Episode 023 = The Weight of Words and Graphene for Turds

2021-09-30
00:51:16

Note: In-person recording again
00:02:11–00:03:39

This episode is being recorded in person. The last previous in-person episode was 002. Listeners are encouraged to tweet "cupboard" or "nupboard", depending on whether they like or dislike this change.

News: Matt had his protractor confiscated
00:06:47–00:11:36

Security at the Shard took Matt's prospector because they said it could be used as a weapon. They also confiscated Hannah Fry's inclinometer. Similar to 022-2, they wanted to measure how far they could see, and then use that to derive the radius of the earth.

Matt once had to get his Rubik's Cube put through an X-Ray machine because he was doing maths sessions in a jail.

"My plumb is just dangling." — Matt

Problem 023-1 = If graphene was rolled to the size of a loo roll, how long would that roll be?
00:13:52–00:25:40

Problem poser: David, from Greensborough
Problem solver: Matt

Problem statement

If you rolled up graphene into a roll the size of a toilet paper roll, how long would it be?

Solution attempt

Graphene is a one atom thick material that's very strong for its mass. According to a paper, an accurate thickness measurement is difficult because measuring it squashes it, but it's rougly 0.5 nm high. Approximating the Achimedean spiral using concentric circles, Matt arrives at a length of 20'000 km, which is halfway around the Earth.

"Give me two rolls of graphene toilet paper and a place to stand, and I will TP the world." — Matt, paraphrasing Achimedes

Ding

A tentative "ding" from Bec

Problem 023-2 = What is the weight of ink in Bec's book?
00:25:43–00:40:46

Problem poser: Samson, from Patreon
Problem solver: Bec

Problem statement

My brother told me that every time he reads a paper book, he wonders how much the book would weigh without any ink. If you had a totally useless representation of a book, how many pages could you save by just printing the ink without any gaps?

Solution attempt

Bec's Horror Heights book is being released on the date of this episode, 2021-09-30, and she got a tour of the factory. She nerds out about the printing process. Bec asked Beth and Ollie from Clays Printing (who printed her book), who estimated 11.2 g per book. Each book is 157.3g, which makes 146.1g per inkless book. The ink is about 7.12% of the mass.

Matt wrote a bit of Python code to count pixels of ink in Bec's book. After some fun stats, he reveals you'd only need 24.22 pages full of ink to equal the 176 actual pages. Matt uses this opportunity to talk about the difference between the mean and median.

Ding

A "solid ding, margin to margin" from Bec and Matt

Update for problem 022-2
00:40:51–00:49:30

People were upset at Matt for not including mountains and sent in lots of suggestions. The highest peak in Tenerife to the highest peak in Gran Canaria are over 100 km apart. From Pico Cristóbal Colón to the ocean (if possible) would be 270 km. From a peak in Arizona to Humphrey's Peak would be 187 km. From Mauna Kea in Hawaii you might get 128 km. From Aconcagua to the ocean would be 298 km. However, these are all just theories.

The world record for the longest photograph from Spain to France is 443 km. This takes into account refraction through the air. Bec criticises that, had Matt googled the answer, he'd found out about this answer straight away.

Ding

A solid ding from Bec, which turns out to be a Beardyman ding

Update for problem 022-1
00:49:30–00:49:51

A bunch of listeners have responded on Twitter with their own writing tips. Matt likes the vibrating pen idea.

Update for problem 021-1
00:49:51–00:50:14

PositronicGirl responded that Bec's solution was adequate.

Ding

A Beardyman ding as a meta-ding