Wednesday, October 28, 2020

Lectures on Polyhedral Topology by J.R. Stallings

 “Lectures on Polyhedral Topology” by J.R. Stallings, of his lectures in TIFR 1967, is available online. It also has bits of my first research. I think that the appendix to Chapter seven is mine. And 8.9.3, the proof of s-cobordism with prescribed torsion is mine. I did not understand Stallings proof which used Stiefel-Whitney classes which I was not comfortable with at that time. I came up with the argument given here which is now standard, I think.

https://www.maths.ed.ac.uk/~v1ranick/papers/stallpl.pdf


Monday, October 26, 2020

Peter Scott

 My friend Peter Scott does not seem to be feeling too well. He had prostrate cancer for a long time and there was a relapse two years ago. Since then, he has been to the hospital off and on, recently to ER for a day. We first met in Liverpool in 1968. Later we corresponded in 1972, he was still in Liverpool and I in Bombay. Some of the resulting work by him was noticed widely and we lost touch, but he seemed to be keeping track of my work and sometimes referred to my work even when it did not seem necessary. Then around 1984, he was one of the organisers of a conference in Warwick. He told me that the conference was organised to understand some of Thurston’s work and I should attend and talk to others since it is difficult to understand it alone. I did attend and it helped. He seems to have decided to resurrect my career since he might have seen some promise in the early days of our contact. We met again in Stillwater in 1986 and he came up with two problems for us to work on, we ended up doing both, one each by correspondence. Then he visited a Melbourne in 1994 and again decided to work with me on some problems of common interest. I was aware of the first one but had no idea how to start. He gave me a paper of Tukia and said what all I had to do was to read about five pages there for the clues. This turned out to be the torus theorem that was completed by others later on. It also started a period of intense collaboration which is still going on. It is probably the hardest work that either of us was ever engaged in and slowly clarified several related problems that interested us. Like many of these things, this kind of difficult technical work may not interest others but was very satisfactory for us. The final clarifications came only this year. Meanwhile we found that we made some mistakes in the early days and since some of this material entered mainstream, it seemed a good idea to publish corrections. But corrections and extensions became another long and difficult affair and seems to be reaching completion now. This will be some thing which nobody may read but compelling to us. Meanwhile Peter keeps chiselling away whenever he is well.

Sunday, September 20, 2020

Long term studies of childhood and later development

The lifelong studies that hold clues to what today’s kids might have in store Book Review of 
The Origins of You: How Childhood Shapes Later LifeJay Belsky, Avshalom Caspi, Terrie E. Moffitt & Richie Poulton Harvard Univ. Press (2020)

Monday, September 14, 2020

Frederick Soddy's economics

It seems that the Nobelm Prize winner in chemistry has written extensively on economics, in particular debt before Michael Hudson.
Frederick Soddy's Debt Economics
Another post in Illogical Economics with some links.
Michael Hudson:"Frederick Soddy pointed this out in the 1920s, describing financial claims as “virtual wealth,” on the opposite side of the balance sheet from tangible capital formation. Adam Smith had argued that money is not real wealth. Bank loans, stocks and bonds are financial claims on wealth. 
The essence of balance-sheet accounting is that assets on the left side equal liabilities on the right-hand side, plus net worth (assets free of debt). It would be double-counting to add an economy’s physical means of production (the asset side of the balance sheet) together with the debt and property claims on these assets (on the liabilities side). Yet most public discourse focuses more on asset prices than on the even faster growth of debt.
Soddy was awarded a Nobel Prize in 1921, showing that good economists sometimes do win – except that he won for his contribution to chemistry, not economics. In an analogy to Ptolemaic astronomy, today’s academic gatekeepers depict an economic system shaped by consumer choice rather than revolving around finance." from https://www.prosper.org.au/2010/05/the-counter-enlightenment/