'Cold Hits'

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

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.

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...

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

 "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

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!

An optical illusion for your entertainment and delectation!:

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

Open Problems...

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" ;-)

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...

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

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...

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

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 ???

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...

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

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

iMourn

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"

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...

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

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!