"The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits." G.K. Chesterton

Sunday, April 25, 2010

{First 10 digit prime in consecutive digits of e}.com

I recently watched a documentary about Google Inc., its beginnings and style of doing business. There was an interesting fact about a recruiting campaign which they launched some years ago. It involved billboards containing a cryptic, and mysterious message: {First 10 digit prime in consecutive digits of e}.com. Finding that prime, and going to the page named after it would take one to a Google jobs page with congratulations of completing stage 1 in the recruiting procedure. Consequently one would be presented with another puzzle to pass further stages. I think that is an avantgarde and clever way of attracting all the IT nerds out there.


Being a bit of a nerd myself, I found the problem itself quite interesting, and since it didn't seem that difficult at first glance, I eventually solved it. The only tricky bit was getting my hands on the 10 digit primes set. Anyway, my approach was to write an algorithm in MATLAB to get the answer.
Directly below is the main function, and further below are some auxiliary functions used in the main one.  
Click on the images to enlarge.


The one below is self explanatory: parity check function.


The one below proved very helpful in the main code, since it allowed to perform arithmetic between vectors (digits of e) and scalars (primes). It converts a 1D array into a scalar (well actually into a string consisting of the original array entries), for any integer array. It does not actually convert it into scalar (consider an array with 0 in the first column), but the sieve in the main code skips all such cases.
 And upon execution ... BINGO!



Tuesday, April 20, 2010

Logic Puzzle: falsification optimization

Below we have four cards, where each has a number on one side and a letter on the other.


Now suppose we make a conjecture about those four cards: "Every card that has P on one side has 3 on the other". Now the question is what's the minimum number of cards we have to turn over in order to check the truth of the conjecture?


Some interesting statistics, concerning the number of people getting this right:
10% - General public
29% - Undergraduates
43% - Mathematicians

So if you got this correct, it means that you did better than an average mathematician :)

SOLUTION IN "COMMENTS"

There's a family of interesting theories concerning the reasons why people get this wrong, and why a more practical set up of this "Watson selection task" reduces the percentage of people who get it wrong.

Thursday, April 15, 2010

Ode to Conformity

Oh the pleasure of reassuring nods,
and the soothing blankness of undisturbed sleep.
You are the loud-speaker which guarantees a vast audience.

You taught me well the value of mass delusion,
and the benefits of ostracizing difficult rivals.

I bow before your power to overwhelm truth - the notoriously elusive dissident.

How I enjoy the smooth ride in your comfortable canoe, meandering swiftly downstream through the difficulties of life.

Sunday, April 11, 2010

TEAISM DOCTRINE


 There exists a Teapot in orbit around the Sun



I    FOUNDATION OF TEAISM

II        DOGMAS OF TEAISM

III            POSTULATES

IV                  PILLARS OF TEAISM

V                        BOOK OF RITES

VI                             GENERAL TEAOLOGY

VII                                  ANNALES OF THE TEAOCRACY

VIII                                         TEAOGONY

IX                                                 ESSENTIAL ANALYTICS




I
FOUNDATION OF TEAISM
This monoteaistic system had its beginning after the existence of the Teapot had been revealed to the Honorable Octavius in a moment of cosmic clarity. The overwhelming certainty of the revelation motivated Octavius to record the truth contained within it, and thus Teaism was founded. This truth has been prophecised, by Bertrand Russell although the message had been still vaguely understood until its formalisation by Octavius. Presently Teaism has a wide following, and its enlightening content is feverously studied by numerous inspired teaologists.


II
DOGMAS OF TEAISM
I    There exists a Teapot in orbit around the Sun.
II   In addition there exists the 'Divine 8 piece Tea set', or just 'The Jolly Good Octave', which consists of the Teapot, 3 cups, 3 saucers and tray. The Teapot cannot be observed in principle, however its other manifestations which are part of the "Jolly Good Octave" appear regularly to the open-hearted folk in the form of flying saucers, often in formations of three which confirms the transcendental structure of the octave.
III  Teatime is the time when Tea is consumed.
IV  The underlying substance of everything is Tea.
V   The essence of the Teapot is Tea.
As a consequence, all Teaists augment the usual set of astrological symbols of celestial bodies as depicted below. This updated chart is more general by virtue of completeness. To distinguish it from its incomplete predecessors it carries the name of The complete chart of astrological symbols of celestial bodies.


THE COMPLETE CHART OF ASTROLOGICAL SYMBOLS OF CELESTIAL BODIES

III
POSTULATES
It follows from the first dogma that there will be two special alignments of the Earth, the Sun and the Teapot; first being a conjunction, and the second an opposition. Also since, by the second dogma, the Teapot can never be observed the dates and time of those alignments will remain unknown. However they will necessarily take place. Hence arbitrary dates for their celebration have been chosen: The conjunction (whether it is a major or minor one remains unknown) shall be called "The great NecessiTEA" and will be celebrated each year on the 8th of August. The opposition shall be called "The golden ImperaTEAve" and shall be celebrated every year on the 21st of March.


IV
PILLARS OF TEAISM
Tea shall be consumed each day at Teatime. The first day of each month is a Tea Party day.


V
BOOK OF RITES
The strength of tea consumed has a sacred relationship to the time of day. In other words strongest tea is consumed at midday and negligible strength at midnight. It follows that consumption of tea is forbidden at midnight.Using teabags is a profanation of the sacred substance. A Tea Party commemorates the origin of Teaism, and is intended to stimulate reflection on its doctrine. This is done over a cup or two of the sacred drink. Biscuits are optional. By the "The Golden Mean Ruling" a liberal use of milk, sugar, honey or any other additives is permitted with Tea only for non ritualistic purposes i.e. no additives shall be mixed with the sacred brew during Tea Party days.
Individuals who choose not to follow the self evident and true path of Teaism are aTeaists. Aside from their limited right to actively participate in the Teaocracy, all care should be taken in healing their their repugnant and inferior cognitive condition.


VI
GENERAL TEAOLOGY
Current Teaological inquiry focuses primarily onsolving the conundrum ever since the existence of the Teapot was revealed to its founder the Honorable Octavius; does Teatime determine the time at which Tea is to be consumed, or is it the temporarily arbitrary act of Tea consumption that determines Teatime? Some progress has recently occured on that front, and it seems that the arrow of Tea i.e. the direction of the flow of Tea may be a key step in solving this conundrum.
Recent Teaological analysis carried out by the "Ponderites" mendicant order has questioned the necessity of both "The great NecessiTea" conjunction and "The golden ImperaTeave" opposition, by pointing out that those alignments would be necessary only if one assumes that Teapot and Earth's orbits are in the same plane.This may require an amendment to the Dogma which explicitly includes that assumption i.e. gives it a status of an axiom. Alternatively, it has been suggested, the necessary conjunction and opposition should be substituted by two truly necessary positions: the closest Earth-Teapot passage, and the most distand Earth-Teapot passage.


VII
ANNALES OF THE TEAOCRACY
Also, strong arguments suggest, that in order to provide the best conditions for Teaism to flourish and preserve the integriTea of moraliTea, its members should strive to establish a Teaocracy. Once established, all care should be taken to maintain it. In a Teaocracy, aTeaists will be free to voice their opinion, but their rights related to participation in the legislative procedures of the Teaocracy will be limited.


VII
TEAOGONY
In the beginning was The Recipe, a purely formal and transcendental tendency to make Tea. An inevitable probability maximalization of The Recipe led to its manifestation. This manifestation resulted in the Big Boil. The Big Boil gave birth to to the Great Brew which appears to be still expanding. At largest observable scales the Great Brew is both isotopic and homogenous. Such homogeneity had baffled Teaologists for some time until a revelation concerning the initial period of Infusion dawned on one of them. This Infusion was a period of rapid expansion of the fabric of existence which initiated the Big Boil and lasted less than one could say "Bob's your uncle".The Big Boil did not occur at some point IN the brew or time. The Great Brew creates its own space and time as it expands. Hence asking what was before the Big Boil is meaningless. This single origin of the Great Brew from the manifest singularitea of The Recipe, justifies a name often used interchangeably with "The Great Brew"; The Unitea. The former name places emphasis on the dynamical and formal aspects of being whereas the latter on its substance and essence.


VIII
BOOK OF NUMBERS
The number 8 has a mystical and fundamental significance in Teaism.


IX
ESSENTIAL ANALYTICS

TEAISM (disambiguation) Teaism is a belief/thought system initiated by the revelation of The Teapot to the Honorable Octavius. It may also refer to:
A term coined by Okakura Kakuzo in his The Book of Tea.

Lucid Sententia XVI

Living systems are some of the most complex forms of being that that have emerged in our universe. In the mandane vastness of space and vacuum punctured occasionally with slightly more sophisticated collections of matter such as stars and galaxies, living beings as far as we know, stand apart in the sheer self sustaining complexity.

Being surrounded by life we have grown to take its complexity for granted; from swatting a mosquito, through slaughtering animals whose flesh we feed on, to finally killing of humans we deprive the universe of its most sophisticated creations.