Idiosyncrasies of Some Great Scientists

Tahmad sahib,

(then there was Philosopher Nasah who was so absent minded that after coming home on a rainy day, he put his umbrella in his bed, and himself went to the umbrella stand and stood there all night. (this one is a joke).)

You will not believe this but this is apparently true. A 19th century Bengali scholar and social reformer, Iswarchandra Vidyasagar achieved such a feat. However it was not a rainy day but a night.

freethinker: life may be short, but it is not short enough not provide time to read the Scientific American. Subscribe to it, and you will become addicted to it. Guaranteed.

Alephnull:
Thanks for the books that you suggested. I`ll take time to pick and choose but now I know which ones to consider when I am choosing. My interests are very diversified.
I wish I knew more of everything. But one`s life is too short. Thanks for your input.
Mohammad Gill

freethinker #35, #38:

Almost anything by Douglas Hofstadter is worth reading – even his translation of ‘Eugene Onegin’. As far as Godel, Turing and company are concerned, an alternative for intelligent laymen is Martin Davis’ recent The Universal Computer. It traces the development of ideas of mathematical logic and computability from Leibniz through Boole, Frege, Cantor, Russell, Hilbert, Godel, and Turing. It has plenty of discussion of the mathematical ideas interspersed with historical and biographical material. Davis doesn’t display Hofstadter’s breadth of interests or his intellectual versatility, and his book had far fewer beautiful pictures than GEB. On the other hand, it’s a good deal shorter … Davis has also edited a collection of the seminal papers of Godel, Turing, Church, Post, etc, called The Undecidable – in case you’d like to have a single source where you can read them all.

Another well-known (and short) exposition of Godel’s best-known work is Nagel and Newman’s Godel’s Proof. The well-known mathematical logician Raymond Smullyan (another extremely interesting character in his own right) has written several books of logic puzzles that develop and explore the ideas that make the proof work.

For a fictionalised account (but based on real incidents and personalities) of Godel and his peers at Princeton, see John Casti’s The One True Platonic Heaven. Again a very compact book – about the same length as Hardy’s A Mathematician’s Apology. There are many other books at various levels for people who’re interested …

And re #17: really, you didn’t have to apologise. I’m not the sort to take offence, least of all at you.

swarrier:

I borrowed ``Godel, Escher, Bach: An Eternal Golden Braid`` today from a local library. I haven`t started reading it seriously but I skimmed through it. It also describes Ramanujan and his work. One of the anecdotes about Ramanujan that I had read in Hardy`s book is also described in it. I would like to share it with the readers here.

Hardy wrote,: I remember once going to see him when he (Ramanujan) was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to me rather dull one, and that I hoped it was not sn unfavourable omen. ``No,`` he replied, ``it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways.`` I asked him, naturally, whether he knew the answer to the corresponding problem for fourth powers; and he replied, after a moment`s thought, that he could see no obvious example, and thought that the first such numbers must be very large.

It turns out that the answer for fourth powers is:
635318657 = 134^4 + 133^4 = 158^4 + 59^4

The answer to the cubes is:

1729 = 9^3 + 10^3 = 1^3 + 12^3

Mohammad Gill

Re: # 38
Dr. Gill
I had forgotten that chapter on Ramanujan. I last read GEB in 1989 so it`s been some time. Digressing a bit from idiosyncracies and physics and mathematics , I have really liked books by Richard Dawkins, ``The selfish gene``, ``The blind watchmaker``, and more recently ``The Ancestors tale``. Morphogenetics by Rupert Sheldrake was interesting, though, scientifically a little iffy.

Another excellent writer on medicine is Dr. Roger Sachs. His book on Migraine and ``The man who mistook his wife for a hat`` (on memory and Alzheimers etc) are worth perusing.

Another intersting writer is Daniel Denett who teaches philosophy close by at Tufts University. He co-authored a book with Hofstadter called ``The Mind`s I``. I have a copy of that but I preferred Hofstadters other books. Maybe I was not quite ready for this one.

Alephnull:
It was reading Raymond Smullyan`s ``The Lady or the Tiger and other puzzles`` that led me to Hofstadter. Another book I have really liked is, ``How to Solve it`` by George Polya. You will have read that. In another couple of years I will get my son to try to read ``One two three infinity`` by George Gamow.

re:#31 by freethinker
I think Hollywood is making a movie on Ramanujam.
Sridhar

swarrier:

I have read Hodges book but not the other two. I have read another biography of Ramanujan. I first learned of Ramanujan in 1969. I was checking out a paper on ``Perturbation`` theory in a mathematical journal and the author quoted Ramanujan. My curiosity immediately led me to Hardy`s book on Ramanujan.

Incidentally, Einstein had many flings outside his marriage. I had written about it in my article ``Einstein`s Love Life`` at Chowk.com on July 20, 2005. Church Turing Tarski thesis to which you have alluded seems interesting. I`ll see if I can procure the book.

Mohammad Gill

Re: # 35

If you get the first book by Hofstadter I would also suggest Metamagical Themas. It has some interesting observations on infinity within bounded sets.

In the 1920`s both the universities in Gottingen and Cambridge (U.K.) did much seminal work in physics and mathematics. I think it was in ``Brighter than a thousand suns`` that Robert Jungk talks about a young student in Gottingen who while cycling through the streets, erratically, fell off his bike and lay on the road. When passer-by`s rushed to his aid , he furiously brushed them off snarling,`` Don`t disturb me, can`t you see I`m thinking``.

Apparently the cafes in Gottingen had standing orders not to remove tablecloths because students and professors would come in and start solving problems sometimes using the table cloths for their calculations. They would be forced to leave when the cafes closed and would come back the next day to finish their problems, and were very unhappy if the tablecloths had been taken away to be washed.

swarrier:

When you talk about Hardy, it is inevitable not to think of Ramanujan also. Ramanujan was an associate of Hardy at Cambridge.

According to Jonathan Borwein and Peter Borwein, Ramaswami Aiyar, the founder of the Indian Mathematical Society, encouraged Ramanujan to ``communicate his results to three prominent British mathematicians. Two apparently did not respond; the one who did was G.H.Hardy of Cambridge, now regarded as the foremost British mathematician of the period.

Hardy, accustomed to receivibg crank mail, was inclined to disregard Ramanujan`s letter at first glance the day it arrived, January 16, 1913. But after dinner that night Hardy and a close colleague, John E. Littlewood, sat down to puzzle through a list of 120 formulas and theorems Ramanujan had appended to his letter. Some hours later they had reached a verdict: they were seeing the work of a genius and not a crackpot. (According to his own pure-talent scale of mathematicians, Hardy was later to rate Ramanujan a 100, Littlewood a 30 and himself a 25. The German mathematician David Hilbert, the most influential figure of the time, merited only an 80.).``

Hardy also wrote, ``The real crises of my career came ten or twelve years later, in 1911, when I began my collaboration with Littlewood, and in 1913, when I discovered Ramanujan. All my best work since then has been bound up with theirs, and it is obvious that my association with them was the decisive event of my life. I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, ``Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.``

Ramanujan was made a Fellow of Royal Society of London and a Fellow of Trinity College in 1917 - the first Indian to be aarded either honor.

Mohammad Gill

Re: # 31
Dr. Gill
We were introduced to Ramanujam in school funnily enough through our English textbooks initially. Then again it is difficult to be a South Indian and not have, Ramanujam, Sir C V Raman, Chandrashekhar Subramanyam etc drilled into one`s head.

Have you read ``The Man who knew infinity`` , the biography of Ramanujan by Robert Kanigel? I heard they are thinking of making a movie on it. It`s an interesting book.

Incidentally there is a very good biography of Alan Turing by Andrew Hodges. It`s a sympathetic potrayal of a enigmatic man.

An interesting discussion on the Church Turing Tarski thesis is present in ``Godel Escher Bach: An Eternal Golden Braid`` by Douglas Hofstadter.

I must thank you for writing this article.

Re: # 31
Great scientists were not always angels and could be terrible characters troo.
Newton was very jealous and very suspicious of others and hpossessed very nasty temper.
Roberst Hook was his equal in his nastiness.
One of the inventors either Shockley or Bardeen was a pukkah racist and published articles stating that blacks were inferrior.
Einstein used to visit smelliest prostitutes in Berlin and used to have sex with women visitors when his wife was working in the kitchen. Actually she died heart broken. He is now no more an icon these days because of this his personal characteristics!
Heisburg was pretty anti-semetic.
But they were all brilliant!

Re: # 32

It was Shockley who was the racist and supported eugenics.

I`m not sure about what you say about Einstein is true. Recently there was a program on PBS called Einstein`s wife (his first wife Mileva Maric) where there were claims that she helped him in his initial papers. However that, in the opinion of a lot of scientists is junk, just wishful theorizing. While it is true that Einstein was a bit vain and liked to be photographed , he may not have been that promiscuous.

However as somebody said , ``Behind every genius lies a flawed human being``.

The British Mathematician G H Hardy claimed all his life not to believe in God, but he spent a lot of time worrying about it.

The anecdote is related by C.P. Snow in his introduction to A Mathematician`s Apology. It is a pleasant May evening some time in the 1930`s and Hardy is in his fifties. He and Snow are walking at Fenner`s cricket ground when the 6 o`clock chimes ring out from the nearby Catholic chapel. ``It is rather unfortunate``, Hardy remarks, ``that some of the happiest hours of my life should have been spent within sound of a Roman Catholic church`

He was also eccentric enough to encompass the God he never believed in. He was also a great cricket fan and loved to watch cricket and hated it to rain during a cricket match . Again from C. P. Snow.

When summer came, it was taken for granted that we should meet at the cricket ground,`` C.P. Snow once recalled. ``[G. H. Hardy] made for his favourite place, opposite the pavilion, where he could catch each ray of sun - he was obsessively heliotropic. In order to deceive the sun into shining, he brought with him, even on a fine May afternoon, what he called his `anti-God battery`. This consisted of three or four sweaters, an umbrella belonging to his sister, and a large envelope containing mathematical manuscripts, such as a Ph.d. dissertation, a paper which he was refereeing for the Royal Society, or some tripos answers. He would explain to an acquaintance that God, believing that Hardy expected the weather to change and give him a chance to work, counter-suggestibly arranged that the sky should remain cloudless, and then he (Hardy) would be able to enjoy the cricket in perfect sunshine.``

This bit from the Andrews Univerity web site.

He also hated being photographed, and hated mirrors so much that he would cover any mirror in a hotel room he entered, with a towel. Another example of him trying to fool God was when on a trip back from Denmark he sent back a telegram claiming he had proved the Reimann hypothesis. He reasoned that God would not allow the boat to sink on the return journey and give him the same fame that Fermat had achieved with his ``last theorem``.

GT #24 Thanks for taking the time to explain, which you have done quite clearly and I get the general idea as a result.

Agreed Outcome 2 in particular is interesting I think since requires both parties to agree on what is fair. Seems to me the popular book ``Getting to Say Yes`` (i.e. the art of negotiating) is on the same lines (and is perhaps inspired by Nash`s work). Thus, that book provides some good pointers towards reaching agreement on any issue - most notable is the pointer that one should separate the respective bargaining positions from the underlying interests . This I think is a good approach to resolving any dispute - namely, for both parties to focus on their own as well as the other parties underlying interest, rather than digging their heels in on the particular position they took at the start of the bargaining session and rejecting solutions that may meet their underlying interests in an equal or even better manner.

I am not sure how much all this is along the lines of Nash`s Bargaining Solution though, although the book seems to be using Agreed Outcome 2 as the take-off point.

Re: # 27 by tahmed

You are perhaps right. However, there are several `hidden assumptions` in Nash`s construct. For starters, imagine you have to divide three cars of the same make between two identical persons. How will you get symmetry (fairness)?

Dr. Gill, sorry for deviating from the topic. Am off for a week:)