# Tag Info

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Documents like the one you linked to were not typed on a typewriter. When writing on typewriters, it was common to leave some space in the document in which the formulas could be inserted by hand. For professional publications, this was then given to a printer (the person, not the machine on your desk ;-)) who hot metal typeset the document. Printers had ...

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We must locate this passage into a double context : the general historical context the specific context of the "rivalry" between Hooke and Newton. See Robert Purrington, The First Professional Scientist : Robert Hooke and the Royal Society of London (2009), Ch.8 : And All Was Light : Hooke and Newton on Light and Color, page 135-on. For the general ...

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I will start by answering why matrix algebra became important, and then discuss approximately when. "Matrices" underpin what is often called operations research. That is, the theory of decision making. They are particularly useful in computer science, which features strings, arrays, etc., with machines substituting for human beings in (mechanical) decision ...

22

The controversy was ostensibly over what gets to be the "true quantity of motion", momentum or vis viva (kinetic energy), with Newton and Leibniz on the opposing sides. While there was some philosophical angle at first, a "skillful attack by Leibniz against an inadequate concept, $m|v|$, and its description of the world", it quickly deteriorated into a ...

22

Hamilton and Klein, Klein was more explicit about it. Hamilton in Lectures on Quaternions (1853) realized that his representation of rotations of rigid bodies by the unit quaternions was not $1$-$1$, but $2$-$1$. Klein in Lectures on the Ikosahedron and the Solution of Equations of the Fifth Degree (1888) replaced the unit quaternions by $2 × 2$ unitary ...

21

Einstein himself told the story in his Kyoto address of 1922, which I quote from Pais's biography titled Subtle is the Lord: "If all systems are equivalent, then Euclidean geometry cannot hold in all of them. To throw out geometry and keep laws is equivalent to describing thoughts without words. We must search for words before we can express thoughts. ...

20

On the other hand, consider this quote from The Feynman Lectures on Physics [In 1869], in a lecture, [Maxwell] said, “I have now put before you what I consider to be the greatest difficulty yet encountered by the molecular theory.” These words represent the first discovery that the laws of classical physics were wrong. This was the first indication that ...

19

It is really funny to read that in the beginning of 21-st century, some young people may think that journals and books printing had something to do with typewriters:-) If you look attentively at the page you scanned you will easily see that this is not a TeX font and not a typewriter. It is more beautiful. Before the middle 1990-th we lived in the "...

19

There is a historical reason. But it was not a fluke of history, the underlying reason is that energy comes up in non-mechanical (thermal, electric) contexts whereas momentum does not. Derived alternative, newton-meter in SI, did not arise naturally in such contexts, and alternative units, like calories, were used prior to the discovery of the general energy ...

19

For context, Tesla was 79 at the time he gave this interview. He had spent his entire life working on electromagnetism within the framework of prerelativistic theories, such as aether theories and a concept according to which "all space is filled with a gaseous substance." He accomplished some important things, but he was also somewhat of a kook and a ...

19

It is not random. These names are of Greek origin, and -ic or -ics are Anglicizations of the Greek suffix -ikos, which meant "pertaining to". In other languages it can be rendered as -ika or -ica, Wolfram's "Mathematica" uses such a version. From the Online Etymology Dictionary: "-ics in the names of sciences or disciplines (acoustics, aerobics, ...

18

All theories of matter, starting with the ancient Greek philosophers, can be classified as either continuous or discrete (i.e., particulate). This dichotomy is due to Aristotle. Aristotle held that matter was continuous: infinitely divisible. Aristotle believed that a vacuum was impossible (indeed, he claimed to prove this). Since a particulate theory ...

18

I'll try with some calculations : please, check it and the formulae used ... A solid ball with a mass $m$ of $1$ kg falls (with the usual approxiamtions : no drag, etc.) with an acceleration $a$ that is about $10 \ m/sec^2$. This means that falling from a tower $80$ meters heigh, it will touch ground after $4$ sec, with a final velocity of about $40 \ m/... 18 According to this, it's a modern fabrication: Although Einstein’s initial application for a doctorate at the University of Bern (he had previously been awarded a PhD by the University of Zürich in 1905) was indeed rejected as insufficient in 1907, and it was not until the following year that he completed a new dissertation that resulted in his being ... 17 According to (the late) William Strauss and Neil Howe in Generations, there are periodic episodes of scientific exhaustion, at least in the United States. For instance, around 1910, the head of the U.S. patent office was (mis)quoted as saying: "Everything that can be invented has been invented." In 1992, Francis Fukuyama famously opined about "the end of ... 17 Note: I present here some information defending Millikan, but please note that I do not necessarily agree with the article it came from. From the feature article "In Defense of Robert Andrews Millikan" by David Goodstein (American Scientist, January-February 2001): Awkwardly, an examination of Millikan's private laboratory notebooks indicates that he ... 16 While it may have been known that a need for safe storage of nuclear waste existed before 1943-1944, it was certainly known by 1944. The Los Alamos National Laboratory began research and development on the first nuclear weapon in 1943 LANL under the Manhattan Project which lasted from 1942 to 1946. The B Reactor at the Hanford site in Washington state was ... 16 I take that your primary goal is to know what Feynman thought of Hawking's work. While it is possible that they have met I would consider it unlikely given that Feynman mentioned several times how his attendance of the Chapel Hill conference (on general relativity) made such a bad impression on him that he never attended another conference on that theme, so ... 15 Unlike Einstein, Planck did not quantize electromagnetic waves themselves, only the exchanged energies, and even them only statistically. So the other two questions have no satisfactory answer because he was not dealing with specifics of emission/absorption at the level of individual quanta. The quanta were meant as mathematical fictions for the purposes of ... 15 In Millikan's publications, he stated categorically that every single oil drop observed had had a charge that was a multiple of$e$, with no exceptions or omissions. But his notebooks are full of notations such as "beautiful data, keep," and "bad run, throw out." Richard Feynman wrote an essay called "Cargo Cult Science," in which he pointed out: ... 15 Max Planck, Scientific Autobiography and Other Papers (Westport, CT: Greenwood, 1949), pp. 33-34:A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.as quoted in:• M. López Corredoira and C. Castro Perelman, ... 14 I'm going to try to answer the question you end with, "Why has atomic bomb instead of another better term become the predominant term?", rather than the question in your title, because that's the historical question. (The other might be interesting to debate, but unlikely to produce a satisfying final answer.) Let's start with the Google ngram, showing the ... 14 Newton used anagrams which are not the usual ciphers. It is not designed for a secret communication, but only for proving at a later time that you knew something. So nobody is supposed to be able to decode the message until you tell what the message was. To do this, he used a simple procedure: he wrote a sentence (in Latin) and then just counted letters in ... 14 This question is based on a misunderstanding. The statement that$\pi$is constant has precise meaning:$\pi\$ is a ratio of the length of circumference to the length of diameter. The statement that it is constant means that it is the same for all circles. (This statement is independent of the representation of this ratio with digits). Contrary to what many ...

14

I do not know how exactly was this picture made, but there are at least two methods. The first one is to compute this potential (which is not too difficult), plot sufficiently many points and connect them by smooth curves. This was still quite common in pre-computer era, in 1970s when a special drawing tool was used, in the shape of a curved ruler of ...

14

The most famous mathematicians who were the members of NSDAP are Ludwig Bieberbach and Oswald Teichmuller. I am not sure which "Hilbert" is mentioned in the question but mathematician David Hilbert certainly was not a party member, and had very negative attitude to the Nazis.

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I am not sure what "explain it like a story" means, but the Bohr–Einstein debates is perhaps the most dramatic story of Einstein making his dissatisfaction known. Pais's scientific biography of Einstein Subtle is the Lord offers an even more comprehensive story of his life and the genesis of his philosophical outlook. As for the main reason for his ...

13

Perhaps one of the most famous computational model discoveries of the 20th century is Lorenz's observation in 1961 of chaotic behavior in a weather model. It overturned the existing consensus in meteorology, and led him to the discovery of a strange attractor in a simplified model of atmospheric convection. The implications are described in the now famous ...

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Who or what attracted Einstein's attention to Mercury, and when? What alerted him to the idea that Mercury's case was different from all those other cases, when a mundane explanation was involved? I know for sure that Henri Poincaré was aware of the problem and of its singularity - had he been in Kelvin's place, he would have added it to the list, and ...

13

Science fiction author Arthur C. Clarke is often credited with the idea of communication satellites. link That was in 1945, long before any artificial satellite had been launched in reality.

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