My father, near the end of his life, considered himself the last Gestalt Psychologist. When I was very young I was fearful of kelp seaweed: my father showed me that it couldn’t hurt me, so I shouldn’t be afraid of it. I learned from him. If you understand something, you can reason about it. If you only have a correlation, you can’t be sure of the factors. He was never afraid to question conventional wisdom or the current fashionable and entrenched ideas (however old or fast those ideas were).
As a clinical school psychologist he was on the front line against invasion of chemical psychiatry into K-12 schools, and he saw how they used “their pseudo-scientific expertise [and argot]” to fool and trap kids and parents into approving the use of brain disabling drugs, within the “educational system” and with the implicit pressure and blessing (and relieving of responsibility) of the teachers and administrators. He also didn’t buy into the dominant paradigms of the first half of 20th century of Freudian psychology and the correlational “blank slate” behaviorism of Watson and Skinner.
“If you don’t understand something said, don’t assume you are at fault.” — David West Keirsey
Throughout my discussions and debates with him in my lifetime, he talked about ideas. We talked about philosophy, science, mathematics, computers, people, and life.
New scientific ideas never spring from a communal body, however organized,
but rather from the head of an individually inspired researcher
who struggles with his problems in lonely thought and unites all his thought
on one single point which is his whole world for the moment.
— Max Planck
… there is something strange going on with Primes
— Paul Erdös
Never mind the mock theta, Ramanujan’s gap, Namagiri dreams.
When Srinivasa Ramanujan wrote to G. H. Hardy in the 16th of January 1913, he had some remarkableformulas in that letter. So remarkable are some of his formulas that mathematicians have been studying Ramanujan’s notebooks of formulas for new mathematical insights to this day, more than a hundred years later.
I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras… I have no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics. I have not trodden through the conventional regular course which is followed in a University course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as “startling”.
Hardy invited him to England because some of the formulas “had to be true, because no one could have the imagination to make them up”. But there were no proofs. However, when this poor vegetarian Indian Hindu came to England, eventually Hardy showed Ramanujan (thru Littlewood) that his formula on Primes was not EXACTLY correct. So Ramanujan had to bend to Hardy and work on his proofs of some of his formulas, so when they tackled the function of Partitions P(n), Ramanujan with the help of Hardy got to point where they “cracked” Partitions (and could prove it). They developed a direct formula that computed the number of partitions pretty accurately, and at the limit (infinity) it was “perfect” — and, could by truncating the number for high partition number to an integer could guarantee to be exact: since the number of partitions of integers is an whole number (i.e., the real number series “formula” converges with an deceasing error rate). Together they “cracked” the problem where neither man could do it alone. Ramanujan supplied the “intuition” (the finding of the hidden pattern) and Hardy provided the rigor to explain why the pattern is true. The method they created, in this instance, was called the “circle method” — and it has been used ever since by numerous mathematicians for various other results.