Golden State and the Mathematical Magic of Seventy-Three (newyorker.com) 102
Charles Bethea has written a fascinating piece on the number '73' for The New Yorker. Below are some tidbits from the story but I urge you to hit the New Yorker link and read the story in entirety there. Bethea writes: "I am aware of the Warriors's push for seventy-three wins," Ken Ono, a professor of mathematics at Emory University and the author of "The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-series," said recently. [...] Professor Ono worked as a math consultant on a film called "The Man Who Knew Infinity," which stars Dev Patel and Jeremy Irons, and which screens this week at the Tribeca Film Festival, in New York. The movie centers on the friendship of the legendary Indian mathematician Srinivasa Ramanujan (Patel) and his Cambridge University colleague G. H. Hardy (Irons), and it depicts a famous story that Hardy once told about Ramanujan. "I remember once going to see him when he was ill at Putney," Hardy said. "I had ridden in taxicab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied. "It is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." One cubed plus twelve cubed, and nine cubed plus ten cubed. This was the first of what came to be known as "taxicab numbers." [...] So what does Professor Ono think of seventy-three? "I really like the number seventy-three," he said. "It is the sixth 'emirp.'" An emirp, he explained, is a prime number that remains prime when its digits are reversed. (Emirp, of course, is 'prime' spelled backward.)
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I'm not trying to give you a hard time here; I've actually never bothered pointing these errors out before because the previous editors didn't seem to care. You do, so I figure it's helpful.
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Gives a damn is good. Deliberately pointing traffic for a story on *sports* while masking it as tech by trying to bring math into the equation... Not so much. An improvement in the attempt for certain but still a paid for traffic generator.
Site owners used to cringe at the threat of being slash-dotted.
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Gives a damn is good. Deliberately pointing traffic for a story on *sports* while masking it as tech by trying to bring math into the equation...
Are you saying Math and Sports do not intersect? Sabremetricians would respectfully disagree!
That said, I thought it was kindof a dumb story about the number 73. I quickly scanned through it to see if there was more to it than the summary that summarized the first two paragraphs of the story, but really, that was about it. It actually had almost nothing to do with sports and was more "here's the number 73. Isn't it cool? Here are some other things that had to do with the number 73." That anecdote about th
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I think I should have summarized it better as 'Low quality click-bait'.
Sorry, but calling it as I see it.
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I think I should have summarized it better as 'Low quality click-bait'.
Sorry, but calling it as I see it.
Oh. Yes, you're absolutely right with that.
I still think the taxi anecdote is amusing, but it's definitely more of a casual numerology blog post and not a newsworthy story.
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Dude, Slashdot is news for nerds; this is news and it's the nerd angle on the story. It's center-bullseye Slashdot material.
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Gushing over a number is not *news that matters*
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That was beyond disgusting.
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You're implying parties are required for social acceptance or affluence.
Please read between the lines.
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It's a shame AOL couldn't keep your kind locked away.
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Not here: https://hardware.slashdot.org/... [slashdot.org]
(second sentence)
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Fixed... you keep using that word, (Score:2)
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At last! News for nerds... (Score:1)
My God, it's full of stars...
Base 10 (Score:4, Interesting)
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Can you provide an example of a number that is prime in base 2, but not prime when converted to base 10?
No, no you can not.
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I hope you brought enough for the whole class, Mr BronsCon.
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Re:Base 10 (Score:4, Informative)
Not to mention, at what point does a number being "interesting" stop being mathematics and start being numerology? I mean, are things like taxicab numbers and 'emirps' useful for anything?
Re:Base 10 (Score:5, Interesting)
Not to mention, at what point does a number being "interesting" stop being mathematics and start being numerology?
There are no uninteresting numbers. Proof: Assume N is the smallest uninteresting number. That property in itself makes it interesting. Therefore there can be no smallest uninteresting number, so logically uninteresting numbers cannot exist. QED.
I mean, are things like taxicab numbers and 'emirps' useful for anything?
There is no requirement that mathematics be useful. Many fields of math, including non-Euclidian geometry, trans-infinite set theory, etc. were developed long before there were any applications. The Greeks and Romans had no use for zero. Some mathematicians consider it a badge of honor to work on a topic that is considered purely theoretical, and therefore useless.
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There are no uninteresting numbers. Proof: Assume N is the smallest uninteresting number. That property in itself makes it interesting. Therefore there can be no smallest uninteresting number, so logically uninteresting numbers cannot exist. QED.
I believe that's the ontological proof that you're a total nerd.
Re:Base 10 (Score:4, Interesting)
Your proof is flawed, because it cannot work recursively. What about the second smallest uninteresting number? Your argument only reduces the set of uninteresting numbers by one, and until proven otherwise, there are an infinity of uninteresting numbers. :)
BTW, 12407 seems to be the smallest uninteresting number http://www.kevinhouston.net/bl... [kevinhouston.net], which, as you mentioned, makes it interesting. The next smallest uninteresting number really is uninteresting, and I don't even know which one it is
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he just "proved" there isn't a first uninteresting number, so there can't possibly be a second. or a third. or so on.
idiot.
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I might be an idiot, but you'll have to prove it ;)
His proof is still flawed. It looks like mathematical induction (https://en.wikipedia.org/wiki/Mathematical_induction), but it really only is the base case, and there's no inductive step.
Let's say that 12407, 12887, 13258, 13794 are the first uninteresting numbers, because they don't have any special property, and for example don't appear in https://oeis.org/ [oeis.org].
12407 is the first uninteresting number, so let's agree this property makes it interesting. What ab
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The proof is indeed flawed, solely for the lack of proper definiton of interesting. But it does not use induction at all, it uses that natural numbers are well-ordered.
- Let S be the set of noninteresting numbers.
- If S is not empty then, since N is well-ordered, there exists a minimum element x of S
- x in interesting, so x is not in S
Contradiction, cannot happen that x belongs to S and does not belong to S.
Hence S is emptyset.
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As long as we're abusing inductive proofs, might as well point out that all prime numbers are odd.
Step One: all prime numbers except "2" are odd numbers.
Step Two: that makes "2" a pretty odd prime number...
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Even if emirps and taxicab numbers are not useful for anything, the techniques developed in proofs of assertions about things have a habit of being useful elsewhere, and the mere pondering of such things is good exercise for mathematical reasoning, and fun for those who like maths. That fun aspect should not be underrated: if you don't enjoy maths, you will tend to limit yourself only to that which has an immediately obvious usefulness. Read up on the history of maths to see how that could be a problem.
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I mean, are things like taxicab numbers and 'emirps' useful for anything?
Who cares? Is the Mona Lisa useful for anything?
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Is the Mona Lisa mathematics?
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Is the Mona Lisa mathematics?
What's that got to do with anything? Is it *useful*.
If not, then what's with the obsession that good things must have use, but only when it comes to mathematics?
Many mathemeticians don't do maths because it's useful in the same way many artists don't do art because it's useful. Both have their uses, but that's not why we do them.
Re:Base 10 (Score:5, Informative)
Primes, in all bases, are highly useful in many areas, encryption being a good one most people likely know of.
Engineering is another area, prime-sizing, matrices and so many practical uses.
Also biology. Cicadas and locusts tend to appear in cycles based on primes, such as every 13 or 17 years. If they instead used a composite period, like, say 12, then they could be prey to predators that had a 3, 4, or 6 year cycle.
For the same reason, machinery sometimes use gears or belts with a prime number of teeth. That can reduce vibrations by eliminating some possible resonances.
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Oetaxicab? What? (Score:2)
This was the first of what came to be known as 'oetaxicab numbers.'
A what number?
"It is the sixth 'emirp.' An emirp, he explained, is a prime number that remains prime when its digits are reversed. (Emirp, of course, is 'prime spelled backward.)
You've got something weird going on with your quotes there.
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"Was also the last really good year for American pop music, before disco took over. "
Also the year of my first really good relationship.
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As I always say at least two great events occurred in 1973. One was the "Dark side of the moon" release, the other....my birth :)
Strange way to promote a movie (Score:4, Informative)
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Simplest Ramanujan anecdote ... (Score:5, Interesting)
But Ramanujan was never taught the process of writing down formal proofs, he self thought everything from a handbook of mathematical identities. Rediscovering several things others had already discovered and proved. He was utterly at a loss to explain how he was able to do math. He simply said, "I look at the equation or a problem. Then Goddess Namagiri Devi writes the answer in my tongue and I recite it". (not an accurate quote, paraphrased by me)
I wish it was Lord Oppiliappan, the family deity of his dad, not Namagiri Devi the consort of the family deity of his mom. Because Lord Oppiliappan is my family deity too. Would have gotten me some bragging rights.
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Interesting, but that leads me to wonder why he was sure it was Namagiri Devi and not another?
Re:Simplest Ramanujan anecdote ... (Score:5, Interesting)
The taxi cab numbers is the simplest anecdote from Ramanujan that could be told to general audience.
It's recently been discovered that there is a specific reason that Ramanujan recognized the property of 1729... and it's even more mind-boggling than the idea that Ramanujan simply saw such obscure properties in random numbers.
As it turns out, Ramanujan was thinking about Fermat's Last Theorem and had written the two sum-of-cubes decomposition of 1729 in some of his papers, as part of an exploration of FLT "near misses", numbers that are almost, but not quite, counterexamples to FLT. What's really incredible, though, was that careful study of his papers reveal that he was in the process of developing a theory of elliptic curves... moving exactly towards the technique that Andrew Wiles used to finally prove FLT in 1994/95, some 75 years after Ramanujan's death.
Given Ramanujan's highly intuitive approach to mathematics, what this most likely means is that Ramanujan somehow just saw the structure of elliptic curve theory and its relation to FLT. Andrew Wiles is clearly one of the most brilliant mathematicians of our day, and he was only able to make and prove this connection with years of intense work and only by building upon a mass of thoroughly developed elliptic curve theory, including the Taniyama-Shimura conjecture which was proposed 35 years after Ramanujan's death, and not observed to be related to FLT until the another 30 or so years after that.
So when Hardy mentioned 1729 to Ramanujan and was surprised at Ramanujan's observation of the number's properties, he thought that it was just evidence that Ramanujan saw odd patterns in numbers, but it was actually evidence of vastly deeper insight into the structure of number theory.
https://plus.maths.org/content/ramanujan
Really sad he died so young.
Really, really sad.
He was utterly at a loss to explain how he was able to do math. He simply said, "I look at the equation or a problem. Then Goddess Namagiri Devi writes the answer in my tongue and I recite it".
That's not completely true. Yes, he did say that, but he was also capable of producing proofs of a sort. He tended to skip a lot of steps that were -- to him -- too obvious to bother stating, and which everyone else had to think very hard about[*], but he could and did produce work that was understandable with appropriate background and sufficient study. It seems likely that had he lived longer and obtained more formal mathematical education that he'd have developed his ability to produce formal proofs for publication.
Ramanujan was a simply incredible mathematical intellect. I have no doubt that if he'd lived a full life he'd have done great work to advance mathematics.
[*] Mathematicians' definition of "obvious" is rather vague. One of my favorite math jokes is about a professor lecturing to his class and saying "It's obvious that...". A student raised his hand and said "Is that obvious? I don't see it". The professor looked at the board for a long minute then walked out of class, went to his office, scribbled furiously for 20 minutes then returned to class and said "Yes, it is obvious." He then continued his lecture without further elaboration.
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Good joke, and interesting story.
I'm kinda good at maths, but an old pal is a few sigmas better than me. During our (math) studies, teachers realized pretty fast that he was more talented than they were. We were jealous of him, not only because he was *that* good, but also because he could write "That's obvious" 10 times in a row during an exam, skip every question till the very last, write only a few sentences and still get the best grade.
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I suspect that deity channelling will be appearing on job requirements for H1Bs pretty soon.
Re:Simplest Ramanujan anecdote ... (Score:5, Interesting)
"But Ramanujan was never taught the process of writing down formal proofs, he self thought everything from a handbook of mathematical identities. Rediscovering several things others had already discovered and proved. He was utterly at a loss to explain how he was able to do math. He simply said, "I look at the equation or a problem. Then Goddess Namagiri Devi writes the answer in my tongue and I recite it". (not an accurate quote, paraphrased by me)"
The other mathematician who was self-taught in the same way was Blaise Pascal. He even invented his own terminology for conventional geometric forms because his family kept him away from formal study.
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What you don't seem to care about though is the fascination with the idea that numbers, in whatever base, express reality.
Working through "the relationships between digits" is simply a primitive form of a deeper insight.
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numbers are just constructs of the human mind; reality is independent of them even if we can make useful models of reality with numbers.
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You may be on to something: 73 is the sixth emirp (as mentioned in the OP). But even more significantly, 73 = 42 + 31, where 31 is the third emirp.
I'm sure that's significant...
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> There are 12 inches in a foot.
Yeah, but there are only 10 toes on my foot.
Real meaning of 73 (Score:3)
"73" is well known in the telegrapher community as the code for "Best Wishes" [wikipedia.org]. It is commonly used in ham radio to this day.
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(or "best regards")
GO SPURS!!! (Score:2)
I think I speak for all of us when I say, (Score:2)
NERDS!
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Beware of the numbers (Score:2)
I know a guy, Walter, who's obsession with a particular number did not end well. [wikipedia.org]
It is not 6th emirp (Score:2)
The article defines emirp as below:
“It is the sixth ‘emirp.’ ” An emirp, he explained, is a prime number that remains prime when its digits are reversed.
Here are the emirp numbers: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73. So it is eleventh emirp.
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-I'm just sayin'
Re:It is not 6th emirp (Score:4, Informative)
The actual definition is "a prime number that results in a different prime when its decimal digits are reversed."
So, single digits, and palindromes (like 11) don't count.
Yes! Available on Netflix (Score:2)
Added to queue. Netflix still rocks.
Sheldon's 73 shirt (Score:2)
I can't believe nobody has yet mentioned this clip: https://www.youtube.com/watch?... [youtube.com]
This is why Sheldon often wears a blue shirt with the number 73 on it.
Penguin (Score:1)
I first saw that story about Rajamujan and Hardy in The Penguin Dictionary of Curious and Interesting Numbers [wikipedia.org] which gave me hours of numerical pleasure.
1729 (Score:2)