User:Dpbsmith/temp

Contents

1 Test, does this produce a warning? 2 History of ebooks 3 So Little Time 4 Stroboscopic effect 5 Notes on possible work in progress on 0/0 5.1 0/0 article 6 Naive arguments to give this expression a value 6.1 Why not just give it a value and be done? 7 See also 7.1 0/0 Opinions 7.2 Mathforum.com 8 Other stuff 9 External Link

Test, does this produce a warning?

?

History of ebooks

As of 2005 ebooks are not a significant vehicle for dissemination of literary work. The meaning of the word ebook, prospects for its future, and interpretation of its history are still subject to debate.

• 1938: H. G. Wells publishes World Brain, a collection of essays and speeches about a dream for a "Permanent World Encyclopedia." Although the technology envisioned is microfilm, the relevance to eBooks is that Wells was nevertheless talking about the low-cost dissemination of words to be read on screens. "There is no practical obstacle whatever now to the creation of an efficient index to all human knowledge, ideas and achievements, to the creation, that is, of a comlete planetary memory for all mankind. And not simply an index; the direct reproduction of the thing itself can be summoned to any properly prepared spot. A microfilm... can be sent anywhere and thrown enlarged upon the screen so that the student may study it in every detail." It is possible that some of the ideas he mentions should be credited to people at Kodak's Recordak division.
• July, 1945, Vannevar Bush publishes As We May Think in the Atlantic Monthly. "The world has arrived at an age of cheap complex devices of great reliability; and something is bound to come of it." Like Wells, taking microfilm as a model, he observed that "The Encyclopaedia Britannica could be reduced to the volume of a matchbox... The material ... would cost a nickel, and it could be mailed anywhere for a cent... The entire material of the Britannica in reduced microfilm form would go on a sheet eight and one-half by eleven inches. Once it is available, with the photographic reproduction methods of the future, duplicates in large quantities could probably be turned out for a cent apiece beyond the cost of materials." He envisioned a personal desk-sized machine, which he called a "memex," with "dry photography" capability for pages laid face-down on the surface of the desk. It would have enough storage for a user to store 5,000 pages a day for hundreds of years. The particular relevance to ebooks lies in the sentence: "Most of the memex contents are purchased on microfilm ready for insertion. Books of all sorts, pictures, current periodicals, newspapers, are thus obtained and dropped into place."
• 1965, INTREX conference
• 1971, Michael Hart types the Declaration of Independence into a networked computer at the University of Illinois and sends it to everyone on the local network. His motivation was to create value through the cost-free electronic propagation of a human readable, general-interest text. Hart maintains this was the beginning of Project Gutenberg and has claimed this as "the first eBook."
• 1974, Ted Nelson publishes Dream Machines, famous for its vision of hypertext.
• 1989, Project Gutenberg releases its tenth title and its first truly "book-length" etext, the King James version of the Bible.
• 1991, Project Gutenberg releases Alice's Adventures in Wonderland by Lewis Carroll, the eleventh PG title and the first book-length piece of fiction.
• 1994, Project Gutenberg releases its hundredth title.
• 1997 (approximate) Entrepreneurs begin planning for production of dedicated eBook devices.
• 1998, the "Rocket eBook" is released in versions badged by Nuvomedia and Franklin. Originally list-priced at $300. (Gemstar's later REB 1100 was a slightly-updated version of the same device).
• 1998, the Softbook is released. (Gemstar's later REB 1200 was a slightly-updated version of the same device).
• 1999, During the Christmas season Barnes and Noble briefly offers the Rocket eBook over the counter in its brick-and-mortar stores, as well as online.
• 1999, September 1st, Microsoft announces release of Microsoft Reader, eBook software for the PC and PocketPC. Contrary to initial announcements, no version capable of reading DRM-protected books is ever offered for PocketPC.
• 2001, Dmitri Sklyarov is arrested by the FBI and briefly jailed for violation of the DMCA. Sklyarov was an employee of ElcomSoft, a Russian company which marketed a program capable of circumventing the DRM system in the Adobe eBook reader software. Adobe eventually drops the lawsuit.

So Little Time

So Little Time is a 1943 novel by John P. Marquand. It is little known today, although when published it reached #1 on the New York Times Bestseller List on September 13, 1943, was a Book-of-the-Month Club selection, and went through eighteen hardbound printings.

The protagonist, Jeff Wilson, is a middle-aged writer who has achieved financial success and security as a script doctor, a rewriter of others' scripts. He has a wife and adult children and has an apartment in New York City and a house in the country. He frequently takes the train to the West Coast to work on movie scripts in Hollywood. He was an aviator in the First World War. This period, when everyone knew that they "did not have much time" has left a permanent stamp on him. The story follows his life during the year leading up to Pearl Harbor, interspersed with flashbacks to his past life.

Like many of Marquand's protagonists, Wilson has foregone the true love of his youth to marry prudently within his station. He lives more or less happily with his wife Madge, but yearns for the lost Louella Barnes. In his last meeting with Louella she makes advances which he is too inexperienced to recognize. She bid genial farewell saying "Good-by, and come back soon, now that you've found your way." The First World War intervenes, he fails to maintain the relationship, and she marries someone else. Wilson never does "find his way" back. Indeed, Wilson appears to have lost his way in life. He views the world with dissatisfaction and ironic distance:

There was one good thing about middle age. There might be new worries, but a lot of old ones were gone. There were a lot of thing which you finally knew you could not do, so that it was logical to give up trying to do them. Jeffrey knew that he would never read all the books in the library, fore example—that it was impossible, simply because of the cold mathematics of time.... Thre was a pack trip, for instance, which had always waned to take in the Rockies. He could think about it still, but he would never have the time.

As war approaches, he is haunted by his memories of World War I and the knowledge of what it was like to live life believing that "he did not have much time." He is disturbed by life continuing as usual, people going about their business when it is obvious to him that, again, there may not be much time.

One ongoing thread concerns his concern over his twenty-one-year-old son, Jim and his girlfriend Sally Sales. Jim enters the military, which Jeff reluctantly accepts as Jim's decision. He snipes with his wife over Sally. Madge, and his old war buddy Minot, disapprove of her social standing. She is "a little common," she does not know how to dress ("Those dreadful little shoes and the bag that matched... Her mother might have taught her—it shows where she came from.") She is "just an ordinary little girl from Montclair." "Not Montclair," says Jeff; "Scarsdale." "All right," says Madge, "Scarsdale." Minot insists that "Jim can't know what he wants. We have to break it up." Jeff does not agree, and encourages Jim and Sally to seize the day. "If you kids want to get married, you'd better get married. It may not work but—you haven't got much time."

In a generally favorable review, Joseph Warren Beach ("The Marquand World," NYT Aug 22, 1943,BR1) comments that the novel "is interesting as one of the first of American novels to make something of the present war. Just what Mr. Marquand does make of it is none to clear. Is he lampooning the vicious stupidity of 'business as usual,' or is he saying that war is life's essence, that even the luckiest of us have so little time to settle our accounts with ourselves?"

Stroboscopic effect

AHD4: stro·bo·scope NOUN: Any of various instruments used to observe moving objects by making them appear stationary, especially with pulsed illumination or mechanical devices that intermittently interrupt observation.

"this led to the spinning slits of the Phenakistoscope invented by Plateau, and the simultaneous independent invention, in 1833, by the Austrian Simon Stampfer of an almost identical device which he named the Stroboscope..." "...Simon Von Stampfer invents the stroboscope, (a phenakistiscope in reverse) which casts regular flashes of light on moving objects - making their motions appear jerky and abrupt...." "....Professor Simon Ritter von Stampfer of the Vienna Polytechnical Institute..."

The pages relating to Television particularly the PAL page does not mention the phonemenon described below. Can anyone help for a name for it plus establish whether it occurs becasue of conversion from film to PAL or from NTSC to PAL or some completely diferent route or reason?: When a fast moving vehcle is shown, particularly a horse drawn wagon or chariot with distinctive spokes, a strobe effect sometimes occurs that makes the wheel appear to move slowly backwards due to the rate at which the film is capturing the picture. Dainamo 10:34, 30 Oct 2004 (UTC)

It's not specifically a conversion issue, although frame-rate conversions sometimes produce more complicated versions of the same issue. It is sometimes called the "stroboscopic effect;" lately it has been called "aliasing;" and it not infrequently is called the "wagon-wheel effect." It has long been noticed in motion pictures. It probably deserves an article if it's not covered already, and stroboscope doesn't cover it, and stroboscopic effect doesn't exist.

It occurs because when a) the view of a moving object is represented by a series of short samples rather than a continuous view, and b) the moving object is engaging in repetitive or cyclic motion at rate that is close to the sampling rate.

For example, consider the stroboscope as used in mechanical analysis. This is a "strobe light" that is fired at an adjustable, variable rate. Let's say you are looking at a moving part that rotates at 60 revolutions per second. Now lets say that instead of illuminating it with a continuous flash, you illuminate it with a series of very short flashes of light 60 times per second. Each light catches the object at the same position in its rotation. Since at 60 flashes per second the persistence of vision smooths out the visual experience, it appears as if the object is standing still. If you illuminate it at 59 flashes per second, each flash will catch it at a slightly different part of its rotation and it will seem to be rotating slowly; it will take 59 flashes = one second before the flash catches it at the starting point again, and the object will look as if it is rotating once a second. If you illuminate it at 61 flashes per second, each flash catches it a little earlier in its rotation and the object look as if it is rotating backwards.

In the case of a television or movie camera, action is captured as a series of brief snapshots and stroboscope effects can occur.

The reason it is seen so often in motion pictures of spoked wheels is this. The wheel of a vehicle doesn't turn at 24 revolutions per second unless the vehicle is going awfully fast. But if you have twelve-spoked wheel, if built precisely, every spoke looks the same as every other spoke and they are all perfectly spaced. So, it turns at only TWO revolutions per second, which is very reasonable, and you film at 24 frames a second, each frame will catch the spokes in the "same" position and the wheel seems to be standing still. Really, the spoke that's at the 12-o-clock position in each frame is a different spoke each time, but they all look the same. If the wheels is turning a little slower than 2 revolutions per second, the position of each spoke is a little further behind in each frame and the wheel seems to be turning backwards.

The reason it's called "aliasing" is that in electrical engineering, when a continuous audio signal is replaced by series of samples--say, a 24.1 Hz signaled is sampled at 24 samples per second--the result looks the same as if an 0.1 Hz signal were sampled at 24 samples per second, so 0.1 Hz is said to be an "alias" for 24.1 Hz. [[User:Dpbsmith|Dpbsmith (talk)]] 15:54, 30 Oct 2004 (UTC)

P. S. I just noticed that we have a damned good article on aliasing, but it doesn't explicitly relate aliasing to stroboscopy or the "wagon-wheel" effect. [[User:Dpbsmith|Dpbsmith (talk)]] 15:56, 30 Oct 2004 (UTC)

In the trade, it's called temporal aliasing. We probably need an article on that. -- Anon.

Notes on possible work in progress on 0/0

Part of the history of mathematics, and one which many individuals recapitulate as they learn it, is the extension of the concept of "number" to include more and more abstract concepts. The first numbers we learn, 1, 2, 3 are so intuitive that it feels as if we do not need to learn the numbers themselves, but only the names for them. As the name for them, the "natural numbers" suggests, they feel like part of the real world. When we are first introduced to them, fractions feel artificial, and negative numbers even more so. As Kronecker said, "Die ganze Zahl schuf der liebe Gott, alles Ubrige ist Menschenwerk" (God created the integers, all else is the work of humankind).

Each extension of the concept of number feels artificial and even paradoxical. The Greeks understood fractions, but were deeply disturbed by the discovery of irrational numbers such as √2. To the extent that we actually use and apply the more advanced forms of number, they become familiar and begin to feel less abstract and more concrete.

The phrase "the real numbers" expresses the mental state of most people with a college-level technical education. Most people do not feel anything deeply disturbing about π or √2. The "imaginary numbers" such as √-1 still feel like artificial abstractions to most people, but not to electrical engineers who work with them every day.

In many cases, the extensions of the set of numbers come in response to a feeling that certain operations ought to have a numerical result. Once we have the natural numbers, we discover the operation of addition. Once we have addition, we discover its inverse subtraction. 6 - 2 = 4. But what does 4 - 6 equal?

It is perfectly possible to have a consistent set of rules in which we simply say that 4 - 6 has no answer, that six cannot be subtracted from four. In fact, traditional forms of bookkeeping, in which assets and liabilities are kept separate columns, allow commercial arithmetic to be performed without ever requiring the use of negative numbers.

The answers to all such questions depend on our definition of the word "number" and our definitions of the operations that can be performed on numbers. Part of mathematics involves the formulation of precise definitions of classes of numbers and operations.

As we shall see, the question "What is the value of zero divided by zero" seems to have a paradoxical quality to it. It is only a paradox in the same sense as the old riddle, "What happens when an irresistable force meets an immovable object?" This riddle can seem mind-boggling, but when analyzed it depends on a set of unexamined, false or contradictory assumptions. In this case, the paradox is solved by observing that if there is such a thing as an irresistable force, then there cannot be such a thing as an immovable object; the two concepts are contradictory.

In the case of zero divided by zero, the unexamined, intuitive assumptions are:

1. Zero is a number
2. Any number can be divided by any number
3. The result of a division is a number
4. A division problem has a single "right answer"

<math>\infty \mathbb{R} \mathbb{R} <math> <math> {\infty, -\infty} <math> <math>\not\mathbb{R}<math>

Indeterminate form L'Hôpital's rule IEEE_floating-point_standard Division by zero Omnipotence paradox Real number

http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html

Topics in mathematics related to quantity

Numbers | Natural numbers | Integers | Rational numbers | Constructible numbers | Algebraic numbers | Computable numbers | Real numbers | Complex numbers | Split-complex numbers | Bicomplex numbers | Hypercomplex numbers | Quaternions | Octonions | Sedenions | Superreal numbers | Hyperreal numbers | Surreal numbers | Nominal numbers | Ordinal numbers | Cardinal numbers | p-adic numbers | Integer sequences | Mathematical constants | Large numbers | Infinity

0/0 article

In mathematics <math>0/0<math> is an indeterminate form.

This means that it is not a valid expression and has no determined value.

Nota bene: That is NOT what "indeterminate form" means.

However if a function F is given by an expression in terms of x and that expression gives us <math>0/0<math> for some value of x=X

"For some value of x=X". Interesting example of a grammatical solecism of a sort that can occur only in mathematical jargon, of the kind often written by students required to take mathematics courses that they'd rather not take, but not by anyone else (if anyone were interested in such things).

then there is often a continuous function that agrees with F everywhere and is defined at the point x=X also.

A correct point, but said much better in the article indeterminate form. If there were a reason to write various articles on various indeterminate forms (and maybe that will be done some day as Wikipedia evolves, then that would be among the less interesting examples to add to that page; the more interesting ones being the less obvious ones.)

For instance if you have the equation <math>y=x/x<math> then it is defined everywhere apart from 0 then we can find a continuous function that agrees with F everywhere but is defined at 0 namely <math>y=1<math>.

A good method for finding such functions is to take the limit of the value of F as x approaches X.

"A good method"? Maybe "a good method" of computing 2 + 2 is for it to be 4. What would be another such "method", besides "taking the limit"?

This will only work if the limit is unique (is the same when approaching from any direction).

Sigh.

Naive arguments to give this expression a value

There are several naive reasons which may be given for considering this expression to have some definite value:

• Anything divided by itself is 1. Hence <math>0/0=1<math>
• Zero divided by anything is 0. Hence <math>0/0=0<math>
• Anything divided by zero is infinity. Hence <math>0/0=\infty<math>

Unfortunately the first two statements (in this form) are rules of thumb only. The third although often mentioned is technically incorrect. It should read that anything divided by zero is undefined. The first two rules correctly stated are:

• Any none zero number divided by itself is 1.
• Any number multiplied by zero is 0.

It should be noted that <math>\infty<math> is not regarded as a number (this is why we don't need to qualify the second point with "any none zero".

The first time I read "none zero", I thought it was a typo. Easily fixed, but not worth it, I think.

There are other arguements used to 'prove'0/0' has a value. Most are based on mathematical fallacies.

Why not just give it a value and be done?

Sometimes in mathematics something has not been defined yet and may not make much obvious sence but yet can be usefuly defined. There are many examples of this in modern mathematics:

• <math>-1<math> was once considered to have no meaning "You can't have -1 cakes". However to aid computation it was found to be useful as a concept and few now doubt its existence as a mathematical entity.
• <math>\sqrt -1<math> was once considered to be undefined. Many people argued that it was just a imaginery construct to solve the cubic and shouldn't be considered real. This is the origin of the terms imaginary and real. However it was found that a whole new beautiful world of complex numbers opened up if you did allow them.
• The logarithm function when used on the positive real numbers (naively) can be thought to be a fairly nice function. However if we consider complex numbers then the logarithm of any given number has an infinite number of values. These values are fairly well behaved (<math>log e^3=3+2i\pi n<math> where n is an integer) and so it is easy to deal with the complexities involved by either Riemann surfaces or by picking a certain branch (mathematics) of the logarithm function (choose one of the values arbitrarily and stick with it).
• The factorial is a function represented by an explanation mark. We have <math>1!=1,\ 2!=2*1,\ 3!=3*2*1<math> and <math>n!=n*(n-1)!<math>. This was considered to only be meaningful with integers (what is (1/2)! ?). However Legendre found a function called the gamma function which agrees with factorial at the integers but is also defined on the positive real numbers (it can be defined at all numbers bar the negative integers by analytic continuation).

So given these examples is it not possible that <math>0/0<math> can be generalised?

Unfortunately not in any realistic way. Whereas in the previous examples the values an expression could take were limited in some reasonable way this is not the case with <math>0/0<math>. To show this we should first note that any reasonable definition would require that the following properties:

• Any expression derived from a continuous function should evaluate in a way that keeps that function continuous.
  • A continuous function does not have any sudden jumps in its value (The function taking the value -1 if x<0 and 1 if x=>0 is not continuous).
• If more than one value is necessary in different circumstances then those values should be limited in some way.
  • For the logarithm (of a real number) you could say that there is only one value which is real.

If we take <math>y=c*(x/x)<math> for any value of c. We can easily see that this equation is the same as <math>y=c<math>. However for any value of c we could still get <math>0/0<math> to make the equation continuous we must allow <math>0/0<math> to take the value c. However this is true for any value of c. Hence the values given are not limited in any realistic way. We cannot satisfy both properties above sensibly. This is why mathematicians decided to leave this expression undefined.

See also

• infinitesimals
• undecidable
• philosophy of mathematics

0/0 Opinions

These are opinions of what 0/0 is. 0/0 has not been solved, therefore, many mathematicians say it is undefinable. Here are the following oppinions:

Mathforum.com

What is zero divided by zero? What I've learned so far is: Anything divided by it's self is 1. Zero divided by anything is 0. Anything divided by zero is undefined.(or some say infinity)

So, given those three rules in math, what is 0/0? Is it 0, because 0 divided by anything is 0? Is it 1, because anything divided by itself is 1? Or is it undefined, because anything divided by 0 is undefinined? (or infinity?) Any input with this would be helpful. I have spent much to much time thinking about this one. What I have come up with is that you get 1 nothing. (lables are important) It still is nothing, you just now have one nothing instead no nothings. Which is very bad grammar. Also, it is to be noted that when the limit of a function produces 0/0, the function needs to be simplfied or have L'Hospital's Rule aplied. In which case the function will no longer be 0/0. This brings up the thought, when will we see 0/0? If we see a 0/0 in a function, it usually can be removed, either by simplfying or L'Hospital's Rule. (I say usually because, though I've never seen a fuction that is 0/0 and can't be simplfied, that doesn't mean that one doesn't exist.) So, is the only time we see this function is when we take it as it appears? 0/0. In other words, is there a way to get 0/0, and not be able to simplify it in anyway to get something else?

0/0 is not 0 OR undefined. It is equal to one. One proof of this is that anything divided by itself is 1. The other involves the fact that 1/0 is equal to infinity. This means, allowing x to equal infinity (for the sake of shortness)...that 1/x = 0. This means that (1/x)/(1/x)= 0/0...and that can be simplified to x/x, which equals 1.

There are many limitations to our notion of zero, the infintesimal, and infinity. Regarding zero divided by zero without getting into the mathematical or logical proof, here's my simple definition: Zero divided by zero simply means Nothing can come from Nothing X divided by zero simply means Some thing can't be divided by no thing So from a purely logical position the former statement is illogical and the latter is impossible.

Mathforum.com

Other stuff

If You Had Wings (June 5, 1972 - June 1, 1987) was an attraction in the Tomorrowland section of Walt Disney World. In the days when most rides required the expenditure of prepaid tickets, this attraction was complimentary. Little-publicized and little known, waiting lines for this attraction were nonexistent or short even when the park was crowded.

It was an undisguised promotion for the then-giant Eastern Airlines, whose corporate slogan at the time was the grandiose (and gender-non-neutral) "The Wings of Man." It was, nevertheless, good entertainment. A sort of dark ride based on Disney's "omnimover" ride system, it conveyed seated passengers slowly, steadily, and smoothly through a series of rooms. The experience began with a vaguely simulated "takeoff" in which the ride ascended a slope, while projections of animated outlines of seagulls and airplanes swooped backwards on the walls giving an enhanced feeling of motion and flight.

Riders then passed through a series of rooms consisting, for the most part, of theatre-like sets that included screens with motion-picture scenes rear-projected. Over forty 16-mm projectors were used in the attraction. The rooms illustrated various Eastern Airlines tourist destinations such as Mexico, the Bahamas, and Trinidad, and showed tourist experiences such as seeing straw-hat markets, fishermen, limbo dancers, and steel drum bands. Repetitive music was accompanied by lyrics that said "If you had wings... if you had wings... you could do these things." The music did not succeed in masking the sound of the hidden projectors, which was audible throughout most of the ride.

The real reward was the final room, an elongated ellipsoid which presented first-person views taken from an airplane taking off, a train, from waterskies, motorcycles, airboats, and so forth. The scenes were projected on the walls by a 70-mm projector. The ellipsoidal room surrounded the riders, producing nearly a 360° surround view. The view was somewhat blurry and distorted. It was not like Disney's razor-sharp Circlevision attractions; it rather resembled the fuzzy "Cinema 180" shows featured in many contemporary amusement parks. Nevertheless, the projection effect combined with the motion of the ride produced a genuinely exhilarating sense of speed, and the bullet-shaped room gave plenty of time to experience the effect.

As the end of the ride approached, the repetitive lyrics gave way to a soothing voice assured you that "you do have wings. You can do all these things. Eastern... let Eastern be your wings."

Ultimately, riders were decanted into an arrival area containing, of all things, an Eastern Airlines reservations desk where, personnel stood ready to assist any riders eager to participate in person in the scenes they had just viewed in simulation. Few seemed to take advantage of this opportunity.

Although remembered affectionately by many, a fan website devoted to the attraction notes that "If you can't remember the public uproar surrounding the closing... one possible reason is that there was none."

External Link

Detailed and affectionate fan site including ride diagrams and photographs (http://home.cfl.rr.com/omniluxe/iyhw-main.htm)