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Topic: Interesting and uninteresting numbers

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Hardy Ramanujan number

	Interesting number paradox - Wikipedia, the free encyclopedia
		The interesting number paradox arises from attempts to classify numbers as "interesting" or "dull".
		1729, for example, 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.
		It arises from Liouville's construction of transcendental numbers, but it was neither the first nor the simplest such number constructed; the construction evidently generates many other similar numbers in the same way.
	en.wikipedia.org /wiki/Interesting_number_paradox (477 words)

	What's Special About This Number?
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is the number of planar partitions of 12.
	www.stetson.edu /~efriedma/numbers.html (7257 words)

	All Numbers Are Interesting (Site not responding. Last check: 2007-11-07)
		Most readers of this paper are undoubtedly familiar with the tongue-in-cheek "proof" that all numbers (usually taken to mean "positive integers") are interesting, which goes a follows: Classify all the positive integers into two sets: the interesting ones (the only even prime, the smallest Smith number, Hardy's taxicab number, etc.) and all the rest.
		Interesting properties of the two small lists of numbers in Conjectures 1 and 2 can be easily found (exercise for the reader!).
		Table 1 (at the end of this paper) shows an interesting property of every positive integer from 10 to 100, except for those which are not expository numbers of any type (marked in the table with an 'o').
	users.aol.com /s6sj7gt/interest.htm (2114 words)

	New Frontiers In Science, Chapter XVIII
		If there were such a number as eighteen it would be impossible to construct a regular polygon of eighteen sides by rule and compass alone.
		Similarly in number theory we can divide the numbers from one to seventeen into four classes: odd primes, powers of two, the product of two odd primes, and the product of two and an odd prime.
		Thus the number of integers and the number of rational numbers would be the same.
	www.tiac.net /~cri/2003/frontiers.html (846 words)

	Notable Properties of Specific Numbers at MROB
		If you replace both numbers with their average, you get 32×32=1024, and 1024 is another number with important properties related to the fact that it is close to 1000.
		Such numbers are odd and don't end in 5, because there is a natural psychological bias to thinking even numbers and numbers that end in 5 are "less random".
		The number that most Americans know best from its use as a speed limit also happens to be a Fibonacci number and the sum of the numbers 1 through 10 (which makes it the 10th triangular number).
	home.earthlink.net /~mrob/pub/numbers-3.html (2965 words)

	sciforums.com - News on Prime Numbers
		Prime numbers hold the key to solving many mathematical problems and play an important role in cryptography — the art of writing or breaking codes.
		because of the prime factorization uniqueness theorem, when the friend factors the number, she will see a list of exponents over her primes, the exponents will be in the range 1-26, each one corresponding to a letter of the alphabet.
		as soon as someone develops a way to easily check whether a number is a prime, then she won t need a key, a list of primes, to decode the message.
	www.sciforums.com /showthread.php?t=10028 (995 words)

	ASA - September 2001: Induction proofs of interestingness and G
		Even given a generous selection of key numbers, all of which were intrinsically interesting from a mathematical point of view (or at leas famous in maths), you were in fact virtually certain not to get a hit.
		This is the essence of the induction proof that all numbers are "interesting".
		interesting kind, and therefore may be said to be part of a deliberate design.
	www.asa3.org /archive/asa/200109/0121.html (1728 words)

	The Howard Center
		The number of Senators elected per voter is far higher in states with small populations than it is in the most populous state, California.
		He said that the interesting poor are those whose misfortunes can be trumpeted to the world, for the benefit of world Communism; the uninteresting poor are those whose misfortunes interest only themselves.
		The Muslims are interesting, the Christians are definitely uninteresting, and Israel and the Jews, opposed by the Muslims, are too close to the right-wing Christians.
	www.profam.org /pub/rs/rs_2105.htm (4411 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Kant prefers finite number of axioms to infinite number of axioms It is interesting to note that many meta-theorems about the existence of finitary and infinitary systems can be proven using the Model Theory.
		In using numbers to describe physical phenomena, it is important to describe the same facet of the object you intend to describe, otherwise it is easy to arrive at an inconsistent numeric description.
		Recall an interesting paradox (due to Chaitin) that the positive integers may be separated into interesting and uninteresting numbers.
	userpages.umbc.edu /~mmisam1/doc.fregenotes.txt (1748 words)

	Faculty Survey for Haumana and MARC Program
		The panel made up of former Haumana and MARC students discussing research careers and their plans for the future was interesting and informative.
		The presentation on the use of human subjects in research was interesting and informative.
		The presentation on the use of vertebrate animals in research was interesting and informative.
	www.pbrc.hawaii.edu /haumana/pride/prePrideProgramStudentEval.html (726 words)

	Amazon.co.uk: Books: The Penguin Dictionary of Curious and Interesting Numbers (Penguin Press Science S.) (Site not responding. Last check: 2007-11-07)
		He fails to notice that it is the fourth trimorphic (and non-automorphic) number: 4, 9, 49, 51 and 75 being the first five cases.
		Hardy, perhaps the greatest number theorist of 20th century, took a taxi from London to the hospital at Putney where Ramanujan was dying of tuberculosis, Hardy noticed its number, 1729.
		The anecdotes and personal stories of mathematicians are interesting, but the majority of entries simply describe the number in question as being 'the start of a remarkable chain of amicable numbers', or consist of formulae.
	www.amazon.co.uk /exec/obidos/ASIN/0140261494 (1244 words)

	Syskill & Webert: Identifying interesting web sites
		First, we believe that many users have multiple interests and it will be possible to learn a more accurate profile for each topic separately since the factors that make one topic interesting are unlikely to make another interesting.
		Its learning time is linear in the number of examples and its prediction time is independent of the number of examples.
		The ten pages with the highest probability were all correctly classified as interesting and the 10 pages with the lowest probability were all correctly classified as uninteresting.
	www.ics.uci.edu /~pazzani/RTF/AAAI.html (5909 words)

	Chaitin / Paradoxes of Randomness
		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.
		Well, interesting means it stands out some way from the herd, and uninteresting means it can't be distinguished really, it's sort of an average, typical number, one that isn't worth a second glance.
	www.cs.umaine.edu /~chaitin/summer.html (6703 words)

	Mr Whitfield's Pi factory
		The other three-digit numbers that equal the sum of the cubes of their own digits are 370, 371 and 407.
		19801 is one of only six 4-digit numbers in which subtracting the reverse of the number, 0891, leaves a number with the same digits, rearranged.
		It is the smallest number to have the property of being uninteresting.
	www.lgfl.net /lgfl/leas/enfield/schools/southgate/accounts/staff/dwhitfield/web/pages/previous_numbers.html (822 words)

	Some paradoxes (Site not responding. Last check: 2007-11-07)
		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.
		Further, if his income was derived from a capital invested at a finite rate of interest (as is usual), the annual payments of income-tax would each be equal in value to the man's whole capital.
		Since it is the smallest uninteresting number it becomes, ipso facto, an interesting number.
	www.wordsmith.demon.co.uk /paradoxes (3977 words)

	Uninteresting Number Proof (Site not responding. Last check: 2007-11-07)
		The Interesting Number property states that every nonnegative integer is an interesting number.
		If so, there must be an uninteresting number that is smaller than all the other uninteresting numbers, by the Well-Ordering Principle.
		This Smallest Uninteresting Number is, by virtue of its unique position among uninteresting numbers, very interesting indeed -- a contradiction.
	mcraefamily.com /MathHelp/JokeProofUninterestingNumber.htm (139 words)

	My Address, Sort Of (Site not responding. Last check: 2007-11-07)
		You don't have to be a Douglas Adams fan to appreciate 42 for the interesting number that it is. 42 is interesting because it's the product of the first perfect-prime pair of consecutive integers, 6 and 7.
		Then assemble these uninteresting numbers in a sequence, in increasing order of "uninterestingness".
		Not to compare people to numbers, but I consider it a true statement that there are no uninteresting people.
	emp.byui.edu /neffr/myaddress.html (282 words)

	Interesting Numbers (Site not responding. Last check: 2007-11-07)
		1729, which he considered to be an uninteresting number.
		Ramanujan immediately perked up, and said that on the contrary, 1729 was a very interesting number: It was the smallest positve integer that could be expressed as the sum of two cubes in two different ways:
		Every integer is interesting, but we may not necessarily be able to see or explain why it is interesting.
	users.pipeline.com.au /owen/Numbers.html (461 words)

	15-399 Constructive Logic / Overview
		Thus we have strong logical guidance in the design of programming languages and type systems, which is the first major application of logic in computer science we consider.
		We briefly investigate arithmetic (the theory of natural numbers), but then generalize to other structure data types and discuss various programming concepts.
		This includes reasoning about data representation (exemplified by an implementation of numbers as bit strings), general recursion (related to complete induction), and reasoning about data structure invariants (captured by dependent types).
	www.cs.cmu.edu /People/fp/courses/logic/overview.html (875 words)

	AusWeb96-Tech: From Hypertext to Flat Text: A Tool for Document Construction
		Parser: it analyses the lexical and syntactic structures of an HTML file from one of the temporary files to determine whether the currently processed HTML tag is of interest or not (see next section for explanation of interesting and uninteresting tags).
		In order to replace the links with the actual documents they point to, we have to analyze all the tags in a source document file to decide whether they should be processed or not.
		The tag can be considered as an uninteresting one, but it can be useful if an index should be created.
	web.comlab.ox.ac.uk /oucl/work/richard.brent/AusWeb96/paper05.html (2284 words)

	[No title]
		It is more like eating\line with one's hands rather than one's feet, which is also universal, but\line we need not invoke a special hand-to-mouth instinct to explain why.\line Language is invaluable for all the activities of daily living in a commu-\line nity of people: preparing food and shelter, loving, arguing, negotiat-\line ing, teaching.
		Chomsky is a paper-and-pencil theoretician who wouldn't\line knowJabba the Hutt from the Cookie Monster, so he suggested that}{\insrsid6427518 }{\insrsid8335715\charrsid16655907 the parents bring their child to the laboratory of the psycholinguist\line Ursula Bellugi in La Jolla.
		The syndrome seems to be\line associated with a defective gene on chromosome 11 involved in the\line regulation of calcium, and it acts in complex ways on the brain, skull,\line and internal organs during development, though no one knows why\line it has the effects it does.
	www.lcc.gatech.edu /~mcnair/Teaching/3206-S2004/Pinker2web.RTF (9121 words)

	Prime Numbers (Site not responding. Last check: 2007-11-07)
		AM finds some simple patterns among these definitions: the set of numbers with zero divisors is empty; the set of numbers with one divisor is itself a singleton (this is found uninteresting); the set of numbers with two divisors (primes without one) is somewhat interesting because there are a reasonable number of examples.
		The excitment begins as AM notices that all numbers with three divisors are also perfect squares;To see this, consider an integer n with three divisors.
		It turns out that the square roots of these numbers are all numbers with two divisors.
	web.media.mit.edu /~haase/thesis/node59.html (197 words)

	Transcript of talk given in Kitakyushu, Japan, July 2001
		Somehow you distinguish between the ones that are interesting, that appeal to you, that stand out, and the positive integers that just merge into the herd, that don't really stand out from the rest in any particular way.
		And the reason you can never prove it, even though I have a mathematical definition of what an uninteresting number is, is that it turns out the most interesting fact about this definition of the uninteresting is that you can never be sure that a number is uninteresting.
		A random number is one that doesn't have structure or pattern, and a number is not random if it has some structure or pattern.
	www.umcs.maine.edu /~chaitin/kitakyushu.html (2674 words)

	The Way of Flesch- Articles - Case Method Teaching - National Center for Case Study Teaching in Science
		The total of these words calculated as a percentage of the total number of words in your text will give you a good measure of how strong the human interest element is. In a dull scientific piece, the percentage will be zero.
		Flesch argues that “a seasoned popular nonfiction writer knows that to interest his readers he must not only turn most of his material into narrative, but he must go one step further and turn a large part of that narrative into dialogue.” The percentage of dialogue varies enormously in different kinds of writing.
		It might interest you to know that this case column you are reading now ranks high on both scales.
	ublib.buffalo.edu /libraries/projects/cases/teaching/flesch.html (2176 words)

	TOUCHSTONE (Site not responding. Last check: 2007-11-07)
		The formal, numerological sources of music hold interesting numbers and uninteresting numbers, clever patterns and banal cliché, and all of these have consequence in phrasing and intonation, good rhythms and bad rhythms.
		But while many cybernauts show a chronic propensity for thinking big, for acclaiming the remote reach of their often vacuous cyberchat, recent technologies also constitute an excellent means for enhancing and appreciating extreme proximity.
		Touch is interested in giganauts and nanonauts, in the full gamut of up- and down-scaled representations afforded by electronic and digital tools, in all things and events made manifest by signal detectors and amplifiers operating beyond the range of normal human perception.
	www.xs4all.nl /~mwais/touch.htm (2157 words)

	On the Number 39 (Site not responding. Last check: 2007-11-07)
		“39 appears to be the first uninteresting number, which of course
		Now, the four corner-threads of the fringe are always tied into a quite precise number of knots: 26 amongst "Eastern" (Sephardic) Jews, and 39 amongst "Western" (Ashkenazi) Jews.
		the number 26 corresponds to the numerical value of the Hebrew letters which make up the name of God, YHWH, and 39 is the total of the number-values of the letters in the expression "God is One", YHWH EHD.
	www.wisdomportal.com /Numbers/39.html (694 words)

	A Fuga Really Big Numbers (Site not responding. Last check: 2007-11-07)
		Power surges through the ten-year-old at the thought of having found a specific, real number that is so big it doesn't even have a name.
		And they have to be actual numbers, not phonies like "jillion," or vague not-quite-numbers like "infinity." Part of the game is to keep using up more number names.
		It implies that there are as many of the number as the number itself.
	members.aol.com /acockburn/papers/fugareallybignumbers.htm (817 words)

	The Ultimate User:Charles Matthews/1729 (anecdote) - American History Information Guide and Reference
		1729 is known as the Hardy-Ramanujan number, after a famous anecdote of the British mathematician G.
		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.
		"No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
	www.historymania.com /american_history/User:Charles_Matthews/1729_%28anecdote%29 (216 words)

	CrapTime.com (Site not responding. Last check: 2007-11-07)
		If there are uninteresting numbers, then we can divide all numbers into two sets - interesting and uninterestingl.
		In the set of uninteresting numbers there will be one number that is the smallest uninteresting number.
		Since it is the smallest uninteresting number it becomes, ipso facto, i.e.
	www.craptime.com (1017 words)

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