Saturday, September 16, 2017

"The Man Who Knew Too Much: Alan Turing"

I just finished reading (i.e. listening to) a great book: "The Man Who Knew Too Much: Alan Turing and the Invention of the Computer" by David Leavitt. (BTW, I just learned he has ties to the University of Florida in Gainesville). It was a great and informative reading about the man so important to both modern sciences and computer sciences alike. What is interesting in the book is perhaps an analysis of some links between Turing's fascination of  the machine intelligence and him being gay. I do not think anyone before Leavitt (who is also openly gay) could touch these topics. While, surely, I do not share many of the Leavitt's opinions being on the thin boundary of objective reading of Turing's papers and, in some way, biased reading from the position of gay person - I must say it was an interesting account, and in some deeper sense explains Turing's fascinations...

Boulogne-Billancourt, September 15, 2017

Monday, September 11, 2017

My "discovery" of the great XX philosophers...

Of course, the "discovery" here is just a metaphor. I knew about them, but did not yet have time to read their works.
This is now changing ...
Tim Maudlin: https://en.wikipedia.org/wiki/Tim_Maudlin
David Lewis: https://en.wikipedia.org/wiki/David_Lewis_(philosopher)

more to come here about them ... :-)

Mirek@Boulogne-Billancourt

Wednesday, August 30, 2017

On recent folly about (corrupt? fake ridden?) media ...

Let me paste here what I recently wrote to a great friend of mine. We differ on politics, yet we have a great respect to each other...

As for the general outcry against media recently. I find it very bad. See, instead of bashing the media, we must find counterbalancing views and the media that present them. THEY EXIST. For many years we were accepting the diversity of the media and we were selecting those who, in our opinion, represent better what is going on. Today the trend is different - we claim the media is corrupt the media spread fakes. Well they sometimes do. But instead of undermining their right to do so, we try to say they have no right to exist. We must be careful, because that usually helps those who come and try to limit the freedom of the media. I saw it here: for years the right wings here were spreading the news of the media corruption, and now they, in power, practically eliminated the freedom of public media (we still have strong private media, thanks God).

In my opinion, the buildup of distrust against the media is exactly what our common enemy likes the most. You know who I have in mind. So, instead of speaking against the media, find the media that speaks well. It exists.

Mirek - Lodz - Poland August 30, 2017

Wednesday, July 26, 2017

Into the serfdom

Say the word

In a totalitarian state
Freedom
Is not evicted
Abruptly
Overnight
From Tuesday to Wednesday
They will stint it slowly
Take it away piece by piece
(Sometimes giving back a piece
But never more than what was taken away)
Day by day in bits
In quantities imperceptible
Until the one fine day,
After a few or several years
We will wake up into the serfdom
Yet we will not even see it
We will be convinced
That so it should be
That so it always was.
This is my, perhaps poor, translation of the poem written by Polish Poet Kornel Filipowicz.

Saturday, February 18, 2017

Can reason emerge from atoms? Reading DeLanda ...

I have been reading, for some long time, an hour a week or so - extremely interesting book I do not quite accept as expressing the philosophical views I subscribe to ...
Manuel DeLanda, "Philosophy and Simulation. The Emergence of Synthetic Reason"

However, I have no time today to review it and explain it all. The only thing I wanted to say today, is that it is a worth reading, profound piece of philosophical work that tries to prove that all higher level objects of this world are emergent properties of the lower level objects. This smells like reductionism, but, and here comes a surprise - it is really not !

I hope to have time to say more about it soon...

Monday, December 12, 2016

Silence by Thich Nhat Hanh

I'm an admirer and a follower (at least intentionally :-)) of the famous Vietnamese Buddhist mont Thich Nhat Hanh. I have read a number of his amazing books. However, I started reading them in the time I stopped blogging, this is why you did not see any review of his books here.

I hope to have some time soon to review the best of them. Now this post is just a signal that my current morning reading (replacing for a short while when I was in hospital, the book about S. Ulam) is now:

Thich Nhat Hanh - SILENCE. The Power of Quiet in a World Full of Noise.


As all books written by him, this one is very simple, modest and bright explanation why we do need silence. Sounds trivial? Perhaps... But when you start reading Thich's words, you will never think it is trivial or naïve ...

"(...) You don't need a lot of modern gadgets in order to be civilized. You need only a small bell, a quiet space, and your mindful in-breath and out-breath. (...) That is what I call true civilization."

"People usually think that their ancestors have died, but that's not correct. Because we are here, alive, our ancestors continue to be alive in us. (...) They are fully present in every cell of our body. (...) We are a community of cells, and all our ancestors are within us. We can hear their voices; we just need to listen."


I will be coming back to this post again...

Cheers
Mirek

"Hope is the power behind love. When hope fails, so does love" - The Ladder of Divine Ascent

By Pvasiliadis - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=2386101
This was quite unexpected discovery and the following  addition of this masterpiece to my library. I was pointed to it by a friend, when we discussed our recent reads of the spiritual and meditative texts from different traditions. After my recent readings from Buddhist, Chinese and Jewish traditions, this was a very profound "return" to some of my roots that are also very important to me. My grandma was Christian Orthodox. My uncle and aunt contributed greatly to the rebuilding of the orthodox church in the city of Bransk (amazing town in eastern Poland known from Eva's Hoffman "Shtetl"). The link here, leads to text in Polish where they are named. Whenever I listen to an Orthodox polyphony I know this Eastern tradition (along with the Western Christian and Jewish) is not in my mind - but in my bones...

My search into meditation and spirituality started decades ago in the Western Christian tradition (among others it was for my friend and a monk Jan Bereza). Before, still in college times I was reading (not understanding too much though :-), John's of the Cross "Dark Night of the Soul". So with deep reverence I just started to read:

John Climacus - The Ladder of Divine Ascent

John Climacus was 7th century, early Christianity Saint reveread by almost all Christian traditions. He was a monk at Vatos monstery at Mount Sinai. He is said to leave decades in a noble isolation, at the foothill of The Mount Sinai. What attracted me to the book and turn me into its (slow) reading (it will perhaps take a year or more in my style of reading of such books) is the opinion of my friend. She said that the book is not very much "religious". That it is universal and is all about the elevation of one's personality and the path through life ...

However, during the reading I also found some thoughts and directions I would like to stay far from ... You can perhaps find some grains of salt in my comments below...

What is below is the selection of the finest quotes from the book I made over almost one year of reading it. I've been typing them here, so this post was evolving since December 2016. Today, while on business in the US, I have just finished reading it....

A quote from the Intro:

"Stillness (besychia) is worshipping God unceasingly and waiting on Him. Let the remembrance of Jesus be present with your every breath. Then indeed you will appreciate the value of stillness"

and another:

"Prayer is the expulsion of thoughts" (ascribed to Evagrius)



(re) starting my reading of this book...

Finally, after some long time (4 months) I'm returning to this book... I finished lengthy intro by bishop Kallistos (which was very good I must say) and started the Ladder itself. And here, I must say a strange surprise... in the third step ("On Exile") I found these words:
"If you long for God, you drive out your love for family." and then quite lengthy explanation why ... which is really strange... And the warning that if you "(...) let the tears of parents or friends fill you with pity (...) you find yourself weeping forever in the afterlife"

This strange. I do want to comment on that yet, will continue reading and thinking ...


"Humility arises out of obedience, and from humility itself comes dispassion, for 'the Lord remembered us in our humility and saved us from our enemies' (Ps. 135:23-24). So we can rightly say that from obedience comes dispassion, through which the goal of humility is attained. Humility is the beginning of dispassion, as Moses is the beginning of the Law, as the daughter is completes the mother and Mary completes the synagogues"


"War against us is proof that we are making the war"



"All he would say was this: 'Please forgive me. No one who has acquired the remembrance of death will ever be able to sin". (...)

Do not search about for the words to show people you love them. Instead ask God to show them your love without you having to talk about it.(...)

Do not deceive yourself, foolish worker, into thinking that one time can make up for another. The day is not long enough to allow you to repay in full its debt to the Lord.



"The first step toward freedom from anger is to keep the lips silent when the heart is stirred; the next, to keep thoughts silent, when the soul is upset; the last, to be totally calm when unclean winds are blowing.

Anger is an indication of concealed hatred, of grievance nursed"

"And this is how anger replies: «I come from many sources and I have more than one father. My mothers are Vainglory, Avarice, Greed. And Lust too. My father is named Conceit. My daughters have the names Remembrance of Wrongs, Hate, Hostility, and Self-justification»"


"Malice is an exponent of Scripture which twists the words of the Spirit to suit itself."



"Talkativeness is the throne of vainglory on which it loves to preen itself and show off.
Talkativeness is a sign of ignorance, a doorway to slander, a leader of jesting, a servant of lies, the ruin of compunction, a summoner of despondency, a messenger of sleep, a dissipation of recollection, the end of vigilance, the cooling of zeal, the darkening of prayer."

"It is hard to keep water in without a dike. But it is harder still to hold in one's tongue."



"Hypocrisy is the mother of lying and frequently its cause. Some would argue that hypocrisy is nothing other than a meditation on falsehood, that it is the inventor of falsehood laced with lies"




Today, I was reading "Step 15" - "On Chastity" and I must say that this is the part of the whole Christian teaching where I start to be its critic, where I start to think that it made a great harm to us. Read this:

"To be chaste is to put on the nature of an incorporeal being. Chastity is a supernatural denial of what one is by nature so that a mortal and corruptible body is competing in a truly marvelous way with incorporeal spirits. A chaste man is someone who has driven out bodily love by means of divine love, who has used heavenly fire to quench the fires of the flesh" (...) "The rule and limit of absolute chastity is to have the same feelings regarding animate and inanimate beings, rational and irrational" (...) "Truly blessed is the man totally unstirred by anybody, any color or any beauty."


Why I'm so enraged by such words? See, we are all on this earth because of love, the physical love that follows the spiritual love. The love finds the best friend in our bodies. The sexual feelings, sitting on the opposite side of chastity are sacred. That is what Bible has taught us through "Song of Songs". That is what is the very essence of our own personal experiences when we truly loved - in both spiritual, higher sense and in "bodily desires" to be with the person we loved, to know her (him). I think that the whole "school of thought" that tries to say that the corporal feelings, the sexual desires, and the physical love are bad - is just sick and harmful. Sure, there is a space between the "sacred and holy" sex and the debauchery and laxity. But to teach good is not to deny the desires, is to show from where they come: from God !!! Why Christianity has not done it well??? 



"When you hear that your neighbor or your friend has denounced you behind your back or indeed in your presence, show him love and try to compliment him. (...)  It is not self-critical who reveals his humility (for does not everyone have somehow to put up with himself?). Rather it is the man who continues to love the person who has criticized him." - The great passage from 'On vainglory' chapter - the 22nd step of the ladder...



" (...) it is sheer lunacy to imagine that one has deserved the gifts of God. You may be proud only of the achievements you had before the time of your birth."

"On Pride" - the 23nd step of the ladder...


"The light of dawn comes before the sun, and meekness is the precursor of all humility."

"Meekness is a mind consistent amid honor or dishonor. Meekness prays quitely and sincerely for a neighbor however troublesome he may be"
"The souls of meek shall be filled with wisdom, but the engry mind will cohabit with darkness and ignorance".

"Evil is deliberate kind of knowledge. Or, rather, it is a deformity of the devil.(...)
Hypocrisy is soul and body in a state of opposition to each other, intertwined with every kind of invention."

"On Meekness, Simplicity, Guilelessness and wickedness" - the 24nd step of the ladder...




"Humility is constant forgetfulness of one's achievements. (..) It is to forestall one's neighbor at a contentious moment and to be first to end a quarrel. (...) It is the disposition of a contrite soul and the abdication of one's own will."

"The sun lights up everything visible. Humility reaches across everything done according to reason. Where there is no light, all is in darkness. Where there is no humility, all is rotten."


"The man who has come to know himself with the full awareness of his soul has sown in good ground. However, anyone who has not sown in this way cannot expect humility to flower within him."


"On Humility" - the 25th step of the ladder...
Not very often in this, otherwise great book, you can find words that puts you off... This is sad remainder that Christian tradition has some darker sides... See this:

"A - obedience, B - fasting (...)  Φ - unhating rejection of parents (...)"

This is strange and something I hardly understand or find acceptable...

"On Discernment" - the 26th step of the ladder...

"This is why a wise man once said: 'You shall obtain a sense of what is divine'"
"On Discernment" - the 26th step of the ladder...

Here a comment from myself: The Bible, through the "Song over Songs" gave us the sense of what is divine... Why Christianity seems to forget that teaching .... ?

"Let us seek to discover the things of heaven through the sweat of our efforts, rather than by mere talk, for at the hour of death it is deeds, not words, that must be displayed."

"On Discernment" - the 26th step of the ladder...

"Keeping guard over one's thoughts is one thing: watching over one's mind another. Distant from each other as the east from the west, the latter is more significant and more laborious than the former."

"On Discernment" - the 26th step of the ladder...

"Eyes show different colors and the sun of the spirit may shine in different ways in the sould. There is the way of bodily tears and there is the way of tears of the soul. There is the way of contemplation of what is before us and the way of the contemplation of what remains unseen. There is the way of contemplation of what is before us and the way of the contemplation of what remains unseen. There is the way of things heard at second hand and the way of spontaneous joy within the soul. There is the way of stillness and the way of obedience. And in addition to these there is the way of rapture, the way of the mind mysteriously and marvelously carried into the light of Christ."

"On Discernment" - the 26th step of the ladder...

"It is impossible to destroy wild beasts without arms. It is impossible to achieve freedom from anger without humility."

"A Brief Summary ..."

" 'God is love' (1 John 4:16). But someone eager to define this is blindly striving to measure the sand in the ocean."
"Hope is the power behind love. Hope is what causes us to look forward to the reward of love. Hope is an abundance of hidden treasure. (...) When hope fails, so does love."

"On faith, hope, and love" - the 30th step of the ladder...



Mirek@Gainesville, last update November 16th, 2017

Tuesday, November 22, 2016

Let's befriend a ... tree ...

I did not expect this book will change so much in my attitude to nature... "The Hidden Life of Trees: What They Feel, How They Communicate—Discoveries from A Secret World" by Peter Wohlleben. (See GoodReads entry) Passionate, scientific, non-fictional - don't know how to label it :-), yet it really changed the way I thought about nature.

There was perhaps something inside me when I was sick seeing a tree cut without a reason or the large parts of forests in North Poland "cultivated" as the lumber industry calls it. Don't take me wrong, I'm not in the camp of people who protest the lumber industry. Not at all. But I saw so many examples of a very bad way the forests were managed... We heard the stories of officials (here in Poland) trying to kill the last pristine forest we have: Puszcza Białowieska...

The book will tell you more about that. I read it audio. Great voice of Mike Grady.

This seems to be my real return to blogging about books. Even short notes are better than nothing.
However, the post like the three earlier, are from my early morning reading of mostly physical books, so they are a bit different in character and the way I write ...

Cheers
Mirek@Lodz

Sunday, November 20, 2016

Stanislaw Ulam - Life & Legacy

I was able to buy a true rarity (through SealsThings via Amazon): the antiquarian volume of "From Cardinals to Chaos. Reflections on the Life and Legacy of Stanislaw Ulam" edited by Necia Grant Cooper and published in 1989 by Cambridge University Press.

While not a very old print, it is generally hard to get.

For long time I was in admiration to Stan Ulam. That dates to my Master Thesis in which I used Monte Carlo simulations, pioneered by Stan. The book gives me a possibility to know about him much more.

Stanislaw Ulam was Polish-American scientist. Educated as mathematician in the pre-war Poland, he worked on Manhattan project and invented many techniques for computer simulations and contributed greatly to both pure and applied mathematics.

In time, this post will perhaps tell you more about him ...

BTW, one, perhaps funny reason I like Stan is for ... his first name! My beloved grandfather was also bearing proud Stanislaw name and my mother is Stanislawa :-)

The book starts with amazing account on Stan by his wife Francoise Ulam. She outlived Stan by 27 years and helped to compose this amazing edition....

"He was a loner, a maverick, a very complicated man, a Pole, and, above all, a study in contrasts and contradictions, which often aroused mixed and conflicting emotions in people. He moved only to the beat of his own drum and never kow-towed to anyone or stopped to promote himself."

FROM STAN'S AUTOBIOGRAPHY

"Banach once told me, 'Good mathematicians see analogies between theorems or theories, the very best ones see analogies between analogies' "

"Contrary to those people who were violently against the bomb on political, moral or sociological grounds, I never had any question about doing purely theoretical work... I felt that one should not initiate projects leading to possibly horrible ends. But once such possibilities exist, is it not better to examine whether or not they are real? An even greater conceit is to assume that if you yourself won't work on it, it can't be done at all. (...) Sooner or later the Russians or others would investigate and build them."

MATHEMATICS AND REALITY

"Of all escapes from reality, mathematic is the most successful ever. It is a fantasy that becomes all the more addictive because it works back to improve the same reality we are trying to evade. All other escapes - love, drugs, hobbies, whatever - are ephemeral by comparison."
(The Lost Cafe, Gian-Carlo Rota)


" ... I always had confidence that if Stan had a feeling for something, it was sure to be significant."Francis H. Harlow



PROBABILITY

I was surprised, down the book, how deep it would go into science!
The chapter "Probability and Nonlinear Systems" reviews the traditional and modern approaches to the probability theory. I deeply enjoyed the description of Bertand's Paradox - an amazing example how deceptive and unclear was traditional probability theory. Seems to me I did not have it mentioned in my probability theory course during my studies !
This paradox reveals that computing a probability using standard definition can deliver much different results for a simple system that obviously should just result in one! Namely, depending on a way we define the set of ALL possibilities, we get 1/4, 1/3 or 1/2 as the probability. Read about it here, a nice demonstration done using Wolfram's Mathematica is here.


THE LUCKY NUMBERS

Stan Ulam was also unquestionable founder of the school of number theory at Los Alamos. Daniel Shanks (about Daniel) named the effort in a nice way: "Los Alamos School of Experimental Number Theory". One of Stan's achievements was the invention (with Gardiner, Lazarus and Metropolis) of LUCKY NUMBERS (the definition here and the sequence here at OEIS). The sequence reads:
1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, 105, 111, 115 (...)
Very nice (awaiting my next "lucky" birthday at 63 :-))

CONJECTURES ABOUT MENTAL PROCESSES

Stan was truly "a renaissance man". In addition to the vast areas of mathematics and physics he covered in his studies he made multiple forays into biology and what we could call today cognitive sciences. In "A Gamow Memorial Lecture" he delivered at the University of Colorado Boulder on October 5, 1982 he made many interesting conjectures about some important mental mechanisms. For example, he speculated about the visual perception, or to be more precise the pattern recognition. The fundamental question is how we recognise handwritten letters, while they differ so dramatically in the two texts written by any two people?
Does the brain store many variants of the letters or some abstract pattern?
Stan conjectures about the third possibility: real-time deformation creation and fast comparison between what we see and what we have in memory:


However, he was fully aware of the speculative character of such conjectures, and when trying to explain why we can not expect that computations would lead to model the brain, he points (as I and many other do) to Gödel theorem:



Amazing !
(Almost) ALL ULAMS PAPERS

I have bought an antiquarian marvel. The 1974 collection of Stanislaw Ulam selected papers: "Sets, Numbers, and Universes" published by MIT Press:


In this book I found amazing sketch of Stan made by famous Polish painter Zygmunt Menkes:


 Can't wait till have time to read Stan's papers !

ENCYCLOPEDIA BRITTANICA ENTRY

http://www.britannica.com/biography/Stanislaw-Marcin-Ulam

CELLULAR AUTOMATA & BIOLOGY

The concept of Cellular Automata was discovered by Stan Ulam and David Newman in 1940s while they both worked at Los Alamos National Laboratory. In the book I review here there is an amazing article (by Brosl Hasslacher) on the applications of Ulam and Newman ideas for fluid dynamics. It shows how the model offered by the cellular automata can lead to Navier-Stokes equations for fluids and their dynamics!

See: "On recursively defined geometrical objects and patterns of growth" R.G. Schrandt & S.M. Ulam (Los Alamos Scientific Laboratory report LA-3762) (Essays on Cellular Automata, ed. A.W. Burks, Urbana, University of Illinois Press,1970)

DNA SEQEUNCING

The key tool in DNA sequence analysis that has been central to genetic science is the ability to measure a distance between DNA sequences. It is not very well remembered but this is one of the greatest of Stan's achievements. In 1972 he proposed how to define a usable metric space of the DNA sequences ("Some ideas and prospects in biomathematics", Annual Review of Biophysics and Bioengineering 1:277-291). The definition enabled sequence comparison and it was one of the most important intellectual achievements of seventies that later led to modern genetics and finally to the Human Genome Project. Stan, speaking of the sequence analysis, with the typical proud wit, once said: "I started all this" :-) (After Walter B. Goad article in the book).


MONTE-CARLO METHOD NAME

To my great amusement I read in Nick's Metropolis account that it was him & Stan who coined the name for one of the most important name in Statistical Physics: MONTE CARLO:

"It was at that time that I suggested an obvious name for the statistical method - a suggestion not unrelated to the fact that Stan had an uncle who would borrow money from relatives because he "just had to go to Monte Carlo"
:-)

BTW, my Masters' thesis was written on a base of my Monte Carlo simulations. I must admit that at that time (30+ years ago), I did not know much about Stan. For some reason he was missing on the author's list of the key paper on that topic: http://bayes.wustl.edu/Manual/EquationOfState.pdf  which was read by, us (by then physicists) while missing the real key (and also earlier) work: http://homepages.rpi.edu/~angel/MULTISCALE/metropolis_Ulam_1949.pdf read usually by statisticians and mathematicians:


NONLINEAR SCIENCE

What is not widely known about Stan's Ulam contributions to science is his contribution to the science of nonlinear processes. Together with Enrico Fermi and John Pasta he created a model system named as "FPU problem" for the authors names.  BTW, we call it today "FPUT Problem", thanks to T. Dauxios ("Fermi, Pasta, Ulam, and a mysterious lady". Physics Today 6, 2008). Earlier, in 1953, they initiated a series of computer simulations exploring how simple, multi-degree nonlinear mechanical systems obeying reversible deterministic dynamics evolve in time.

However, what was great about Ulam's contribution to the field of research was ... his wit in naming it. He once remarked on its naming (non-linear science) saying that it is like "defining the bulk of zoology by calling it the study of 'non-elephant animals'" :-) Using this funny expression he simply stressed that both in mathematics and nature the nonlinear processes prevail!
More telling, in this context, is the another Stan's bon mot:

"Ask not what mathematics can do for biology, Ask what biology can do for mathematics"

See also what David K. Campbell (Boston University) said in his Lilienfeld Prize Lecture :

"FPU was a watershed problem: marked birth of nonlinear science (and computational physics/ ”experimental mathematics”) with its paradigms of  chaos, solitons, and patterns, and produced many specific insights into physical phenomena including ILMs, anomalous heat transport, and a deeper understanding of statistical mechanics. The FPU problem was, as Fermi remarked, quite a “little discovery.”

He also wrote:

"In all these respects, non-linear science represents a singularly appropriate intellectual legacy for Stan Ulam: broadly interdisciplinary, intellectually unfettered and demanding, and - very importantly - fun" :-)



All that goes even deeper. In the next article of the book ("The Ergodic Hypothesis"), Adrian Patrascioiu considers how the solution of the FPUT (Fermi, Pasta, Ulam and Tsingou) problem can be linked to Quantum Mechanics:


"So perhaps quantum mechanics is nothing more than classical statistical mechanics done the right way in a universe filled with particles interacting primarily via electromagnetic and gravitational forces."




ON QUANTUM MECHANICS

I must say that Ulam had an incredibly deep understanding of Quantum Mechanics. In his discussions with Gian-Carlo Rota (Italian mathematician and philosopher) he once said:

"Quantum mechanics uses variables of higher type. Instead of idealized points, or groups of points or little spheres or atoms or bodies, the primitive notion is a probability measure. Quite a logical leap from the classical point of view. Nevertheless you find in quantum mechanics the strange phenomenon that a theory dealing with variables of higher type has to be imaged on variables of lower type. It is the complementarity between electron and wave."

The notion of the variables of higher type, particularly in the probability context, where we speak about probability AMPLITUDES instead of themselves, is indeed very important and, for many, the hardest to grasp...


FRIENDS

Stanislaw Ulam had many friends. Let me name only two great minds I was not very much aware before reading this book. The first is Paul Erdős, genial Hungarian mathematician (https://en.wikipedia.org/wiki/Paul_Erd%C5%91s). Ulam and Erdős exchanged about 200 letters on science... It is a demonic paradox that Paul died in Warsaw in 1996 at the mathematical congress. In the country of Ulam's childhood...

The second was aforementioned  Gian-Carlo Rota (Italian mathematician and philosopher - https://en.wikipedia.org/wiki/Gian-Carlo_Rota).

The notes left in Ulam files, discovered after he passed away, revealed a deep level of friendship, respect, good humor and focus on deep problems of science...

What was specially pleasent to me was the discovery that so many of these dialogs happened in ... Gainesville Florida - my adopted "home town" in the US....


LAY TO REST ...

Both Françoise and her husband are buried with her French family in Montparnasse Cemetery in Paris.

http://www.legacy.com/obituaries/santafenewmexican/obituary.aspx?n=francoise-ulam&pid=150769924
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=7205311
https://en.wikipedia.org/wiki/Gian-Carlo_Rota



(Some extra links: Borsuk-Ulam theorem: https://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam_theorem 
Ulam's Cardinals: https://en.wikipedia.org/wiki/Measurable_cardinal
with Everett on Projective Algebra: https://doi.org/10.2307/2266746)


The post finished on June 25th in Lodz, Poland