last digit would be approximately random.
There are two "bases" that actually work: (120)_b = 114 where b = -1 +/- sqrt(115) ~= 9.72381 or -11.7238.
For the curious, I'm using this definition of an irrational base. It's mildly entertaining to think through some of the properties of these systems. Wikipedia's base-phi article has a bit of detail, though note that it limits the "digits" to 0 and 1 to ensure (near-)uniqueness. I had to allow at least 0, 1, and 2 for (120)_b to be well-defined, but then there are infinite expansions using only 0 and 1 which equal (2)_b.
If you allow the digits to be arbitrary rational numbers, you start exploring some field extension and Galois theory. Base pi then is quite pretty and enjoys a very strong uniqueness property, considering how free we are with our digits--any number with a finite representation in this system has only that one representation. Perhaps unexpectedly, this fact implies the impossibility of squaring the circle, since it is equivalent to the transcendence of pi, which is equivalent to pi being in an infinite dimensional field extension over the rationals, whereas the compass-and-straightedge-constructable lengths all lie in power-of-two (so finite) extensions..
I imagine you meant each month was 29 days? If so, how many months were there? More to the point, what's the ratio of old year to new year length? (Living 80 * 29 = 2320 days or less than 7 current years is not notable.)
I have a Hotmail account I use to send (legitimate) zipped executable attachments. It's set to forward to my gmail, though. I don't have a spam problem with either.
Appealing to some fundamental part of the fabric of the universe that treats humans differently from other matter is more than a little arrogant. Quite frankly, the universe doesn't give a damn what humans do.
But, one doesn't need to make such an appeal anyway. I want slavery to be wrong because I myself don't want to be a slave, and I can empathize with an imagined slave enough that I don't want them to be a slave either. I am willing to accept the conceit, "humans have the right to be free," if it means there will be fewer slaves. Fundamentally there is no such right. The term "right" is too vague to carry much meaning anyway. It is, however, a useful rhetorical device. One must be careful not to take it too literally.
If you were to justify making someone a slave by saying things are not absolutely "right" or "wrong", I would listen patiently and ignore you. My reasons are unaffected--I can still empathize with slaves. If you forcibly made someone a slave, I would not be bothered by putting you in jail for it. My lack of a sense of intrinsic rights is irrelevant; I still want society to be a certain way even if I can't justify that with appeals to universal truth. I'm quite content with appeals to human-scale truth. I also understand that different people would apply essentially the same algorithm I use differently for subtle reasons. This also does not perturb me: getting at the truth of a matter difficult and error-prone, and we usually can't behave perfectly anyway. That's not a reason not to try your best, though.
Slashdot Mirror
Since the info above was informative, here are a few other statistics that interest me and help put minority issues into perspective. They're at best tangentially related to TFA, though.
There are perhaps 100,000 furries in the US, or around 1 in 3000 people. [Furries at a glance: the majority are young white men; they're pretty much evenly split between hetero and homosexual, with many at varying degrees of bisexuality; very few own fursuits; to be clear, furries primarily have an interest in anthropomorphic characters, so "it's not about sex" (though as always it can be).]
30% of those over 24 in the US have a bachelor's degree. Only 3% have doctorates or professional degrees.
Around 25% of all people in Swaziland have HIV/AIDS. The number jumps to over 50% for women 25-29. [Yes, this is unbelievably tragic.] Around 0.4% of the US population has HIV/AIDS, though around 20% of men who have sex with men do (accounting for around half of all cases; receptive anal sex spreads it more quickly than any other common sex practice; interestingly, fellatio is almost entirely safe in this regard; condoms reduce transmission rates by only ~80%, depending on specifics).
Around 1% of the US population is some variety of Native American. Around 15% are poor.
Sorry for the self reply.... I forgot to add that I'm not an expert in these issues by any means. Non-standard human sex/gender are just minor interests of mine.
It's worth noting that conditions apart from standard XX female and XY male do occur in humans:
Turner syndrome: usually, single X chromosome, no second X or Y. Creates females who are almost always infertile with varying physical problems. Incidence is around 1 in 2000 to 1 in 5000 (phenotypic) females.
Triple X syndrome: XXX chromosomes. Makes females with essentially no physical differences from XX females (including reproductively). Incidence: 1 in 1000 females.
Klinefelter's Syndrome: XXY chromosomes. Produces sometimes-infertile males, sometimes with developmental problems. 1 in between 500 and 1000 males affected.
XYY Syndrome: XYY chromosomes. Almost no physical differences with XY males (slightly taller). 1 in 1000 males.
XX Male Syndrome: XX chromosomes. Produces always-infertile males who usually appear to be XY males. 4 or 5 in 100,000 people.
Swyer Syndrome: XY chromosomes. Produces females without developed gonads, though a developed uterus may be able to carry another person's embryo.
The above is only a partial list. There are quite a few related conditions that fall under the general heading of "Intersex" (sometimes you see the acronym LGBTI; that's the I). They vary widely from producing (some type of) hermaphrodites to causing a large number of non-standard sex characteristics. From the article,
According to Fausto-Sterling's definition of intersex, on the other hand, 1.7 percent of human births are intersex.
and
Between 0.1% and 0.2% of live births are ambiguous enough to become the subject of specialist medical attention, including surgery to disguise their sexual ambiguity.
To give a very approximate comparison (these numbers vary a lot by region, time period, and definition), around 1% of the population is bisexual, and around 5% is gay. It's perhaps even more difficult to get an accurate transgender incidence number; I've seen between 0.2% and 0.003%. Those who get sex reassignment surgery are in the minority. (There's a lot more to gender than the type of gonads you have, and female-to-male surgery isn't terribly effective.)
But he's one cannoli short of a heart attack
Hah, thanks for the laugh.Your post deserves a Funny mod.
While I thank you for your post, the fact that its contents are not completely obvious to everyone is very sad.
It would also be nice if they could also ignore gay marriage, contraception, abortion both pro or con, and also just about every other distracting hot button issue out there.
Forgive the presumption, but are you a white heterosexual male? Perhaps if any of those "hot button" issues touched you personally you'd feel differently. I, for instance, would like to get married someday, so gay marriage is an important issue to me. I'm actually fine with Obama ignoring it right now, though. I suspect he'll come out in support of it sometime in his second term when he'll take less political flack. I certainly don't want Santorum winning so he can reinstitute DADT or otherwise set gay rights in the US back a decade or so. More than that, Santorum is just not that smart, and I don't want an(other) idiot for a president.
The MSM offers all kind of reasons why there's not much enthusiasm for Romney
Well of course men who have sex with men don't like Romney--he's opposed to gay marriage!
Only one: that we live in a logical and consistent universe. In other words, that if we reproduce the conditions under which a phenomenon was observed, then the phenomenon itself will be reproduced.
Three things:
1. Defining "logic" is extremely difficult; that problem should not be swept under the rug. There are a great many different systems of logic with different axioms and different styles of reasoning. The law of the excluded middle has been controversial in the past (that is, "either X is true or not X is true"). Mathematicians are often uncomfortable with the axiom of choice (one can make an arbitrary choice from each of infinitely many buckets simultaneously) and sometimes try to avoid it or use a weakened form like dependent choice. Aside from which axioms to include in your system of logic, there are formal systems that are fundamentally different from the "intuitive" first order predicate logic most people probably use naturally, like infinitary logic which allows infinitely long proofs. It might seem like splitting hairs to the uninitiated, but there are worlds of fundamental questions to explore in this vein.
2. "Science" is often (ironically) romanticized. The truth is that modern humans have cobbled together a set of effective heuristics and rules which we now call science. I imagine the same basic process gave us religion, though those heuristics and rules aren't as good at predicting how reality will behave. In any case, God did not come down and hand humanity the scientific method (which is actually a rather vague phrase), or mathematical models, or the logical systems those models are based on. We've created them. Perhaps something better will come along and several thousand years from now today's "science" will be tomorrow's "religion". [OT: I sometimes dislike sci-fi for making aliens not nearly alien enough. Who's to say aliens haven't discovered a better set of rules than "hypothesize, experiment, revise, repeat", or a better logical system than what we use? Maybe they have halt checkers that aren't paradoxical since they don't meet the requirements of Rice's theorem.]
3. Preface: I might be reading too far in to what you've written here. You seem to have a classical, deterministic view of the universe. Quantum mechanics was particularly revolutionary because it fundamentally altered this view of the world. If you repeat an experiment under the same conditions, you do not in general get the same result--only the probabilities involved can be predicted. This of course raises fundamental questions about the nature of knowledge, but that's been hashed over to death (and as far as I can tell there's little practical point in discussing the matter).
I thought "mathematical parrot reveals his genius with posthumous paper" was referring to some human who spent his life repeating other people's mathematical ideas but then was validated by some original paper found and published only after his death.
Your complaints seem directed at WinForms. I much prefer WPF--for instance, finding all the functions on a button can be done manually by going to the XAML file, finding the button's UI code, seeing which events go to which functions, and finding those functions in the code-behind file. WPF's separation between business logic and the interface is very appealing to me, as are a bunch of the features WPF offers, like recursive templates.
My evaluation of WPF and C#.NET along the points outlined by the OP: .NET development framework".
(A) Check; strong IDE.
(B) Unclear. Being locked in to a particular mindset is too vague for me to quantify and evaluate.
(C) Check, probably. Certainly you can make your own custom interface elements with whatever graphics you feel like. I'm unfamiliar with WPF/.NET 3D capabilities, though they almost certainly would suit the OP's needs.
(D) Not check. C#.NET is largely Windows-only, and WPF is not part of Mono, the "cross platform, open source
(E) Unsure. Licensing isn't my area. Probably no problem.
Hah, that was hilarious, thank you.
While I don't quite agree with you about the quality of his exposition, I also don't see the point of discussing it further since it's such a minor issue. I will if you wish, though.
I'm not sure where "[Nash was] not in any way predictable out-of-house" came from. I'm no Nash expert, but his mental disturbances didn't start until 1959, several years after these letters were written. From the letters, the impression I got was that his ideas simply weren't advanced enough to merit him further time, rather than him being unsuitable for being in-or-out-of-house with the NSA.
To be clear, "continuous" linear programming has polynomial-time algorithms. Integer linear programming does not, however.
Did he invent modern cryptography?
No. His "machine" (the letters don't imply it was ever built) certainly wasn't the only one of its kind. If anything, the letters might give him some vague claim on the beginnings of computability and/or computational complexity theory, though his "exponential conjecture" isn't really developed enough to earn him much credit for either, IMO.
Is it ironic that around this time the UK was injecting Turing with hormones?
It's certainly coincidental. There are some rumors that Nash was bisexual (inasmuch as he had some sort of maybe-sexual relationship with some men, or was attracted to some men), though he allowed his wife to deny it in a 60 Minutes interview. There's some discussion of the issue in the book A Beautiful Mind was based on.
While it's a bit off topic, I hope for a day where society doesn't care about a person's sexuality, and where I stop keeping a mental list of the non-heterosexual celebrities I know of. Until that day comes, thank you Anderson Cooper, Ellen Degeneres, Wanda Sykes, Alan Turing, ....
I agree that just because they were handwritten doesn't necessarily indicate a lack of thoughtfulness. He probably wanted to avoid having a secretary type them up to keep them secret. That they're sloppily handwritten does indicate a lack of thoughtfulness, though not necessarily about the key ideas: mostly, his presentation could have been better. Beyond the stylistic issues I mentioned above, there is for instance this sentence:
"Recently a conversation with Prof. Huffman here indicated that he has recently been working on a machine with similar objectives."
A more thoughtful presentation might replace the second "recently" with "lately" or similar. His description of his exponential conjecture could also have used a second draft. As an example, he says "n is the maximum span of the 'memory' of the process" when in fact he (probably accidentally) put n+1 x_k's in his function, so the 'memory' would be n+1, not n.
(Just so I don't give the wrong idea, I found the letters fascinating. That I found flaws in them is not terribly important.)
I think we actually agree. By "insecure", I meant he was not secure in his reputation with the NSA. He seemed quite confident about the correctness and worth of the ideas he presented. I suppose he may or may not have literally felt fear about getting ignored. Perhaps it's not standard, but to me the phrase "X was afraid of Y" is an idiom that doesn't necessarily imply X feels fear. For instance, take "I'm afraid you'll have to leave" or "He's afraid the door will be locked and he'll have to go around back in the cold."
To be clear, I understand your "translation" of his "1950's politeness". It's so obvious that I didn't feel the need to explicitly agree with you. I only bring it up now since you repeated your translation in different words as if I didn't understand the first version (or the original text).
I don't know why you keep obliquely insulting me ("Your first mistake was..." [you never got to my second mistake, by the way; did you have one?]; "Wow. You really don't understand how academic politeness works?"). It's distracting.
Yup, and in fact I did think of that when I wrote the post above. My main complaint was his sloppy writing style. He could certainly have done a more professional job of writing his letters by hand. Using the ones we have as drafts and copying their corrected contents carefully to new paper would have made a big difference, for instance. Of course these are minor points; I was just pleasantly surprised the NSA gave him the attention he seems to have deserved in spite of his stylistic flaws.
I wonder if he could type--or, more generally, if academics and particularly mathematicians generally had that skill in the mid 50's.
(I don't think TeX would have been much more helpful than a standard word processor to him since there were so few equations, and typesetting them would be extremely simple. I'd use some other program like OmniGraffle to generate the diagrams.)
What about the "crank or circle-squarer" bit? He was afraid of getting put in a crank file. See this article for a fascinating discussion of mathematical cranks, among them angle trisectors and circle-squarers:
"Many mathematics departments do not bother with crank work, throwing it out or putting it in a file labeled 'nuts' or 'crackpots.'"
That he was at all afraid of that outcome implies his insecurity, regardless of his work in game theory (which is of course distinct from cryptography) or his own opinion of it. By the way, Nash hadn't won any major awards by 1955 (as far as I can tell). His Nobel came in the 90's, for instance. He used MIT math department stationary, probably for convenience and also as proof that he was at least somewhat respectable. Conversely, he wasn't not respectable either; his mental problems didn't develop until around 1959. He was just afraid of getting ignored.
Actually I was surprised by how much interest the NSA showed. Here was a young (~27) assistant professor of math writing to the government largely out of the blue. Nash himself was relatively insecure in his reputation, at least to this audience:
"I hope my handwriting, etc. do not give the impression I am just a crank or circle-squarer. My position here is Assist. Prof. of math. My best known work is in game theory (reprint sent separately)."
Even though he's insecure, he still chose to hand-write his letters sloppily with relatively poor penmanship and words crossed out. Still, the NSA dutifully corresponded with him and analyzed his machine, concluding
"[it] has many of the desirable features of a good auto-key system; but it affords only limited security, and requires a comparatively large amount of equipment. The principle would not be used alone in its present form and suitable modification or extension is considered unlikely, unless it could be used in conjunction with other good auto-key principles."
The letters certainly don't give me the impression of someone who is serious about making a working cypher machine. He's pretty clearly just dabbling in cryptography because it's a nice mental game for him to play. That doesn't necessarily mean his ideas should be ignored, and (somewhat surprisingly) the NSA didn't ignore them.
To be fair, IE10 includes spell checking (and auto correct), though only preview versions have been released. The final version of IE9 was released in March of last year. I'm curious, what other "must-have features" are absent from IE10 (or IE9, for that matter)?
I'm used to people disliking IE for how it was years ago and not giving it a fair chance today--and of course Microsoft hate is popular here (TFS opens with the "grandiose bluster" of an "aging juggernaut"--thanks so much for excellent and fair reporting of facts, slashdot). I apologize if you're not one of them.
You described the plot of Office Space and Superman III. It's a practice apparently known as "salami slicing" or "penny shaving". In real life I imagine the rounding mostly evens out. You'd have eg. $0.99 going to $1, though on multiple-item purchases the last digit would be approximately random.
How does this interpretation get around people living 120 * 29 / 365 = under 10 years at most? It seems completely unworkable.
There are two "bases" that actually work: (120)_b = 114 where b = -1 +/- sqrt(115) ~= 9.72381 or -11.7238.
For the curious, I'm using this definition of an irrational base. It's mildly entertaining to think through some of the properties of these systems. Wikipedia's base-phi article has a bit of detail, though note that it limits the "digits" to 0 and 1 to ensure (near-)uniqueness. I had to allow at least 0, 1, and 2 for (120)_b to be well-defined, but then there are infinite expansions using only 0 and 1 which equal (2)_b.
If you allow the digits to be arbitrary rational numbers, you start exploring some field extension and Galois theory. Base pi then is quite pretty and enjoys a very strong uniqueness property, considering how free we are with our digits--any number with a finite representation in this system has only that one representation. Perhaps unexpectedly, this fact implies the impossibility of squaring the circle, since it is equivalent to the transcendence of pi, which is equivalent to pi being in an infinite dimensional field extension over the rationals, whereas the compass-and-straightedge-constructable lengths all lie in power-of-two (so finite) extensions..
I imagine you meant each month was 29 days? If so, how many months were there? More to the point, what's the ratio of old year to new year length? (Living 80 * 29 = 2320 days or less than 7 current years is not notable.)
I have a Hotmail account I use to send (legitimate) zipped executable attachments. It's set to forward to my gmail, though. I don't have a spam problem with either.
Appealing to some fundamental part of the fabric of the universe that treats humans differently from other matter is more than a little arrogant. Quite frankly, the universe doesn't give a damn what humans do.
But, one doesn't need to make such an appeal anyway. I want slavery to be wrong because I myself don't want to be a slave, and I can empathize with an imagined slave enough that I don't want them to be a slave either. I am willing to accept the conceit, "humans have the right to be free," if it means there will be fewer slaves. Fundamentally there is no such right. The term "right" is too vague to carry much meaning anyway. It is, however, a useful rhetorical device. One must be careful not to take it too literally.
If you were to justify making someone a slave by saying things are not absolutely "right" or "wrong", I would listen patiently and ignore you. My reasons are unaffected--I can still empathize with slaves. If you forcibly made someone a slave, I would not be bothered by putting you in jail for it. My lack of a sense of intrinsic rights is irrelevant; I still want society to be a certain way even if I can't justify that with appeals to universal truth. I'm quite content with appeals to human-scale truth. I also understand that different people would apply essentially the same algorithm I use differently for subtle reasons. This also does not perturb me: getting at the truth of a matter difficult and error-prone, and we usually can't behave perfectly anyway. That's not a reason not to try your best, though.