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Topic: Interesting number paradox

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	Interesting number paradox - Wikipedia, the free encyclopedia
		The interesting number paradox is a semi-humorous paradox that arises from attempting to classify numbers as "interesting" or "dull." 1729, for example, may be called an interesting number because it is the smallest number expressible as the sum of two positive perfect cubes in two different ways.
		This version of the paradox applies only to the natural numbers, as it depends on mathematical induction, which is only applicable to sets that are well-ordered; the argument does not apply to the real numbers.
		As the paradox lies in the definition of "interesting", it applies only to persons of sufficiently sophisticated taste in numbers: if one's view is that all numbers are boring, and one is unmoved by the observation that 0 is the smallest boring number, there's no paradox.
	en.wikipedia.org /wiki/Interesting_number_paradox (530 words)

	1729 (number) - Wikipedia, the free encyclopedia
		I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen.
		It is a centered cube number, as well as a dodecagonal number, a 24-gonal and 84-gonal number.
		Because in base 10 the number 1729 is divisible by the sum of its digits, it is a Harshad number.
	en.wikipedia.org /wiki/1729_(number) (718 words)

	List of numbers - (Site not responding. Last check: 2007-11-06)
		A perfect number is an integer which is the sum of its positive proper divisors (all divisors except itself).
		Keep in mind that rational numbers like 0.12 can be represented in infinitely many ways, e.g.
		Number Gossip - a searchable database of interesting properties for numbers upto 10000
	psychcentral.com /psypsych/List_of_numbers (775 words)

	The Telegraph - Calcutta : KnowHOW (Site not responding. Last check: 2007-11-06)
		Interesting paradoxes arise from attempts to classify numbers as ‘interesting’ or ‘dull’.
		For example, 1729 is often considered an interesting number, because it is the smallest number expressible as the sum of two positive perfect cubes in two different ways.
		In a classification of numbers as to whether they have interesting properties or not, there would be a smallest number with no interesting properties whatsoever.
	www.telegraphindia.com /1051024/asp/knowhow/story_5379443.asp (429 words)

	Category:Number theory - RSCI, The Science Classification Index (Site not responding. Last check: 2007-11-06)
		Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers and contains many open problems that are easily understood even by non-mathematicians.
		More generally, the field has come to be concerned with a wider class of problems that arose naturally from the study of integers.
		Number theory may be subdivided into several fields according to the methods used and the questions investigated.
	www.scienceindex.org /Category:Number_theory.html (136 words)

	Press Releases - National Motorists Association (Site not responding. Last check: 2007-11-06)
		Ironically, the paradox of no posted speed limits and low fatalities is no surprise to the traffic safety engineering community.
		The paradox is that the desired effect from posting speed limits was achieved by removing them.
		*Interesting side bar: During this 6 year period, Montana's rural interstates daytime speeds (no speed limit) were consistently lower (on average 5-10 mph and more) than the speeds being reported on many sections of Southern California's 65 mph posted urban interstates.
	www.motorists.org /pressreleases/montana.html (1229 words)

	Certain Doubts » Paradox vs. Surprise (Site not responding. Last check: 2007-11-06)
		Historically ‘paradoxical’ sometimes carried overtones of being contrary to common sense or general belief: so when, for instance, people in the 18th century called Hume a ‘paradoxical author’ they meant not merely that he said surprising things but that he said things contrary to what everyone believed.
		So what’s paradoxical is the lost logical distinction between actual universally known truth and possible universally known truth, and that contravenes our pre-theoretical assumptions about modality–not just mine, and not just those of philosophers, but of those who reflect on the matter even for the briefest time.
		Paradoxes and surprises are similar in that they can be put in the form of a set of mutually inconsistent but individually plausible claims.
	bengal-ng.missouri.edu /~kvanvigj/certain_doubts/index.php?p=95 (1654 words)

	Olbers's Paradox
		To calculate the number of shells, we note that there is roughly 1 star per cubic parsec in our galaxy ===> average distance between stars in our Galaxy (shell thickness, T) is ~ 1 parsec (explain why).
		The fact that the Universe has a finite age is the principal explanation of Olbers's Paradox.
		It is interesting that in asking and answering the seemingly trivial question, "Why is the night sky dark?" one could have inferred that the Universe is expanding and that the Universe has a finite age (or at the least the stars and galaxies have finite ages).
	zebu.uoregon.edu /~imamura/209/apr7/olbers.html (1022 words)

	What's a number?
		Given the difficulty of establishing whether a given number is algebraic or not, this was one of Cantor's early surprising results.
		The rest of the complex numbers could also be defined by adding this new number i to the set of reals and postulating that usual arithmetic operations (addition, subtraction, multiplication) apply to the expanded set and all the laws known to hold for these operations hold for the new set as well.
		The rest of surreal numbers (included are the numbers we discussed so far and myriads of numbers some of which I have a difficulty imagining.) are formed starting with 0 and applying just two simple rules.
	www.cut-the-knot.org /do_you_know/numbers.shtml (3546 words)

	Time Supplement [Internet Encyclopedia of Philosophy]
		This paradox, also called the clock paradox and the twin paradox, is an argument about time dilation that uses the theory of relativity to produce a contradiction.
		The group of natural numbers, or counting numbers, was envisioned by Aristotle not as pre-existing before counting begins, but as being generated as someone counts over an interval of time, so he said the natural numbers were potentially infinite and not actually infinite.
		That number is picked so that the new meter will be nearly the same distance as the old meter, which was the distance between two marks on a platinum bar that was kept in the Paris Observatory.
	www.iep.utm.edu /ancillaries/time-sup.htm (13049 words)

	Review of Conte, Rosaria and Paolucci, Mario: Reputation in Artificial Societies: Social Beliefs for Social Order
		This increasing interest comes from the fact that reputation and other related social mechanisms (such as trust, reciprocity, altruism, and mutual monitoring) are understood as an appropriate framework to institutionalise the smooth running of complex and decentralised societies.
		Furthermore, in repeated encounters, a number of factors may favour co-operation over mutual defection, according to uncertainty about the future (the famous "shadow of the future"), about the rationality of the co-player, and about the possible influence of social embeddedness.
		While the interest in infosocieties and online communities as social laboratories is unsurprising, in view of the fact that designers of artificial systems face difficult challenges in dealing with the problems of social order and collective action, it is impossible to deny a fundamental difference between social systems and infosocieties.
	jasss.soc.surrey.ac.uk /7/3/reviews/squazzoni.html (4348 words)

	Mathematicians (Site not responding. Last check: 2007-11-06)
		She taught herself Latin and Greek and because her parents opposed her interest in mathematics (in their eyes it was not a subject suitable for a thirteen-year-old girl), she read Newton and Euler secretly at night.
		Ramanujan replied that it was very interesting number since it was the smallest number that could be expressed as the sum of two cubes in two different ways.
		Think about this paradox because it became very important in the theory of sets and a version of the paradox is the key to Gödel's results on the axiomisation of maths.
	www.mayer.dial.pipex.com /maths/mathms.htm (1522 words)

	EPAA Vol. 9 No. 6 Ludlow: Teacher Test Accountability
		First, of the 1644 total number of items administered over the first four dates, 332 items (20.19%) had point-biserial correlations that are lower than the industry minimum standard criterion of.20.
		It is not in the short-term business interests of a testing company to conduct disconfirming studies on the technical quality of their commercial product.
		Given the national interest in “higher standards” for achievement and assessment, it must be recognized that there are no “gold” standards by which a testing program such as the MECT can be evaluated (Haney & Madaus, 1990; Haney, 1996).
	epaa.asu.edu /epaa/v9n6.html (8361 words)

	Butterflies and Wheels Article
		Again, this was not a biography in the usual sense of the word; I was interested in Gödel’s life only insofar as it related to his theorems: what they meant to him as well as to others, and how the latter facts affected him.
		I was able to read the memoirs of those who had known Gödel and to make use of their observations and speculations; and I was fortunate to have met him once, though only very briefly, during a small window of his life when he was somewhat more outgoing than usual.
		We are all of us, not to speak of mathematical/philosophical geniuses, far too complicated and self-contradictory to be contained in a “narrative framework.” The biographer, as much as the mathematical logician, is keenly aware of the incompleteness necessarily inherent in her project.
	www.butterfliesandwheels.com /articleprint.php?num=116 (2978 words)

	P
		However, to consider these possibilities further, we should move into the areas of Symbolic, involving modes of transubstantiation, rituals of rebirth, whereby the individual identifies himself in terms of the collective motive (an identification by which he both is and is not one with that with which and by which he is identified).
		At present it is enough to note in a general way how the paradox of the absolute figures grammatically in the dialectic, making for a transcending of none term by its other, and for the reversed ambiguous derivation of the term from its other as ancestral principle'.
		It is assumed that beyond a limited number of propositions, the proposition sequence of the text base is not fully accessible for recall....
	www.sil.org /~radneyr/humanities/P.htm (17509 words)

	PrudentBear.com (Site not responding. Last check: 2007-11-06)
		The private financing gap must widen as we subtract less of a negative number (fiscal deficit) and then more of a positive number (fiscal surplus) from a widening current account deficit (which is chronically in the US a negative number).
		Unless interest rates fall in an offsetting fashion, debt servicing loads must also rise in a period when the private sector balance is growing faster than GDP.
		The interesting losses on the Lipper convertible arb funds, however, is worth paying attention to, as convertible bonds have been a key longer term financing channel in recent quarters for the corporate sector.
	www.prudentbear.com /guest.htm (3133 words)

	Some paradoxes (Site not responding. Last check: 2007-11-06)
		In this paradox, Epimenides, the Cretan, says, "All Cretans are liars." If he is telling the truth he is lying; and if he is lying, he is telling the truth.
		The number of syllables in the English names of finite integers tend to increase as the integers grow larger, and must gradually increase indefinitely, since only a finite number of names can be made with a given finite number of syllables.
		The paradox arises from a disguised breach of the arithmetical prohibition on division by zero, occurring at (5): since a = b, dividing both sides by (a - b) is dividing by zero, which renders the equation meaningless.
	www.wordsmith.demon.co.uk /paradoxes (3977 words)

	Answering Advocates of Gay Marriage
		Legalizing gay marriage would certainly increase interest in newer technologies and probably lead to demands for access to them in order to equalize their ability to have children.
		But other interests are involved, including not only those of children and those of society at large but also those of many religious communities.
		They have restricted the number of spouses, restricted the institution to those who can afford more than one household, specified the amount of attention that must be paid to each spouse, and so on.
	www.catholiceducation.org /articles/homosexuality/ho0064.html (10448 words)

	Chaitin / Paradoxes of Randomness
		I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole number", which is itself a rather interesting number, since it is precisely the first uninteresting number.
		So there are only a finite number of words in English, and therefore if you consider all possible texts with up to a billion words, there are a lot of them, but it's only a finite number, as mathematicians say jokingly in their in-house jargon.
		And there are only a finite number of numbers that you can name with this finite number of texts, because to name a number means to pick out one specific number, to refer to precisely one of them.
	www.umcs.maine.edu /~chaitin/summer.html (6703 words)

	Thomas Jefferson, on Aristocracy - letter to John Adams
		Here every one may have land to labor for himself if he chooses; or, preferring the exercise of any other industry, may exact for it such compensation as not only to afford a comfortable subsistence, but where-with to provide for a cessation from labor in old age.
		Every one, by his property, or by his satisfactory situation, is interested in the support of law and order.
		And such men maysafely and advantageously reserve to themselves a wholesome control over their public affairs, and a degree of freedom, which in the hands of the Canaille of the cities of Europe, would be instantly perverted to the demolition and destruction of every thing public and private.
	www.bigeye.com /aristocracy.htm (2111 words)

	Parrondo's Paradox Simulation
		The simulator runs a specified number of trials and reports the average of the results from all of the trials.
		The number of games per trial and the total number of trials are parameters that can be changed below.
		If you do want to change the seeds please note that they must be specified between parentheses, that the first number must be an integer in the range [0-31328], and that the second number must be an integer in the range [0-30081].
	hampshire.edu /lspector/parrondo/parrondo.html (691 words)

	Law and Letters
		Interesting to me about the article is how it has more to do with income and socionomic class, but barely mentions race or gender dynamics.
		And it is interesting enough to limit the discussion to American divisions in class, race, and ethnicity.
		But if you take an intellectual interest in your law school courses (and I mean all of them, so choose wisely after 1st year), then law school is very intellectually rewarding.
	lawandletters.blogspot.com (13751 words)

	Paradox: Queries — Part One (Site not responding. Last check: 2007-11-06)
		Paradox queries are written with the DISTINCT clause if the primary key is selected.
		A feature I found quite interesting, was how easy it is to have Paradox create a table based on the results of the query instead of only displaying the results on the screen.
		This is a handy feature if you are ever in a situation where you have to extract data to be transferred to another database.
	www.windowatch.com /paradox6_3.html (1322 words)

	Paradox: Treatment with a Twist - Counselor Magazine (Site not responding. Last check: 2007-11-06)
		Paradox is excellent for eliminating manipulative or genuine feelings that the treatment isn’t working since paradox is really prescribing the problem with an exaggeration or a twist.
		Paradoxical assignments are a little like risky surgery: Such interventions can be lifesavers; nevertheless, they are not always appropriate.
		Some practitioners who practice paradox insist that this weakens the impact of the paradox, though I would suggest that it generally does not negate its total impact.
	counselormagazine.com /pfv.asp?aid=august03ProfessionalDevelopment.htm (1234 words)

	Sentient Developments (Site not responding. Last check: 2007-11-06)
		If this is the case, humans may be among any number of intelligent beings in the Galaxy at similar stages, or possibly, the only one.
		There are many problems with the anthropic argument, namely the realization that complex life has existed on Earth for millions of years (for example, the dinosaurs ruled for 250 million years).
		These fears are fueled by a number of factors, including recent breakthroughs in technology, the sweeping effects of globalization in the economic, social, and political realms, and the prevalence of existentialism/materialism/naturalism in popular thought and culture.
	www.sentientdevelopments.com /fermi.html (1953 words)

	MILE HIGH COMICS presents THE BEAT at COMICON.com: You can't apparate within the grounds of Hogwarts...or DC Comics (Site not responding. Last check: 2007-11-06)
		These numbers cannot be directly compared, however, as one is sell-in and one is sell-through.
		Such elementary number crunching does nothing but show that the numbers are of the same magnitude, however.
		However, given the number of complaints by people who are much smarter than me, I've changed the equation, which, IMHO, is still meaningless except to show degree.
	www.comicon.com /thebeat/2005/11/you_cant_apparate_within_the_g.html (1588 words)

	Black Hole Information Loss
		For instance, in our example we took a state described by a set of eigenvalues and coefficients, a large set of numbers, and transformed it into a state described by temperature, one number.
		In that case, people probably still would not believe Bekenstein and instead of the information loss paradox we'd still be wondering how to reconcile fl holes with the second law.
		The thermal spectrum of Hawking radiation is one of the most serendipitous results in modern physics, in my opinion, which is another way of saying that something deep and not understood is going on.
	math.ucr.edu /home/baez/physics/Relativity/BlackHoles/info_loss.html (882 words)

	[No title]
		The number is used as an administrative mechanism for a variety of purposes.
		It is interesting to note that residents of countries which have ID documents or papers, often refer to these in the English as ICs or Identity cards.
		The key area of interest, from the perspective of benefit agencies, lies in creating a single numbering system which would be used as a basis for employment eligibility, and which would reduce the size of the fl market economy.
	www.privacyinternational.org /issues/idcard/idcard_faq.html (6283 words)

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