A visual companion to the audio edition of Mathematica
The full set of illustrations and tables from the print edition
In several languages, the audio edition of Mathematica: a Secret World of Intuition and Curiosity comes without an accompanying booklet with the illustrations and tables. Many listeners have justifiably raised the issue, and I want to thank them and apologize for this oversight.
For everyone’s convenience, here’s the full set of illustrations and tables from the print edition. A few comments:
All the drawings and mathematical diagrams were commissioned for the original French edition and created by Éléonore Lamoglia — I thank her for her patience, precision, and dedication. The elephant looks easy, but it took a while to get it right.
The photograph selection varies a bit from one print edition to the other, due to copyright technicalities and also each publisher's specific art guidelines. E.g., the Russian edition use a different Ben Underwood picture, the French edition a different Fosbury picture, and the US edition a different Tom Hales picture.
In the print editions, the pictures are free-floating without any legend, as their content is always obvious from context.
The print editions are all black & white. Whenever possible, I’m including here the original color photographs.
Some historical photographs are only available in low resolution, and some lack credits. It took some effort (and AI upscaling) to convince my publishers that these pictures were still worth printing.
Chapter 2: The Right Side of the Spoon
A cognitive transformation program with no historical precedent:
Chapter 5: Unseen Actions
A shape-sorting toy:
A tail-walking dolphin:
A tail-walking human:
Chapter 6: Refusing to Read
Bill Thurston:
Chapter 7: The Child’s Pose
Alexander Grothendieck right before he left mathematics:
Alexander Grothendieck as a child:
Chapter 9: Something’s Going on Here
An icosahedron:
Cartesian coordinates:
A 2-dimensional shadow of an hyper-icosahedron (aka 600-cell, aka hexacosichoron.)
Chapter 10: The Art of Seeing
Bill Thurston as a child:
Ben Underwood:
Chapter 11: The Ball and the Bat
How the correct answer to the ball and bat problem can be intuitive, despite Kahneman’s claim of the contrary:
Thinking fast, slow, and super slow:
Chapter 12: There Are No Tricks
How to visualize and compute the 1 + 2 + … + 99 + 100 sum (note: there’s more than one way to do, and mine is in no way superior nor canonical.)
“Staircase” visualization of the sum (shown here for 1 + 2 + … + 17 + 18, but you get the idea.)
How to get to 5000 (Thurston’s initial approximate answer): it’s the surface area of the white triangle. To get to 5050, one must add the area of the small shaded triangles.
An alternate way to get to the correct answer: it’s half the surface of this 100x101 rectangle. This is where the double-sum “trick” comes from.
Different domains of mathematics, studying different types of intuitive objects:
Chapter 14: A Martial Art
René Descartes after Frans Hals. Note the “tough-guy” gaze of this former mercenary, ready to jump for his sword. This is fairly typical of 17th century Dutch art and compares well to modern gangsta rap iconography.
Chapter 15: Awe and Magic
An infinite grid:
An infinite line:
A trefoil knot:
A different way to draw the trefoil knot:
The unknot:
Another way to draw the unknot:
Yet another way to draw the unknot:
A very messy way of drawing the unknot (can you mentally untangle it?):
What makes you so sure that the trefoil can’t be deformed into the unknot? Would you bet your life on it?:
A maximum density stacking of oranges:
Tom Hales:
The densest way to arrange coins:
Maryna Viazovska:
Chapter 16: Controlling the Universe
Ted Kaczynski at age 26 (as the youngest assistant professor in the history of UC Berkeley) and 53 (at the end of the longest search in the history of the FBI):
Chapter 18: The Elephant in the Room
Two languages, two sets of rules:
Chapter 19: Abstract and Vague
My favorite page in the entire book is one that is plainly impossible to adapt for audio. It’s a good reason to reproduce it in full:
A neuron:
Epilogue
G.H. Hardy (left) and Srinivasa Ramanujan (right).
The infamous page 379 from Russell & Whitehead’s Principia Mathematica:
I am currently listening to Mathematica on Audible, and it is a delight - I wish my teenage self had been able to read it in the 70s. I had ambitions to do Maths with Computer Science at Edinburgh University, but their 2nd year 2X course nearly did me in, especially complex analysis and linear algebra; the latter had a dysfunctional lecturer with microscopic paper notes - so I just stuck to CS (which worked out great).
I was initially upset when I saw that the audio edition did not have the illustrations, but had a look about and found this post - many thanks for making them available. Your illustration for the ball and bat had me scratching my head at first, and then flash bulbs exploded. I had solved it algebraically when I first read Kahneman's book years ago, but your 2D visualisation makes it pop, and is doable in one's head - your whole point.
Great work, and I hope it helps young-uns persist at the splendid adventure which is maths. I'm going to dig out some old Maths 2X papers and revisit my daemons.
I enjoyed your book. I have always loved math. This book furthered my understanding of what it was that I loved about it. I love the idea about how 'understanding' math profoundly enhances our perception of the world we inhabit. The consequence of reading your book is a reinvigoration for pursuing new math ideas. Where should I start? Any good sites or YouTubers making related content for the generally lay mathematician (bachelor is engineering)?