Wednesday 27 October 2010

The Piffle Paradox - or how pure mathematicians have fun

Ever wondered how pure mathematicians have fun? The following is from the 1967 paper Modern Research in Mathematics by A. K. Austin, from the Department of Pure Mathematics at the University of Sheffield. It's a send-up, by the way...

A note on piffles by A. B. Smith

A. C. Jones in his paper "A Note on the Theory of Boffles," Proceedings of the National Society, 13, first defined a Biffle to be a non-definite Boffle and asked if every Biffle was reducible.

C. D. Brown in "On a paper by A. C. Jones," Biffle, 24, answered in part this question by defining a Wuffle to be a reducible Biffle and he was then able to show that all Wuffles were reducible.

H. Green, P. Smith, and D. Jones in their review of Brown’s paper, "Wuffle Review, 48", suggested the name Woffle for any Wuffle other than the non-trivial Wuffle and conjectured that the total number of Woffles would be at least as great as the number so far known to exist. They asked if this conjecture was the strongest possible.

T. Brown, "A collection of 250 papers on Woffle Theory dedicated to R. S. Green on his 23rd Birthday" defined a Piffle to be an infinite multi-variable sub-polynormal Woffle which does not satisfy the lower regular Q-property. He stated, but was unable to prove, that there were at least a finite number of Piffles.

T. Smith, L. Jones, R. Brown, and A. Green in their collected works "A short introduction to the classical theory of the Piffle," Piffle Press, 6 gns., showed that all bi-universal Piffles were strictly descending and conjectured that to prove a stronger result would be harder.

It is this conjecture which motivated the present paper.


Not to be outdone, S. J. Farlow from the Department of Mathematics, University of Maine, wrote in the seminal A rebuke of A. B. Smith's paper, 'A Note on Piffles':

In A. B. Smith's recent paper, 'A Note on Piffles', The American Mathematical Monthly, 84, p. 566 he completely fails to mention one of the most significant results yet discovered in Piffle Theory, namely A. K. Puddle's paper, 'Products of Planar Piffles'.

In this short but succinct note Puddle proves that a denumerable product of Pi Piffles is in fact a P-Pi Piffle (assuming of course pairwise permutation of the Piffles). That Puddle's condition was only necessary and not sufficient did of course not detract from this significant work—but did in fact open the door to the well-known Piffle Paradox (of which I'm afraid Professor Smith is completely unaware).

Readers interested in obtaining a complete up-to-date history of the Piffle should consult P.U. Piper's comprehensive review, The Piffle: 1840-1978 (Pauper Press). Here Piper describes some modern approaches taken by American Mathematicians during the last fifteen years. I am sorry to say that the classical treatment of Piffles taken by most English Mathematicians, notably the work of author Smith, is, by American standards, obsolete even before it hits the printing press. In particular the classic theorem of Smith, Jones and Brown on Polynomial Piffles would be only a simple corollary to Puddle's basic result on Homological Piffles. In fact it is fairly safe to say that all the English results so far on Piffle Theory can be subsumed in Piper's short note, 'Spectral Decompositions of Partial Piffles', American Piffle Review, 27, pp. 1-2.


Hat-tip to Let ε < 0 where I first saw this lovely work. I believe the original paper came out of discussions between mathematicians and educators regarding good (and presumably bad and confusing) forms of mathematics education. I dare say that had I seen this treatise in undergraduate maths, or had Homological Piffles been mentioned at least once, I wouldn't have transferred from Metric Spaces to Astronomy....

Austin, A. (1967). 3183. Modern Research in Mathematics The Mathematical Gazette, 51 (376) DOI: 10.2307/3614400

Farlow, S. (1980). Three Mathematical Satires A rebuke of A. B. Smith's paper, 'A Note on Piffles' International Journal of Mathematical Education in Science and Technology, 11 (2), 285-304 DOI: 10.1080/0020739800110222

Tuesday 19 October 2010

Ep 136: Sexual Selection

It's about time we put out a new podcast!

In this edition, I chat to Associate Professor Robert Brooks, Director at the Evolution and Ecology Research Centre, UNSW about sexual selection.

Charles Darwin described sexual selection as "struggle between the individuals of one sex, generally the males, for the possession of the other sex" and nature abounds with strange examples of where animal features have evolved way past their survival needs - for example, reindeer antlers, peacock plumes and quite possible human vocabulary - humans and other primates survived quite nicely without a wide vocabulary, why do we now possess one?

Rob is a leading world expert in the area, listen in to find out what he had to say.
Listen in to this show here (or press play below):

If you would like to hear more about the science of sex, check out The Beer Drinking Scientists episode Let's talk about sex.

Brooks, R. (1999). The dark side of sexual selection Trends in Ecology & Evolution, 14 (9), 336-337 DOI: 10.1016/S0169-5347(99)01689-4

Brooks, R., Hunt, J., Blows, M., Smith, M., Bussiére, L., & Jennions, M. (2005). EXPERIMENTAL EVIDENCE FOR MULTIVARIATE STABILIZING SEXUAL SELECTION Evolution, 59 (4), 871-880 DOI: 10.1111/j.0014-3820.2005.tb01760.x

Monday 11 October 2010

2SER Subscriber Drive - subscribe and I will give you a cuddle

Between October 11 and October 23, Sydney community radio station 2SER is running its annual subscriber drive. 2SER is home to the science program Diffusion Science Radio to which I regularly contribute, and I also record interviews and podcasts using their studios.

Community radio stations are partially funded by various levels of government, but in the main, they draw their revenue from sponsors and listeners. Subscribing to 2SER is pretty cheap:

$33 - Concession
$66 - Working
$120 - Passionate
$120 - Bands / Artists
$120 - Organisation
$250 - Business
$600 - Lifetime

The theme for this year's drive is Hello Radio, my old friend - so go on, help out a friend in need! Check out the subscriber page to contribute and for more information on the subscriber packs that will be delivered to your door, and the prizes you could win, should you subscribe.

Subscribing to 2SER helps keep independent radio on air - for instance, you will be hard pressed to find quality science radio in Australia outside of the ABC - generally, community radio stations house this type of broadcasting. And as Diffusion is a relatively small operation, we can respond to listener questions in a personal way. Each member of the team is an actual trained and working scientist, as opposed to a journalist, which means that we can bring authority to the topics at hand, as well as having access to Australia's best scientists. The same can be said of 2SER's other talk shows.

To the freebies - if you subscribe, you will receive:
  • Spunk Subscriber Pack containing tracks from Bear Hug, Menomena, Holly Throsby, Sufjan Stevens, Wild Nothing, Caitlin Rose, Active Child, Sonny and the Sunsets, The Books, Olof Arnalds, Mountain Man, Joanna Newsom, Gold Panda, Anthony and the Johnsons plus Jeff The Brotherhood;
  • Three months subscription to Time Out Sydney:
  • Sticker, Fridge Magnet.
The major prizes are:
  • Return flights To Malaysia for two - valued at $1890;
  • A $1000 bike pack;
  • A 12 month membership to Boxing Works, Surry Hills - valued at $1308;
  • 12 months of music - valued at $1440;
  • 2 courses at 2SER School Of Radio - valued at $1320;
  • A DJ course and music production course with DJ warehouse - valued at $540;
  • Oxx Digital and Internet radios - valued at $300;
  • 10x Double Passes To Peats Ridge 2010/11 - Valued At $600.
Plus, if you subscribe and mention Diffusion (or, if you want, me!) then I will give you a cuddle. What more could you want? Check out the subscriber page for more.