Chistopher Columbus

Christopher Columbus

October 9, 2023
Remembering and honoring the great explorer...

Happy Columbus Day!

Stanislaw Ulam

Thoughts on the AP Calculus Exam

Without the invention of the infinitesimal calculus, most of our technology would have been impossible. Should we therefore say that calculus is bad?
-- Stanisław Ulam

Max Born

Einstein, Born, and Inflation

Inflation is taxation without representation.
-- Milton Friedman

Lev Landau

Lev Landau and Math Education

In nature's infinite book of secrecy
A little I can read.

-- Shakespeare

Blue Ribbon

TJHS, Satellites, and the Asian Quota

Superior quality or worth; excellence.
A quality deserving praise or approval; virtue.


Thanksgiving 2020

Happy Thanksgiving!

Fourth of July

The Day Before

Fourth of July
Happy 4th of July!
Merry Christmas

Merry Christmas!

John C Reynolds
John C Reynolds

Contravariance and Covariance

The ideas of contravariance, and covariance, long of great utility in physics, were introduced into C# beginning with .Net Framework 3.5... At first glance there seems to be no relation between the physics and computer science usages...It might therefore be of interest to show the history of these ideas and how they found their way into the theory of computer languages...
Charles Townes

Charles Townes

The great Charles Townes (7/28/1915 - 1/27/2015) inventor of the maser/laser, celebrates a birthday this week.


Pyotr Ufimtsev

When I was a kid, we had a neighbor whose job it was to translate Russian literature. This seemed to me at the time to be a rather peculiar job. German and French, sure, but Russian was not particularly popular. Why Russian? In retrospect, given that this was during the time of the cold war between the US and the USSR, it should have been obvious...
Scottish Cafe

The Scottish Cafe

AS an undergraduate mathematics student, I had a topology professor who would tell his students about the early days of topology. There was it seemed a cafe where the Polish mathematicians would congregate and discuss mathematics for hours on end.
When some mathematician stumbled upon a problem or conjecture that was interesting but he could not solve, he could ask the coffee house staff for a book that was kept there just for the mathematicians...and in which the problem would be recorded as a challenge for any mathematician who visited the coffee house. From this cafe sprung many of the early results of topology and measure theory, and the book became rather famous, at least among topologists...
Well, it's a rather romantic story, but one that students tend to put aside as they concentrate on the job of actually learning the subject of topology!
But fast forward to the present -- and that cafe is now a bank...and that part of Poland is now Ukraine, and the Polish city of Lwow where the coffee house was located is now the Ukrainian city of Lviv ( "Lvov/Lviv translated from Russian/Ukrainian means "Lion". By the way, if you visit Lviv, you will discover many wonderful statues and sculptures, some quite old, of lions.)
Having visited Lviv a few times I have tended to concentrate on exploring the usual tourist attractions...but on a recent visit, I had to see if I could find this Scottish Cafe....

Richard Feynman, Corrected

A while ago, Vladimir Putin was shown on Russian television cavorting around Kyzyl, Tuva. (The same Tuva after which Microsoft named its excellent Tuva Project). Tuva was made famous in the physics world in 1991 by the publication of "Tuva or Bust, Richard Feynman's Last Journey"... At the time, the Tuva media attention caused me to dust off and re-read that book...leading, interestingly enough, to the discovery of a previously unknown, but unfortunately somewhat widely propagated, Feynman error. Yeah, Feynman published an error. So here is the story, along with my correction...


Recently, I talked to somebody who mentioned they had worked with coordinate systems and gimbals, which reminded me I have a backlog of old blog entries that have not been ported to .Net core... Here then is the port of an old post, on the great William Rowan Hamilton, quaternions, and gimbal lock...


Complex Numbers

Our ultimate goal is to explain, simply, how the classical idea of a bit -- something that can have a value of only zero or one -- may be extended to a quantum system. Because quantum mechanics uses "complex numbers", it is natural to start there...

Quantum Bits

The quantum analog of a two valued sytem gives rise to the idea of a quantum bit, also known as a qubit.

Orion and Mars

Sometime ago, NASA launched its Orion rocket, with the goal of sending man to Mars. A cost and benefit analysis is interesting...

Magic of Reality Review

A review of Dawkins' work that he wrote for a younger audience. A careful analysis of Dawkins' work is given. Dawkins' book utlimately turned out to be a missed opportunity for Dawkins.