Book Review: A divine language : learning algebra, geometry, and calculus at the edge of old age.

Alec Wilkinson, staff writer for The New Yorker magazine, recently wrote about his quest to study math later in life. Here is a link to his September 6, 2022, article: How Mathematics Changed Me | The New Yorker. He started his quest five years ago at age 65. He also writes about this in his book, A divine language : learning algebra, geometry, and calculus at the edge of old age. I have the book on order and look forward to reviewing it.

From his article, I understand much of what Wilkinson learned during his quest as I started this math blog late in my life. This blog started as a Covid project two years ago when I was 61. We both learned strangeness of different types of infinities, mystery of design of our world, and how God in unknowable.

11/8/2022 Update - my local library got this book, and I just finished it. Wilkinson included stories about many of my favorite mathematicians. I liked that he was able to interview Chris Ferguson, who won $1,000,000 in the World Series of Poker in 2000, shortly after earning his PhD from UCLA. 

Book Review: We Have No Idea, A Guide to the Unknown Universe by Jorge Cham and Daniel Whiteson

 

(Jacket design by Jorge Cham, Penguin Random House Riverhead Books)

If you are looking for an entertaining book on cosmology, We Have No Idea fits the bill. Authors Cham and Whiteson begin the book with a few chapters on what makes up the universe where we learn that it consists mostly of dark matter and dark energy. Fitting for the title of the book, scientists still know little about 95% of the universe.

To make the material easier to read, the book is generously illustrated by Cham with cartoon-style drawings.

Footnotes include science humor topics. For example, footnote 68 refers readers to the website: Has the Large Hadron Collider destroyed the world yet?

While providing a humorous example, I found their explanation of the difference of philosophical and scientific theories to be very easy to understand. Essentially, theories need to be testable to be deemed scientific.

 Another topic explored is string theory. Those who like the post, The Very Samll and the Very Big will like the chapter "How Many Dimensions are There?" 

Book’s website: We Have No Idea by Jorge Cham, Daniel Whiteson: 9780735211520 | PenguinRandomHouse.com: Books

Kruskal Chains

 

For an introduction to the Kruskal chain, watch this video by CountVsauce2: (1853) The Number Illusion You Won't Believe - YouTube. The video shows a popular magic trick using the hours of a clock and is based on a Kruskal chain. The host explains how the trick works and once you understand how it works, the principal can be applied to other situations.

Here is how to expand the Kruskal chain to a card trick. Shuffle a normal 52-card deck of playing cards. Deal them out face up into 4 rows of 10 cards and a 5^th row of 12 cards.  Ask your audience member to pick one card from the top row but not to reveal it to you. Instruct them to count ahead in the matrix of cards based on the number of the card (aces = 1 and face cards = 5). When they land on the next card, they repeat the procedure based on the value of the card they land on, and they keep counting until they cannot proceed any further. As your participant is choosing the starting card, you need to pick any starting card and complete the exercise to the last row. Before your participant begins the counting process, announce you know which card they will be their final landing card – this will be the last card you landed on. Based on the Kruskal chain, most starting cards will have “chains” that intersect and once they do, the remainder of their sequences will be the same. There are some instances, where there will be one or more starting cards that produce a sequence that doesn’t intersect the other chains. This will occur about 15% of the time. If one uses two decks and therefore allowing for more chances of chains intersecting, the trick will fail to work only 5% of the time.

Update 4/9/2023

Interesting note - if one takes a new, unshuffled deck and deals it out in order as described above, the ending point will be the third card from the end of the last row - the three of spades.

Update 8/24/2024 - another post feature a Kruskal count has been added to this blog and it will become a proposed sequence for the OEIS.