Book Review: Pluses and Minuses

 

Stefan Buijsman, philosopher of mathematics, earned his PhD at age 20. His book, Pluses and Minuses, How Math Solves Our Problems, covers several mathematical concepts in a very easy-to-read and understandable format. Many topics he reviews includes systems that we interact with everyday such as mapping the shortest route, Google searches, and Netflix movie recommendations. There are also examples of how mathematics models scientific observations and also predicts the possible existence of yet undiscovered phenomena. Most notable was Paul Dirac's prediction of the positron or anti-electron.

Another topic Buijsman writes is why early civilizations developed mathematics. Related to this topic, he also explains how certain indigenous cultures get by without having words for numbers. 

I particularly liked his chapter on probability and statistics. As an instructor of statistics myself, I will use Buijsman's examples in future classes.

Publisher link: https://www.penguinrandomhouse.com/books/611373/pluses-and-minuses-by-stefan-buijsman/

How Does a Math Formula Highlight the Creator?

(Image: https://www.iconfinder.com/atifarshad)

The Ken Ham Blog recently had a thought-provoking post about the Golden Ratio: see link. It speaks how this ratio is related to many things in nature. A video by the Institute for Creation Research presents their argument for God as evidenced by intelligent design in the Fibonacci series and the Golden Ratio.

See also:

Speed Limit Conversions 

OEIS Sequence

42

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In Douglas Adams' Hitchhiker Guide to the Galaxy, the answer to the ultimate question of the universe was 42. BigThink.com had an article today listing 5 actual questions of science that have the answer 42: 42 really is the answer to these 5 fundamental questions - Big Think.

More on Adams' classic: The Hitchhiker's Guide to the Galaxy - Wikipedia.

Update, 1/10/2024: Also see https://www.iflscience.com/life-the-universe-and-everything-why-42-really-is-the-ultimate-answer-72379 for additional questions answered with 42.

Book Review: Gödel, Escher, Bach: an Eternal Golden Braid

 

I recently re-read Gödel, Escher, Bach: an Eternal Golden Braid, an epic book weaving the similar patterns found in mathematics, art/design, and music. First published in 1979, just a few years after the author, Douglas Hofstadter earned his PhD from the University of Oregon in 1975. I first read the Pulitzer Prize-winning book in 1983 while I was earning my PhD from the University of Illinois. So, I found it very inspiring that someone could produce such a great work early in his career.

In addition to the math of Gödel, the designs of Escher, and the music of Bach, Hofstadter includes dialogues between Tortoise and Achilles in the style of Lewis Carrol to reinforce the ideas he puts forward. He also includes a number of puzzles, discussions on computer coding, recursion (on many levels), and most interesting, artificial intelligence. 

Wolfgang Haken, 1928 - 2022

 

(Image:  Wolfgang Haken in 2008 - own work)

One of my favorite math professors passed away last year and I regret not being timelier in reporting this. Wolfgang Haken, University of Illinois at Urbana- Champaign, together with Ken Appel, solved the four-color problem. This is the subject of an earlier post: Math Vacation: Four Color Map (jamesmacmath.blogspot.com). I really enjoyed his lectures and the enthusiasm he shared about mathematics.

 

Word Clouds

 

If you ever wondered how to produce a "Word Cloud," there is an easy function built into the program Wolfram Mathematica. I've been slowly taking tutorials on using Mathematica and a key to learn a new programming language is to apply newly introduced functions in your own work. 

If you don't have access to Mathematica, Wolfram Mathematica has a cloud-based version available for no cost - you just have to set up an account: see this link: Wolfram Cloud.

Next, copy the line of code below into a new notebook and replace "mathematics" with the subject of your choice.

WordCloud[WikipediaData["mathematics"]]

For example, to produce a word cloud for the city of Chicago, use: WordCloud[WikipediaData["Chicago"]].

The result is below.

More information specific to the WordCloud Function, see example 18 of: Strings and Text: Elementary Introduction to the Wolfram Language.

Tutorials on using Mathematica can be found here: An Elementary Introduction to the Wolfram Language by Stephen Wolfram.

Note: Stephen Wolfram is the author of A New Kind of Science. See: Math Vacation: My Favorite Math Websites (jamesmacmath.blogspot.com)

3,628,800

This post is inspired by a recent puzzle published by Alex Bellos in the Guardian: Did you solve it? Puzzles you can do in the pub | Mathematics | The Guardian

The title of the post is 10! = 1x2x3x4x5x6x7x8x9x10 = 3,628,800. Interestingly, this value is the same number of seconds in six weeks. The challenge in Bellos's puzzle was to make the comparison without using a calculator.

One can confirm this without a calculator. Write out the number of seconds in six weeks as:

6 (weeks) x 7 (days) x 24 (hours) x (60 minutes) x (60 seconds)

Now one can cancel factors in the above equation by matching up with terms in the equation for 10!.

Cancel the 6 in both equations.

Cancel the 7 in both equations.

Cancel the 24 by matching with the 3 and 8 in the 10! equation

Reduce the 60 to 6 in the seconds equation by cancelling the 10 in the 10! equation.

Reduce the other 60 to 6 in the seconds equation by canceling the the 2 and the 5 in the 10! equation.

These canceling operations leaves us with 6x6=36 in the seconds equations and 4x9=36 in the factorial equation, therefore the number of seconds in six weeks equals 10!.

Alex Bellos is also the author of one of my favorite math books: Math Vacation: My Favorite Math Websites (jamesmacmath.blogspot.com)