A Mathematician Reads the Newspaper

September 23, 2016 Leave a comment

I was looking through my bookshelf when I came across this book. I had not read it!

The book is ‘old’. However, the delightfully humorous and clear lessons to us remain relevant (and perhaps are even needed more now than ever). The newspaper was a wonderful launching pad for these explorations.

Categories: books

Rationality

September 1, 2016 Leave a comment

This is another post motivated by a Mathematica Stackexchange post adapting code by user  halmir (visualization of a sample of the consecutive decimal representation). The following is visualization of rational which are either finite or recurring).

vphd

Categories: Mathematica, Mathematics

Finely Tuned

August 31, 2016 Leave a comment

This post is motivated by an answer on Mathematica Stackexchange.

This is based on the Lotka Volterra predator-prey model.

lv

Categories: Mathematica, Mathematics

Not To Too Hot to Handle

August 15, 2016 Leave a comment

This is a tentative play with Mathematica 11…in this case solving a 3D heat PDE over cup geometry (free STL format download)…

mug

Categories: Mathematica

Idea Makers

August 4, 2016 Leave a comment

ideamakers

I thoroughly enjoyed this book from beginning to end.I have read various biographies of some of the notable people in the book. This back examines their ideas and their lives through the lens of current idea maker. The book is a collection of essays by the author. This does not, as one might expect, lead to a disjointed style. Each chapter is self contained but also part of a coherent whole.  I particularly enjoyed the chapter on Ada Lovelace (and Charles Babbage). The graphics in the book provide a visual access to these singular minds (some centuries old).

 

 

 

Categories: books

Two Roads

June 9, 2016 Leave a comment

tworoads

This post is homage to the amazing power of approximation of asymptotics. A finite number of terms of a divergent series can rapidly approach the value of a function while a convergent series needs an extremely large number of terms to get to the same accuracy and precision.

1/\Gamma (x) is the illustrative function (chosen as  mentioned in Professor Bender lecture on Mathematical Physics). The plot shows the single term Stirling approximation/function (obviously begs the question what algorithm does Mathematica used) v partial sums of power series/function.

 

asymptotic

 

Categories: Mathematica, Mathematics

Hazard

June 6, 2016 Leave a comment

Hoffman et al provided an interesting article on the underlying mechanism of aging. This was a clearly written and strong argument that aging is a matter of physics not biology.

This post explores the age distribution of a population (in equilibrium) with a constant hazard (age independent of mortality).

In the following, a population of 1000 “individuals” all 1 years old. The time evolution individuals are removed from the population and replaced by 1 year olds who then age. 100 cycles are shown. The red line is equilibrium distribution.

This is not the human situation as the author remarks. We are fortunate to have repair mechanisms that protect us for as long as they do.

poppopm

Categories: Uncategorized