The Mathematical Spammer (feat. Matt Parker) - Objectivity 254
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- Опубліковано 13 бер 2022
- William Shanks deluged the Royal Society with precise calculations - and he checked them carefully. More links below ↓↓↓
Featuring Matt Parker from Stand Up Maths speaking with Keith Moore and Brady Haran.
Matt Parker's Pi Day video:
• Can we calculate 100 d...
Numberphile Shanks video: • The Reciprocals of Pri...
Matt Parker website: standupmaths.com
Objectivity on Patreon: / objectivity
Subscribe to Objectivity: bit.ly/Objectivity_Sub
Films by James Hennessy and Brady Haran
Royal Society website: bit.ly/Royal_Society
The Royal Society's own UA-cam channel: / royalsociety
Facebook: / objectivityvideos
Twitter: / objectivity_vid
Patron thank you page: www.bradyharanblog.com/objecti...
Objectivity T-Shirts: teespring.com/stores/objectivity - Наука та технологія
3 Matt Parker video with the same hour ? That's yet another Parker approximation of pi
He's 14% of the way into producing this next video.
If only he appeared in someone else's video for about 1/7 of the duration.
@@vigilantcosmicpenguin8721 Ideas for next year?
This video had me cackling. What a guy. What an absolute, insufferable legend.
That look he had at the start was epic, because he knew what he did, it was calculated af.
William Shanks be like:
Unacceptable conditions!! UNACCEPTABLE!!!
Another of my favorite historical hand computations is the factorization of the Mersenne number 2^67 - 1 by F. N. Cole in 1903. The story goes that Cole took "three years of Sundays" to find its two prime factors, then delivered a silent hour-long lecture to the American Mathematical Society where he worked out 2^67 - 1 on one side of the chalkboard, then multiplied his two prime factors on the other side, and he got a standing ovation. Today my computer can find those factors in less than a second.
It's hysterical imagining that lecture. Everyone at the edge of their seat for an hour but it's so quiet you could hear a pin drop.
For whatever reason, this is the funniest thing I've read in a while. The thought of a bunch of mathematicians leaning over in their chairs in anticipation.. he writes the last digit with a huge sweeping flourish of the chalk, sweating like a madman. And as people lose their absolute minds (I'm imagining papers being throw into the air for some reason), he takes a bow. Glorious.
Edit: probably ladies throwing their panties on the stage too, right? That *_is_* how math works, right guys? I haven't been getting my degree for nothing? Right?!
@@idontwantahandlethough Is there scope for a Masters in Doing all of the noteboard apperences in "Big Bang Theory" pure and applied maths ?
@@idontwantahandlethough I'm sure the ladies swooned daintily. Not sure about the undergarments though, they were different times then
@@dielaughing73 Tossing their handkerchiefs onto stage in a girlish fervor!
All I could kept thinking is that this guy would’ve loved the OEIS. Definitely would have made regular contributions.
This is great throughout, but Matt saying "Look, everyone knows I'm that guy!" out loud is the highlight of this episode.
His certainty is vindicated.
Sure Shank Redemption.
Keith mentioned Babbage, but left out Donald Knuth who created an entire typesetting system from scratch to maintain control over his printed work. I see that he’s been on Numberphile and Computerphile, but I don’t remember whether or not y’all discussed LaTeX. It would be great to delve into that, as it brings together so many cool areas of history and technology.
To be fair, they're different goals. Knuth created TeX because of math typesetting - how it looks. Babbage created the difference engine, in part, to calculate log tables to avoid mistakes in the actual calculations of similar tables of the time. Typesetting wasn't the concern there.
Someone could make an entire channel dedicated to discussing different things Donald Knuth worked on and not run out of video ideas.
Knuth would be TeX, not LaTex. Though Lamport seems a pretty interesting character too.
This week I have submitted several trivia and goof items to IMDb, and three or four comments on UA-cam videos, correcting small errors made by their creators. Sounds like W. Shanks was a man after my own heart!
Fire up the cloud car
I think your YT comment needs a typo correction
It is very rare that someone writes legibly enough that someone other than Keith is able to read something
Indeed, I have tried reading some census returns and they are a waste of time , but then some enumerators were under a pressure of time to get it completed.
Maybe it has something to do with him being a teacher haha
06:32, the /verso/ in a different hand, is just the draft of the erratum sheet needed to make the corrections that Mr Shanks notified in his letter, i.e. the 3 -> 2 and 7 -> 1.
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.
Every time he says "welcome to the Royal Society" I expect the next words to be "for Putting Things on Top of Other Things"
I'm so envious of their handwriting. But I almost never write anything by hand anymore so that's probably why.
I have acquired an expenses and history journal from someone whom didnt really have a great education (worked as a plantsman for the royal parks), perfect handwriting, me gets 2nd class degree, but might have got a first as my writing refuses to be anything other than marks on a page, that even I cannot read back
I love Keith's comment about Northumberland as my grandmother was from Rothbury - location of William Amstrong's engineering centre of the universe.
I always think, given the weather , that Northumbria must have seemed like the Med to the Vikings from Scandinavia, but to us soft southerners , nope, too much like iceland.
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.)
Wouldn't of thought we could have machine learning tech that can crush human go masters but still have issues getting text on or from paper in the right order.
Nice to see Bradley teaming up with Pat Marker again!
Why would someone pat marker
@@volodyadykun6490 I sometimes pat my markers when they do a good job writing
I've never been, but I understand that Northumberland IS in fact the finest bit of British soil that exists.
Now that I'm in Keith's good graces, can I come over and just rummage through the archives? Please?
Become a member FIRST.
the Royal Society is a goldmine of content. great stuff :)
This is one of my favorite channels in youtube. Thank you a lot
You’re welcome. Thanks for watching.
Very insightful. I enjoyed watching this.
Love these videos so much ☺️☺️
Matt looks so wonderfully smug in that opening shot!
This channel deserves so much more than its got
We’ve got you, and that’s enough.
Superb!
Happy Pi Day!!
i love his handwriting! so neat!
Do they have any videos about the process of archival? Like the method of putting these letters, etc. into the books and what kind of glue they have to use?
I watched it. But I'll watch it again soon.
Matt Parker: posts video about a spamming mathematician.
Also Matt Parker: spams three videos about the same subject from three channels at the same time, and adds a plug in his podcast to boot. 🤣
Including a video where he makes a bunch of students help him calculate pi by hand.
I've literally got three a Matt Parker videos in a row on my stream. This man must be stopped.
Oh it's matt, I haven't seen him on UA-cam today...
He has a channel standupmaths
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.
I think I may have seen this video before...I thought I would have commented on it then.....especially 4:23
All three of you guys are great.
3:13 "Do we get any more sense of the man from these documents?"
Well, I gather that he had an awful lot of free time.
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.
The world need more like Shanks.
I can imagine that corrections would be even more important historically since errors would be copied and continued in future works making them very difficult to stamp out. The same thing happens today but not often with math errors since we're able to check more easily. Also we have Snopes.
Early ideas of COVID transmission were based on a typo. Some number got changed in a... I think Biology journal that was transcribing an idea from physics so all the bio guys had the wrong number until the publicity around COVID had physics folks saying "that doesn't look right, we need to compare notes". I think it was something about how long water-borne particles stayed viable and they had the size wrong so they thought it was longer? That's why there were early warnings about leaving packags in quarantine before bringing them inside.
And thus meet the plight of CGP Grey
Please keep anything even tangentially related to sham organizations like Snopes away from math.
@@RamAurelius The debunking done by Snopes, while well regarded, rigorous, peer reviewed and largely unbiased, deals with historical facts, not timeless ones like math proofs.
From some searching online there seem to be virtually no people disputing their fact checks. The worst I could find is that they aren't very transparent about their internal staff and processes. I couldn't find any valid complaints about their actual fact checking.
Notice that William Shanks wrote the dates Month/Day/Year. I wonder when that standard changed in the UK.
I paused 2 seconds in to open a packet of crisps and Brady looks FURIOUS!
I’m really not. Enjoy your crisps.
@@ObjectivityVideos 😂 Is it because I didn't offer you one? I'll try to remember next time :)
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
Incredible, hahaha!
I don't have a lot of experience in prime numbers (engineering student) but I recognized a pattern in the book. The number of digits before repeating seems to always be a factor of the prime number - 1... Does anyone else see that?
Well spotted! You can see that at 3:05 where the frequency of 65291 is 65290/20 = 3296 for example. Hoping someone will shed some more light on why.
@@haulin Without delving into too many details for a UA-cam comment, Fermat's Little Theorem for a=10 (and p not 2 or 5) gets you what you want here.
@@radu.moldov2115 I don't know how you guys do this stuff but I am mighty impressed anyways 😯😀
@@haulin I think it was part of the process that Shanks used - Matt aluded to it in his video on the Primes in this book , but didnt fully explain it, but did the explanation of how to do the long division
Let p be a prime. The integers mod p form a group of order p-1. In other words, every integer (mod p) has an inverse (number that multiplies to 1) and this multiplication is associative. We also have an identity element, namely 1. Fermat's little theorem gives us an upper bound on the order, namely p-1.
A primitive root of p is a number n such that for any number m (mod p), there is some positive integer k such that n^k is m (mod p). the primes for which the decimal expansion includes 1,2,3,...,9 are the primes for which 10 is a primitive root. when 10 is not a primitive root of p, its powers still form a cyclic subgroup of the integers mod p; the order of the subgroup always divides the order of the group. the order of the cyclic subgroup is the number of digits before repeating, and the order of the group is p-1. hence, the number of digits before repeating will divide p-1.
roughly speaking. consult a group theory textbook. do not learn group theory from random yt commentors like me. :)
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!
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..
SHANK'S THEOREM: For all prime numbers p, the reciprocal 1/p is a repeating decimal where the length of the repeating pattern is LESS than p.
Even better - the length is always a factor of p-1 (so if it doesn't happen by half of p-1... no need to keep dividing to find the length)
@@radu.moldov2115 You see something relating to this via the corrections; Almost all of them are just x2 or /2 of the stated number.
@@comma_thingy Matt alluded to how the errors would have arisen, but didnt do the full explanation
@@radu.moldov2115 proof please?
It seems to me that most reciprocals digit count are n-1, (n-1)/2 and so on
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.
"There's no way it's gonna be Pi this time!! ... Aww, pi."
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.
Just a shot in the dark, but I think Keith may be from Northumbria... :)
Can't think of a better way to celebrate Pi Day then by celebrating someone who, apparently, really liked pi.
4:05 Brady removes his white gloves.
This one is pretty fun. I will say the things he's doing is validating existing results and sometimes, well incredibly rarely, you find something wrong or you get a better process that could lead to a new discovery.
Pi is roughly 3. Thats close enough for me.
Why is Brady the only one wearing white gloves for handling delicate archived documents, but then at 6:10 when they’re actually touching pages the gloves are off?
This channel has explained that they don't usually use gloves for paper. You're actually more likely to do damage. They have a video on the subject.
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.
It's the largest possible for that specific prime. The period of a prime p is at most p-1. Of course many (infinitely, I guess) primes have that property. And as there's no largest prime, there's no absolute longest period. A mistake Matt made though is the method Shanks used. I'm very sure he calculated the order of 10 mod the respective prime. Still impressive, but hand division of 60000+ digits is impossible.
@@bur2000 I think you completely missed the point of what I said.
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.
Soooo, was Shanks right with the corrections he sent in? Both for his own work and for others' work?
I am not sure if he corrected other persons. Perhaps what is remarkable for the pi book ONLY two errors, and those are in part due to the problem with the numeral system we use.
What is the pattern of primes (P) with (P-1) digits before repeating?
10 is a primitive root modulo all those P
There's a measure for diligence.
W. Shanks is a monster!!!!!!
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
Parker's been busy lately
1/2 = .5 and 1/5 = 0.2. If we were doing these calculations in a prime base, would we have no exceptions like this?
True that those are only exceptions because they divide evenly into our base of ten, though of course if you pick a prime base like seven, then one seventh is exactly 0.1, if that counts as an exception to you.
@@radu.moldov2115 Ohh, is there a relationship of the base to the divisor that can be plotted on a table that would show a pattern ?
happy pi day everyone
maybe could have benefited from a a higher f stop for that first closeup on matt
Definitely! :)
"Spam, spam, spam, spam
Spam, spam, spam, spam
Spammity spam, spammity spam."
Librarians are wizards
Why is Brady wearing gloves and the head librarian is not? 😂
Happy Pi Day!
2:31 Would someone please explain this to a dummy (me)? It seems like it could take more digits to repeat.
He was a pedantic perfectionist. i understand him all too well... except about the numbers thing. To my consciousness numbers are mind-numbing !:-)
Is it just me, or is Keith's tie looking quite long today?
It seems like Shanks had his finger in a number of pies.
Pi Day, 22/7
I imagine there are a fair few Shanksian viewers here. Not I, for my intellect, mathematical or otherwise, is not up to par. Believe me, yours very sincerely, Christopher.
P.S. Charles Darwin, no intellectual slouch, to be sure, often closed his letter to his professor and mentor J. S. Henslow in a manner much the same as did Shanks. What a charming habit. -C.M.
This Shanks dude sounds interesting.
Pretty sure he’s the founding father of r/counting
A guy who calculates in all of his free time won't be up to much mischief. Shanks couldn't have been that bad.
0:28 this is wrong.
Everyone by now should know Cardiff is the middle point and anchorpoint of the universe.
Since there is a rift, which can also be used to refuel your TARDIS.
Intelligent beings! #mathematician 👍🧠
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.
I hope the proof for the Riemann hypothesis isn't sitting in someone's junk folder :\
Maybe it was too wide to fit in the margin.
I wonder how many children he had.
people in the past have such elegant handwriting. i'm ashamed😂
You just can't get around π
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....
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.
So, this Shank guy actually had OCD.
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!!!
Tau 🖖
Honestly parker, you need to stop trying to make 'mathS' happen, it's not going to happen. Math. Singular. Give up bro, it's embarrassing.
Some people get uptight about the weirdest stuff
Everyone in the world who speaks Commonwealth English: *Am I a joke to you?*
Matematika. Problem solved.
It's only "math" in the land of the Imperial measurements and where dates are written the wrong way round. Maths (with the ess) is a contraction of mathematics (also with an ess).
Matt is bilingual. When he films a video in the US he uses "math", when he films a video in commonwealth countries he uses "maths". Get over it; you are embarrassing yourself.