Richard Feynman on Math

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

Fun With Mr. Honner... and the PSAT

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)

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"....

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

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)

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"

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')

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

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

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...

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

 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!." 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 270+ 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

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')

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

Friday Puzzle

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

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

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

Physicist Max Tegmark muses on math and reality:

What's Math Good For…

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)

 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'

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'

A recent tweet from Clifford Pickover:

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

Yes She Khan!

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

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

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!)