numeracy

improving first principles, statistics and math and increased detection of errors of (c)omission

How Not To Be Wrong (J. Ellenberg)

Math gives us a way of being unsure in a principled way: not by giving up, but rather making a firm assertion: "I'm not sure, this is why I'm not sure, and this is roughly how not-sure I am." Or even more: "I'm unsure and you should be too."

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Significance: In common language it means something like "important” or “meaningful.“ But the significance test that scientists use doesn’t measure importance. When we‘re testing the effect of a new drug, the null hypothesis is that there is no effect at all; so to reject the null hypothesis is merely to make a judgment that the effect of the drug is not zero. But the effect could still be very small - so small that the drug isn’t effective in any sense that an ordinary non-mathematical Anglophone would call significant.

The lexical double booking of “significance” has consequences beyond making scientific papers hard to read. On October 18, 1995, the UK Committee on Safety of Medicines (CSM) issued a “Dear Doctor” letter to nearly 200,000 doctors and public health workers around Great Britain, with an alarming warning about certain brands of “third-generation” oral contraceptives. “New evidence has become available,” the letter read, “indicating that the chance of a thrombosis occurring in a vein is increased around two-fold for some types of pill compared with others.” A venous thrombosis is no joke; it means a clot is impeding the flow of the blood through the vein. If the clot breaks free, the bloodstream can carry it all the way to your lung, where, under its new identity as a pulmonary embolism, it can kill you.

The Dear Doctor letter was quick to assure readers that oral contraception was safe for most women, and no one should stop taking the pill without medical advice. But details like that are easy to lose when the top-line message is “Pills kill.” The AP story that ran October 19 led with “The government warned Thursday that a new type of birth control pill used by 1.5 million British women may cause blood clots...It considered withdrawing the pills but decided not to, partly because some women cannot tolerate any other kind of pills.”

The public, understandably, freaked out. One general practitioner found that 12% of pill users among her patients stopped taking their contraceptives as soon as they heard the government report. Presumably, many women switched to other versions of the pill not implicated in thrombosis, but any interruption makes the pill less effective. And less-effective birth control means more pregnancies. (What—you thought I was going to say there was a wave of abstinence?) After several successive years of decline, the conception rate in the United Kingdom jumped several percentage points the next year. There were 26,000 more babies conceived in 1996 in England and Wales than there had been one year previously. Since so many of the extra pregnancies were unplanned, that led to a lot more termination, too: 13,600 more abortions than in 1995.

This might seem a small price to pay to avoid a blood clot careening through your circulatory, wreaking potentially lethal havoc. Think about all the women who were spared from death by embolism by the CSM's warning! But how many women exactly is that? We can't know for sure. But one scientist, a supporter of the CSM decision to issue the warning, said the total number of embolism deaths prevented was "possibly one."

History of Pi (P. Beckmann)

The attitude of the ancient Greeks to Euclidian geometry was essentially this: “The truth of these five axioms is obvious; therefore everything that follows from them is valid also." The attitude of modern mathematics is somewhat different: "If we assume that these axioms are valid, then everything that follows from them is valid also." At first sight the difference between the two seems to be a chicken-hearted technicality. But in reality it goes much deeper. In the 19th century it was discovered that if the fifth postulate was pulled out from under Euclid’s cathedral, not all of the building would collapse; a part of the structure (called absolute geometry) would remain supported by the other four axioms. It was also found that if the fifth axiom was replaced by its exact opposite, namely, that it is possible to draw more than one straight line through a point parallel to a given straight line, then on this strange fifth foundation stone (together with the preceding four) one could build all kinds of weird and wonderful cathedrals. Riemann, Lobachevsky, Bolyai and others built just such crazy cathedrals; they are known as non-Euclidean geometry.

The non-Euclidean axiom may sound ridiculous. But an axiom is unprovable; if we could prove it, it would not be an axiom, for it could be based on a more primitive (unprovable) axiom. We just assume its validity or we don’t; all we ask of an axiom is that it does not lead to contradictory consequences. And non-Euclidean geometry is just as free of contradictions as Euclidean is. One is no more “true” than the other. The fact that we cannot draw those parallel lines in the usual way proves nothing.

Nevertheless, some readers may feel that all this is pure mathematical abstraction with no relation to reality. Not quite. Reality is what is confirmed by our experience. Euclidean geometry is convenient for describing this kind of experience; which is not the same thing as saying it is “universally true.” For there are other experiences for whose description Euclidean geometry is extremely inconvenient. Suppose point A is on this page of the book and point B is on some star in a distant galaxy; then what does “straight" mean? In that case we have no experience with ropes, but we do have experience with light rays. And this experience shows that light rays traveling through gravitational fields do not behave like ropes stretched between stakes. Their behavior is described by Einstein's General Theory of Relativity, which works with non-Euclidean geometry. This is more convenient in describing the laws that govern our experience. If we were to express these laws in Euclidean space they would assume very complicated forms, or alternatively, we would have to revamp all of our electromagnetic theory from scratch (without guarantee of success), and this is not considered worth while (by the few physicists who have even given this alternative any thought). And so the chicken-hearted technicality of saying "if" is neither chicken-hearted nor a technicality.

Innumeracy (J. A. Paulos)

These matters are not merely academic, and there is a direct way in which the mass media's predilection for dramatic reporting leads to extreme politics and even pseudoscience. Since fringe politicians and scientists are generally more intriguing than mainstream ones, they garner a disproportionate share of publicity and thus seem more representative and significant than they otherwise would. Furthermore, since perceptions tend to become realities, the natural tendency of the mass media to accentuate the anomalous, combined with an innumerate society's taste for such extremes, could conceivably have quite dire consequences.

The Pleasure of Finding Things Out (R. Feynman)

The first matter of judging evidence...you begin by being very uncertain as to what the answer is. For if you already know the answer there is no need to gather any evidence about it. There are usual rules for judging evidence; it's not right to pick only what you like, but to take all of the evidence, to try to maintain some objectivity about the thing. Authority may be a hint as to what the truth is, but it is not a source of information. As long as it's possible, we should disregard authority whenever the observations disagree with it. And finally, the recording of results should be done in a disinterested way. That's a very funny phrase which always bothers me—because it means that after the guy's all done with the thing, he doesn't give a darn about the results, but that isn't the point. Disinterest here means that they are not reported in such a way as to try to influence the reader into an idea that's different than what the evidence indicates.

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Epaulettes and the Pope

One of the things that my father taught me besides physics (LAUGHS), whether it’s correct or not, was a disrespect for respectable...for certain kinds of things. For example, when I was a little boy, and a rotogravure—that’s printed pictures in newspapers—first came out in the New York Times, he used to sit me again on his knee and he’d open a picture, and there was a picture of the Pope and everybody bowing in front of him. And he’d say, “Now look at these humans. Here is one human standing here, and all these others are bowing. Now what is the difference? This one is the Pope—he hated the Pope anyway—and he’d say, “the difference is epaulettes”—of course not in the case of the Pope, but if he was a general it was always the uniform, the position, “but this man has the same human problems, he eats dinner like anybody else, he goes to the bathroom, he has the same kind of problems as everybody, he’s a human being. Why are they all bowing to him? Only because of his name and his position, because of his uniform, not because of something special he did, or his honor, or something like that.” He, by the way, was in the uniform business, so he knew what the difference was between the man with the uniform off and the uniform on; it's the same man to him.


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It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. In that simple statement is the key to science.

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Oh, yes. I’m very proud of not having a Ph.D. I think the Ph.D. system is an abomination. It was invented as a system for educating German professors in the 19th century, and it works well under those conditions. It’s good for a very small number of people who are going to spend their lives being professors. But it has become now a kind of union card that you have to have in order to have a job, whether it’s being a professor or other things, and it’s quite inappropriate for that. It forces people to waste years and years of their lives sort of pretending to do research for which they’re not at all well-suited. In the end, they have this piece of paper which says they’re qualified, but it really doesn’t mean anything. The Ph.D. takes far too long and discourages women from becoming scientists, which I consider a great tragedy. So I have opposed it all my life without any success at all.

Thinking Physics (L. C. Epstein)

Relativistic Bike and Trolley

Consider a motorcycle powered by super-powerful electric batteries, and a common electric street-car (powered by overhead wire) that are each driven to speeds approaching the speed of light. In turn, each drives over a scale which we read in our stationary frame of reference. An increase in mass of the ______ will be registered:

A) motorcycle

B) streetcar

C) both

D) neither


Answer:

B), despite the widespread misconception among relativity buffs that the mass of a moving thing always increases, going to infinity as the speed of the thing approaches the speed of light. It so happens that the mass of a thing increases not if speed is added to it, but only if energy is added to it. Energy is poured into the streetcar from the powerhouse through the overhead trolley wire. But the motorcycle carries its own energy supply with it. While new energy is added to the streetcar, no new energy is added to the motorcycle. Energy has inertia. So the mass of the streetcar increases with speed while the mass of the motorcycle remains unchanged whatever its speed.

Interestingly enough, all the mass gained by the streetcar is compensated by a like decrease in mass at the power source. If the streetcar gains a thousand kilograms then the mass of the fuel and its products at the power plant is minus one thousand kilograms! And with the motorcycle, any gain in mass of the bike and rider is compensated by a like decrease of mass of the battery so there is no net change in mass. So the mass of all things does not go to infinity simply because their speed goes to the speed of light. After all, light moves at the speed of light and its mass is certainly not infinite.

context

non-fiction narrative of human decisions and technological progress

The Making of the Atomic Bomb (R. Rhodes)

Placzek pointed out that uranium and thorium both exhibit a capture resonance for neutrons with medium-range energies of about 25 electron volts. That meant, first of all, that although fission was one behavior uranium could exhibit under neutron bombardment, capture and subsequent transmutation continued to be another. Bohr was not ever to be rid of those inconvenient “transuranians.” Some of them were real.

If a neutron penetrated a uranium nucleus, for example, the result might be fission. But if the neutron happened to be traveling at the appropriate energy when it penetrated—somewhere around 25 eV—the nucleus would probably capture it without fissioning. Beta decay would follow, increasing the nuclear charge by one unit; the result should be a new, as-yet-unnamed transuranic element of atomic number 93. That was one of Placzek’s points. It would prove in time to be crucial.

The other source of confusion was more straightforward. It was also more immediately relevant to the question of how to harness nuclear energy. It concerned differences between uranium and thorium.

Thorium, element 90, a soft, heavy, lustrous, silver-white metal, was first isolated by the celebrated Swedish chemist Jons Jakob Berzelius in 1828. Berzelius named the new element after Thor, the Norse god of thunder. Its oxide found commercial use beginning in the late nineteenth century as the primary component of the fragile woven mantles of gas lanterns: heat incandesces it a brilliant white. Because it is mildly radioactive, and radioactivity was once considered tonic, thorium was also for some years incorporated into a popular German toothpaste, Doramad. Auer, the company that made German gas mantles, also made the toothpaste. Hahn, Meitner and Strassmann, the Joliot-Curies and others had regularly studied thorium alongside uranium. Its behavior was often similar. Otto Frisch had first demonstrated that it fissioned. He bombarded it next after uranium in the course of his January experiment in Copenhagen, the experiment he had discussed with Bohr after he returned from Kungälv and Bohr had worked so hard in the United States to protect.

Frisch was then also the first to notice that the fission characteristics of thorium differed from those of uranium. Thorium did not respond to the magic of paraffin; it was unaffected by slow neutrons. Richard B. Roberts and his colleagues at the Department of Terrestrial Magnetism of the Carnegie Institution of Washington had just independently confirmed and extended Frisch’s findings. With their 5 million volt Van de Graaff they could generate neutrons of several different, known energies. Continuing their experiments after their Saturday-night show for the Washington Conference group, they had compared uranium and thorium fission responses at varying energies as Frisch with his single neutron source could not. They found to their surprise (Frisch’s paper had not yet appeared in Nature) that while both uranium and thorium fissioned under bombardment by fast neutrons, only uranium fissioned under bombardment by slow neutrons. Some energy between 0.5 MeV and 2.5 MeV marked a lower threshold for fast-neutron fission for both elements. (Bohr and John Wheeler, beginning work at Princeton on fission theory, had estimated the threshold energy to be about 1 MeV.) The slow neutrons that also fissioned uranium were effective at far lower energies. “From these comparisons,” the DTM group concluded in a February paper, “it appears that the uranium fissions are produced by different processes for fast and slow neutrons.”

Why, Placzek now prodded Bohr, should both uranium and thorium have similar capture resonances and similar fast-neutron thresholds but different responses to slow neutrons? If the liquid-drop model had any validity at all, the difference made no sense. Bohr abruptly saw why and was struck dumb. Not to lose what he had only barely grasped, oblivious to courtesy, he pushed back his chair and strode from the room and from the club. Rosenfeld hurried to follow. “Taking a hasty leave of Placzek, I joined Bohr, who was walking silently, lost in deep meditation, which I was careful not to disturb.” The two men tramped speechless through the snow across the Princeton campus to Fine Hall, the Neo-Gothic brick building where the Institute for Advanced Study was then lodged. They went in to Bohr’s office, borrowed from Albert Einstein. It was spacious, with leaded windows, a fireplace, a large blackboard, an Oriental rug to warm the floor. No peripatetic like Bohr, Einstein had judged it too large and moved into a small secretarial annex nearby.

“As soon as we entered the office,” Rosenfeld remembers, “[Bohr] rushed to the blackboard, telling me: ‘Now listen: I have it all.’ And he started—again without uttering a word—drawing graphs on the blackboard.”

The first graph Bohr drew looked like this: The horizontal axis plotted neutron energy left to right—low to high, slow to fast. The vertical axis charted cross sections—the probability of a particular nuclear reaction—and served a double purpose. The lazy S that filled most of the frame represented thorium’s cross section for capture at different neutron energies, the steep central peak demonstrating the 25 eV resonance in the middle range. The tail that waved from the horizontal axis on the right side represented a different thorium cross section: its cross section for fission beginning at that high 1 MeV threshold. What Bohr had drawn was thus a visualization of thorium’s changing response to bombardment by neutrons of increasing energy. Bohr moved to the next section of blackboard and drew a second graph. He labeled it with the mass number of the isotope most plentiful in natural uranium. “He wrote the mass number 238 with very large figures,” Rosenfeld says; “he broke several pieces of chalk in the process.” Bohr’s urgency marked the point of his insight. The second graph looked exactly like the first:

But a third graph was coming.

Francis Aston had found only U238 when he first passed uranium through his mass spectrograph at the Cavendish. In 1935, using a more powerful instrument, physicist Arthur Jeffrey Dempster of the University of Chicago detected a second, lighter isotope. “It was found,” Dempster announced in a lecture, “that a few seconds’ exposure was sufficient for the main component at 238 reported by Dr. Aston, but on long exposures a faint companion of mass number 235 was also present.” Three years later a gifted Harvard post-doctoral fellow named Alfred Otto Carl Nier, the son of working-class German emigrants to Minnesota, measured the ratio of U235 to U238 in natural uranium as 1:139, which meant that U235 was present to the extent of about 0.7 percent. By contrast, thorium in itsnatural form is essentially all one isotope, Th232. And that natural difference in the composition of the two elements was the clue that set Bohr off. He drew his third graph. It depicted one cross section, not two: Having made a hard copy of his abrupt vision, Bohr was finally ready to explain himself.

Both thorium and U238 could be expected on theoretical grounds to behave similarly, he pointed out to Rosenfeld: to fission only with fast neutrons above 1 MeV. And it seemed that they did. That left U235. It followed as a matter of logic, Bohr said triumphantly, that U235 must be responsible for slow-neutron fission. Such was his essential insight. He went on to explore the subtle energetics of the several reactions. Thorium was lighter than U235, U238 heavier, but the middle isotope differed more significantly in another important regard. When Th232 absorbed a neutron it became a nucleus of odd mass number, Th233. When U238 absorbed a neutron it also became a nucleus of odd mass number, U239. But when U235 absorbed a neutron it became a nucleus of even mass number, U236. And the vicissitudes of nuclear rearrangement are such, as Fermi would explain one day in a lecture, that “changing from an odd number of neutrons to an even number of neutrons released one or two MeV.” Which meant that U235 had an inherent energetic advantage over its two competitors: it accrued energy toward fission simply by virtue of its change of mass; they did not.

Lise Meitner and Otto Frisch had realized in Kungälv that a certain amount of energy was necessary to agitate the nucleus to fission, but they had not considered in detail the energetics of that input. They were distracted by the enormous 200 MeV output. In fact, the uranium nucleus required an input of about 6 MeV to fission. That much energy was necessary to roil the nucleus to the point where it elongated and broke apart. The absorption of any neutron, regardless of its velocity, made available a binding energy of about 5.3 MeV. But that left U238 about 1 MeV short, which is why it needed fast neutrons of at least that threshold energy before it could fission.

U235 also earned 5.3 MeV when it absorbed a neutron. But it won Fermi’s “one or two MeV” in addition simply by adjusting from an odd to an even mass. That put its total above 6 MeV. So any neutron at all would fission U235—slow, fast or in between. Which was what Bohr’s third graph demonstrated: the probably continuous fission cross section of U235. From slow neutrons on the left only a fraction of an electron volt above zero energy, to fast neutrons on the right above 1 MeV that would also fission U238, any neutron an atom of U235 encountered would agitate it to fission. Natural uranium masked U235’s continuous fissibility; the more abundant U238 captured most of the neutrons. Only by slowing the neutrons with paraffin below the U238 capture resonance at 25 eV had experimenters like Hahn, Strassmann and Frisch been able to coax the highly fissionable U235 out of hiding. In a burst of insight Bohr had answered Placzek’s objections and replenished his liquid drop.

__________

At Trinity gloom was everywhere. A physical chemist from Los Alamos, Joseph Hirschfelder, remembers Oppenheimer’s discomfort that Saturday evening at the hotel where the guests invited to view the test had begun to assemble: “We drove to the Hilton Hotel in Albuquerque, where Robert Oppenheimer was meeting with a large group of generals, Nobel laureates, and other VIP’s. Robert was very nervous. He told [us] about some experimental results which Ed Creutz had obtained earlier in the day which indicated that the [Trinity] atom bomb would be a dud.”

Back at Base Camp Oppenheimer slept no more than four hours that night; Farrell heard him stirring restlessly on his bunk in the next room of the quarters they shared, racked with coughing. Chain-smoking as much as meditative poetry drove him through his days. Sturdy Hans Bethe found a way back from the precipice, Kistiakowsky remembers: "Sunday morning another phone call came with wonderful news. Hans Bethe spent the whole night of Saturday analyzing the electromagnetic theory of this experiment and discovered that the instrumental design was such that even a perfect implosion could not have produced oscilloscope records different from what was observed. So I became again acceptable to local high society." When Groves called, Oppenheimer chatted happily about the Bethe results.

__________

Oppenheimer appreciated the salutary effect of Bohr’s presence. “Bohr at Los Alamos was marvelous,” he told an audience of scientists after the war. “He took a very lively technical interest...But his real function, I think for almost all of us, was not the technical one.” Here two texts of the postwar lecture diverge; both versions illuminate Oppenheimer’s state of mind in 1944 as he remembered it. In unedited transcript he said Bohr “made the enterprise which looked so macabre seem hopeful”; edited, that sentence became: “He made the enterprise seem hopeful, when many were not free of misgiving.” How Bohr did so Oppenheimer and even Bohr had work to explain. Oppenheimer outlines an explanation in his lecture:

Bohr spoke with contempt of Hitler, who with a few hundred tanks and planes had tried to enslave Europe for a millennium. He said nothing like that would ever happen again; and his own high hope that the outcome would be good, and that in this the role of objectivity, the cooperation which he had experienced among scientists would play a helpful part; all this, all of us wanted very much to believe.

“He said nothing like that would ever happen again” is a key; Austrian emigré theoretician Victor Weisskopf supplies another: In Los Alamos we were working on something which is perhaps the most questionable, the most problematic thing a scientist can be faced with. At that time physics, our beloved science, was pushed into the most cruel part of reality and we had to live it through. We were, most of us at least, young and somewhat inexperienced in human affairs, I would say. But suddenly in the midst of it, Bohr appeared in Los Alamos.

It was the first time we became aware of the sense in all these terrible things, because Bohr right away participated not only in the work, but in our discussions. Every great and deep difficulty bears in itself its own solution...This we learned from him. “They didn’t need my help in making the atom bomb,” Bohr later told a friend. He was there to another purpose.

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“This time,” he told Weil, “take the control rod out twelve inches.” Weil withdrew the cadmium rod. Fermi nodded and ZIP was winched out as well. “This is going to do it,” Fermi told Compton. The director of the plutonium project had found a place for himself at Fermi’s side. “Now it will become self-sustaining. The trace [on the recorder] will climb and continue to climb; it will not level off.” Herbert Anderson was an eyewitness:

At first you could hear the sound of the neutron counter, clickety-clack, clickety-clack. Then the clicks came more and more rapidly, and after a while they began to merge into a roar; the counter couldn’t follow anymore. That was the moment to switch to the chart recorder. But when the switch was made, everyone watched in the sudden silence the mounting deflection of the recorder’s pen. It was an awesome silence. Everyone realized the significance of that switch; we were in the high intensity regime and the counters were unable to cope with the situation anymore. Again and again, the scale of the recorder had to be changed to accommodate the neutron intensity which was increasing more and more rapidly. Suddenly Fermi raised his hand. “The pile has gone critical,” he announced. No one present had any doubt about it.

Fermi allowed himself a grin. He would tell the technical council the next day that the pile achieved a k of 1.0006. Its neutron intensity was then doubling every two minutes. Left uncontrolled for an hour and a half, that rate of increase would have carried it to a million kilowatts. Long before so extreme a runaway it would have killed anyone left in the room and melted down. “Then everyone began to wonder why he didn’t shut the pile off,” Anderson continues. “But Fermi was completely calm. He waited another minute, then another, and then when it seemed that the anxiety was too much to bear, he ordered ‘ZIP in!’ ” It was 3:53 P.M. Fermi had run the pile for 4.5 minutes at one-half watt and brought to fruition all the years of discovery and experiment. Men had controlled the release of energy from the atomic nucleus. The chain reaction was moonshine no more. Eugene Wigner reports how they felt:

Nothing very spectacular had happened. Nothing had moved and the pile itself had given no sound. Nevertheless, when the rods were pushed back in and the clicking died down, we suddenly experienced a let-down feeling, for all of us understood the language of the counter. Even though we had anticipated the success of the experiment, its accomplishment had a deep impact on us. For some time we had known that we were about to unlock a giant; still, we could not escape an eerie feeling when we knew we had actually done it. We felt as, I presume, everyone feels who has done something that he knows will have very far-reaching consequences which he cannot foresee.

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Dr. Oppenheimer...suddenly told me that we had [made] a terrible scientific blunder,” Groves testified after the war. “I think he was right. It is one of the things that I regret the most in the whole course of the operation. We had failed to consider [thermal diffusion] as a portion of the process as a whole.” From the beginning the leaders of the Manhattan Project had thought of the several enrichment and separation processes as competing horses in a race. That had blinded them to the possibility of harnessing the processes together. Groves had partly opened his eyes when barrier troubles delayed K-25; then he had decided to cancel the upper stages of the K-25 cascade and feed the lower-stage product to the Beta calutrons for final enrichment. So he was prepared to understand immediately Oppenheimer’s similar point about the value of a thermal-diffusion plant: “I at once decided that the idea was well worth investigating.”

Development of Searles Lake Brine (J. E. Teeple)

"Responsible men should have an accurate knowledge of all money values involved. I don’t like to see men working in the dark. It is particularly distressing to have research and development men struggling with problems that might at the most mean $10 or $20 per day, and calmly ignoring factors that may involve hundreds or thousands simply because they lack an accurate knowledge of proportional money values. Many firms are exceedingly secretive regarding all money figures. It may be a petty misdemeanor to allow your cost figures to reach a competitor, particularly if your costs are such that you ought to be ashamed of them, but it is a major folly to keep your own good men in ignorance of them. A still greater folly is not to know them yourself."

"The brine in the pans foamed like soapsuds, which was not particularly the fault of the evaporators, and in order to keep this foam under control it was customary to blow live steam at times into the second or third effects; also not economical. A brine of this type depositing large quantities of salts requires rather vigorous positive circulation through the heating tubes, but these pans were equipped with a type of propeller which used nothing stronger than moral suasion, and the liquors were of such an unregenerate type that moral suasion was not effective. Because of the slow circulation, the tubes salted up very rapidly and frequent stops were necessary for washout. Due to some of the minor constituents in the brine the tubes of the first effect were frequently found coated with an impervious and insoluble enamel which so cut down the heat transmission that frequent resort to mechanical violence was necessary to remove it."

"The matter of maintaining an atmosphere of mutual respect is of course advisable anywhere, but it becomes exceedingly important when dealing with technical men from whom you expect constructive work and ideas. My lecture to young men who are about to assume a position giving them some authority over other technical men runs about as follows: Don't strut; the fact that you now have a certain title or position is extremely unimportant to everyone but yourself. It doesn't prove anything. Maybe in selecting you someone made a mistake which will he rectified later. The essential thing is what can you do, what can you contribute, how much better are you than a vacancy in the office? Crazy Ludwig was king of Bavaria. and Caligula's horse was consul of Rome. These were important events to Ludwig and maybe to the horse but they can hardly he counted as factors in successful progress."

Turing's Cathedral (Dyson)

Bigelow compiled a list of fourteen “Maxims for Ideal Prognosticators” starting with MIP I: “Make all observations in same coordinate system as will finally be used by the gun-pointer.” Maxims 2-4 advised separating the available information into that needed immediately and that needed later, While Maxim 5 added that “if noise is ever to be filtered from signal, it must be done at the earliest possible stage rather than after the two are tangled with other noises and signals, for the same reason that repeater stations are used on a signal line rather than filters and amplifiers at the ends.” Maxim 7 advised “Never estimate what may be accurately computed”; Maxim 8 advised “Never guess what may be estimated” and, if a guess was absolutely necessary, “Never guess blindly” was Maxim 9.

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As they refined their models. Charney's group needed a benchmark by which to gauge their predicrions. For his test case, Richardson had used the otherwise uneventful morning of May 20, 1910. Charney's group chose Thanksgiving 1950 when a severe storm struck the central and eastern United States. The weather system, whose development was missed by the forecasts available at the time, caused three hundred deaths, unprecedented property damage, and even blew part of the roof off the Palmer Physical Laboratory at Princeton University It was the perfect storm.

"Because of the spontaneity and intensity of its development this storm was selected as an ideal test case for the prediction of cyclogenesis." Charney explains. Despite the unpredictability of turbulence, he believed that “the inception and development of cyclones are determinate and predictable events." Although cyclogenesis might appear random, ”the initial perturbation will have a preferred location in space and time, and its amplitude, though it may be small initially, will be entirely determined by the basic flow. It is like an automobile being pushed slowly but inexorably over a cliff.“

”The storm of November 25-27 was first noted on the surface weather map of 1230 GMT, November 24 as a small low developing over North Carolina and western Virginia," began the summary in the November 1950 Monthly Weather Review. Over the next forty-eight hours the disturbance grew to become the worst storm ever recorded over the United States. Coburn Creek, West Virginia, received sixty-two inches of snow. Records of minus 1 degree Fahrenheit were set in Louisville, Kentucky, and Nashville, Tennessee, and thirty inches of snow fell in Pittsburgh, bringing the steel industry to a halt.

"The two-and-a-half-dimensional model did not catch the cyclogenesis, [although] there was some vague indication of something going on," Charney later reported. "And so we went to a three-level model, that is, a two-and-two-thirds dimensional model, and we did catch the cyclogenesis. It wasn‘t terribly accurate, but there was no question that [we did]. And I always thought that this was a terribly important thing...I wanted the world to know about that!"

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Viewing the problem of self-replication and self-reproduction through the lens of formal logic and self-referential systems, von Neumann applied the results of Gödel and Turing to the foundations of biology—although his conclusions had little effect on working biologists, just as his Mathematical Foundations of Quantum Mechanics had little effect on the day-to-day work of physicists at the time. Applying Turing's proof of the unsolvability of the Entscheidungsproblem to the domain of self-reproducing automata, he concluded, in December 1949, that "in other words you can build an organ which can do anything that can be done, but you cannot build an organ which tells you whether it can be done!'”

"This is connected with the theory of types and with the results of Gödel." he continued, "The question of whether something is feasible in a type belongs to a higher logical type. It is characteristic of objects of low complexity that it is easier to talk about the object than produce it and easier to predict its properties than to build it, But in the complicated parts of formal logic it is always one order of magnitude harder to tell what an object can do than to produce the object.”

Can automata produce offspring as complicated, or more complicated, than themselves? ‘Complication' on its lower levels is probably degenerative, that is, every automaton that can produce other automata will only be able to produce less complicated ones." Von Neumann explained. There is a certain level of complication, however, beyond which "the phenomenon of synthesis, if properly arranged, can become explosive, in other words, where syntheses of automata can proceed in such a manner that each automaton will produce other automata which are more complex and of higher potentialities than itself.”

This conjecture goes to the heart of the probability or improbability of the origin of life. If true, then the existence of a sufficiently complicated self-reproducing system may lead to more complicated systems and. with reasonable probability, either to life or to something lifelike. Self-reproduction is an accident that only has to happen once. “The operations of probability somehow leave a loophole at this point," explained von Neumann, "and it is by the process of self-reproduction that they are pierced." Von Neumann had intended to return to the question of self-reproduction after leaving the AEC.

Growth Company - Dow Chemical's First Century (E. N. Brandt)

Herbert Dow visited the bromine plant and "I found it shut down with most of the men on the roof. The coke tower was plugged with iron hydrate and needed to be scraped out. But, there was considerable odor of bromine and the men claimed they were waiting for it to clear up. I was satisfied that the amount of bromine was not more than it had been customary for me to soak up on many occasions and I presumed the foreman was equally familiar with the amount of bromine the men could absorb without injury. So I told him to set the example by going down and taking out the first pail of coke. He started to climb down the ladder and when his head got inside the door, he changed his mind and came out again, saying there was altogether too much bromine. So I took my coat off, threw it to one side, went down myself and told them to pass down the tools. I filled one pail full of coke and they pulled it out, and by that time the ladder was full of men trying to get down to help me, and very promptly enough coke was removed to restart the plant.

If I had not gone up on the roof and if I had not known by experience how much bromine irritation a man can stand before it becomes a serious matter, that plant might have been shut down all day and several hundred dollars lost thereby." - H. H. Dow, written in 1930

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A year after Dow began making phenol, fishermen downstream began to complain their fish tasted bad, and it was soon clear that phenol was the culprit. From 1928 to 1935 waste ponds were used to hold back millions of gallons until high river flow. When released, Al Edmunds would follow the river flow taking samples until it reached the town water intake, which he closed until the contaminated water passed by. Fish were grown in various river water samples and served to Dow's taste-test panel every day at 11:30 AM and 4:30 PM.

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Dow had an excess of caustic from the chlorine-caustic cells, so during the 1930's Willard Dow asked the lab to come up with some way to consume it. Edgar Britton (who has a lab named after him) read a German formula for Ethocel that used 3 pounds of caustic per pound product. An Ethocel fiber spinning/weaving system was set up making "Ethorayon" a soft, silky fabric and many of the scientist's wives were soon wearing underwear made of it. But, in the 1930's, an iron had only one setting for cotton, which melted this material. The textile industry wouldn't modify irons for just one new material. The material was a failure. It took DuPont with Nylon to finally get a reduced-heat setting. Ethorayon was probably 10 years ahead of the time when it would have been successful.

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Rifamycin was discovered by Dr. Pagani, a microbiologist who picked up a soil sample in a pine forest on the French Riviera while on vacation in 1957. Back in Milan, the sample was checked for any antibacterial microorganisms. Rifamycin became Dow's biggest pharmaceutical. Zoalene coccidiostat was developed by Brown, Harris & Fischback. This product revolutionized the poultry industry by making it possible to raise chickens on a large scale without risking catastrophic losses from coccidiosis, a major poultry disease. Once under control, chicken became the most economical form of animal protein available, and the status of chicken changed from Sunday dinner for the prosperous to everyday food for the masses. Chicken would soon turn up in fast-food franchises across the land.

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Lee Iacocca took a new Lincoln equipped with new disc brakes, brand new at the time. Apparently Iacocca was riding his brake pedal and overheated his brake fluid, resulting in poor braking performance. The next morning he said: "I want a 450-degree boiling point brake fluid, and I want it now. Whoever can do it gets all of our business." Dow employed a researcher named Joe Schrems, who was a genius at formulating brake fluid. He was also blind. He created the formulation and won Dow the business.

people

minds, decisions, logic and preferences

On Intelligence (J. Hawkins)

“Prediction” means that the neurons involved in sensing your door become active in advance of them actually receiving sensory input. When the sensory input does arrive, it is compared with what was expected. As you approach the door, your cortex is forming a slew of predictions based on past experience. As you reach out, it predicts what you will feel on your fingers, when you will feel the door, and at what angle your joints will be when you actually touch the door. As you start to push the door open, your cortex predicts how much resistance the door will offer and how it will sound. When your predictions are all met, you’ll walk through the door without consciously knowing these predictions were verified. But if your expectations about the door are violated, the error will cause you to take notice. Correct predictions result in understanding. The door is normal. Incorrect predictions result in confusion and prompt you to pay attention. The door latch is not where it’s supposed to be. The door is too light. The door is off center. The texture of the knob is wrong. We are making continuous low-level predictions in parallel across all our senses. But that’s not all. I am arguing a much stronger proposition. Prediction is not just one of the things your brain does. It is the primary function of the neocortex, and the foundation of intelligence. The cortex is an organ of prediction. If we want to understand what intelligence is, what creativity is, how your brain works, and how to build intelligent machines, we must understand nature of these predictions and how the cortex makes them. Even behavior is best understood as a byproduct of prediction.

Gödel, Escher, Bach (D. Hofstadter)

It is cause for joy when a mathematician discovers an isomorphism between two structures which he knows. It is often a “bolt from the blue” and a source of wonderment. The perception of an isomorphism between two known structures is a significant advance in knowledge—and I claim that it is such perceptions of isomorphism which create meanings in the minds of people. A final word on the perception of isomorphisms: since they come in many shapes and sizes, figuratively speaking, it is not always totally clear when you really have found an isomorphism. Thus, “isomorphism” is a word with all the usual vagueness of words—which is a defect but an advantage as well.


In this case, we have an excellent prototype for the concept of isomor-

phism. There is a “lower level” of our isomorphism—that is, a mapping

between the parts of the two structures:




How to Win Friends and Influence People (D. Carnegie)

If a person makes a statement that you think is wrong—yes, even that you know is wrong—isn’t it better to begin by saying: “Well, now, look. I thought otherwise, but I may be wrong. I frequently am. And if I am wrong, I want to be put right. Let’s examine the facts.” There’s magic, positive magic, in such phrases as: “I may be wrong. I frequently am. Let’s examine the facts.” Nobody in the heavens above or on the earth beneath or in the waters under the earth will ever object to your saying: “I may be wrong. Let’s examine the facts.”

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If a man’s heart is rankling with discord and ill feeling toward you, you can't win him to your way of thinking with all the logic in Christendom. Scolding parents and domineering bosses and husbands and nagging wives ought to realize that people don’t want to change their minds, they can’t be forced or driven to agree with you or me. But they may possibly be led to, if we are gentle and friendly, ever so gentle and ever so friendly.

Sapiens (Y. Harari)

The First Wave Extinction, which accompanied the spread of the foragers, was followed by the Second Wave Extinction, accompanied the spread of the farmers, and gives us a perspective on the Third Wave Extinction, which industrial activity is causing today. Don’t believe tree-huggers who claim that our ancestors lived in harmony with nature. Long before the Industrial Revolution, Homo sapiens held the record among all organisms for driving the most plant and animal species to their extinctions. We have the dubious distinction of being the deadliest species in the annals of biology.

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Eventually, people were so smart that they were able to decipher nature’s secrets, enabling them to tame sheep and cultivate wheat. As soon as this happened, they cheerfully abandoned the gruelling, dangerous, and often spartan life of hunter-gatherers, settling down to enjoy the pleasant, satiated life of farmers. That tale is a fantasy. There is no evidence that people became more intelligent with time. Foragers knew the secrets of nature long before the Agricultural Revolution, since their survival depended on an intimate knowledge of the animals they hunted and the plants they gathered. Rather than heralding a new era of easy living, the Agricultural Revolution left farmers with lives generally more difficult and less satisfying than those of foragers. Hunter-gatherers spent their time in more stimulating and varied ways, and were less in danger of starvation and disease. The Agricultural Revolution certainly enlarged the sum total of food at the disposal of humankind, but the extra food did not translate into a better diet or more leisure. Rather, it translated into population explosions and pampered elites. The average farmer worked harder than the average forager, and got a worse diet in return. The Agricultural Revolution was history’s biggest fraud.

Defeating Darwinism by Opening Minds (P. Johnson)

Here is what I want to say to the scientists and educators: History has taught us that an established religion tends to fall into bad habits, and the same thing may be true when a scientific establishment starts to act like a governmental body with an official ideology to uphold. The price of having that kind of position is that you are tempted to protect your power and wealth by defending things you shouldn't be defending, with methods (like doubletalk and intimidating threats of legal action) that you shouldn‘t be using. These become bad habits, and they eventually lead you into massive hypocrisy and self-deception. When you preach baloney detecting as the essential tool of science but make students turn their baloney detectors off when they get to the really important questions of origins, you convict yourselves every day of hypocrisy. You also lose the ability to think critically about your own beliefs, and eventually you set yourself up for the kind of embarrassment that destroyed Matthew Harrison Brady.

There is only one cure. No matter how badly you want to bury the tough questions, you have to acknowledge that those questions really are too tough to be settled with misleading slogans like “Evolution is a fact” and "Science and religion are separate realms." You have to admit that people have reasons for objecting to the materialist philosophy you are presenting in the name of science. If you are going to be educators instead of dogmatists, you are going to have to start dealing honestly with those objections.

unforgettable

stories

Smoke Gets In Your Eyes (C. Doughty)

Prior to resurfacing, the floors [of the crematory] had begun to resemble the topography of the Alps. Large chunks of concrete dislodged themselves from years of wear and tear. With the floors in this condition, sweeping out the bones and ashes had become a test of dexterity and will that outstripped the job description. With these new floors I could rake the bones out with graceful, luxurious strokes, and without even breaking a sweat.

Day one of freshly floored machines went off without a hitch. Day two began with me loading in Mrs. Greyhound. In marked contrast to her sleek surname, Mrs. Greyhound was a pleasantly plump woman in her eighties. Her permed white hair and soft hands reminded me of my paternal grandmother, a schoolteacher in a one-room schoolhouse in small-town Iowa who raised seven children and made cinnamon rolls from scratch. One summer when I was a child, I visited her in Iowa and was awoken in the middle of the night to find her crying in the dark living room because she knew "that there are some people who don’t know the love of Jesus." My grandmother had died almost ten years before I began working at Westwind, but only my father had been able to fly back to Iowa for the funeral. It was easy to see your own grandmother in people...well, bodies...like Mrs. Greyhound.

Using the principles of Cremation 101, Mrs. Greyhound went in at the beginning of the day, when the cremation retorts were still cool. We needed the cremation chambers stone cold in the morning to accommodate our larger men and women. Without a cold chamber, the flesh would bum up too quickly, going up the smokestack in thick, dark puffs, potentially summoning the fire department. People with additional body fat (such as the zaftig Mrs. Greyhound) were cremated first. while smaller, older ladies with zero body fat (and babies) were generally saved for the end of the day. I loaded Mrs. Greyhound into the cold retort and went about my morning business When I returned moments later, there was smoke pouring out the door. Billowing, black smoke. I made my “assessing an emergency situation” noise, a cross between a choke and scream, and ran to get Mike in his front office. “Oh shit, the floor,” he said, steely-eyed. Mike and I came screeching around the corner back into the crematory. At that same moment, from the chute where the bones are swept out, came a sluice of gushing, molten fat. Mike pulled out the bone-collecting container, roughly the size of a large shoebox, to find a pool of what had to have been a gallon of opaque slop. And it kept coming. And coming. The two of us replaced container after container at the bottom of the bone chute like we were bailing out a leaky boat.

Mike ran the containers to the prep room, washing the fat down the same drain as the blood from the embalming process. Meanwhile I plunked down on the floor with a pile of rags, sopping and swabbing up the fat as it cascaded out. Mike kept apologizing, the first time Mike had apologized for anything in my whole time at the crematory. Even he was on the verge of heaving after the tenth round of smoke, heat, scrub, swab, repeat. "It’s the floor,” he said, defeated. "The floor? The beautiful new retort floor?’ I said. "The old floor had all of those craters, the fat could pool then burn up later in the cremation. Now the fat has nowhere to go, so it's gliding out the front door."

When at last the situation was under control, I looked down to find my dress stained with warm human fat. Would you call this color burnt sienna, or is it more of a marigold? I wondered. I was sweaty but I felt alive. Cremation was supposed to be the “clean" option, bodies sanitized by fire into a pile of inoffensive ashes, but Mrs. Greyhound would not go, as Dylan Thomas said, gentle into that good night. We did not succeed in making her disposal tidy, despite all the tools of the modern death industry, the hundreds of thousands of dollars of industrial machinery. I wasn't sure we should he trying as hard as we were for the perfect death. After all, “success" meant using all the plastic and wires In present the idealized corpse of Elena Ionescu. "Success" meant dead bodies taken from their families by professionals whose job was not ritual but obfuscation, hiding the truths of what bodies are and what bodies do. For me, Mrs. Greyhound blew the truth of the matter wide open. Death should be known. Known as a difficult mental, physical, and emotional process, respected and feared for what it is.

"Jesus, do you need, like, a dry-cleaning stipend or something?" Mike asked, standing over me. I cackled helplessly, sitting on the crematory floor in my fat-stained dress, my legs sprawled in front of me, surrounded by rags. It was a moment of release. “I think this dress is done. man. You can buy me lunch or something. Fucking hell." I was horrified that this had happened to Mrs. Greyhound, but it would be a lie to describe the experience as anything less than exhilarating, the repulsive going hand in hand with the wondrous. My work at Westwind had given me access to emotions I didn‘t know I was capable of, I would start laughing or crying at the drop of a damn hat. Crying at a particularly beautiful sunset or a particularly beautiful parking meter, it didn‘t matter.

It felt as if my life up to this point was spent living within a tiny range of sensations, rolling hack and forth like a pinball. At Westwind that emotional range was blasted apart, allowing for ecstasy and despair like I had never experienced. Everything I was learning at Westwind I wanted to shout from the rooftop. The daily reminders of death cast each day in more vivid tones. Sometimes in mixed company I would share the story of molten fat or some other cringe-inducing tale from the Crematory People performed their scandalized reactions but I felt less and less connected to their revulsion. The most salacious stories—bones ground in a metal blender or torture-spike eye caps—had the power to disrupt people's polite complacency about death. Rather than denying the truth, it was a revelation to embrace it, however disgusting it might sometimes be.

The Making of the Atomic Bomb (R. Rhodes)

As of July 9 Kistiakowsky did not yet have enough quality lens castings on hand to assemble a complete charge. Oppenheimer further compounded his troubles by insisting on firing a Chinese copy of the gadget a few days before the Trinity shot to test its high-explosive design at full scale with a non-fissionable core. Each unit would require ninety-six blocks of explosive. Kistiakowsky resorted to heroic measures:

"In some desperation, I got hold of a dental drill and, not wishing to ask others to do an untried job, spent most of one night, the week before the Trinity test, drilling holes in some faulty castings so as to reach the air cavities indicated on our x-ray inspection films. That done, I filled the cavities by pouring molten explosive slurry into them, and thus made the castings acceptable. Over night, enough castings were added to our stores by my labors to make more than two spheres."

"You don't worry about it." he adds fatalistically. "I mean, if fifty pounds of explosives goes off in your lap, you won't know it."