
The Eccentric Lives of Steinhaus, Banach and Ulam (2014) - nyankosensei
http://culture.pl/en/article/maths-madness-and-the-manhattan-project-the-eccentric-lives-of-steinhaus-banach-and-ulam
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siliconunit
I wonder sometimes if our modern structured and red taped upper education
model could ever cope with such exceptional individuals at all. I cannot stop
thinking they will never get the unbridled space they need to express their
ideas and concot together without an heavy amount of supervision and
channeling toward 'agreed' topics and behaviours, I think education and the
application of the law should be very flexible when exceptional individuals
are at stake...

~~~
GuiA
That is already the case. Many Hollywood stars walk penalty free from repeated
drug incidents, while poorer people spend many years in prison for one time
minor offenses, for one example amongst many.

You might argue that these people are not the “exceptional” you have in mind,
but many are likely to not argue with your definition either.

~~~
NotSammyHagar
They get off crimes mostly because they can hire good lawyers. A lot of
successful entrepreneurs didn't finish college and instead ran out to do their
own thing (gates, jobs, zuckerberg).

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boxerab
Steinhaus, Ulam and many other mathematicians in the Lviv school were Jewish,
and had to flee or go into hiding to survive the German occupation.
Interesting that there is no mention of this in the article.

~~~
osipov
Unfortunately today, Lviv remains hostile to Jews by celebrating[1] extreme
nationalism. Something I experienced first hand due to my Jewish heritage.

[1]
[https://en.wikipedia.org/wiki/Stepan_Bandera#Jews](https://en.wikipedia.org/wiki/Stepan_Bandera#Jews)

~~~
bobthechef
> Lviv remains hostile to Jews

I'm not sure how that relates to the OP since the article is on a Polish
website. "Remains hostile" seems to suggest it was hostile before WWII.
Remember, Lviv today is largely Ukrainian (as was Bandera). Most Poles, Jew or
gentile, were either expelled after or killed during the war.

~~~
NotSammyHagar
The wikipedia page on the city has a great description of the history.
[https://en.wikipedia.org/wiki/Lviv](https://en.wikipedia.org/wiki/Lviv)

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graycat
Notice Ulam, Feynman, and von Neumann at Los Alamos in

[http://www-history.mcs.st-and.ac.uk/BigPictures/Ulam_Feynman...](http://www-
history.mcs.st-and.ac.uk/BigPictures/Ulam_Feynman_von_Neumann.jpeg)

For the Banach match box problem, that is, flip a fair coin x + y times and
find the probability of getting heads exactly x times. So, it's a binomial
probability problem.

A _Banach space_ is a complete, normed linear space. There is a nice chapter
on Banach space in

Walter Rudin, _Real and Complex Analysis_.

There are some nice applications of the Hahn-Banach theorem in

David G. Luenberger, _Optimization by Vector Space Methods_.

In

Patrick Billingsley, _Convergence of Probability Measures_.

is a nice presentation of Ulam's result in measure theory Le Cam called
_tightness_ : Roughly, IIRC, for any probability measure P and any a > 0 no
matter how small, there exists a sphere S of finite radius so that P(S) > 1 -
a. Intuitively the probability mass can't just keep avoiding all spheres;
eventually some sphere, if large enough, must cover nearly all the mass. There
are some cute technical details.

Once in a paper I used Ulam's result to show that a goofy distribution-free
statistical hypothesis test was not trivial. And I've seen other applications.

The hypothesis test was to improve on our work in artificial intelligence for
zero day monitoring for problems in server farms and networks. So, Ulam's
tightness has played a role in at least one piece of work intended to be
practical!

IIRC, Ulam was long head of Los Alamos. Once I heard his lecture on the role
in evolution of having two sexes.

There was a Time-Life book on math with a few pages on Ulam. IIRC, Ulam did by
hand or mechanical calculator some of the early Monte-Carlo evaluations of
critical mass.

At

[http://www.brainyquote.com/quotes/quotes/s/stanislawu312043....](http://www.brainyquote.com/quotes/quotes/s/stanislawu312043.html)

is

"It is still an unending source of surprise for me how a few scribbles on a
blackboard or on a piece of paper can change the course of human affairs."

Stanislaw Ulam

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mannykannot
There is an intriguing reference here: "...the concept of a spatial x-ray
locating device came to [Steinhaus] during a winter stroll spent observing
snowflakes falling on his fur coat." Elsewhere, I have found the comment
"Steinhaus designed and instrument for localization of strange bodies in the
body of a sick person by means of X-rays, based on a simple and elegant
geometrical conception (1938) [1]." Does anyone know what this is? A form of
tomography, perhaps, or an application of stereology? - which is distinct from
tomography, according to this article [2], and is apparently somehow related
to his Longimeter, recently discussed here [3].

[1]
[http://prac.im.pwr.edu.pl/~hugo/HSC/Steinhaus.htm](http://prac.im.pwr.edu.pl/~hugo/HSC/Steinhaus.htm)
[2]
[https://en.wikipedia.org/wiki/Stereology](https://en.wikipedia.org/wiki/Stereology)
[3]
[https://news.ycombinator.com/item?id=16647821](https://news.ycombinator.com/item?id=16647821)

~~~
Someone
From that description, I would guess a form of focal plane tomography
([https://en.wikipedia.org/wiki/Focal_plane_tomography](https://en.wikipedia.org/wiki/Focal_plane_tomography)),
but
[http://far.in.tum.de/pub/sielhorst2008jdt/sielhorst2008jdt.p...](http://far.in.tum.de/pub/sielhorst2008jdt/sielhorst2008jdt.pdf)
says

 _”The first setup augmenting imaging data registered to an object was
described in 1938 by the Austrian mathematician Steinhaus. He described the
geometric layout to reveal a bullet inside a patient with a pointer that is
visually overlaid on the invisible bullet. This overlay was aligned by
construction from any point of view and its registration works without any
computation. However, the registration procedure is cumbersome and it has to
be repeated for each patient. The setup involves two cathodes that emit X-rays
projecting the bullet on a fluoroscopic screen (see Fig. 2). On the other side
of the X-ray screen, two spheres are placed symmetrically to the X-ray
cathodes. A third sphere is fixed on the crossing of the lines between the two
spheres and the two projections of the bullet on the screen. The third sphere
represents the bullet. Replacing the screen with a semi-transparent mirror and
watching the object through the mirror, the third sphere is overlaid exactly
on top of the bullet from any point of view. This is possible because the
third sphere is at the location to which the bullet is mirrored. Therefore,
the setup yields stereoscopic depth impression. The overlay is restricted to a
single point and the system has to be manually calibrated for each
augmentation with the support of an X-ray image with two X-ray sources.”_

~~~
jagger11
> by the Austrian mathematician Steinhaus

Steinhaus was Polish, the confusion probably comes from the fact that he was
born in then occupied by Austro-Hungary part of Poland (city of Jaslo, now
within borders of Poland).

~~~
bobthechef
I've noticed more than a few Poles saddled with non-Polish roots in various
history books. Banach himself was at one point incorrectly identified as a
Russian mathematician in an old edition of the Encyclopedia Britannica.
Sometimes the cause of error may be the historian's ignorance, sometimes
nationalistic appropriation by others. Many Poles also often worked abroad
during the 19th and 20th centuries because of foreign oppression by the
Germans, Russians, and the Austrians (the last to a lesser degree than the
first two).

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pjmorris
'Adventures of a Mathematician' is an autobiography of Ulam. I've not read it,
but it was recommended by one of my math professors.

~~~
dannylandau
I have read it, and remains one of my favorite biographies -- Highly
recommended. Never thought it would get a mention on HN!

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cafard
Ulam's memoirs are still in print, I think, and very readable.

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chmaynard
> .. mathematicians who dreamt big, wrote poems, constructed the atomic bomb
> and helped organise the first flights to the moon.

Wow! I want to purchase the movie rights -- where do I sign?

