Showing posts with label Math Nerds. Show all posts
Showing posts with label Math Nerds. Show all posts

Tuesday, October 27, 2009

Dunbar's Number


150 is a special number for tribes. Our social networks can not surpass 150 people. What would be the response from a mega-church?

Dunbar's Number (Seth Godin's remarks on 150)

Friday, October 16, 2009

Hh: Hertz


The SI derived unit used to measure the frequency of vibrations and waves, such as sound waves and electromagnetic waves. One hertz is equal to one cycle per second. The hertz is named after German physicist Heinrich Hertz (1857-1894).
click for a larger image
hertz
the ranges of sound frequencies, measured in hertz, that humans and a variety of animals are able to hear

The American Heritage® Science Dictionary Copyright © 2005 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.


Sunday, October 11, 2009

Gg: Geodiscs


In mathematics, a geodesic (pronounced /ˌdʒiː.ɵˈdiːzɨk, ˌdʒiː.ɵˈdɛsɨk/ JEE-o-DEE-zik, JEE-o-DES-ik) is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. In the presence of an affine connection, geodesics are defined to be curves whose tangent vectors remain parallel if they are transported along it.

The term "geodesic" comes from geodesy, the science of measuring the size and shape of Earth; in the original sense, a geodesic was the shortest route between two points on the Earth's surface, namely, a segment of a great circle. The term has been generalized to include measurements in much more general mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph.

Geodesics are of particular importance in general relativity, as they describe the motion of inertial test particles. (Read More)

Saturday, October 10, 2009

Gg: Golden Mean-Golden Ratio


Golden Mean: In philosophy, especially that of Aristotle, the golden mean is the desirable middle between two extremes, one of excess and the other of deficiency. For example courage, a virtue, if taken to excess would manifest as recklessness and if deficient as cowardice.

In Context:
...the planets correlate with each other via simple mathematical relationships, but they also do so with an uncanny and profound association with various forms of The Golden Mean.

The Golden Mean or Golden Ratio is one of the most intriguing number in mathematics. It is commonly denoted by the Greek letter, phi, and is given in either to two forms by the equalities: F º 1.618033989... and f º 0.618033989... (where “...” means a continuation of the numbers -- See Transcendental Numbers). The Golden Mean was known to the ancients (and moderns), who considered these numbers so sacred that monuments from the Giza Pyramids and Greek Parthenon to Notre Dame Cathedral and the United Nations Building in New York City have been based on these fundamentals of Sacred Geometry.

Thursday, October 8, 2009

Mm: Monad (Gr. Monas, a unit)



1. In Greek usage, originally the number one. Later, any individual or metaphysical unit.
2. Bruno named his metaphysical units monads to distinguish them from the Democritean atoms. The monads, centers of the world life, are both psychic and spatial individuals.
3. Leibniz (borrowing the term possibly from Augustine, Bruno or Protestant scholastics) identified the monads with the metaphysical individuals or souls, conceived as unextended, active, indivisible, naturally indestructible, teleological substances ideally related in a system of pre-established harmony.
4. By extension of Leibnizian usage, a soul, self, metaphysical unit, when conceived as possessing an autonomous life, and irrespective of the nature of its relations to beings beyond it.

-- W.L.

Wednesday, October 7, 2009

Ff: Fractions


n.
1. Mathematics An expression that indicates the quotient of two quantities, such as 1/3 .
2. A disconnected piece; a fragment.
3. A small part; a bit: moved a fraction of a step.
4. A chemical component separated by fractionation.

[Middle English fraccioun, a breaking, from Anglo-Norman, from Late Latin frcti, frctin-, from Latin frctus, past participle of frangere, to break; see bhreg- in Indo-European roots.]
Word History: Our word fraction did not originally have a mathematical sense. It goes back ultimately to the Latin verb frangere, "to break." From the stem of the past participle frctus is derived Late Latin frcti (stem frctin-), "a breaking" or "a breaking in pieces," as in the breaking of the Eucharistic Host. In Medieval Latin the word frcti developed its mathematical sense, which was taken into Middle English along with the word. The earliest recorded sense of our word is "an aliquot part of a unit, a fraction or subdivision," found in a work by Chaucer written about 1400. One of the next recorded instances of the word recalls its origins, referring to the "brekying or fraccioun" of a bone.

The American Heritage® Dictionary of the English Language, Fourth Edition copyright ©2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.


Tuesday, October 6, 2009

Rr: Reductio ad absurdum



Reductio ad absurdum (Latin: "reduction to the absurd")[1] in formal logic is an argument to refute a proposition (or set of propositions), by showing that it leads to a logically absurd consequence.[2] In other words: the proposition is shown by proper inspection to be simply untenable within the rules of logic, because it necessarily leads to a self-contradictory consequence.

An unstable hypothesis creates an improbable seam. (Paraphrased from Lee Smolin Trouble with Physics)

Thursday, October 1, 2009

Pp: Propinquity Effect


propinquity
Noun
Formal nearness in time, place, or relationship [Latin propinquus near]

Collins Essential English Dictionary 2nd Edition 2006 © HarperCollins Publishers 2004, 2006


The sense of the word "propinquity" as given here is a specialised one. For a more general definition of the word, see in the Wiktionary.

In social psychology, propinquity (from Latin propinquitas, nearness) is one of the main factors leading to interpersonal attraction. It refers to the physical or psychological proximity between people. Two people living on the same floor of a building, for example, have a higher propinquity than those living on different floors. Propinquity can mean physical proximity, a kinship between people, or a similarity in nature between things. Propinquity is also one of the factors, set out by Jeremy Bentham, used to measure the amount of pleasure in a method known as felicific calculus.

Propinquity effect

The propinquity effect is the tendency for people to form friendships or romantic relationships with those whom they encounter often. In other words, relationships tend to be formed between those who have a high propinquity. It was first theorized by psychologists Leon Festinger, Stanley Schachter, Kurt Lewin and Kurt Bach in what came to be called as the Westgate studies conducted at MIT (1950). The typical venn diagram used to represent the propinquity effect is shown below where U = universe, A = set A, B = set B, and S = similarity:



The sets are basically any relevant subject matter about a person, or persons, or non-persons, etc; depending on the context of the use of the word. Propinquity can be more than just physical distance. Residents of an apartment building living near a stairway, as an example, tend to have more friends from other floors than others. The propinquity effect is usually explained by the mere exposure effect, which holds that the more exposure a stimulus gets, the more likeable it becomes.

Saturday, September 26, 2009

Ii: Imaginative Community



whose ethic and organization incroporates a belief in the inevitability of progress and openess to the future.
Defined by Lee Smolin in the (Trouble with Physics)

Friday, September 25, 2009

Ss: Science


Defined by Richard Fenyman and Lee Smolin in the Trouble with Physics page 307;

Science is the organized skepticism in the reliability of expert opinion.


Wednesday, September 16, 2009

Tt: Tangent


tangent (tnjnt)
1. A line, curve, or surface touching but not intersecting another.
2. The ratio of the length of the side opposite an acute angle in a right triangle to the side adjacent to the angle. The tangent of an angle is equal to the sine of the angle divided by the cosine of the angle.
3. The ratio of the ordinate to the abscissa of the endpoint of an arc of a unit circle centered at the origin of a Cartesian coordinate system, the arc being of length x and measured counterclockwise from the point (1, 0) if x is positive or clockwise if x is negative.
4. A function of a number x, equal to the tangent of an angle whose measure in radians is equal to x.

The American Heritage® Science Dictionary Copyright © 2005 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.

ThesaurusLegend: Synonyms Related Words Antonyms
Noun1.tangenttangent - a straight line or plane that touches a curve or curved surface at a point but does not intersect it at that point
straight line - a line traced by a point traveling in a constant direction; a line of zero curvature; "the shortest distance between two points is a straight line"

2.tangent - ratio of the opposite to the adjacent side of a right-angled triangle
circular function, trigonometric function - function of an angle expressed as a ratio of the length of the sides of right-angled triangle containing the angle
Based on WordNet 3.0, Farlex clipart collection. © 2003-2008 Princeton University, Farlex Inc.





Then I tossed him a Yorker which he missed and it went off at a tangent as soon as it had reached the tree.
The Little White Bird by Barrie, James Matthew

Tuesday, September 15, 2009

Bb: Black Hole Information Paradox



The black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could "disappear" in a black hole. It is a contentious subject since it violates a commonly assumed tenet of science—that information cannot be destroyed. _Wikipedia (Black hole Information Paradox)


The scenario John Myers describes "is true, but it's really an issue of information getting scrambled, not lost." In the black hole paradox, the problem is that the information appears to be truly lost, not merely scrambled, yet "the foundations of classical mechanics and statistical mechanics are based on the exact conservation of information." Finally, "a number of the letters express a very common misconception, namely, that because an outside observer sees an infalling observer slow down, that the in falling observer sees the outsider speed up. This is simply not so. The in falling observer looks back and sees nothing unusual."--R. COWEN