The Mathematical Spammer (feat. Matt Parker) - Objectivity 254

I've literally got three a Matt Parker videos in a row on my stream. This man must be stopped.

Superb!

So, this Shank guy actually had OCD.

This was a fantastic video. The brief discussion by Keith and Matt was interesting, and another example of what a great interviewer Brady is. One question, and the depth of the conversation goes to infinity.

YOU can't figure out how he did it, yet lambast him for doing it anyway? YOU are earning money based on a guys life work, only to deride him in the process? If you think so poorly of the man, don't do a F%CKING video on his work.

Matt, it's a different Shanks (Daniel Shanks, mathematician in the 50s), but you should do a video on the Shanks Transform, and summing divergent series

i love his handwriting! so neat!

He was a pedantic perfectionist. i understand him all too well... except about the numbers thing. To my consciousness numbers are mind-numbing !:-)

I paused 2 seconds in to open a packet of crisps and Brady looks FURIOUS!

I got three videos in a row with Matt Parker in them today. One from standupmaths, one from objectivity, and one from numberphile. No complaints.

The conversation about editing and printing errors... makes me wonder if there's a way to distill Gaiman's Law down to a mathematical formula? (Neil Gaiman has postulated that without fail, when you receive a copy of a book you wrote, if you open it to a random page, you will find a typo.)

Pi is roughly 3. Thats close enough for me.

Okay, but why does mat keep avoiding 60029 repeating in 60028 steps in favor of 60017 repeating in 60016 steps. It just doesn't make sense!!!

Notice that William Shanks wrote the dates Month/Day/Year. I wonder when that standard changed in the UK.

Librarians are wizards

Pi Day, 22/7

All I could kept thinking is that this guy would’ve loved the OEIS. Definitely would have made regular contributions.

The closed captions on the first prime reciprocal example say "6013" instead of "60013", and 6013 could not have a period of 5001, since the period not only needs to be less than the prime, it needs to be a divisor of p-1. 5001*12 = 60012 = 60013 - 1 so the actual example works, but the auto-generated closed captions number 6013 could not have a period that large.

I'm really surprised for every time you pointed out the period associated with 60013 being the longest possible, that you never also noted that the number immediately after it shows the same property.

"Spam, spam, spam, spam
Spam, spam, spam, spam
Spammity spam, spammity spam."

Very insightful. I enjoyed watching this.

Oh, I guess I don't need to explain how automated punch-hole mechanical computers were developed by Babbage and others at this time in this region that could spit out binary lists that could accidentally be misread, resulting in the binary shift errors seen in William Shanks work.... you guys already know....

I have sheets of paper from when I was in first or second grade where I was just writing out things like what the square of each number were up to a few thousand. I wish any of my education afterwards was geared toward maths but it wasn't..

This Shanks dude sounds interesting.

This is how we think.
Thinkers. I did this for
Two decades in reverse
Working in the financial
Services industry.
We need to keep the conversation going.
Pi is an operator
Pi is a number
Pi is a number of numbers
Primes indicate complete sets
The set of complete sets is defined as pi
By pi
Of pi
To the pi
Yesterday was Sunday
Today is Sunday
Tomorrow is a dream

What is the pattern of primes (P) with (P-1) digits before repeating?

That is not what he is doing. He is taking powers of 10 modulo the given prime p. And then he looks for the smallest power of 10 which is equal to 1. This is always a divisor of p-1, and the powers of 10 are found by repeated squaring and combining the squares using the binary representation of the power you want to get. That is much faster than calculating the reciprocal by long division for large primes, it takes order (log p) steps, not order p steps, as long as you know how to factor p-1.

maybe could have benefited from a a higher f stop for that first closeup on matt

"There's no way it's gonna be Pi this time!! ... Aww, pi."

My favourite factorisation story:

The mathematician Fortuné Landry (1799--1895) devoted a considerable amount of time to factorising numbers of the form $2^n \pm 1$. To be more specific, all those numbers with $n\le 64$, except four. In 1869 he published his results [Landry], and of $2^{58} + 1$ he wrote

No one of the numerous factorisations of the numbers $2^n \pm 1$ gave as much trouble and labour as that of $2^{58} + 1$. This number is divisible by 5; if we remove this factor, we obtain a number of 17 digits whose factors have 9 digits each. If we lose this result, we shall miss the patience and courage to repeat all calculations that we have made and it is possible that many years will pass before someone else will discover the factorisation of $2^{58} + 1$.

The large factors are $L = 107367629$ and $M = 536903681$.

Two years later Aurefeuille noticed that $M - 5L = 2^{16}$, from which he then found that

2^{58} + 1 = (2^{29} - 2^{15} + 1)(2^{29} + 2^{15} + 1)

This is a special case of the identity,

4a^4 + 1 = (2a^2 - 2a + 1)(2a^2 + 2a + 1)

which is special case of the identity, found by Sophie Germain,

4a^4 + b^4 = (2a^2 - 2ab + b^2)(2a^2 + 2ab + b^2)

with $a = 2^{14}, b=1$. If Landry had known that, his task would have been much easier!

So Shanks hold the Parker record number of Pi digits calculated by hand.
Which is very different from the record number of Parker Pi digits calculated by hand, which has 11 correct decimal digits.

Would be great to hear about the actual algorithms and work methods used by the human calculators for the atomic bomb and early space travel. How did they make use of many people working side by side without waiting for a previous result. Perhaps next attempt to calculate pi will give more digits!

If it were not for the now too rare "pedant", we'd just be swimming in mistakes and misinformation, intentional or otherwise (see: the 'internet'). Put another way, if one is not happy to be corrected when truly wrong, then one is an egoist, if not just a putz. We need more Shanks and far less politicians, priests, and....pundits.

Heaven for me would be having free run to explore all the various bits of minutiae, illustrations, and arcane curiosities hidden in those wonderful old forgotten books piled all over the shelves.

Every time he says "welcome to the Royal Society" I expect the next words to be "for Putting Things on Top of Other Things"

You just can't get around π

I am not sure if him saying "I have more time to devote to checking the proofs than you" would have been taken as a self-burn back then. The modern neurotic obsession with being constantly busy and loathing of leisure didn't get invented until later.

Incredible, hahaha!

Why is Brady wearing gloves and the head librarian is not? 😂

There's a measure for diligence.

CORRECTION - Houghton-le-Spring is NOT in Northumberland. It is a town in the City of Sunderland, Tyne and Wear, North East England which has its recorded origins in Norman times. Historically in County Durham, it is now administered as part of the Tyne and Wear county.

Just a shot in the dark, but I think Keith may be from Northumbria... :)

I wonder how many children he had.