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Terms from Mathematics

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July 01, 2004, 06:56

Terms from Mathematics

Yesterday's term, "begging the question", meant "making a circular argument". So says the dictionary.

- He had been right not to speak to her; there were no more words to be said, only a

– Maeve Binchy,

The moderator was gettitng panicky now. He could see the clock telling him he had six minutes to bump this squabble out of the endless

– Thomas Perry

We must crack the supply side by making broadband affordable and available to create network access for application services, but to a degree it is a

– Peter McCarthy-Ward, East of England regional director at BT

July 01, 2004, 07:16

I recall something from Jonson, "A net is an object composed of interstitial vacuities (sic)."

RJA

July 02, 2004, 08:50

- His description of the Lewinsky affair is just as

In his statement Fed[eral Reserve] chairman Alan Greenspan, just reappointed to his fifth term, was less

- This research leads us to one

Kansas is a state prone to extreme temperatures and

July 04, 2004, 20:43

In proper mathematical use an

- Microsoft continues to appeal a huge fine … by the time anything is decided the result will matter

As hard as the cowboy life was for Wilcox, life was

Melani said, "... It's an

Beleaguered by

public libraries … are turning to stronger tactics to track down overdue material. Ignore the traditional overdue notice, and you may hear from a debt-collection agency. … "The value of this service is

. . . .Exponential change can be negative (shrinkage), as in the decay of a radioactive substance, in which the shrinkage-per-year diminishes each year.

¹ Compounding of interest creates exponential growth, which is rapid if the bank pays 15% interest - but is slow if the bank pays 1% interest. Exponential change can be negative (shrinkage), as in the decay of a radioactive substance, in which the shrinkage-per-year diminishes each year.

July 04, 2004, 22:42

Real exponential growth almost never occurs in reality, because exponential growth, slow or fast, eventually gets infinitely large. Bacteria colonies approximate exponential growth when they are small and have plenty of nutrients, but they will eventually outgrow their energy and nutrient sources, and growth ceases to be exponential.

One area where things can grow exponentially is mathematical complexity. This is exploited by encryption algorithms in which the number of possible solutions grows exponentially with the size of the key, and adding an extra bit to the key makes the solution exponentially more difficult.

Exponential decay, on the other hand, happens all the time.

July 05, 2004, 09:56

July 06, 2004, 00:33

Simply take a sheet of paper, one hundredth of an inch thick (and as large in area as you wish) and cut or fold it into two (which makes it a fiftieth of an inch thick). Take that and repeat the process which makes it a twenty-fifth of an inch. Repeat the process fifty times. The question is, how thick will the pile of paper be?

The answer, which few believe until they try it and find that their calculators overflow, is many thousands of MILES.

Try it for yourself - you'll need to divide by 63,360 (the number of inches in a mile) after about the thirtieth multiplication or your calculator, too, will overflow.

Richard English

July 06, 2004, 01:31

quote:If no-one believes you, it might be an idea to give a different example.

... and I have never yet had a delegate believe the answer.

July 06, 2004, 09:11

- Branching in nature is often

– Walter Witschey,

A computer program can make factals recursively. The procedure is to apply a rule to make a simple starting figure more complicated; then reapply the same rule to the resulting figure; then re-reapply; etc.¹ One can add to the mix other elements, such as randomness.

Fractals are important in computer graphics, for they can generate wonderfully detailed images of such natural features or textures such as mountains, clouds, trees and forests. (For these images, credit Vistapro Pictures Vistapro Pictures and Kevin Meinert respectively.) Fractals can also be beautiful as abstract art, and one can buy programs to generate them.

I have simplified quite a bit, but this gives the basic idea.

¹ In this example starts with an equal-sided triangle. At each step, a triangle of 1/3 the prior size is added atop the middle third of each side.

July 07, 2004, 08:46

A useful word -

It's next to impossible to search for usage, since a google search brings up cites to IFF meaning 'International Flavors and Fragrances' or 'Illinois Facilities Fund' or the like.

July 08, 2004, 09:08

Memory played near but not quite. I did not find "iff," but did see "wff," defined as "well formed formula."

RJA

July 08, 2004, 14:59

July 08, 2004, 19:26

Hmmm, can't say that I have had much occasion to write to mathematicians. Hab must keep better company than I do

July 09, 2004, 01:40

July 09, 2004, 11:21

The French for 'iff' is 'ssi', which I presume is pronounced 'si et seulement si'.

To search for mathematical uses of 'iff' combine it with another term: {iff exists} brings up a lot.

July 12, 2004, 20:53

QT from the Sun Times had a good column today, talking about

"...the legendary King Arthur..."

"...the legendary Robin Hood..."

"...the legendary Dennis Rodman..."

"...the legendary Hard Rock Cafe..."

"...the legendary Tigers [sic] administrator Graham Richmond..."

"...legendary customer service..."

July 13, 2004, 01:01

And customer service in many parts of the world is also legendary - in other words, it's a myth that it ever happened - and it doesn't happen now!

What seems to be happening is that the word legendary is shifting in meaning and is often taken to mean "famous" or "excellent"

Richard English