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.
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?!
This week I have submitted several trivia and goof items to IMDb, and three or four comments on RUclips videos, correcting small errors made by their creators. Sounds like W. Shanks was a man after my own heart!
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.
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.
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.
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.
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.
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.
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'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?
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.
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 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?
@@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
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.
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. 🤣
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?
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.
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 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..
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.
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.
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.
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
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.
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.
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 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.
@@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.
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.
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.
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.
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.
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....
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.
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!
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!!!
All I could kept thinking is that this guy would’ve loved the OEIS. Definitely would have made regular contributions.
This week I have submitted several trivia and goof items to IMDb, and three or four comments on RUclips 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
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.
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 is great throughout, but Matt saying "Look, everyone knows I'm that guy!" out loud is the highlight of this episode.
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.
His certainty is vindicated.
Sure Shank Redemption.
Every time he says "welcome to the Royal Society" I expect the next words to be "for Putting Things on Top of Other Things"
This is one of my favorite channels in youtube. Thank you a lot
You’re welcome. Thanks for watching.
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
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.
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.
This channel deserves so much more than its got
We’ve got you, and that’s enough.
the Royal Society is a goldmine of content. great stuff :)
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
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.
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 :)
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.
Matt looks so wonderfully smug in that opening shot!
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?
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.
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 RUclips 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
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.
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.
Love these videos so much ☺️☺️
I've literally got three a Matt Parker videos in a row on my stream. This man must be stopped.
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.
Very insightful. I enjoyed watching this.
Oh it's matt, I haven't seen him on RUclips 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.
The world need more like Shanks.
Superb!
Happy Pi Day!!
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.
4:05 Brady removes his white gloves.
"There's no way it's gonna be Pi this time!! ... Aww, pi."
Notice that William Shanks wrote the dates Month/Day/Year. I wonder when that standard changed in the UK.
It seems to me that most reciprocals digit count are n-1, (n-1)/2 and so on
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?
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 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..
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.
2:31 Would someone please explain this to a dummy (me)? It seems like it could take more digits to repeat.
I watched it. But I'll watch it again soon.
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.
i love his handwriting! so neat!
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.
Can't think of a better way to celebrate Pi Day then by celebrating someone who, apparently, really liked pi.
I sometimes wish I was as much of a "workaholic" as these guys centuries ago.
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.
What is the pattern of primes (P) with (P-1) digits before repeating?
10 is a primitive root modulo all those P
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
Is it just me, or is Keith's tie looking quite long today?
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.
Incredible, hahaha!
Just a shot in the dark, but I think Keith may be from Northumbria... :)
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.
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 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.
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! :)
There's a measure for diligence.
Pi is roughly 3. Thats close enough for me.
Librarians are wizards
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.
Why is Brady wearing gloves and the head librarian is not? 😂
It seems like Shanks had his finger in a number of pies.
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.
"Spam, spam, spam, spam
Spam, spam, spam, spam
Spammity spam, spammity spam."
Parker's been busy lately
W. Shanks is a monster!!!!!!
Pretty sure he’s the founding father of r/counting
He was a pedantic perfectionist. i understand him all too well... except about the numbers thing. To my consciousness numbers are mind-numbing !:-)
A guy who calculates in all of his free time won't be up to much mischief. Shanks couldn't have been that bad.
Happy Pi Day!
This Shanks dude sounds interesting.
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.
Pi Day, 22/7
people in the past have such elegant handwriting. i'm ashamed😂
Intelligent beings! #mathematician 👍🧠
I wonder how many children he had.
You just can't get around π
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!!!
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.
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....
So, this Shank guy actually had OCD.
Fifty copies of pi...
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.