Glorious tables of numbers

At some point, in one of the many universities where I have spent time, I ran across a pile of old books that were being given away to anyone who wanted them. I was attracted (who wouldn’t be?) by the Table of Circular and Hyperbolic Tangents and Cotangents for Radian Arguments, which was published in 1943 by the Columbia University Press; mine is the second (1947) printing. It consists of page upon page of digits, row upon row and column upon column of tan(x), cot(x), tanh(x), and coth(x), enumerated to roughly eight significant digits.

This was before the time of calculators and computers, and I really was attracted by the sprawling, rippling, hypnotic lists of numbers. It sits proudly on my bookshelf next to the copy of Gradshteyn and Ryzhik’s Table of Integrals, Series, and Products that I bought as an undergrad (and which has actually proven useful to me in my career, since computers are not unmatched along that dimension). But the truly and surprisingly beautiful portion of the book of tables turned out to be the Foreword, written by one H. T. Davis of northwestern university.

I highly recommend clicking on the link above and reading the entire text (don’t miss the “note” at the end!), which is only about two pages. But if you are in a rush (or just need a teaser to spur your interest), here are some highlights:

  • …discovery and measurement have gone hand in hand.
  • The mathematical functions’ origin in some universal principle has endowed them with a kind of immortality, and hence they appear over and over again in disciplines [including economics!] far removed from the one in which historically they first appeared.
  • The figures seen on the printed page may appear dull reading to the uninitiated, but behind them there is a realm that challenges the imagination … usually there is a long story of scientific achievement.
  • Even the old table of chords, computed probably by Hipparchus in the second century BC and transmitted to us through Claudius Ptolemy, could be adapted readily to the use of modern students of trigonometry.
  • The present volume … adds another pillar to this great monument of science, which, in the words of Horace, “is more enduring than bronze.”

It is marvelous to me to imagine the concentrated time and effort, stretching back continuously over centuries, that fed these and similar tables — and to imagine the many discoveries and adventures that would not have been possible without them.…

Continue reading

Category: Philosophy, Science

Women in science

A facebook friend recently posted a link to the following image:


I will try to ignore the spelling and grammatical errors, although they are not a promising start. I was surprised by the first one in particular, so I looked into it a bit. Cecilia Payne-Gaposchkin (1900-1979) was a brilliant early astrophysicist. She did indeed, along with others, make startling discoveries about the molecular composition of stars. The much more senior Russell did indeed suggest (probably quite strongly) that she not publish some of the more startling conclusions. But the text here implies that he stole her idea, repeated it exactly, and then published the same thing and took all the credit. According to wikipedia, this is not what happened at all:

When Payne’s dissertation was reviewed, astronomer Henry Norris Russell dissuaded her from presenting her conclusion that the composition of the Sun was predominantly hydrogen and thus very different from that of the Earth, as it contradicted the accepted wisdom at the time. However, he changed his mind four years later after having derived the same result by different means and publishing it. Although he acknowledged her work briefly in his paper, Russell was still often given credit for the discovery even after Payne had been proved correct.

But perhaps you don’t trust wikipedia, even if it does manage to spell Russell correctly. Fortunately I happen to own Payne-Gaposchkin’s autobiography, so I looked up references to Russell. She describes him (20 years after his death, and shortly before her own) as “a great man” – “not sensitive, vain, or vindictive”, although she admits that he did not have the “gift of letting his associates share the sense of achievement” (p.178).

Interestingly, in the same paragraph where she says that the “feminine urges to cook, to sew, to entertain were natural to me”, she concludes by writing: “during my whole scientific life I have never had a sense of being inferior, never been conscious that my fellow-scientists considered me inferior, on account of my sex” (p.167) . Of course she was at a disadvantage in many ways as a woman, and for every man who went out of his way to support her there was another man who actively discriminated against her. She understood this dynamic perfectly well, and she makes a point of saying how much better was the situation in america (harvard) than in her native england (cambridge).

It is also undoubtedly true that her discoveries are remembered less well because she was a woman (as the wikipedia description attests), so I agree completely with the sentiment of the image above. In fact I know for a fact that this still happens (albeit less often and less explicitly) and it is a disgrace. But advocates do themselves a disservice through slipshod research (especially regarding scientists!), by defaming people who were not (in this case) at fault, and by distorting the facts – facts which require no distortion at all in order to serve the intended purpose.

It seems fitting to close with Payne-Gaposchkin’s own words from a late chapter “On being a woman” (pp.226-7):

As I look back I ask myself what difference it has made to me as a scientist that I was born a woman. As concerns the intellectual side of the matter, I should say that it has made very little. [...] On the material side, being a woman has been a great disadvantage. It is a tale of low salary, lack of status, slow advancement. But I have reached a height that I should never, in my wildest dreams, have predicted 50

Continue reading

Category: Science

That Happened: the barkley marathons 2015









The barkley entry form (which begins: It can be done. You can’t do it, but it can be done.) has a quiz every year. This year included questions on such topics as quasars, solitary numbers, red oak, and the Etruscan language. Question 2 asked for the meaning of the name of the element dysprosium, and my response was as follows:

It comes from the Greek δυσπρόσιτος meaning “hard to get”. This phrase also describes (a) the answers for this exam; (b) five loops at the Barkley; and (c) anything worthwhile in life.

As two-time barkley finisher Brett Maune recently wrote to the barkley listserv: “Acute discomfort can produce the most treasured lifelong memories.” [Yours truly may have been similarly quoted in the barkley documentary opining that most people could use a little more pain in their lives.] The barkley is the epitome of and the ultimate referendum on this approach to life.

After having gotten to book 4 (Indian Head) of loop two in 2012 and then crewed in 2013 and 2014, I was back in the race for 2015. My training was consistent but modest at best, with 5-7 hours per week since the beginning of December. My biggest weekend was a fun trip to Nova Scotia to hang out with fellow barker Jodi Isenor and his wife Karine (and friends), where I managed over 10,000’ of vertical in the snow. Alas it also left me with some heel blisters (still not sure why; I haven’t had anything like that before – see below right), requiring that much of my remaining training be done barefoot in my apartment building – either on the treadmill at max incline or going up and down the ten flights of stairs (e.g. 7500 steps in two scintillating hours).










Race weekend I got to the campground thursday evening, and found it fairly quiet with rain expected, so I ended up at the slightly sketchy motel in wartburg… where I immediately ran into Laz (i.e. race director Gary Cantrell) and Frozen Ed Furtaw and chatted for a bit. Slept surprisingly well and went back friday morning to set up my tent, say hello to everyone gathering, and test out my blister patches on still-sensitive heels (verdict: it only hurt on the uphills). It was more exciting than I expected to be back in the game!

Eventually Laz handed out the course directions for this year (see various excerpts in italics below), as well as the individualized Univac computer predictions for each runner (Julian Jamison: taken by poachers and sold into slavery). Later (around 5pm?!) the official map finally appeared, and we all crowded around it trying to carefully mark the route; see pics.

I decided not to take the official instructions out on the course with me, but I made some notations on the map from them, from my memory of previous loops, and from conversations in previous weeks with Jodi and with Jared Campbell: thank you both! The weather was brisk (in the 20s in camp at night on both friday and saturday, cooler and windier up in the hills) but looked mostly clear. Back to my cozy tent, read for a bit, and lights out at 10:30p, just half an hour before the earliest possible blowing of the conch shell.

Except that of course this year he didn’t blow the conch until 10:22a on saturday, the latest in history. I hadn’t slept all that well, but this gave me time in the morning to …

Continue reading

Category: Running

Subscribe to tunes for bears

Name (required)

Email (required)

Julian C. Jamison

I'm an economist, researcher, traveler, runner, and astronaut-in-waiting. I enjoy pondering human behavior, including both what we do and what we ought to do - either to maximize our well-being or in pursuit of some other goal.

More about me
About TFB (this blog)
Contact me
Site policies




The views and opinions expressed on this website are solely those of Julian C. Jamison and other occasional authors, and they do not necessarily represent the views of the Consumer Financial Protection Bureau or the United States.