Saturday, June 19, 2010

Tile Switch Plate Covers The case against \

when one uses the approach of nonstandard calculus. However, these shortcuts can be easily adopted in a standard calculus course.

Let me elaborate.

\MLXC Derivatives are similarly computed without taking a limit. Continuity of functions is defined as \ows to infinity is Represented by an "unbounded hyperreal number", the sequence Could Quickly Grow, or very Quickly, or slowly, or very slowly, and for Each Conceivable "growth rate" there is a hyperreal number of the Corresponding "order of magnitude ". There is an uncountable number of Different Growth rates. The set of hyperreals Complicated is quite a thing to imagine! No wonder a textbook Can not Give specific examples of infinitesimals and Keeps writing "dx" or "epsilon." However, students will Have a hard time Trying to Understand this concept Without an intuitive picture. I think it is Not Productive to require students to Understand the hierarchy of Growth Such orders at an early stage in a beginner's calculus course. I see this as the first major problem. The secon d problem is that not all limits can be computed simply by \third problem is That I Will Have students trouble with the notion of convergence of series after seeing all WHERE Calculations So Many Powers of "epsilon" are Automatically infinitesimal. The convergence of series is an Especially shady spot in nonstandard analysis. That says a truncated one series has the sum S (n) Where n is the number of terms. Then one Substitutes an "unbounded integer" instead of n. This is impossible to do in practice unless Already one has S (n) as an analytic function of n. Also, the idea of "unbounded integers" is very complicated. For example, "cos (2 * Pi * n)" should be "almost equal" to 1 When n is an "unbounded integer." (Or Should it be

Exactly equal to 1?) However, as we Have Seen, "cos x" is undefined Actually if x is unbounded, like when to x = 1/epsilon with infinitesimal epsilon. It appears that \e bounded function, then x=y when we finally take the limit epsilon=0.\

Monday, June 7, 2010

Does A Prolapsed Uterus Go Away?

In a previous post ( http://chaource.livejournal.com/58109.html ) I viewed the scientific community as a clique whose primary visible purpose is to extract money from the public. Here is another view of the humanity's scientific activity that may explain what is wrong with the funding of science.

I focus on scientists who work on basic theoretical research --- the \ (arxiv.org) that permits them to exchange results quickly and somewhat informally. It is precisely these scientists who do not feel particularly motivated by money, who resent the idea of deadlines or reporting to a boss, who like choosing their projects based on fascination and interest, and who may come to the office at 4 pm to stay there until 3 am and continue working on weekends and holidays. In other words, scientists seem to have have all the attitudes typical for people engaged in a purely volunteer effort.

This volunteer effort happens to be moderately remunerated and in certain countries may even look like a career, but this has not always been the case. It used to be the case that you got money only for performing a tangible service that other people wanted renThe mind CAN Develop A Certain aptitude and liking for a particular task That Does Not Actually Have Anything to do with the real world But, to the mind Fascinated, Appears To Be as Relevant and important as real-world task and Stock (or even more important !). Fascinated by the Saami people find activity Each Other and continue to Pursue Their Common Interest. Any Remuneration for Their Work Is Purely incidental (eg the miserly book royalties) and is Not Regarded as important. One obvious difference

Between the scientific community and to local scientists Interest That club is publish, and SP, ie produces visible results (one counter That Could Also Sometimes players chess games publish Their, Which Are Useful for future chess players). The "amount of science Produced"y, especially in the internet age where it costs almost nothing to publish. I recently learned that Ebay sells $1 billion/yr worth of junk, Amazon sells $3 billin/yr worth of books, while Elsevier makes $8 billion/yr mostly on sales of subscriptions to its online publications, with a profit margin of 22%. This money is paid by universities, who then force scientists to attract more funds. Scientists then find themselves fighting for grant money.

Conclusions:

1. Basic scientific research must be openly recognized as a volunteer effort. Money should be paid only for actual services rendered, e.g. teaching or computer programming or consulting. Governments should not be allowed to directly sponsor science because this leads to massive abuses and a decline in the quality of work. Private persons do it sponsoring science discretion and at Their Own Risk. (Rich indivuduals with an Interest in science of course Pursue That May Interest.)

2. Scientists publish dog for free on the Internet using Any free license (GNU FDL or Creative Commons ", or whatever). The best way to make a volunteer effort "is to make it visible Commonly accessible. The Basically noncommercial, volunteer nature of the scientific publishing Effort Should Be Made explicit, in That the results of Effort That Are Freely accessible.

3. Such publishers as Elsevier, Springer, etc., Who Routinely take camera-ready texts from scientists
Them And Then sell back to scientists at monopoly prices
, Should Be boycott. It Would Be Much Better if science Monographs and Textbooks Were Freely accessible. Cheap print shops sell dog-on-demand printed copies of Textbooks to students at $ 0.05 per page. Poor students CAN buy a $ 200 computer and read the Textbooks on the screen.