It turned out that the higher ranges were more easily mastered by the AIC's programmers. At an IQ setting of 160, the computer held its own with a Professor of postmodern literary theory, and at 180, produced a witty critique of Stephen Hawking's latest book.
The effort to simulate all levels of human IQ was initially frustrated, however. The first time the IQ dial was set to 40, sparks flew, the screen went blank, and the voice-synthesizer burnt out.
After several months of additional effort a new round of testing was begun. As before, the AIC handled itself beautifully at IQ levels of 140, 160, 180 and even 200. With bated breath, the team's chief engineer set the dial to 40 once again. At the first words from the computer's voice synthesizer, the team broke into cheers, for they knew they had convincingly simulated even a minimal human intelligence. It said:
The two hundred year interval from the brilliant discoveries of Huygens and Newton to the geometrization of mathematics by Riemann and Poincaré seems a mathematical desert, filled only by calculations....
For modern mathematicians it is generally difficult to read their predecessors, who wrote: ``Bob washed his hands'' where they should simply have said ``There is a
t_1 < 0 such that the image Bob(t_1) of the pointt_1 under the natural mappingt -> Bob(t) belongs to the set of people having dirty hands and at_2 of the half-open interval(t_1,0] such that the image of the pointt_2 under the same mapping belongs to the complement of the set concerned when the pointt_1 is considered.''
The most obvious reason for teaching [students] to use calculators is that they are all around us in the world outside of school, and most people who have access to them do not use them very intelligently. Since calculators can be very powerful tools in doing mathematics, one of the obligations of a good mathematics education program in a school is to teach students how to use calculators intelligently, including when not to use them because there are better tools available for the task at hand. Beyond that, it is hard to convince children that school mathematics has something to do with the real world if they see everybody outside of school doing mathematics with calculators but they are not allowed to use them in school.
Many teachers have put forward the view ... that the limit concept should be given in terms of a relation between epsilon and delta regions. We must assert quite definitely that we consider this form to be unsuitable. Even as regards acquiring a purely formal mastery of the definition, many years' experience has shown that this form gives rise to very considerable and sometimes insurmountable difficulties, and not only with schoolchildren, but also with students in the early courses at the higher schools. ... [T]he concept of limit if formulated in this way will be mastered at best abstractly, at the price of a large gulf between the concept itself and the real considerations with which it is associated.The domain of definition of a function:
The well-known text-book tradition ... is to work out this domain from the formula; it is said, for example, that 'the function +\sqrt{1-x^2} exists only for |x| <= 1'. Such terminology must be considered mathematically imprecise and pedagogically dangerous, for at its base lies the thought that the function defined for |x| <= 1 by the formula +\sqrt{1-x^2} cannot be defined outside this interval; that the existence of the function comes to an end where the analytical expression used to describe it ceases to make sense.Definitions in mathematical pedagogy:
When we require that definitions should sometimes be learnt by the pupils in full, this has its sound methodological basis. A logical definition is a formula from which nothing can be dropped and to which not a word can be added, or otherwise the sense will be distorted. In demanding that the pupils learn such definitions by heart we are therefore instilling in them just that scrupulous attitude towards a definition which, by its logical nature, the definition deserves. It is useful, we would suggest, to show even schoolchildren how quickly the sense of a definition is distorted if we change even so much as a single word; such examples would help the pupils to understand that the word-by-word memorization of a definition is an act of high logical culture and not a piece of scholastic cramming.
All teaching of arithmetic and algebra in the schools should be carried on ... under the banner of a fight against formalism.
[``... pure chaos is completely uninteresting.'']
I will not watch it on TV, I will not watch on DVD. I will not watch on VHS, I will not watch on CBS. I will not watch it in a car, I will not watch it in a bar. I will not watch it with my dad, I will not watch it when I'm sad. I will not watch it in my bed, I will not watch with my friend Fred. I will not watch it on a box, I will not watch it shown on FOX. I will not watch it on a table, I will not watch when it's on cable. I will not watch it in a chair, I will not watch it anywhere. I wish I had not paid eight bucks, This movie really really sucks.
Because the all which is on the table begins to address the big cost drivers. For example, how the benefits are calculate, for example, is on the table; whether or not benefits rise based upon wage increases or price increases.There's a series of parts of the formula that are being considered. And when you couple that, those different cost drivers, affecting those changing those with personal accounts, the idea is to get what has been promised more likely to be or closer delivered to what has been promised. Does that make any sense to you? -- George W. Bush
Steve King, congressman of Iowa, has introduced HR 997, a bill to make English the official language of the United States of America. -- News Item
As democracy is perfected, the office of president represents, more and more closely, the inner soul of the people. On some great and glorious day the plain folk of the land will reach their heart's desire at last, and the White House will be adorned by a downright moron. -- H.L. Mencken
To A Quick Young Fox:
Why jog exquisite bulk, fond crazy vamp,
Daft buxom jonquil, zephyr's gawky vice?
Guy fed by work, quiz Jove's xanthic lamp --
Zow! Qualms by deja vu gyp fox-kin thrice.
-- Lazy Dog
Such indeed is the tendency to such a coalition, and such its corrupting influence on both the parties, that the danger cannot be too carefully guarded agst. And in a Govt. of opinion, like ours, the only effectual guard must be found in the soundness and stability of the general opinion on the subject. Every new & successful example therefore of a perfect separation between ecclesiastical and civil matters, is of importance. And I have no doubt that every new example will succeed, as every past one has done, in shewing that religion & Govt. will both exist in greater purity, the less they are mixed together.
It was the belief of all sects at one time that the establishment of Religion by law was right & necessary; that the true religion ought to be established in exclusion of every other; And that the only question to be decided was which was the true religion.
The example of Holland proved that a toleration of sects dissenting from the established sect was safe & even useful. The example of the Colonies, now States, which rejected religious establishments altogether, proved that all Sects might be safely & advantageously put on a footing of equal & entire freedom; and a continuance of their example since the declaration of Independence, has shewn that its success in Colonies was not to be ascribed to their connection with the parent Country.
If a further confirmation of the truth could be wanted, it is to be found in the examples furnished by the States which have abolished their religious establishments. I cannot speak particularly of any of the cases excepting that of Virga. where it is impossible to deny that Religion prevails with more zeal and a more exemplary priesthood, than it ever did when established and patronised by Public authority.
We are teaching the world the great truth that Govts. do better without Kings & Nobles than with them. The merit will be doubled by the other lesson that Religion flourishes in greater purity, without than with the aid of Govt. #
The power of the executive to cast a man into prison without formulating any charge known to the law, and particularly to deny him judgement by his peers for an indefinite period, is in the highest degree odious, and is the foundation of all totalitarian governments whether Nazi or Communist.
The slide rule was the prime symbol of the engineering profession until the 1960s, after which it was made obsolescent by digital computers. Current computer calculations, yielding a dozen or more significant figures, are more precise than slide-rule calculations, which yield but three significant figures, but they are seldom more accurate. Most of the data used in engineering are, by nature, approximate. In general, the precision and the speed of the computer are bought at the cost of the visual sense of the reasonableness of a numerical answer that many engineers cultivated as they learned to make calculations on their slide rules....
When nearly all engineers used slide rules, carried out structural analyses using graphic statics, and resorted to whatever nomograms they might find to solve immediate problems, the advantages of visually monitoring one's calculations (Does it look right? Are the numerical answers reasonable?) were built into the graphical mathematics they used. Even though digital computers are making graphical methods seem both old-fashioned and insufferably slow, a few younger engineers, along with the old fogeys, are beginning to understand that speed has sometimes been bought at the cost of understanding.
I believe that the motion picture is destined to revolutionize our educational system and that in a few years it will supplant largely, if not entirely, the use of textbooks.
...the fact that a Prohibition enforcement officer is universally regarded in America as a licensed blackmailer and scoundrel, even when he shows all the outward signs of integrity, is due to a sound instinct in the common people. They sense the plain fact that his business is unescapably anti-social--that it is, in fact, quite as anti-social as that of the porch-climber, pickpocket or private detective. Decorating him with a badge and a pad of black warrants doesn't change him in the slightest. He is intrinsically a criminal, and before many moons have waxed and waned mob justice will begin to deal with him as such.
The American people, taken one with another, constitute the most timorous, sniveling, poltroonish, ignominious mob of serfs and goose-steppers ever gathered under one flag in Christendom since the end of the middle ages. -- H. L. Mencken
Let us suppose we are given a set of linear equations A x= b to solve. ... We may either treat this problem as it stands and attempt to find x, or we may solve the more general problem of finding the inverse of the matrix A, and then allow it to operate on b giving the required solution of the equations as x= A^{-1} b. ...It seems probable that with the advent of electronic computers it will become standard practice to find the inverse.
better !pout !cry
better watchout
lpr why
santa claus <north pole >town
cat /etc/passwd >list
ncheck list
ncheck list
cat list | grep naughty >nogiftlist
cat list | grep nice >giftlist
santa claus <north pole > town
who | grep sleeping
who | grep awake
who | egrep 'bad|good'
for (goodness sake) {
be good
}
The profound study of nature is the most fruitful source of mathematical discovery. Not only does this study, by proposing a fixed goal for our research, have the advantage of excluding vague questions and calculations without result. It is also a sure way of shaping Analysis itself, and discovering which parts it is most important to know and must always remain part of the subject. These fundamental principles are those which are found in all natural phenomena.
The Scotsman is mean, as we're all well aware, And bony and blotchy and covered with hair. He eats salty porridge and tosses huge trees, And wears pretty dresses to show off his knees.
mark- sman ren- owned McCo- rmick Ave. Ames Tribune pentach- lorophenol dish- armonies Pete- rson ISU Daily, 2/5/90 electrol- uminescence Wang, Semiconductor & Device Physics
... the standard tests have almost nothing to do with the acquisition of mathematical understanding and put a premium on brute knowledge and memory, speed and slickness. They provide no opportunity for the student to explain his or her answer and treat all 'wrong' answers as equally wrong. Thus their effect is to distort the teaching and learning processes and the curriculum, in the direction of unmitigated skill-acquisition. They are, in short, inimical to mathematics itself.
