These books of random digits were an important plot point in a 1968 science fiction novel titled _His Master's Voice_ by Stanislaw Lem. A statistician sued the publisher of one after showing that the digits weren't random but actually a very long repeating sequence. The publisher had been using noise from a radio telescope, but now they discovered that one source wasn't random and must be an extraterrestrial signal.
i like the bit about the crank who correctly asserts that the original data is an alien message, but what he thinks is the message is just the sequence of the detector switching on and off. That character reminds me a lot of conspiracy guys--if they encountered actual evidence of extraterrestrials they probably wouldn't be able to recognize it.
modern one is cos(x)~1. When I was studying electro-mecanics there was two kinds of people. Those trying to go with full precision and failing and those knowing where 12=10. Same when reading graphs, there was people trying to use the rule of third, then those who knew when to round or change the curve shape for best approximation. Being able to get close to the real answer without doing too much calculation was an art and the speed difference was huge. There, it was possible because of tolerance in components. We were taught how to calculate the error margin, but those calculations are themselves quite involved...so we approximated them too, talk of inception ^^ The only place where we wouldn't approximate, it's when tracing. Traces had to be crystal clear!
I know I’m going to piss off the mathematicians (which is, like, everyone on here except me) but for the rest of us mortals doing real-world practical things, if you’re within 2 or maybe 3 decimal places, you’re good. My grandfather was a metallurgist and that was his mantra. And if you ever did need to work out the full problem, there’s always a calculator, a piece of paper, or a whiteboard. The Apollo astronauts carried Pickett slide rules to the moon. As far as I’m concerned, that’s pretty much the gold standard.
@@jaytc3218 Depends on your calculations though. If you end up multiplying by 100 for some reason, then you need more precision in the intermediary steps. Likewise, when I was doing electro mecanics and had components with 20% tolerance, then "10+2=10", especially if there was a square root later on ^^ Even for statistics, you can get away with very aggressive rounding thanks to differences, square root and divisions all over the place. But when enumerating, it's usually a string of factorials, "combinatorials", squares and multiplications. So, any early rounding can totally change your answer up to the scale! So, you've to glance at the calculation, evaluate the possible error margin, see what error margin you are allowed then do your rounding (or not). It's also possible to do symbolic computation (algebra) then reduce at the very end. I remember that at the end of my curriculum in electro-mechanics, we looked at a circuits and eyeballed the whole output signal shape because we needed to shape the signal later on to drive mechanics. (so, building the circuits step by step according to our needs) I also remember that in my graduate in industrial computing (programming automatons), my lab teacher asked me to do a program to pilot a 6DOF polar arm to draw a straight line. I said "NO", I was unable to do so, because you've to compute the speed of all joints as such that the tip goes into a straight line. Easy in 2D, because your joints are in the same plane, much harder in 3D as one of the joints is in a perpendicular plane (And the stroke can have any direction!). Instead, I programmed a mini factory ^^ (Which was way easier as the arm had the ability to record poses and tween from one pose to another + the ability to drive every joint independently) All of that to say that rounding is an exercise by itself and can't be done blindly. Really depends on the problem at hand.
Absolutely LOVELY video once again. Clear, thoughtful, informative, well-produced -- and just the right length. I also really liked your more philosophical comments at the end. You make complex ideas really "human" -- and that's (IMO) a really great skill -- and service to your viewers. Please do carry on -- take care of yourself. I look forward to your output very much! CHEERS! Patrick.
In 2020 a RAND Engineer analyzed the numbers in the book and found a flaw in the statistical distribution. Check out the WSJ article - it was quite interesting.
I stumbled across your channel somehow a few months ago and subscribed. I realized I haven’t ever really left a comment. Just thought I’d say I watch each of your new videos as soon as I see it in my feed, and I thoroughly enjoyed your other videos too. I hope you keep making these! They are a great mix of history, math, science, and a delightfully dry sense of humor. Thanks for making videos!
Good random numbers were very hard to come by even on computers (as John von Neuman said: if you use deterministic methods to generate random numbers you are off course in state of sin) and several Monte Carlo methods, measure areas, in bootstrap methods, etc. The best book of Stanislav Lem (Solaris author) and all begins when a random number book is published, the numbers were created based on random background neutrino detection. Ten used begin to complain that they are not random and .... well it is one the best books I already read I won't spoil for you.
My statistics textbooks still reference these books, especially for sampling: "Use a random number table (or generator) to produce the required quantity of random numbers"
Way back in the 1970s when I was a newly minted graduate in one of my first jobs, I spotted a colleague using a table of random numbers for some statistics work he was doing. After a short chat I wrote a BASIC program to do it for him. Saved him a lot time, and earned me some brownie points.
@@RetroNerdstalgia it had all the numbers of the book in it, and picked one at random. The trick was how to program the random pick, without using the entered numbers. On a more serious note. The numbers in the book are real random (unless one sees "printed" numbers as a source of destroying randomness), the numbers in a program are always pseudorandom (at least those quick solutions), so less robust.
@@pierQRzt180 These days there are online services offering true random numbers generated by thermodynamic or quantum processes--very useful for cryptographic or statistical purposes. I think if you want them generated at a high rate, there's a price.
Well RAND co. did know to make money from a prank. Generate random numbers->publish them in a book->tell people they need a book full of random numbers-> earn the money. Thats a way to do it :-)
Published for the government during the height of the Cold War, my first guess was to foil code breaking or as passcodes. Fresh on their minds was the cautionary tale of the titan of cryptography, the Enigma Machine. The "uncrackable" cipher defeated by human error... The WW2 equivalent of setting your password to "password."
I vaguely remember a movie in which a computer was running malware (heavy mainframe) that transferred some data from one place to another place where they were not supposed to be. I really do not remember what - perhaps money. But at one point the heroes were inspecting a core dump. One remarked that the dump just seemed like random numbers, not a program. And then one of them remembered that the numbers were a page from this book and that proved that the memory had been written over to hide traces of the malware being present. That is the nerdiest nerd ever to appear in a movie.
Wow. The spoiler warning given in this video was not even nearly sufficient. I planned on reading the entire book cover to cover but now that I know that it ends with 8 I have no reason to. Next time, please give ample warning before you ruin the enjoyment for others.
Thank you for doing justice to this authentic product of human ingenuity. Too many ignoramuses write sarcastic reviews while never having thought about Rand's objectives.
Thank you Chris, for your deep and inspirational homily. It's possible the universe itself is an infinitely symmetrical object, the realm of all possibilities. But the current spacetime we reside in is a restricted state, with some of those symmetries broken by either spatial expansion or temporal evolution or combinations/synergies of both. It's possible that Cantor and Church were right then, maybe we do live in some subset of the set V, en.wikipedia.org/wiki/Von_Neumann_universe
Greek professors were paid for their books from the state in accordance to the number of the pages! Most of them were putting a few pages with random numbers just to increase their fee!!!
i know some older engineers that have books like this. and you can still buy custom lists of random digits from a few different companies that use radioactive isotopes to generate "true" random digits and not pseudo random digits. i suppose in some cases the difference really does matter
heres the real question. every number in this book is paired to a number in sequence. instead of reading the numbers in turn, you could go to the number in order and instead take the random number thats paired to it
I think the first column in each page is just the indexing column. It does not show a random number, but rather the number associated with the column, so that it can be referenced more easily.
Update: I found a library in, of all places, Ankara that was selling it. I've started taking jinking routes to work to reduce the likelihood of interception by my enemies
Thanks! There is no "full" version- I made it just for these videos. The weird cowbell is one of the stock sounds in GarageBand for MacOS- they call it "echolocation synth". Like a true expert, I found it because it's close to the top of the alphabetical list! (See also- the intro song which is stock iMovie "Breakbeat")
Another math channel had a book of the number of digits to the first repeat for the reciprocals of prime numbers. It was the hobby of a 19th century school master to calculate them. They said it was useful for computing some other useless thing.
And what I would like to know from a mathematician is: there is somhow a link between randomness and prime number. ( yes the point means that’s not a question.)30mars2022
Not a question but I'm answering anyway! The prime numbers are not random, since they are a specific sequence that looks the same every time we measure it: 2, 3, 5, 7, etc. But there are many important statistical properties that the primes have which resemble numbers which are chosen at random. It's a similar situation with the digits of pi- they are not random but when measured at large scales statistically they have properties which look the same as randomness.
Looks lke lots and lots of codes, now just imagine if these were codes and a hackers wants to figure out wich of those codes is the right one to break in, that will take hundreds of years to track down the right code ,out of “millions” of codes.
The book was a necessary and useful tool for its time. The need for such a book has vanished with the advent of modern computers and the capability of anyone being able to generate TRULY random numbers (Not Pseudo-Random). I would love to have that book as a collector's item, however!
afaik random number generator programs \ libraries are pseudo-random, that's why organizations that require true-randomness and are able to afford it use different kinds of whacky methods that rely on physical changes such as the method used to make this book. the problem with this book isn't that the numbers it contains are pseudo-random, because they are random, but rather that from the moment it was printed in a certain order this order is now a repeating series
@@pubcollize Today's home computers CAN generate TRUE random numbers. They can use things such as mouse movements, timing between clicks of the mouse, timing between keystrokes, and other sources to generate a SMALL pool of TRULY random numbers. In fact, this is done in a crypto program that I have used for a number of years: PGP If you need a LARGE pool of truly random numbers, however, then you need to resort to other external means.
@@gedstrom You didn't mention the most obvious one -- grabbing least significant bit from microphone ADC. Even if no mic is connected in most cases ADC is sensitive enough to catch up some radio signals / static electricity / whatever. These bits are (sort of) truly random. I would write a program at some point to test resulting numbers distribution.
Curses!!! I was reading that! The prose, the character development, the intricately layered suspense... and then you go and spoil the ending for me. 8.
I believe the machine used ambient noise from the electromagnetic spectrum. So reconstructing the machine’s output would require complete knowledge of the electromagnetic environment at the time. Not really possible, even if you know exactly how they did it.
Yep, it sounds like they used chaotic input rather than a true source of randomness. I've heard of radioactive sources to generate true random numbers. Same with photon emitters aimed at half-silvered mirrors with detectors on either path. At some point you do have to ask what the practical difference is between a deterministic random number generator which is impossible to predict and a true random number generator. I think my favorite system for generating randomness is covering a wall in lava lamps and pointing a digital camera at it, then generating numbers based on the data output by the camera. It's not truly random, but the movement of wax in the lava lamps is essentially unpredictable. (It's my favorite because it's the most fun to look at.)
These books of random digits were an important plot point in a 1968 science fiction novel titled _His Master's Voice_ by Stanislaw Lem. A statistician sued the publisher of one after showing that the digits weren't random but actually a very long repeating sequence. The publisher had been using noise from a radio telescope, but now they discovered that one source wasn't random and must be an extraterrestrial signal.
I love Lem!
i like the bit about the crank who correctly asserts that the original data is an alien message, but what he thinks is the message is just the sequence of the detector switching on and off. That character reminds me a lot of conspiracy guys--if they encountered actual evidence of extraterrestrials they probably wouldn't be able to recognize it.
Ancient calculating devices joke: An engineer is someone who, if you ask him what's 2x2, whips out his slide-rule and says 3.9
What's so funny? I just got out my old Pickering log-log and got the same answer.
modern one is cos(x)~1.
When I was studying electro-mecanics there was two kinds of people. Those trying to go with full precision and failing and those knowing where 12=10.
Same when reading graphs, there was people trying to use the rule of third, then those who knew when to round or change the curve shape for best approximation.
Being able to get close to the real answer without doing too much calculation was an art and the speed difference was huge.
There, it was possible because of tolerance in components.
We were taught how to calculate the error margin, but those calculations are themselves quite involved...so we approximated them too, talk of inception ^^
The only place where we wouldn't approximate, it's when tracing. Traces had to be crystal clear!
@@programaths sin(x) = x
I know I’m going to piss off the mathematicians (which is, like, everyone on here except me) but for the rest of us mortals doing real-world practical things, if you’re within 2 or maybe 3 decimal places, you’re good. My grandfather was a metallurgist and that was his mantra. And if you ever did need to work out the full problem, there’s always a calculator, a piece of paper, or a whiteboard. The Apollo astronauts carried Pickett slide rules to the moon. As far as I’m concerned, that’s pretty much the gold standard.
@@jaytc3218 Depends on your calculations though. If you end up multiplying by 100 for some reason, then you need more precision in the intermediary steps.
Likewise, when I was doing electro mecanics and had components with 20% tolerance, then "10+2=10", especially if there was a square root later on ^^
Even for statistics, you can get away with very aggressive rounding thanks to differences, square root and divisions all over the place.
But when enumerating, it's usually a string of factorials, "combinatorials", squares and multiplications. So, any early rounding can totally change your answer up to the scale!
So, you've to glance at the calculation, evaluate the possible error margin, see what error margin you are allowed then do your rounding (or not).
It's also possible to do symbolic computation (algebra) then reduce at the very end.
I remember that at the end of my curriculum in electro-mechanics, we looked at a circuits and eyeballed the whole output signal shape because we needed to shape the signal later on to drive mechanics. (so, building the circuits step by step according to our needs)
I also remember that in my graduate in industrial computing (programming automatons), my lab teacher asked me to do a program to pilot a 6DOF polar arm to draw a straight line. I said "NO", I was unable to do so, because you've to compute the speed of all joints as such that the tip goes into a straight line. Easy in 2D, because your joints are in the same plane, much harder in 3D as one of the joints is in a perpendicular plane (And the stroke can have any direction!). Instead, I programmed a mini factory ^^ (Which was way easier as the arm had the ability to record poses and tween from one pose to another + the ability to drive every joint independently)
All of that to say that rounding is an exercise by itself and can't be done blindly. Really depends on the problem at hand.
When you were flipping though this looked like a first edition. On page 168, in the second column in the top half was a 3 that is supposed to be an 8.
the ghost of william shanks!
@@ehfik what kind of weird youtube rabbit hole did i fall down to not only read this comment but also understand it
@@jacobburfield4622 numberphile ties it all together. have a great day!
If it was "supposed to be" then it wasn't random.
Absolutely LOVELY video once again. Clear, thoughtful, informative, well-produced -- and just the right length. I also really liked your more philosophical comments at the end. You make complex ideas really "human" -- and that's (IMO) a really great skill -- and service to your viewers. Please do carry on -- take care of yourself. I look forward to your output very much! CHEERS! Patrick.
In 2020 a RAND Engineer analyzed the numbers in the book and found a flaw in the statistical distribution. Check out the WSJ article - it was quite interesting.
I stumbled across your channel somehow a few months ago and subscribed. I realized I haven’t ever really left a comment. Just thought I’d say I watch each of your new videos as soon as I see it in my feed, and I thoroughly enjoyed your other videos too. I hope you keep making these! They are a great mix of history, math, science, and a delightfully dry sense of humor. Thanks for making videos!
Thanks a lot!
Good random numbers were very hard to come by even on computers (as John von Neuman said: if you use deterministic methods to generate random numbers you are off course in state of sin) and several Monte Carlo methods, measure areas, in bootstrap methods, etc. The best book of Stanislav Lem (Solaris author) and all begins when a random number book is published, the numbers were created based on random background neutrino detection. Ten used begin to complain that they are not random and .... well it is one the best books I already read I won't spoil for you.
My statistics textbooks still reference these books, especially for sampling: "Use a random number table (or generator) to produce the required quantity of random numbers"
Caude Shannon would love how much information is in this book.
Way back in the 1970s when I was a newly minted graduate in one of my first jobs, I spotted a colleague using a table of random numbers for some statistics work he was doing. After a short chat I wrote a BASIC program to do it for him. Saved him a lot time, and earned me some brownie points.
How did the program work?
@@RetroNerdstalgia it had all the numbers of the book in it, and picked one at random. The trick was how to program the random pick, without using the entered numbers.
On a more serious note. The numbers in the book are real random (unless one sees "printed" numbers as a source of destroying randomness), the numbers in a program are always pseudorandom (at least those quick solutions), so less robust.
@@pierQRzt180 You put all the numbers in the book in a BASIC program?
@@pierQRzt180 These days there are online services offering true random numbers generated by thermodynamic or quantum processes--very useful for cryptographic or statistical purposes. I think if you want them generated at a high rate, there's a price.
Well RAND co. did know to make money from a prank. Generate random numbers->publish them in a book->tell people they need a book full of random numbers-> earn the money. Thats a way to do it :-)
It's the Numberwang Code!
41988...And that's Numberwang!
Published for the government during the height of the Cold War, my first guess was to foil code breaking or as passcodes. Fresh on their minds was the cautionary tale of the titan of cryptography, the Enigma Machine. The "uncrackable" cipher defeated by human error... The WW2 equivalent of setting your password to "password."
This is a great channel. Only just beginning to explore the content. Thank you for taking the time to make them.
I vaguely remember a movie in which a computer was running malware (heavy mainframe) that transferred some data from one place to another place where they were not supposed to be. I really do not remember what - perhaps money. But at one point the heroes were inspecting a core dump. One remarked that the dump just seemed like random numbers, not a program. And then one of them remembered that the numbers were a page from this book and that proved that the memory had been written over to hide traces of the malware being present.
That is the nerdiest nerd ever to appear in a movie.
Woah- this might be a good math props episode
Wow. The spoiler warning given in this video was not even nearly sufficient. I planned on reading the entire book cover to cover but now that I know that it ends with 8 I have no reason to. Next time, please give ample warning before you ruin the enjoyment for others.
CVivian I managed to mute the video and look away before the spoiler but reading your comment revealed the last digit! WHYYYY????
And the last normal deviate is -.122.
NOBODY IS SAFE FROM THE SPOILERS
Thank you for doing justice to this authentic product of human ingenuity. Too many ignoramuses write sarcastic reviews while never having thought about Rand's objectives.
Thank you Chris, for your deep and inspirational homily. It's possible the universe itself is an infinitely symmetrical object, the realm of all possibilities. But the current spacetime we reside in is a restricted state, with some of those symmetries broken by either spatial expansion or temporal evolution or combinations/synergies of both.
It's possible that Cantor and Church were right then, maybe we do live in some subset of the set V, en.wikipedia.org/wiki/Von_Neumann_universe
Greek professors were paid for their books from the state in accordance to the number of the pages! Most of them were putting a few pages with random numbers just to increase their fee!!!
After your review, this book has been moved to the poetry section.
I want to know what the two middle numbers are
i know some older engineers that have books like this. and you can still buy custom lists of random digits from a few different companies that use radioactive isotopes to generate "true" random digits and not pseudo random digits. i suppose in some cases the difference really does matter
heres the real question. every number in this book is paired to a number in sequence. instead of reading the numbers in turn, you could go to the number in order and instead take the random number thats paired to it
Brilliant video love the randomness of the ururrurrr. Earned a sub in my books
This one was deep. Thank you
Not sure if I oversold the ending- that stuff is a super-exaggerated version of my true feelings, but I wanted it to feel epic.
@@ChrisStaecker imho it was an appropriate crescendo built on a wonderful concept. Bravo!
Do you have a lecture on “Binfords Law “ I think that would work well in your RUclips series
I love Benford’s law- mostly I focus on physical objects, but maybe I’ll work it in someday.
Could be something radical encoded in there no one's ever noticed, or figured out.
cryptonomicon style
The lack of a pattern is a pattern in itself
Great topic, thanks for the video
I think the first column in each page is just the indexing column. It does not show a random number, but rather the number associated with the column, so that it can be referenced more easily.
Yes that’s right. Each row is numbered sequentially.
How did you get a hold of the 1st edition? I've been looking for one for literal years now
Yes- very hard to find. My University library has it! So this copy isn't mine.
@@ChrisStaecker the hunt continues!
Update: I found a library in, of all places, Ankara that was selling it. I've started taking jinking routes to work to reduce the likelihood of interception by my enemies
Awesome! But also: Did you upload that end song in full somewhere? Really dig the cowbell from space
Thanks! There is no "full" version- I made it just for these videos. The weird cowbell is one of the stock sounds in GarageBand for MacOS- they call it "echolocation synth". Like a true expert, I found it because it's close to the top of the alphabetical list! (See also- the intro song which is stock iMovie "Breakbeat")
I see! thanks :)
Any chance for a third edition?
7:03 «...history calls them heroes»
Plot twist: history is written by the victors.
Plot twist twist: Victor is the only classic adding machine manufacturer that still exists.
Lol! You twisted the plot too much. :-)
The sequence 86753 occurs 10 times, and 75309 is repeated 8 times.
Rand? Such a random name
Another math channel had a book of the number of digits to the first repeat for the reciprocals of prime numbers. It was the hobby of a 19th century school master to calculate them. They said it was useful for computing some other useless thing.
I have a book that is one volume of an infinite volume random book
So actually fundamentally the universe is random. Only macroscopiccally order arises
Heroes!
And what I would like to know from a mathematician is: there is somhow a link between randomness and prime number. ( yes the point means that’s not a question.)30mars2022
Not a question but I'm answering anyway! The prime numbers are not random, since they are a specific sequence that looks the same every time we measure it: 2, 3, 5, 7, etc. But there are many important statistical properties that the primes have which resemble numbers which are chosen at random.
It's a similar situation with the digits of pi- they are not random but when measured at large scales statistically they have properties which look the same as randomness.
Do I need this book? No. Do I want this book? Yes, yes I do.
Looks lke lots and lots of codes, now just imagine if these were codes and a hackers wants to figure out wich of those codes is the right one to break in, that will take hundreds of years to track down the right code ,out of “millions” of codes.
The book was a necessary and useful tool for its time. The need for such a book has vanished with the advent of modern computers and the capability of anyone being able to generate TRULY random numbers (Not Pseudo-Random). I would love to have that book as a collector's item, however!
afaik random number generator programs \ libraries are pseudo-random, that's why organizations that require true-randomness and are able to afford it use different kinds of whacky methods that rely on physical changes such as the method used to make this book.
the problem with this book isn't that the numbers it contains are pseudo-random, because they are random, but rather that from the moment it was printed in a certain order this order is now a repeating series
@@pubcollize Today's home computers CAN generate TRUE random numbers. They can use things such as mouse movements, timing between clicks of the mouse, timing between keystrokes, and other sources to generate a SMALL pool of TRULY random numbers. In fact, this is done in a crypto program that I have used for a number of years: PGP If you need a LARGE pool of truly random numbers, however, then you need to resort to other external means.
@@gedstrom None of the sampling methods you mentioned are true-random, and PGP uses pseudo-random generator.
@@gedstrom You didn't mention the most obvious one -- grabbing least significant bit from microphone ADC. Even if no mic is connected in most cases ADC is sensitive enough to catch up some radio signals / static electricity / whatever. These bits are (sort of) truly random. I would write a program at some point to test resulting numbers distribution.
Volume 1 out of 10^10^6.
Shockingly, I think I saw this book in a library once. Not 100% sure though. Also, I prefer to avoid deviants ;)
Curses!!! I was reading that! The prose, the character development, the intricately layered suspense... and then you go and spoil the ending for me.
8.
It's not that deep.
The numbers are technically not random. If you knew how the machine worked you could predict the next number. These are seemingly random
I believe the machine used ambient noise from the electromagnetic spectrum. So reconstructing the machine’s output would require complete knowledge of the electromagnetic environment at the time. Not really possible, even if you know exactly how they did it.
@tim You are talking about psudo-random number, not random number.
Yep, it sounds like they used chaotic input rather than a true source of randomness. I've heard of radioactive sources to generate true random numbers. Same with photon emitters aimed at half-silvered mirrors with detectors on either path.
At some point you do have to ask what the practical difference is between a deterministic random number generator which is impossible to predict and a true random number generator.
I think my favorite system for generating randomness is covering a wall in lava lamps and pointing a digital camera at it, then generating numbers based on the data output by the camera. It's not truly random, but the movement of wax in the lava lamps is essentially unpredictable. (It's my favorite because it's the most fun to look at.)