Math-Frolic !

MathLove

2012-02-14T06:30:00.006-05:00

For Valentine's Day I was looking, naturally, for something to post connecting mathematics and love... a lot of possibilities, but in the end decided I could do no better than to re-run a link I posted just 3 months ago -- Jennifer Ouellete's fun ode ("Love Among the Equations") bearing on the subject here:

http://blogs.scientificamerican.com/cocktail-party-physics/2011/09/29/love-among-the-equations/

an excerpt:

"It turns out that the world is filled with hidden connections, recurring patterns, and intricate details that can only be seen through math-colored glasses. Those abstract symbols hold meaning. How could I ever have thought it was irrelevant?

This is what I have learned from loving a physicist. Real math isn’t some cold, dead set of rules to be memorized and blindly followed. The act of devising a calculus problem from your observations of the world around you – and then solving it – is as much a creative endeavor as writing a novel or composing a symphony."

Ian Stewart on Black-Scholes

2012-02-13T10:45:00.009-05:00

(Black-Scholes Equation)

Good piece (as usual) from Ian Stewart on some of the mathematics underlying the financial crash:

http://www.guardian.co.uk/science/2012/feb/12/black-scholes-equation-credit-crunch

From the article:

"Anyone who has followed the crisis will understand that the real economy of businesses and commodities is being upstaged by complicated financial instruments known as derivatives. These are not money or goods. They are investments in investments, bets about bets. Derivatives created a booming global economy, but they also led to turbulent markets, the credit crunch, the near collapse of the banking system and the economic slump. And it was the Black-Scholes equation that opened up the world of derivatives."

Seife, Wallace, and Infinity, Oh My!…

2012-02-11T06:30:00.001-05:00

If by any chance you're not familiar with science-writer Charles Seife's work, I highly recommend it (one of my favorite science expositors). More recently he put up a simple 'tweet' that caught my eye, noting that he was now in possession of "David Foster Wallace's annotations" to his (Seife's) book "Zero: the biography of a dangerous idea." He actually linked to an image (pdf) of one of the pages, which included the following passage, with Wallace's simple annotation, "Heavy." :-)

"How big are the rational numbers? They take up no space at all. It's a tough concept to swallow, but it's true.
Even though there are rational numbers everywhere on the number line, they take up no space at all. If we were to throw a dart at the number line, it would never hit a rational number. Never. And though the rationals are tiny, the irrationals aren't, since we can't make a seating chart and cover them one by one; there will always be uncovered irrationals left over. Kronecker hated the irrationals, but they take up all the space in the number line.
The infinity of the rationals is nothing more than a zero."

Fascinating stuff… and, 'heavy' indeed!; all the moreso, no doubt, for someone who was essentially an English major/novelist/writer, like Wallace, with a brilliant/eclectic mind (he did deeply study logic and mathematics in college though).

About 3 years after Seife's "Zero" came out, Wallace produced "Everything and More: A Compact History of Infinity" -- a remarkable take (300 pages that he calls "a booklet"), from a non-mathematician, on the whole history and thought surrounding mathematical infinity. I happen to like this quirky volume a lot for its sheer uniqueness (I still can't imagine the mind that could write such a book, and if you are familiar with Wallace's innovative writing style, you know it is unique!), but I've seen professional mathematicians give the volume both negative and positive reviews. In any event, we may now have at least some inkling as to what moved Wallace to even tackle such subject matter. As Paul Harvey would say, perhaps from Wallace's Seife-annotations we will get a glimpse of "the rest of the story."
[-- Tragically, Wallace took his own life at age 46 in 2008, after lifelong bouts with depression.]

Friday Fun

2012-02-10T06:00:00.003-05:00

Wow!, it's not April 1st yet, so I can only assume that someone spiked Vi Hart's coffee for her latest video escapade ;-):

http://tinyurl.com/7s4ggmf

And for a Friday puzzle, a simple, straightforward riddle (requires more thinking through than mathematics):

Sally notes that the day before yesterday she was 22 years-old, yet next year she will be 25. What day does her birthday fall on, and when did she voice the above statement?
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Answer: Her birthday is on Dec. 31, and her statement was made on New Year's Day, Jan. 1.

The Traveling Salesman Problem... and Art

2012-02-09T11:30:00.003-05:00

Alex Bellos addresses the Travelling Salesman Problem and William Cook's new book on the subject, and also artwork, here:

http://alexbellos.com/?p=1629

Wolfram Education Portal

2012-02-08T10:30:00.000-05:00

I grew up up at the wrong time (woe is me!). There are SO many cool digital applications for education these days; particularly math education. And the not-so-new kid on the block comes from venerable Wolfram Alpha with the "Wolfram Education Portal." If you're an educator (or, even NOT), check it out -- it's in beta and they want feedback:

http://education.wolfram.com/

Elsevier… Can You Hear Us NOWWWW!?

2012-02-07T05:45:00.002-05:00

Wow!… back on January 22, I linked to what I called an "interesting, inspired post" from mathematician Tim Gowers recommending a boycott of scientific publisher Elsevier for various ill-publishing practices. Little did I know how much pent-up, anti-Elsevier feeling was out there, nor how quickly the boycott idea would snowball. Below, are some of the many blog entries that have joined in the effort:

http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/
http://freethoughtblogs.com/pharyngula/2012/01/16/elsevier-evil/
http://blogs.discovermagazine.com/cosmicvariance/2012/01/30/boycott-elsevier/
http://www.michaeleisen.org/blog/?p=890
http://thecostofknowledge.com/
http://www.scottaaronson.com/blog/?p=891
http://tylerneylon.com/b/archives/136
http://cscs.umich.edu/~crshalizi/weblog/864.html
http://terrytao.wordpress.com/2012/01/26/the-cost-of-knowledge/
http://www.newappsblog.com/2012/02/more-on-the-elsevier-boycott.html
http://michaelnielsen.org/blog/on-elsevier/

...and for a slightly broadened take on matters, the always-interesting Doron Zeilberger:

http://www.math.rutgers.edu/~zeilberg/Opinion120.html

Meanwhile, 4000+ scientists have signed a petition supporting the boycott idea. This isn't simply a mathematics issue, since Elsevier publishes in several different subject areas -- but frankly, I'm kinda proud (even though I'm not even a professional mathematician myself) that this whole movement was raised to the forefront by a major mathematician. More generally, I'm proud of the pioneering work that mathematicians have done in utilizing the Web as a collaborative force to accomplish things.
The public often perceives mathematicians in a 'geeky,' loner sort of light, working quietly away in a corner, but in fact, when the spirit moves them ;-) they can be among the most powerful (and unselfish) movers of science and society! Give Tim Gowers a high-five!

ADDENDUM: I don't plan to do continuous "Addendums" on this issue, as related pertinent Web posts appear, but I do think the following update from Tim Gowers is worth noting:

http://gowers.wordpress.com/2012/02/08/a-more-formal-statement-about-mathematical-publishing/

"The Math Book"… ho hum?…..

2012-02-05T07:45:00.003-05:00

In recent years there have been a number of what I call math "nugget" books written for a mass audience -- books covering a range of interesting mathematical topics in a brief way, and introducing math to lay folks who might otherwise not give it much attention. I've especially liked certain volumes from Tony Crilly and Richard Elwes that I've mentioned here previously. They do a good job of giving readers enough interesting material to chew on to possibly seduce them into further study, without overwhelming them.

Clifford Pickover is a well-known polymath (I would almost say poly-polymath) and math popularizer. He's authored several books I've enjoyed, and is just an all-around fascinating fellow! His "The Math Book," came out a couple of years back as a sort of "nugget"/coffee-table/math volume that met with wide acclaim and awards. I don't think I've read a single bad review of it! Still, I hesitated buying it because it just never much enticed me despite frequent scans of it at my local bookstore. But, with a major discount coupon ;-), I did finally purchase it, and continue to have mixed feelings about it, including some difficulty recommending it to math fans, despite its wide acclaim.

But first let's cover the positives, since it is a book with so many fans. The style and format is beautiful; very glossy, very glitzy; very, as I say, coffee-tablish; unlike most math books. It also touches upon a very wide range of topics, or as the book says, "milestones" (250 by its own count), and does so in an organized, chronological way, that pulls the reader along from antiquity to modern times (although it need not be read from beginning to end, but can be read in a much more random order). The language and level of material is appropriate to a lay audience. Pickover's own love of math shines through on each page, and it seems clear that his goal for the book is not so much to educate people, as perhaps to imbue them with some of the same excitement about the field that he feels. Every page seems to say, 'Isn't this wondrous!'
All of that is obviously to the positive…

My problems with the volume however are these:

Starting with the practical: it is a thick, square, heavy book (especially the hard-back version), not conducive to reading in bed, on one's back, as I often like to do -- a small quibble to many, but for me a major drawback in what is essentially a 'pleasure' book, not a textbook. It's coffee-table quality almost makes it more a volume for show than for reading (which is unfortunate)... Stephen Hawking's "Brief History of Time" was called perhaps the most widely-selling, UNread book in publishing history -- I fear Pickover's book could suffer a similar fate (even though it is more readable than Hawking's). I realize Pickover is probably trying to reach out to a very broad audience, but for my taste it is simply TOO glossy and glitzy; almost gaudy, and almost a turn-off. Moreover, the short, bite-size text entries are simply too brief to really afford the reader much substantive information on the subjects at-hand. Whereas, Crilly and Elwes, give the reader enough, as I say, to chew on, Pickover often just scratches the surface here, instead of fleshing things out. Each page leaves me wanting more, and feeling shortchanged. Take away the artistic presentation and you are left largely with a pithy, somewhat pedantic regurgitation of quite interesting historical math tidbits, for which you need Google standing by if you wish to explore further… it's a somewhat "Cliff"Notes version of math history (...although I also realize Pickover likes to experiment with math writing styles and presentation -- still, this volume seems a bit of a 'puff-piece' compared to some of his other fine works, and it would be ashamed, I think, if he became better known for this book than his other contributions). Overall, I am still glad I bought the book, as a reference source... but am also glad I got it at a heavy discount ;-))

In short, I can recommend this volume to young people beginning their journey in mathematics, as a sort of starter book, an initiation into the field of math, but am more reluctant recommending it to readers who are further-along, for whom there may be many better selections... including fuller text and less glitz. Still, many may (and clearly DO) find its style, format, elegance, and sheer breadth of topics, captivating enough to want it for their bookshelf (...or coffee table) -- indeed, mine seems to be a minority view; those who are particularly enamored of this book, feel free to chime in, in the comments, about what makes it so laudable or useful from your standpoint…

(Also, if you DO like this offering from Pickover, it is worth noting that he followed it up with a similarly-styled volume called "The Physics Book.")

By the way, the books I cited above from Crilly and Elwes that I very much liked and do recommend are:

"The Big Questions: Mathematics" and "50 Mathematical Ideas You Really Need to Know" -- both by Tony Crilly

and, "Mathematics Without the Boring Bits" -- by Richard Elwes
Also, Elwes did an even more encyclopedic/comprehensive volume of math topics than Pickover's book, called "Mathematics 1001," but minus the glossiness -- I prefer the Elwes offering, if you're looking for terse treatments, but understand it won't carry the popular appeal of Pickover's effort.

Finally, for anyone who especially likes Pickover's book for its 'historical' format, I might just mention that Pat Ballew does a wonderful job of regularly noting mathematics history in his "On this Day in Math" entries over at "Pat's Blog."

Clock Geometry

2012-02-03T06:15:00.001-05:00

For a Friday puzzle, another one lifted from William Poundstone's recent "Are You Smart Enough To Work at Google":

At 3:15, what is the angle formed between the minute hand and hour hand on an analog (regular) clock?
(if the answer seems immediately obvious to you, you likely have the wrong answer)

I'll be giving the correct answer in the comments section below.

Math Genius of the Female Persuasion

2012-02-02T09:30:00.014-05:00

It seems like most stories of young math savants or geniuses involve males, but here's one of a German female, 21-year-old (at the time) Julia Ruscher, whose specialty is stochastic processes:

...and speaking of gender and math talent, consult this old take from xkcd:

http://xkcd.com/385/

Out of the Mouths of Babes...

2012-02-01T12:50:00.000-05:00

Haggis finds that children ask the darndest things (...about space-filling curves):

http://haggisthesheep.wordpress.com/2012/01/29/most-random-masterclass-question-ever/

Richard Feynman on Math

2012-01-31T06:30:00.002-05:00

...'cuz, hey, you can never watch too much Feynman:

Fun With Mr. Honner... and the PSAT

2012-01-30T12:15:00.000-05:00

Making a boring (yaaawn) test question, a bit more challenging:

http://mrhonner.com/2011/10/26/fun-with-the-psat/

Greatest Math Equations Ever (including 1+1=2)

2012-01-29T07:30:00.004-05:00

A list of the world's 20 greatest math equations (Maxwell beats out Euler):

http://benvitalenum3ers.wordpress.com/2012/01/28/why-is-112-on-the-20-greatest-equation-list/

And in regards to Russell and Whitehead proving that 1+1=2 in Principia Mathematica, this:

...actually, a more serious take on the Russell/Whitehead work here:

http://blog.plover.com/math/PM.html

"Most mathematicians believe in heaven"....

2012-01-28T07:00:00.004-05:00

In an older, interesting (and critical) NY Times piece, Jim Holt reviews John Allen Paulos' review of arguments for/against God in his book "Irreligion." The Platonist/Non-Platonist debate is alive-and-well as Holt takes Paulos to task for some of his arguments and writing style (but also has some positive things to say):

http://tinyurl.com/6o36w4y

I've repeatedly linked at times to a prior Bloggingheads/TV clip with John Horgan and Jim Holt that I enjoyed (where Holt gives his take on math), but for newcomers to the blog here it is again :

http://math-frolic.blogspot.com/2010/10/math-talking-heads.html

Friday Puzzle

2012-01-27T06:00:00.001-05:00

I'll probably pull a few puzzles for the blog from the new volume I referenced a short while back, "Are You Smart Enough To Work At Google?"

We'll start with a pretty easy and straightforward one here:

How many integers are there between 1 and 1000 that contain at least one 3 as a digit?

(By the way, the last puzzle that I referred to over at Richard Wiseman's site is also included in the above book.)

answer below for today's riddle:
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Answer: 271

Maths Education (as those Brits would have it)

2012-01-24T19:30:00.001-05:00

Alex Bellos on why math education ought be compulsory through the teenage years... and, why it ought be enjoyable:

http://www.guardian.co.uk/science/2012/jan/23/how-learn-love-maths

an excerpt:

"Maths is justified in this country[Britain] because it is useful. Sparks said his proposals were necessary because young people need a better grasp of maths to compete in the job market, where an understanding of technology and numeracy are increasingly important.
I agree. But maths should also be studied for the same reasons we study Shakespeare – it is our intellectual and cultural heritage. Maths makes us more creative and gives us a deeper understanding of the way things really are."

"A Paean to Beautiful Mathematics"

2012-01-23T13:00:00.000-05:00

Bit of a book review from another blog here (of "Proofs From THE BOOK"):

http://mathforlove.com/2012/01/beautiful-mathematics/

…not a volume I'll be reading myself, but I can still appreciate its impetus (as I like to say myself, 'math iz a beautiful thang!')

From the reviewer: "Now here’s the thing: this is a book that is decidedly not for the layperson. To read it, you need to be extremely comfortable with calculus and limits, infinite sums, and some serious subtleties, both conceptual and notational. But if you are, the surprises keep coming. The results on primes are nothing short of astonishing (especially to me, as a non-number theorist who’s always loved the subject)."

Elsevier (which happens to be an anagram of 'evil seer')

2012-01-22T08:30:00.001-05:00

Mathematician Tim Gowers writes an interesting, inspired post about the abuses of journal publishers here (directed specifically at Elsevier, which he is boycotting):

http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/

excerpt:

"...I am not only going to refuse to have anything to do with Elsevier journals from now on, but I am saying so publicly. I am by no means the first person to do this, but the more of us there are, the more socially acceptable it becomes, and that is my main reason for writing this post."

As a side-note, PZ Myers, over at Pharyngula also isn't joyously thrilled with Elsevier:

http://scienceblogs.com/pharyngula/2012/01/elsevier_evil.php

Coding, Learning, the Future

2012-01-21T15:44:00.002-05:00

More and more is being written about coding/programming skills becoming part of basic literacy for upcoming generations.

Here's a recent take:

http://chronicle.com/blognetwork/castingoutnines/2012/01/14/programming-for-all/

and the same author gives some jumping-off points here:

http://chronicle.com/blognetwork/castingoutnines/2012/01/16/so-you-want-to-learn-to-program/

(hat tip to the latest Math Teachers at Play Carnival for pointing me to these 2 posts)

I'll also refer folks back to this prior Conrad Wolfram video on the subject (and many others have expressed a similar viewpoint):

http://wildaboutmath.com/2011/07/16/conrad-wolfram-on-teaching-math/

Friday Puzzle

2012-01-20T06:30:00.000-05:00

I adapted this from a Lewis Carroll conundrum recently posted over at "Futility Closet":

(caution though, this one may give you a headache ;-))

Mitt says that Newt always lies.
Newt says that Ron always lies.
Ron says that both Mitt and Newt always lie.
So, who is telling the truth?

answer below....
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.Answer: Newt tells the truth (...but then we all know better than that)

Whatevuh...

2012-01-19T13:15:00.000-05:00

In the next sentence, the number of occurrences of "0" is 1, of "1" is 7, of "2" is 4, of "3" is 1, of "4" is 1, of "5" is 1, of "6" is 1, of "7" is 1, of "8" is 2, and of "9" is 1.

In the previous sentence, the number of occurrences of "0" is 1, of "1" is 8, of "2" is 2, of "3" is 1, of "4" is 2, of "5" is 1, of "6" is 1, of "7" is 2, of "8" is 1, and of "9" is 1.

Is the Answer Obvious, or, Obscure

2012-01-18T06:30:00.002-05:00

Verbatim from Richard Wiseman's blog:

"Imagine there is a country with a lot of people. These people do not die, the people consists of monogamous families only, and there is no limit to the maximum amount of children each family can have. With every birth there is a 50% chance its a boy and a 50% chance it is a girl. Every family wants to have one son: they get children until they give birth to a son, then they stop having children. This means that every family eventually has one father, one mother, one son and a variable number of daughters. What percent of the children in that country are male?"

Wiseman's Friday puzzles are frequently devious… but, often once the answer is given and explained, one feels impelled to slap one's forehead and exclaim "DOH!, well, of course, obviously!." So perhaps his best offerings are those that, even once explained, are still not totally clear, and generate a lot of ongoing discussion/debate...

The one from last Friday (above) is such an effort, once again proving how tricky and misleading, probabilities can be. I confess to requiring extra time to convince myself that 50% was the correct answer, and it stiiiill rankles my intuition (…reminds me of Cantor's "I see it but I don't believe it" reaction! ;-)). This seems to be one of those quirky puzzles that is patently obvious to many, yet hugely thorny for others (one of the keys, I think, is to remain tightly focused on strict statistical probability, and not let your brain get distracted by what could theoretically happen). Read all the discord for yourself:

http://richardwiseman.wordpress.com/2012/01/16/answer-to-the-friday-puzzle-139/

(...peruse as many of the 250+ comments as you care to -- in fact you have to read some to get the answer, since Richard neglected to post an answer or explanation in his own post)

Collaboration via NY Times

2012-01-17T06:25:00.000-05:00

The NY Times "Numberplay" column this week addresses "open science," collaboration, and the Traveling Salesman Problem:

http://wordplay.blogs.nytimes.com/2012/01/16/open-science-numberplay-style/

The column poses two problems (one involving numbers/distances and one involving words/letters) for readers to work on. I'll be interested to see how well collaboration succeeds, in particular, on the first, enormous problem.

(The inspiration for this column, by the way, was the following, more general Times piece on collaborative science in the digital age: http://tinyurl.com/78apwyy )

Autistic Prodigy ('1 in 10 million')

2012-01-16T06:00:00.014-05:00

In case you missed it, last night CBS's "60 Minutes" profiled autistic (math & science) prodigy Jake Barnett. Fascinating!:

Friday Puzzle

2012-01-13T07:00:00.004-05:00

Adapted from a Richard Wiseman post:

From a normal playing deck of 52 cards, 4 cards are pulled at random and placed face down on a table. IF it is the case that by picking any two of those selected cards at random, the chance of getting 2 red cards is 50%, then what is the chance of picking, at random, two black cards from the 4?
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answer: 0% (for there to be a 50% chance of getting 2 red cards, there MUST be 3 red cards and 1 black card total)

Prime Thoughts

2012-01-12T08:23:00.002-05:00

a couple of prime number observations from an Indian mathematician (who wonders about the universality of the 2 properties he is noting):

http://gonitsora.com/some-interesting-properties-about-some-prime-numbers/

Abstraction and the Senses

2012-01-11T09:40:00.000-05:00

Joselle over at "Mathematics Rising" recommends 3 internet talks (one by Marcus du Sautoy, one by David Deutsch, and one by Benoit Mandelbrot) in this recent post :

http://mathrising.com/?p=708

(The subjects, broadly speaking, are symmetry, empiricism, and fractals, and what Joselle believes unites the 3 talks is a consideration of how abstraction emerges from sensory data; I also think these ideas piggy-back nicely onto the short Max Tegmark video I posted yesterday.)

One Physicist's Slant on Math

2012-01-10T09:00:00.004-05:00

Physicist Max Tegmark muses on math and reality:

What's Math Good For…

2012-01-09T10:45:00.001-05:00

why, constructing Sudoku puzzles of course!

I'm not much of a Sudokohalic myself, but still find it interesting that an Irish mathematician has apparently proven (yet to be confirmed) that Sudoku puzzles MUST contain a minimum of 17 clues (out of 81 squares) in order to insure a unique solution to any given puzzle:

http://www.nature.com/news/mathematician-claims-breakthrough-in-sudoku-puzzle-1.9751

A Couple of Books (…and, a Dig at Microsoft)

2012-01-08T07:15:00.001-05:00

Am reading a couple of books at the moment worth passing along:

"Math For the Frightened" by Colin Pask is yet another volume that purports to make math more accessible to those who have an aversion to it -- there are a plethora of such offerings around; almost a genre unto themselves -- and I am glad such volumes exist, but I do think they tend to oversell themselves. Math takes effort; it doesn't come easy for most of us, especially beyond certain levels. Assuredly some approaches to math introduce a bit more fun or interest or understanding to the subject than some other approaches, but for those with genuinely weak analytical skills or simply 'afraid' of math, such volumes likely won't turn the tide.
The Pask effort is a good and sincere attempt, but I imagine will still leave non-math-types in the dust at many points. I'm more comfortable recommending the book to those already inclined to math, or to math educators, than to any who are genuinely "frightened" of math (I'm probably more a fan of the "For Dummies" series of mathematics offerings for the math-averse). However, I'm only half-way through Pask's volume, and scanning ahead it looks like some of the best material may be yet to come. And here's a couple of quotes I like from the book that touch upon why reaching out to the math-challenged is so important:

From Arnold Toynbee: "I chose to give up mathematics, and I have lived to regret this keenly after it has become too late to repair the mistake. The calculus, even a taste of it, would have given me an important and illuminating additional outlook on the Universe."

And this from W.H. Auden: "I was cut off from mathematics. And this is a tragedy. That means half the world is lost. Scientists have no difficulty understanding all the humanities, but if you don't have mathematics you can't understand what they're up to."

A bit of a diversion, but a second book I'm reading and enjoying is William Poundstone's new "Are You Smart Enough to Work at Google?" -- a volume centered interestingly around the questions, puzzles, techniques currently employed by hiring interviewers at many top-flight high-tech companies -- an entertaining and breezy read (I recommend); I'll probably pull a few 'Friday Puzzles' from it for the blog.
Nothing to do with mathematics, but I'll close out with this joke from the volume that gave me a good chuckle:

"A helicopter was flying around above Seattle when a malfunction disabled all of its electronic navigation and communications equipment. The clouds were so thick that the pilot couldn't tell where he was. Finally, the pilot saw a tall building, flew toward it, circled, and held up a handwritten sign that said WHERE AM I? in large letters. People in the tall building quickly responded to the aircraft, drawing their own large sign: YOU ARE IN A HELICOPTER. The pilot smiled, looked at his map, determined the route to Sea-Tac Airport, and landed safely. After they were on the ground, the co-pilot asked the pilot how he had done it. 'I knew it had to be the Microsoft building,' he said, 'because they gave me a technically correct but completely useless answer.' ;-))

'Ant and Honey'

2012-01-06T07:00:00.006-05:00

For a pre-weekend puzzle, another recent Presh Talwalkar offering (especially for the geometers out there... or, the entomologists):

http://mindyourdecisions.com/blog/2011/12/26/puzzle-ant-and-honey/

Of 'Delight and Awe'

2012-01-05T09:00:00.002-05:00

A recent tweet from Clifford Pickover:

"Gaze in delight and awe: 22222 + (33333)^2 = 1111111111."

Yes She Khan!

2012-01-04T07:00:00.005-05:00

In news that is circling the mathosphere Vi Hart is joining forces with non-profit educator Khan Academy to…. well, er, uhh, I'm not actually sure just how Vi's quirky, creative, rapid-fire talents will be used by the more standard fare of the online Academy, but still one assumes it will be a very productive association indeed!
Congrats to Vi… and, more especially to Salman Khan for snagging her. We all eagerly await whatever production surprises may lie ahead…

Polymath Eric Lander Profiled

2012-01-03T07:15:00.001-05:00

Fascinating, inspiring profile (via NY Times) of a mathematician turned biologist:

http://www.nytimes.com/2012/01/03/science/broad-institute-director-finds-power-in-numbers.html?pagewanted=1&_r=1

Math is The Cat's Meow

2012-01-01T07:00:00.006-05:00

I like math... and, so does Paul Krugman:

http://krugman.blogs.nytimes.com/2011/12/31/i-like-math/?smid=tw-NytimesKrugman&seid=auto

(p.s.: Happy 2012!)

Friday Puzzle

2011-12-30T06:15:00.003-05:00

For the probability buffs out there, here's a tricky problem from another site:

What is the probability that in a group of 31 people, NONE of them have birthdays in February or August? (assume equal probability of birthday for all days throughout the year)
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the answer (I presume correct), 0.41%, is computed here:
http://tinyurl.com/7h3nh23

Delightful Math

2011-12-27T09:59:00.005-05:00

I've seen this particular puzzle presented many times in the form of a typical word or story problem, but don't recall if I'd seen it rendered in poetical form before:

http://tinyurl.com/7j4dlcs

6 and Primes

2011-12-26T07:30:00.002-05:00

It is an interesting fact that ALL prime numbers beyond 2 and 3 are either 1 more, or 1 less, than a multiple of 6. If you were unaware of this simple factoid you can check out these links for a discussion/explanation of it:

a short explanation: http://www.jimloy.com/number/prime6.htm

a longer explanation: http://tinyurl.com/77l94cc

Quickie Friday Puzzle

2011-12-23T07:00:00.003-05:00

Just a quickie on this day of Festivus! ;-)

How many Santa's helpers must there be total in a group, if all but 2 are named Smith, all but 2 are named Jones, and all but 2 are named Wilson?
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answer: 3 total (1 Smith, 1 Jones, 1 Wilson)

Year-end Review...

2011-12-22T08:30:00.003-05:00

For newer readers here, just a year-end list of some personal favorite posts from the last 12 months. Nothing particularly profound or deep about most of these; just touching on matters I happened to find interesting:

1) A Seemingly Impossible Task That Isn't
(a favorite paradox/puzzle coming from Raymond Smullyan)

2) Of Wheels and Circles and Points, Oh My
(another old mind-bending paradox)

3) Couple of Videos
(couple of fun YouTube videos)

4) Fermat's Last Theorem
(a video on Andrew Wiles solving Fermat's Last Theorem)

5) Marilyn Rolls the Dice
(Marilyn vos Savant introduces another puzzle)

6) The Cantor Set
(the Cantor Set)

7) A Video Re-run
(A Bloggingheads/TV video with John Horgan and Jim Holt)

8) The Blind Spot
(Review of William Byers' book "The Blind Spot")

9) Kickin' Back With Cantor
(BBC documentary on Cantor)

10) Loser…
(just for fun)

Explaining the Riemann Hypothesis

2011-12-21T08:47:00.000-05:00

For anyone who woke up this morning and muttered to themselves, "Hmmm, what is that there Riemann Hypothesis all about anyway?...":

http://www.askamathematician.com/2011/12/q-what-is-the-reimann-hypothesis-why-is-it-so-important/

Are These Folks Humans or Cyborgs!?

2011-12-20T06:28:00.001-05:00

Some people's brains are definitely wired very differently from mine....

When I first read of autistic savant Daniel Tammet's recitation of pi to over 22,500 decimals back in 2004, it seemed like a stunt beyond human comprehension, likely not to be surpassed in my lifetime… BOY, WAS I WRONG!!
It was a couple years later that I learned that Tammet's effort merely set a British and European record for pi recitation, but wasn't even close to the world record. As far back as 1981, an Indian had already recited pi to almost 32,000 digits, and a couple of Japanese blokes later greatly surpassed that endeavor. Then in 2005, a Chinese fellow, Chao Lu, would more than TRIPLE Tammet's puny ;-) performance, by reciting from memory, a phenomenal 67,890 digits of pi, and is still listed as the official record-holder by some accounts. Here's one listing of the world's top pi record-holders:

http://pi-world-ranking-list.com/lists/memo/

I'm not sure how these "official" designations are established though, because the current proclaimed record-holder is a former Japanese engineer, named Akira Haraguchi, who recited pi to 100,000 digits in 2006 (breaking his own prior record of almost 84,000):

http://www.foxnews.com/story/0,2933,217765,00.html

Simply UNNNreal! (...Having said that though, pi has now been computed to 10 trillion digits, so HEY Akira, ya gotta ways to go yet!)

...Now, if only I could remember where I left my car keys last night.

A Little Bit On Randomness

2011-12-19T06:00:00.003-05:00

h/t to Dan Meyer for this one:

The Depths and Intuition of Mathematics...

2011-12-18T10:00:00.007-05:00

A long, interesting, insightful answer to a simple question posed on Quora.com:

http://www.quora.com/What-is-it-like-to-have-an-understanding-of-very-advanced-mathematics

Booklist

2011-12-17T08:30:00.002-05:00

One blogger's list of 46 "interesting" math books from 2011 here:

http://tinyurl.com/8xmgf83

A variety of subject matter and material level is represented.

Friday Puzzle

2011-12-16T06:00:00.002-05:00

A recent geometry puzzle from 'Futility Closet' here (with a possibly surprising answer):

http://www.futilitycloset.com/2011/11/28/rolling/

Carny Time!

2011-12-15T08:00:00.003-05:00

Someone apparently submitted one of my year-old posts to the current Math Teachers At Play blog carnival (thank you to whoever you are!). The whole diverse Carnival is worth a look here:

http://letsplaymath.net/2011/02/18/math-teachers-at-play-35/

Infinite Trees Finitely Discussed

2011-12-14T07:15:00.001-05:00

Keith Devlin takes on infinity via mathematical trees in this recent blog post:

http://devlinsangle.blogspot.com/2011/12/christmas-trees-from-land-of-santa.html

Of Higgs and Sigmas

2011-12-13T06:30:00.002-05:00

What are the confidence intervals of confidence intervals, and other thoughts....

With a significant announcement from CERN on the Higgs boson presumed to be just hours away, KW Regan enters the fray with this interesting post about science, sigmas, and levels of significance:

http://rjlipton.wordpress.com/2011/12/13/the-higgs-confidence-game/

…an excerpt therefrom:

"The high rate of disappearing significance overall is still puzzling. Its extent in human sciences was detailed exactly one year ago in a disturbing article by Jonah Lehrer for The New Yorker. If 250 researchers try the same experiment, one would expect 2 or so of them to get deviations (in either direction). The world will then see 2 or so published papers from them, but nary a peep from the 248 who failed and gave up quickly and forgot about it. Thus a significant result may appear independently confirmed when it was actually just by chance, and those failing to reproduce it will then peep up loudly. The effect is equally pernicious with 250 different experiments, especially given a fair chance of a lower-confidence positive from a test deemed related enough to corroborate the original."

Holiday Shopping For All Ye Merry Math Fans

2011-12-10T16:00:00.004-05:00

Order early & order often ;-)

http://www.zazzle.com/sheckyr/gifts

Richard Elwes... Again

2011-12-09T16:00:00.000-05:00

I've been aware of Brit Richard Elwes for barely over a year now, but he's already vaulted to one of my favorite math expounders. An interview with him here from Q Blog (and great to see that he has a new volume out, "The Maths Handbook," and yet another on the way! ....his first two books are two of my favorites):

http://www.quercusbooks.co.uk/blog/2011/12/07/the-quercus-couch-richard-elwes/

Another Friday Puzzle

2011-12-09T07:37:00.012-05:00

Update: I had quickly adapted the original problem below from another site, only to realize it was far too easy as a problem of 2 equations with 2 unknowns, so have now re-stated it below in at least a slightly more challenging form:

"x" and "y" are two different 2-digit prime numbers composed of the same digits, but in reverse order. If it is true that x - y = 36, then what must the numbers x and y be:
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answer: x=73 and y=37

Game Show Math

2011-12-08T09:16:00.011-05:00

...or, why doing math in your head with a bazillion eyes upon you is no picnic!
(h/t to Presh Talwalkar for this)

Halting Problem In Verse

2011-12-07T06:00:00.002-05:00

The Halting Problem, Dr. Seuss, poetry, and Geoffrey Pullum here... ohh my:

http://ebiquity.umbc.edu/blogger/2008/01/19/how-dr-suess-would-prove-the-halting-problem-undecidable/

quite cool!

Phi

2011-12-04T18:00:00.001-05:00

The stream of popular books out on pi, the Fibonacci sequence, or the Golden Ratio seems unending… and, now we have another: Alfred Posamentier and Ingmar Lehmann are newly out with "The Glorious Golden Ratio" -- haven't read it, but for geometry fans, anything by these two is certainly worth some high anticipation!

Friday Puzzle

2011-12-02T06:15:00.004-05:00

I adapted this problem directly from a recent NPR Car Talk puzzler, so if you heard that show you'll know the answer:

My brother Morty and I took a drive up to the mountains this weekend to see the Golden-breasted Flooglebird. Morty drove the first 40 miles and I drove the rest of the way. We saw the Flooglebird right away (or something closely resembling it) and immediately returned home on the exact same route.

On the return trip Morty again drove the first part of the trip, and I drove the final 50 miles this time.
In total who did the most driving, me or Morty, and how many more miles than the other brother did that driver do? (yes, there's enough information to reach an answer!)

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answer: I drove 20 more miles than Morty
(the Car Talk guys explain it their way here: http://www.cartalk.com/content/car-trip-trigonometry-0?answer )

Today's Statistics Lesson...

2011-11-28T16:49:00.000-05:00

From Professor Dilbert:

http://tinyurl.com/bowyu86

A Few Books

2011-11-27T18:30:00.001-05:00

Haven't mentioned any books for awhile, so will just briefly cite 3 that have been around for a little while now, though I've only read the last one:

"The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy," Sharon Bertsch McGrayne's volume on Thomas Bayes and the statistical theory he formulated has received mostly favorable reviews, including this one from no less than The Lancet:

http://www.thelancet.com/journals/lancet/article/PIIS0140-6736%2811%2961728-5/fulltext

A book I received a review copy of but never got around to reading, is "Magical Mathematics" by Persi Diaconis and Ron Graham, recounting the mathematics that underlies a lot of magic tricks. Even though it didn't engage me, I won't argue with success, as it has received almost unanimous thumbs-ups in reviews I've seen, including this one from CTK Insights:

http://www.mathteacherctk.com/blog/2011/10/magical-mathematics/

(...As a sidenote, speaking of magic, a book I did love, but on neuroscience not mathematics is now out in paperback: "Sleights of Mind" by Macknick and Martinez-Conde.)

Finally, the one review volume I have had a chance to peruse, is this year's issue of "The Best Writing On Mathematics 2011," edited once again by Mircea Pitici. I almost feel I could duplicate the short review I gave of last year's initial edition for the current volume. It is again a fine compendium of great variety. If anything, I would say it has a bit more philosophical reading and other material that a layperson can readily follow (while still also including several quite technical entries). And again, whatever your own proclivities in math it will contain some contributions of interest and others probably not-so-much, but all-in-all a very worthwhile volume. I look forward to this series continuing well into the future.

Thanksgiving

2011-11-23T06:15:00.001-05:00

no math today….

"If the only prayer you ever say in your whole life is 'thank you,' that would suffice."
-- Meister Eckhart

Of Numbers and Colors...

2011-11-20T07:15:00.000-05:00

A recent medical study looks at synesthesia (the cognitive blending of sensory information) and numbers, and the differences in cortical activity between "synesthetes" and others:

http://www.medicalnewstoday.com/releases/237908.php

Well-known autistic savant Daniel Tammet is famous for his synesthetic experience. He expounds upon what it all means in this TEDTalk from earlier this year:

Tammet is also famous for his depiction of how he visualizes the number pi in color (a number he has recited from memory to over 22,500 digits -- no, that's NOT a misprint):

see here: http://www.newscientist.com/gallery/mg20227111500-savant-art

The "Dr Square Puzzle"

2011-11-18T05:45:00.003-05:00

Visit the "math4love" blog to see a fun, interesting, iterative-type math problem, inspired by a 3rd grader!:

http://mathforlove.com/2011/11/the-dr-square-puzzle/

Food For Thought? (math instruction)

2011-11-14T09:30:00.004-05:00

This TEDtalk by John Bennett seems a tad overly pedantic, but I do find the endpoint (last couple minutes) regarding deductive and inductive reasoning interesting, as well as his general take that middle and high school math ought NOT be mandatory for students:

Numberphile

2011-11-13T08:00:00.003-05:00

YouTube is introducing a new channel for math buffs, called "Numberphile":

http://www.youtube.com/user/numberphile

(...not too much up on it yet, but worth keeping an eye on; I'm adding a link to right-hand column under "Misc. Resources")

Thinking vs. Rote Knowing

2011-11-11T07:30:00.005-05:00

Assessing a 14-yr.-old math whiz for entrance to Cambridge (...and a nice thought puzzle):

http://www.bbc.co.uk/news/magazine-15574889

"The Unplanned Impact of Mathematics"

2011-11-10T08:30:00.003-05:00

"Time and again, pure mathematics displays an astonishing quality. A piece of mathematics is developed (or discovered) by a mathematician who is, often, following his or her curiosity without a plan for meeting some identified need or application. Then, later, perhaps decades or centuries later, this mathematics fits perfectly into some need or application."

…and Peter Rowlett looked for (and talked about) more examples of such here:

http://travelsinamathematicalworld.blogspot.com/2011/07/unplanned-impact-of-mathematics.html

Of Love and Fourier Transforms...

2011-11-09T06:45:00.002-05:00

Jennifer Ouellette's ode to mathematics... and love (...and some physics guy) here:

http://blogs.scientificamerican.com/cocktail-party-physics/2011/09/29/love-among-the-equations/

an excerpt:

"It turns out that the world is filled with hidden connections, recurring patterns, and intricate details that can only be seen through math-colored glasses. Those abstract symbols hold meaning. How could I ever have thought it was irrelevant?

This is what I have learned from loving a physicist. Real math isn’t some cold, dead set of rules to be memorized and blindly followed. The act of devising a calculus problem from your observations of the world around you – and then solving it – is as much a creative endeavor as writing a novel or composing a symphony."

Math Documentaries Available

2011-11-08T07:45:00.004-05:00

In case you have a lot of free time to fill in, a nice listing of math documentaries that look very good (mostly from BBC) available on the Web here:

http://www.cosmolearning.com/mathematics/documentaries/

(and I've inserted a permament link to same in right-hand column under "Misc. Resources.")

More of What's-Math-Good-For

2011-11-07T08:45:00.003-05:00

Here's a list of 15 diverse folks who have, or may have, used their geeky math skills to gain some lucrative money-making advantage:

http://tinyurl.com/6koc8wp

(hat tip to Steven Colyer)

Good Math, Not-So-Good Math

2011-11-06T09:30:00.003-05:00

Mark Chu-Carroll over at 'Good Math Bad Math' has never suffered math cranks very well (...and he gets his share of them):

http://scientopia.org/blogs/goodmath/2011/11/05/yet-another-cantor-crank/

For more crankish entertainment you can visit here:

http://www.crank.net/maths.html

83rd Carnival of Mathematics

2011-11-05T13:58:00.001-04:00

The latest Carnival of Mathematics is up-and-running here:

http://teachbesideme.blogspot.com/2011/11/cafrnival-of-mathematics-83.html

The Title of This Post is Recursive

2011-11-02T18:30:00.001-04:00

Keith Devlin waxes not-quite-poetic on "The Recursion Principle" and its underlying importance to mathematics:

http://devlinsangle.blogspot.com/2011/11/how-multiplication-is-really-defined-in.html

From the posting:

"Though recursion is ubiquitous in modern mathematics, even at the most basic level of the analysis of the arithmetic of natural numbers, it is a subtle concept, easily misunderstood…

"This may all seem like a great deal of fuss about nothing. But what is going on here is really very deep. Much of modern mathematics involves finding ways to handle the infinite - calculus exclusively and spectacularly so. Mathematicians learned over many years of painful lessons that the step from the finite to the infinite is a tricky one that requires considerable finesse. In particular, you have to exercise great care to set it up correctly and do it right. The Recursion Theorem is one of those crucial bridges that allow us to go beyond the finite to the infinite, to extend human intellect from its finite physical limitations to the infinite world beyond that our minds can construct. By getting the mathematics right, we can make that step with total confidence. Confidence both in that abstract world itself and in the concrete conclusions it allows us to reach about our lives, our science, and our technologies. That is huge for Humankind."

(...ohh, and by the way, multiplication is NOT just repeated addition. ;-)

Loser....

2011-11-01T06:00:00.004-04:00

Enjoy... stumbled upon this in the comments to a Richard Wiseman posting:

'Cold Hits'

2011-10-31T07:00:00.003-04:00

Nice treatment of probability, fingerprint analysis, and the birthdays-in-a-room example via a recent John McGowan post:

http://tinyurl.com/6y5ad4o

Obviously, Pi = 4

2011-10-28T08:30:00.001-04:00

For any who have never seen it, an oldie-but-goodie puzzle today... simple proof that pi = 4 :

http://i.imgur.com/AzeYc.jpg

From the What-Is-Math-Good-For-Anyway-Dept.

2011-10-26T09:30:00.006-04:00

Wow, who knew:

"Six of the 10 writers of 'The Simpsons' are high-level mathematics PhDs and for years they have been making mathematical jokes to each other in the series, such as writing formulae up on blackboards or on car numberplates. The jokes have developed a cult following among the scientific community."

Simon Singh knew... see:

http://www.thebookseller.com/news/science-book-deals-frankfurt.html

[image via wikimedia commons]

Marilyn Rolls the Dice...

2011-10-25T06:20:00.005-04:00

Marilyn Vos Savant, who brought the Monty Hall Problem to public view, stirs the probability pot again with this Sunday magazine problem asking which result is the more likely outcome from 20 throws of a die: a) 11111111111111111111 or b) 66234441536125563152

http://tinyurl.com/3zsb7tf

[Addendum: I've now gotten around to reading many of the comments to the above link, and interestingly, once again Marilyn has opened a can of worms. Her logic/math is correct, yet many misinterpret the problem and once again think she is wrong, as they did originally in the case of the Monty Hall Problem.
The problem reminds me slightly of Newcomb's Paradox where a notion of 'backwards causation' comes into play to confuse the issues; except that Newcomb's Paradox is essentially unresolved, whereas this dice problem is clearly resolvable.]

Rumbling In Cantor's Paradise

2011-10-22T14:17:00.001-04:00

"No one will drive us from the paradise which Cantor created for us." -- David Hilbert

I wasn't aware there was very much serious controversy over Cantor's proof that the real number set is uncountable (versus the set of integers which is countable), but RJ Lipton is aware of the naysayers out there and takes a stab at reaching them here:

http://tinyurl.com/3mo7mt4

(Not sure Lipton will win over any doubters with his argument, but for most, Cantor probably doesn't even require a defense; at any rate some interesting comments below Lipton's post.)

A Wiseman Puzzle... and Martin

2011-10-21T08:00:00.001-04:00

Richard Wiseman's puzzle for today might keep you busy for awhile:

http://richardwiseman.wordpress.com/2011/10/21/its-the-friday-puzzle-132/

(he'll post the answer on Mon. -- answer HERE)

p.s.... Happy Birthday to Martin Gardner today, wherever he is Recreationing In Peace.
(a 4-min. NPR remembrance at the time of his death here)

Four Circles... Really!

2011-10-20T16:36:00.000-04:00

An optical illusion for your entertainment and delectation!:

http://i.imgur.com/RYHtQ.jpg

Open Problems...

2011-10-19T07:00:00.002-04:00

interesting older post on some "embarrassing" open problems in math:

http://angryfaic.wordpress.com/2011/02/26/embarrassing-open-problems-in-maths/#more-42

"Problem Solving Flowsheet" ;-)

2011-10-18T06:30:00.005-04:00

Not exactly math, but problem-solving for all you lab rats... Yesterday, in a lab, I ran across a technical ;-) "problem solving flowsheet" taped to the wall -- when I got home I looked it up on the internet and of course found lots of references to the very same sheet, so I may be among the last to have seen this (don't know how long it's been going around).
In case you've missed it too you can check it out here (adult language):

http://renivstheblog.files.wordpress.com/2011/05/problem-solving-flowsheet.gif

Reuben Hersh's Mathematical Experience...

2011-10-17T06:35:00.007-04:00

Reuben Hersh has written often of the history, culture, and deeper nature of mathematics. And he is, famously, a NON-Platonist... one who believes mathematics is more a by-product of the human mind than a real extant part of the physical Universe. One of his classic works (with Philip Davis), that most of you have likely read, was "The Mathematical Experience," which Martin Gardner reviewed quite critically back in 1981. I enjoy reading Hersh, and I've been re-reading this particular volume on its 30th anniversary, but having said that, his writing sometimes seems to skim the surface of the material he is tackling. The content bounces back-and-forth between regurgitation of standard pedagogical material and more interesting, but not always convincing, arguments of deeper philosophy. I'm sometimes reminded of the old Wendy's commercial, "Where's the beef?" in reacting to certain subjects broached in this book that don't seem fleshed out as fully as they deserve (the second half of book though is richer than the first half, and Hersh provides plenty of good references for "further study"). Perhaps I just miss the nuance of Hersh's stance on some matters, but I usually find Gardner's arguments more persuasive and articulate. Having said that, more and more respected mathematicians these days seem to be moving toward the minority non-Platonist stance that Hersh has long expounded, so the debate is hardly settled (...indeed, it is probably more UNsettled than ever!).

I mention all of this only because of recently stumbling across this informal response, I'd not seen before, from Hersh to Gardner's original review, and it makes for interesting reading:

http://cs.nyu.edu/pipermail/fom/1997-November/000128.html

The below page links to an Edge interview where Hersh further spells out his notions:

http://edge.org/3rd_culture/hersh/hersh_p1.html

"The Mathematical Experience" remains a classic mathematical opus, with a great breadth of math subject matter (and there is a newer, updated version which I don't own, so not sure how much it differs from the original), and I'm definitely finding it worth a re-read decades later.

Benford's Law vs. Finance and Accounting Data

2011-10-13T06:15:00.000-04:00

uhh-ohhh...

http://econerdfood.blogspot.com/2011/10/benfords-law-and-decreasing-reliability.html

"...overall, the picture looks grim."

Of Hula Hoops and Geometry, and...

2011-10-12T07:15:00.001-04:00

http://www.futilitycloset.com/2011/09/22/johnson-circles/

...and in other news, Keith Devlin has a brand-spanking newly-launched blog here (1st post on Steve Jobs):

http://profkeithdevlin.wordpress.com

Coordinated Web Effort Proposed to Solve Riemann Hypothesis

2011-10-11T06:15:00.002-04:00

I don't hold out a lot of optimism for this, but what do I know: Indian mathematician organizing online collaborative effort to tackle the Riemann Hypothesis (based on an approach originally proposed by Freeman Dyson highlighting quasicrystals):

http://www.microfinancemonitor.com/2011/10/10/indian-mathematician-raises-storm-over-riemann-riddle/

also, see here:

http://fadereu.posterous.com/knk103-the-crystals-of-mt-zeta

which includes this quote from Dyson: "...if we take a Baconian point of view, the history of mathematics is a history of horrendously difficult problems being solved by young people too ignorant to know that they were impossible."
:-)

[Bernhard Riemann image via Wikimedia Commons]

Math at Science Online 2012 ???

2011-10-09T07:00:00.020-04:00

Scientific American's Bora Zivkovic is one of the co-organizers of the premier annual 3-day "Science Online" conference (focusing on science blogging and science communication more generally in the digital age), held in central North Carolina every January -- this year in Raleigh. Attendees come from all over North America as well as internationally. There has always been a strong emphasis on the biological and medical sciences in the multitudinous sessions of this conference, and increasingly the physical sciences are represented as well. Mathematics has been rather less prominent, and Bora recently tweeted "Where's the math?" in regards to proposals for the coming get-together.

If you're a blogger or other math educator/communicator and you've never been to one of these conferences I highly recommend the experience (in fact, I'd defy you to find any individual who's attended that didn't feel richly rewarded by the content, variety, and camaraderie of the meeting -- even if your interests are very narrowly 'mathematical' and not so much 'scientific' you will find very worthwhile, instructive sessions to choose from).

Session suggestions for this coming January (19th-21st) are listed at:

http://bit.ly/hhu4f2

Anyway, Bora is actively soliciting for more math-oriented content; if you have ideas/suggestions that fit into any of the above subject areas (especially if you would like to be a presenter/contributor yourself) contact him SOON at: coturnix@gmail.com

DO note that the conference is actually billed as an "Unconference" and sessions are not intended to be the typical 45-min. Powerpoint lecture format, but rather short presentations that generate active and knowledgeable audience participation/engagement. Everyone (including presenters) goes away learning from others.

If you're on Twitter you can follow the progress of Science Online 2012 at the hashtag #scio12. Even though the conference isn't until January, online planning and conversation about it will be ramping up considerably starting about now. And registration for the conference will likely close (fill up) very shortly after it opens!

Perplexing Art...

2011-10-08T08:00:00.002-04:00

If you're a fan of optical illusions or Escher-like artwork you may enjoy this blog-site:

http://impossible-world.blogspot.com/

iMourn

2011-10-06T00:05:00.006-04:00

Dreamer, Doer, Visionary, Sage, Wizard, Virtuoso.....

(1955 - 2011)

THANKS for all the MAGIC!!!

[“Any sufficiently developed technology is indistinguishable from magic.” -- Arthur C. Clarke]

(Jobs' 2005 commencement address at Stanford HERE)

(David Pogue's tribute HERE)

"Paraconsistent Mathematics"

2011-10-05T09:50:00.011-04:00

As a bit of followup to yesterday's post I just discovered this couple-month-old article from plus.maths.org on "paraconsistent mathematics," which addresses the sort of 'truth' issues of statements raised yesterday, and allows for certain 'logical' contradictions:

http://plus.maths.org/content/not-carrot

Just Some Classic Hofstadter...

2011-10-04T08:20:00.001-04:00

From chapter 17 of "The Mind's I"(1981) by Douglas Hofstadter and Daniel Dennett:

"One variant is: 'Thiss sentence contains threee errors.' On reading it, one's first reaction is, 'No, no - it contains two errors. Whoever wrote the sentence can't count.' At this point, some readers simply walk away scratching their heads and wondering why anyone would write such a pointless, false remark. Other readers make a connection between the sentence's apparent falsity and its message. They think to themselves, 'Oh, it made a third error after all - namely, in counting its own errors.' A second or two later, these readers do a double-take, when they realize that if you look at it that way, it seems to have correctly counted its errors, and is thus not false, hence contains only two errors, and... 'But...wait a minute. Hey! Hmm...' The mind flips back and forth a few times and savors the bizarre sensation of a sentence undermining itself by means of an interlevel contradiction, possibly on the purpose or interest of the idea, possibly on the cause or resolution of the paradox, possibly simply to another topic entirely."

And in some further self-referential fun Tanya Khovanova recently offered these two sets of sentences that come from David Bernstein (where a sentence and its 'negation' are either both true or both false):

This sentence contains five words.
It is not true that this sentence contains five words.

This sentence contains ten words.
It is not true that this sentence contains ten words.

Questioning Peano

2011-10-03T07:55:00.004-04:00

For those inclined toward epistemology and formal logic, another wonderful post from RJ Lipton below, this time on the possible inconsistency of Peano Arithmetic:

http://rjlipton.wordpress.com/2011/10/01/what-if-peano-is-inconsistent/

This stuff makes my head hurt... but I always enjoy watching others pursue it!

Friday Puzzle

2011-09-30T07:05:00.003-04:00

Yeah, I'm a sucker for basic (but clever) geometry puzzles, so here's another one from "Futility Closet" from a month+ ago:

http://www.futilitycloset.com/2011/08/17/rest-stop/

(click where indicated in the posting to see the surprisingly simple answer)

New Aczel Book

2011-09-29T17:14:00.000-04:00

The always-interesting Amir Aczel has a new volume out that should be of interest, "A Strange Wilderness: The Lives of the Great Mathematicians":

http://www.amazon.com/Strange-Wilderness-Lives-Great-Mathematicians/dp/1402785844

Here's the blurb from Publisher's Weekly:

http://www.publishersweekly.com/978-1-4027-8584-9

"Math In the Real World"

2011-09-28T11:30:00.001-04:00

"Home School Math" has put up a nice page of resource links (entitled "Online Math Resources For Math in the Real World") for math teachers/homeschoolers/students or just math fans:

http://www.homeschoolmath.net/online/real_life_math.php

Popcorn Time... Math Movie

2011-09-27T07:45:00.001-04:00

A movie for math buffs! Hooray!! "Julia Robinson and Hilbert's Tenth Problem," a 1 hour movie about... Julia Robinson (1 of the major female mathematicians of her day) and Hilbert's 10th problem (dealing with the algorithmic solvability of Diophantine equations) will be playing in various locales in October. See here for possible air dates in your area:

http://www.zalafilms.com/films/jrairdates.html

Wikipedia entry for Hilbert's 10th problem here:

http://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem

entry for Julia Robinson here:

http://en.wikipedia.org/wiki/Julia_Robinson

And here's the movie trailer to whet your appetite:

(David Hilbert image via Wikimedia Commons)

Gödel Simplified... sort of

2011-09-26T06:45:00.001-04:00

I got a big kick out of this 1994 1-page (pdf) explanation of Gödel's Second Incompleteness Theorem from George Boolos, all in single-syllable words (literally)... pretty impressive!:

http://bit.ly/bWrBqz

Geometry Lovers...

2011-09-25T10:40:00.004-04:00

I only recently discovered this great site with a great many cool geometry problems (mostly high school level):

http://gogeometry.com/problem/index.html

the more general home page for the site here:

http://gogeometry.com/

Friday Puzzle

2011-09-23T07:00:00.002-04:00

For a Friday puzzle I'll just link you to this one from Presh Talwalkar from several weeks ago (...another geometry-oriented puzzle, involving string-cutting; with the answer included in the comments to Presh's post):

http://mindyourdecisions.com/blog/2011/08/29/geometry-puzzle-string-cutting-game/

(Math) Teaching and Twitter

2011-09-22T06:20:00.000-04:00

Mr. Honner recently noted how much he now uses Twitter for ideas and connections to assist his math teaching activities. I suspect most of you already use Twitter, but if not, he offers a straightforward basic introduction to its use and benefits here:

http://mrhonner.com/2011/09/18/math-teachers-and-twitter/

He includes a list of some of the mathematically-inclined Twitter feeds he follows for his purposes. And if you want a much longer, broader list of math-related Tweeters you can check out this list from Listorius:

http://listorious.com/search/people?q=math&search=Search