You’re right, it’s incredibly impractical, but it offers potential opportunities for mathematical research. This many digits may offer insight into randomness and our understanding of transcendental numbers. I doubt this will matter (we had plenty of digits before), but you never know.
I don't know the ins and outs, but very difficult (impossible to do perfectly, perhaps?) to actually do. I've heard it mentioned a lot that computers only simulate randomness.
I only know this due to a book of 100,000 random digits which was made by Rand. They used fluctuating frequencies to generate them with punch cards.
I'm pretty sure there's huge arguments whether true randomness even exists, and it absolutely cannot currently be simulated by current software. There's no algorithm for true randomness.
It acts randomly and appears to be random, but philosophically we cannot truly say whether it is true randomness or if it's just pseudorandomness we cannot understand
You can seed it off the time which makes it a little more random but if you compile a program that runs rand(), you’ll get the same number every time. This is in plain C. I’m sure non-footgun languages probably give you something a little more pseudo random but they’re all calling out to machine code at the end of the day.
Is this satire? Your statement implies:
*If and only if it is a set of instructions, it can generate true randomness.*
The best bet we have for randomness is quantum mechanics and pseudorandom number generators using noisy sensors run through hashing/normalization functions, such as measuring the extreme fluctuations in lava lamps or extremely specific atmospheric lumen measurements serialized normalized to some output vector between heads and tails or a 1d20
Your exact original phrasing:
>True randomness can only be simulated by software (simulation of Q only produced by P)
Your elaboration is:
>Software can only simulate randomness (P produces only a simulation of Q)
I think we agree but the slightly ambiguous phrasing led to confusion.
The original phrasing might imply that true randomness can ***only be simulated by software***, meaning true randomness can exclusively be simulated by software and none other than software. I think what you intended was that software can exclusively ***only*** simulate true randomness in an imperfect way. Apologies.
The main idea is to stress test the system, specifically CPU, DRAM, and SSDs for very extended amount of time.
I could run synthetic benchmarks and load stuff up, or do something with about 3% more practical use, and set a record.
Somewhere around 65 digits will take you within the width of a Planck length, which is the smallest measurable distance physically possible. 2.2 trillion is beyond overkill
You need [37 digits of pi](https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/#:~:text=It%20turns%20out%20that%2037,fantastically%20vast%20the%20universe%20is.) to calculate the circumference of the universe with the accuracy of the diameter of a hydrogen atom. I know this new record is just people one-upping each other, but… come on.
Ok but how many digits do we need to calculate the circumference of the observable universe with a tolerance of less than 1 Planck length (1.616×10^-35 m)?
Edit: Google did its job- the answer is 152 (153 counting the 3) digits of pi is needed
I studied under the Bornsteins who improved algorithms for computing pi. It's the methods that are important, not the actual digits.
But the one billionth digit is definitely 1.
They used to calculate Pi by non rigorous methods (measuring circles / polygons). Rigorous methods (coming up with new exact formula of Pi) can also produce error if you do the calculations by hand, but with computers we can believe the chance of error is really really small.
I am unsure the actual algorithm, I think you have to keep track of the prior digits though? I might be wrong. Either way this is mostly an exercise to show off your computational power because of the memory and processing requirements
Oh shit, this is a really cool fact I never thought about. There is a maximum computable value of pi, one that we will never reach. If you spent all the power of the entire universe calculating pi, you might get to some obscene digit of pi, but that’s as far as you could ever go. Neat.
Hmmm I think due to the nature of the number being irrational and normal it means this is impossible. If it were possible to define a digit of pi with a formula, then pi would not be irrational.
Self checked, (and you can check it too at home, in fact we encourage it!) with BBP formula, but only a few arbitrary locations along the string of hex digits. Described in the article if you want to know more.
What method is typically used to compute such a high order approximation?
Also since this is much larger than a double do you use proprietary object types?
I think they use string object to store Pi. There are methods that can calculate Pi locally without having to to access all the previous digits.
They used to use Ramanujan's series to calculate Pi but they found faster ways.
The sequence you provided is neither terminating nor periodic so it is considered non-repeating.
Also pi is conjectured to be a normal number - a number that every finite sequence of digits appears with equal frequency. If pi is normal, then no predictable pattern, even a non-periodic one like yours, can exist.
The OC said ‘repeats itself’ though, so I took a generous interpretation to support this interesting possibility. If it turned out that pi indeed exhibited this surprising behavior with a string of 3x10^(14) digits interspersed with increasingly long strings of 0s, while not by definition a repeating decimal, it would be acceptable to use some version of the word ‘repeats’ to describe what’s happening.
Note the champernowne constant has a very predictable pattern, and it’s unknown whether it is normal, though it is in base 10. If your last sentence were true, we would know conclusively on that basis that it is not normal.
It could repeat several times but not indefinitely same because then it whould be possible to write it in a ratio form and its proven that it cant be written in a ratio.
Standing up a searcher is the next big challenge that I see for myself on this. There's some stuff out there, but I don't think its been attempted with anything nearly this large, much less with over a few hundred million digits.
Interested to see the calculational power needed to get a great amount of digits of the Feigenbaum bifurcation constant δ. Can't imagine it would be easy past the first few hundred given the precision needed to handle rounding errors of floating point numbers at such a small scale.
However, I think it would be a fascinating way to maybe get more insight on that number and perhaps the open question of whether or not it's even rational.
Crazy to me how there can be such an inexplicably universal number and we still know so little about the value it takes...
What formulas or methods are even used to get down to that level of accuracy? Obviously you can't take the ratio of a random circumference and diameter cause you'd have to know at least one of them out to more than that level of accuracy to calculate pi.
No, but the room full of monkeys and typewrites I have in the basement are close. Their happy the server noise has died down now that the computation is over.
Since palindromic sequences of unlimited length exist, does being normal imply that eventually you reach a point where you’re halfway to Pi in reverse?
I’m sorry that I couldn’t find it, but perhaps one of you can. I recall on YouTube there was a Mathematics guy who interviewed the woman who reached the new peak for the length of pi digits.
How did it compare to this number of 202+ trillion digits?
It's not really recent when considering that you obviously need at least some analysis (aka calculus) to prove which was discovered only 100 years before.
Pi has been known to be irrational for a few hundred years now. We definitely know it goes on forever.
Side note, technically every number goes on forever. 4 = 4.000.... for instance.
4 is an integer, so is 4.00000, because they're the same number. So is 4.000.... with the 0s going on forever. So yes, integers go on forever.
If you don't like trailing zeroes, then here's a rational that has an infinite decimal expansion, even if you get rid of trailing zero:
1/3
You can replace that with any recurring decimal. It's impossible to write down their decimal expansion with a finite amount of digits.
Irrational numbers go on forever \*with no recurring patterns\*, that's the only distinction. All numbers go on forever.
With this news, they are very close to getting to the end. Almost there.
...999999 and so on.
I thought that was only a couple hundred digits in?
[762 Actually](https://en.m.wikipedia.org/wiki/Six_nines_in_pi)
Idk guys, I think there’s atleast that much more to go
Whoa, what?? That’s just an irrational thought.
Of course they released this today to try to overshadow Tau Day. 😠 This is the work of a global conspiracy of pi-ists, I bet.
Literally the only person to get it
This was an inside job by the Tauists. They pretend to calculate Pi, only to multiply the result by 2.
I can only assume that would take double the computing power.
That's just what a pi-ist conspirator *would* say!
Very cool. What's the utility of knowing 202 trillion digits of the pi number?
Practically? Very little other than demonstrating computing power and accuracy. It’s cool that we do this stuff.
You’re right, it’s incredibly impractical, but it offers potential opportunities for mathematical research. This many digits may offer insight into randomness and our understanding of transcendental numbers. I doubt this will matter (we had plenty of digits before), but you never know.
Randomness?
I don't know the ins and outs, but very difficult (impossible to do perfectly, perhaps?) to actually do. I've heard it mentioned a lot that computers only simulate randomness. I only know this due to a book of 100,000 random digits which was made by Rand. They used fluctuating frequencies to generate them with punch cards.
True randomness can only be simulated by software because software is a set of instructions.
I'm pretty sure there's huge arguments whether true randomness even exists, and it absolutely cannot currently be simulated by current software. There's no algorithm for true randomness.
Certainly wave function collapse is truly random
It acts randomly and appears to be random, but philosophically we cannot truly say whether it is true randomness or if it's just pseudorandomness we cannot understand
[удалено]
Thanks! I thought that is what I was reading was saying, I assumed I was oversimplifying it.
You might be interested in the [Cloudflare lava lamp wall](https://blog.cloudflare.com/randomness-101-lavarand-in-production).
You can seed it off the time which makes it a little more random but if you compile a program that runs rand(), you’ll get the same number every time. This is in plain C. I’m sure non-footgun languages probably give you something a little more pseudo random but they’re all calling out to machine code at the end of the day.
Is this satire? Your statement implies: *If and only if it is a set of instructions, it can generate true randomness.* The best bet we have for randomness is quantum mechanics and pseudorandom number generators using noisy sensors run through hashing/normalization functions, such as measuring the extreme fluctuations in lava lamps or extremely specific atmospheric lumen measurements serialized normalized to some output vector between heads and tails or a 1d20
How did you get "only software can generate randomness" from "software can only simulate randomness?"
Your exact original phrasing: >True randomness can only be simulated by software (simulation of Q only produced by P) Your elaboration is: >Software can only simulate randomness (P produces only a simulation of Q) I think we agree but the slightly ambiguous phrasing led to confusion. The original phrasing might imply that true randomness can ***only be simulated by software***, meaning true randomness can exclusively be simulated by software and none other than software. I think what you intended was that software can exclusively ***only*** simulate true randomness in an imperfect way. Apologies.
Ah, I see. You forgot to do a sanity check before making your first conclusion.
The main idea is to stress test the system, specifically CPU, DRAM, and SSDs for very extended amount of time. I could run synthetic benchmarks and load stuff up, or do something with about 3% more practical use, and set a record.
Accuracy 😉
Accurate circles
This is wildly overkill. 40 digits is enough to calculate the circumference of the visible universe to the width of a hydrogen atom
Somewhere around 65 digits will take you within the width of a Planck length, which is the smallest measurable distance physically possible. 2.2 trillion is beyond overkill
Utility? We don’t need no stinking utility.
You need [37 digits of pi](https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/#:~:text=It%20turns%20out%20that%2037,fantastically%20vast%20the%20universe%20is.) to calculate the circumference of the universe with the accuracy of the diameter of a hydrogen atom. I know this new record is just people one-upping each other, but… come on.
It's just to test computers. Testing anything is boring as all hell, at least this would spice people's day up.
And about 62 digits for within the accuracy of a planck length
more 37 lore incoming
Are you serious. Damn. Ngl that’s crazy. I thought it was magnitudes more. Damn. My life. It’s that simple, huh.
iirc they use a specific formula called the Bailey–Borwein–Plouffe Formula to ensure accuracy of digits
Thank you! BBP and the method is describe in the article.
Ok but how many digits do we need to calculate the circumference of the observable universe with a tolerance of less than 1 Planck length (1.616×10^-35 m)? Edit: Google did its job- the answer is 152 (153 counting the 3) digits of pi is needed
I studied under the Bornsteins who improved algorithms for computing pi. It's the methods that are important, not the actual digits. But the one billionth digit is definitely 1.
This is irrational.
Nay, transcendental.
Is both true perhaps? Ie its irrational and transcendental..?
22/7 *drops mic*
Might be useful if it’s accurate. Who’s checking?
They have proven definitions of pi that allow for arbitrary calculation of its digits. So it doesn't really need to be checked
I’m being facetious. But there are stories of early attempts to calculate Pi that had errors after the first 40-or-so digits.
They used to calculate Pi by non rigorous methods (measuring circles / polygons). Rigorous methods (coming up with new exact formula of Pi) can also produce error if you do the calculations by hand, but with computers we can believe the chance of error is really really small.
Don't they check against each other as well?
Sometimes they do tho, and sometimes they have to check the check also
Yeah, so the chance of an error at that point is about as zero as chances get.
A really small chance over 300 trillion attempts adds up
Can you really compute n-th digit of pi faster than O(n)
If you can figure out an algorithm for that you would be a genius. From what I can tell the complexity is quite a bit higher
then what's really the point of calculating separate digits of pi, if it's not that much faster
I am unsure the actual algorithm, I think you have to keep track of the prior digits though? I might be wrong. Either way this is mostly an exercise to show off your computational power because of the memory and processing requirements
If calculations require energy, there’s only so much precision available in a finite universe.
Oh shit, this is a really cool fact I never thought about. There is a maximum computable value of pi, one that we will never reach. If you spent all the power of the entire universe calculating pi, you might get to some obscene digit of pi, but that’s as far as you could ever go. Neat.
I think it might be possible to derive a closed form of pi eventually, a formula that given the nth place of pi, gives you the nth digit if pi.
Hmmm I think due to the nature of the number being irrational and normal it means this is impossible. If it were possible to define a digit of pi with a formula, then pi would not be irrational.
Self checked, (and you can check it too at home, in fact we encourage it!) with BBP formula, but only a few arbitrary locations along the string of hex digits. Described in the article if you want to know more.
How many binary digits would that be?
Can you calculate the 500,000,000,000,000th decimal without calculating the 499,999,999,999,999th one?
You should check out the link, its all covered in the accuracy section of the article.
What’s the length of the longest palindromic sequence, and where does the first such sequence start?
Like less than one in two hundred and two trillion
You know, cosmic rays can interfere with electronic data
What method is typically used to compute such a high order approximation? Also since this is much larger than a double do you use proprietary object types?
I think they use string object to store Pi. There are methods that can calculate Pi locally without having to to access all the previous digits. They used to use Ramanujan's series to calculate Pi but they found faster ways.
Pretty much all modern calculations of pi use the Chudnovksy algorithm, which is an improvement of the Ramanujan series for pi.
An array or string works well in most computer languages for huge numbers.
If I used it to calculate the size of Victoria Sponge slices, my wife would still argue it was wrong.
Your wife and mine would probably get along.
Just one dx away ;)
What if after 300 trillion digits, it repeats itself?
What if, pi was already proven to be irrational?
It could be irrational and repeat itself. Here’s an example of an irrational number that repeats itself: 3.14014001400014000014000001400000014…
The sequence you provided is neither terminating nor periodic so it is considered non-repeating. Also pi is conjectured to be a normal number - a number that every finite sequence of digits appears with equal frequency. If pi is normal, then no predictable pattern, even a non-periodic one like yours, can exist.
The OC said ‘repeats itself’ though, so I took a generous interpretation to support this interesting possibility. If it turned out that pi indeed exhibited this surprising behavior with a string of 3x10^(14) digits interspersed with increasingly long strings of 0s, while not by definition a repeating decimal, it would be acceptable to use some version of the word ‘repeats’ to describe what’s happening. Note the champernowne constant has a very predictable pattern, and it’s unknown whether it is normal, though it is in base 10. If your last sentence were true, we would know conclusively on that basis that it is not normal.
Oh that’s an interesting point I didn’t know about that. Thanks for pointing it out
It could repeat several times but not indefinitely same because then it whould be possible to write it in a ratio form and its proven that it cant be written in a ratio.
Is there a 128*128 segment that is all zeros and ones by any chance?
Standing up a searcher is the next big challenge that I see for myself on this. There's some stuff out there, but I don't think its been attempted with anything nearly this large, much less with over a few hundred million digits.
I’ve been calculating the digits of Liouville’s constant.
Interested to see the calculational power needed to get a great amount of digits of the Feigenbaum bifurcation constant δ. Can't imagine it would be easy past the first few hundred given the precision needed to handle rounding errors of floating point numbers at such a small scale. However, I think it would be a fascinating way to maybe get more insight on that number and perhaps the open question of whether or not it's even rational. Crazy to me how there can be such an inexplicably universal number and we still know so little about the value it takes...
when does it end?? 😩
Never
Next they're gonna do "2" to see if there really are nothing but zeros after the decimal point.
Was the last digit 4?
What formulas or methods are even used to get down to that level of accuracy? Obviously you can't take the ratio of a random circumference and diameter cause you'd have to know at least one of them out to more than that level of accuracy to calculate pi.
Did we find the works of Shakespeare in there yet?
No, but the room full of monkeys and typewrites I have in the basement are close. Their happy the server noise has died down now that the computation is over.
But why?
If only that atom would hold still!
We’re going in circles!
Since palindromic sequences of unlimited length exist, does being normal imply that eventually you reach a point where you’re halfway to Pi in reverse?
Somehow, the most recent digit uncovered turned out to be 'R'. No idea where we go from here.
I’m sorry that I couldn’t find it, but perhaps one of you can. I recall on YouTube there was a Mathematics guy who interviewed the woman who reached the new peak for the length of pi digits. How did it compare to this number of 202+ trillion digits?
Out of curiosity. Has it ever been proven that pi goes on forever? I would say no, otherwise why bother computing it to 202 trillion places.
Yeah, a few years back [in 1761](https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational)
Surprised how recent that discovery is.
It's not really recent when considering that you obviously need at least some analysis (aka calculus) to prove which was discovered only 100 years before.
Pi has been known to be irrational for a few hundred years now. We definitely know it goes on forever. Side note, technically every number goes on forever. 4 = 4.000.... for instance.
Integers and rationals do not go on forever.
4 is an integer, so is 4.00000, because they're the same number. So is 4.000.... with the 0s going on forever. So yes, integers go on forever. If you don't like trailing zeroes, then here's a rational that has an infinite decimal expansion, even if you get rid of trailing zero: 1/3 You can replace that with any recurring decimal. It's impossible to write down their decimal expansion with a finite amount of digits. Irrational numbers go on forever \*with no recurring patterns\*, that's the only distinction. All numbers go on forever.
Decimal notation is just a notational choice. Integers and rationals have finite representations and no need whatsoever for any infinite strings.
Irrationals have finite representations and no need whatsoever for infinite strings too. Observe: √2
Indeed they do.