Switzerland's University of Applied Sciences Graubünden [...] yesterday claimed it had broken the record, asserting it beat the previous record of 50 trillion digits, set by Timothy Mullican last year, by 12.8 trillion digits, and completed the task in just over 108 days versus Mullican's 303.
[...] A pair of 32-core AMD Epyc 7542 processors powered the uni's rig. AMD states the CPU cores spend most of their time at 2.9GHz, can burst to 3.4GHz, have 128MB L3 cache and happily run 64 threads apiece. A server with 1TB of RAM was also employed, with Ubuntu Linux 20.04 installed on a pair of solid-state disks of unspecified size.
A JBOD housed 38 7200RPM hard disks, each with 16TB capacity.
[...] Hard disks were chosen over SSDs because SSD performance degrades over time and the university's designers feared their intensive calculations could cause problems. In all, the uni said 510TB of disk space was used.
(Score: 4, Interesting) by Mykl on Wednesday August 18 2021, @03:32AM (42 children)
Calculating to this distance is really just a vanity project - the area of a galaxy in square nanometres is unaffected once you go past about 100 digits.
What we really want to know (and would be much more impressive) is if there has been any attempt to search for a pattern in those 62.8 trillion digits.
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @04:09AM (15 children)
I thought there was a math proof that pi was an irrational number - no pattern.
(Score: 3, Informative) by Beryllium Sphere (r) on Wednesday August 18 2021, @04:20AM
Not just irrational, transcendental.
(Score: 4, Informative) by maxwell demon on Wednesday August 18 2021, @05:25AM (13 children)
Being irrational does not necessarily mean that there is no pattern. For example, the following number is irrational, but has a clear pattern:
0.1101001000100001000001…
Numbers without pattern are called normal; it is conjectured that pi is normal, but it has not been proved.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by stormwyrm on Wednesday August 18 2021, @06:23AM (6 children)
No, you can also have normal numbers that have a pattern. For instance, Champernowne's Constant:
0.123456789101112131415161718192021222324252627282930...9899100101102103104...99799899910001001...
Champernowne's constant also has a very clear pattern, but it is normal in base 10.
Numquam ponenda est pluralitas sine necessitate.
(Score: 2) by tangomargarine on Wednesday August 18 2021, @02:55PM (5 children)
Who comes up with these whacky numbers? I don't suppose there's any actual mathematical use for this thing, like pi or e?
"Is that really true?" "I just spent the last hour telling you to think for yourself! Didn't you hear anything I said?"
(Score: 3, Interesting) by stormwyrm on Wednesday August 18 2021, @04:14PM (3 children)
Numquam ponenda est pluralitas sine necessitate.
(Score: 2) by tangomargarine on Thursday August 19 2021, @06:52AM (2 children)
Okay...after I'm done bleeding from the eyes trying to parse this definition...
What's the point of coming up with the term "normal numbers", then? We're just kicking the can down one layer.
"Is that really true?" "I just spent the last hour telling you to think for yourself! Didn't you hear anything I said?"
(Score: 2) by tangomargarine on Thursday August 19 2021, @07:06AM (1 child)
I'll be the first to admit that I absolutely suck ass at advanced math (and it's been real detrimental to me as a programmer /s), but god damn, dude...
"Oh no"
So the term he was defining out of thin air, he had a hard time coming up with an example for? The tragedy.
uh huh
Oh really? He somehow managed to prove that the category of numbers that already existed that was more or less "any number you can think of (minus imaginary numbers (basically anything multiplied by i))" was a superset of the thing he just made up?
Math majors are so weird.
Random aside, I had to take Discrete Math back in college to complete my Comp Sci major. That was an "interesting" class...I got the impression that the only people who ever took it were Comp Sci students (because it was a core requirement class) and math majors (who as we've already established are crazy ;).
And supposedly the statistic was that 50% of students failed the course on their first try. Naturally I hazarded a guess that it was a popular class to pawn off on the low-person-on-the-totem-pole new professor, which I'm sure had nothing to do with students having a hard time passing it.
"Is that really true?" "I just spent the last hour telling you to think for yourself! Didn't you hear anything I said?"
(Score: 0) by Anonymous Coward on Thursday August 19 2021, @07:34AM
We know that the vast majority of numbers are normal numbers. The fact that we know of only a handful of examples out of that majority and we had to purposefully design them to be such is a stunning illustration of how little we actually know not just about numbers but mathematics in general.
(Score: 3, Funny) by Tork on Wednesday August 18 2021, @06:59PM
It all makes more sense when you realize the numbers they're messing with are imaginary.
🏳️🌈 Proud Ally 🏳️🌈
(Score: 2) by wirelessduck on Wednesday August 18 2021, @06:28AM
Would it be significant in any way if pi was found to be not normal?
(Score: 1, Interesting) by Anonymous Coward on Wednesday August 18 2021, @06:49AM (4 children)
That isn't what normal means. Normal means that the finite subsequences of digits making up the irrational number occur according to the natural density. Your number isn't normal because the sequences with zeros occur much more commonly than sequences with ones. For example, all of the subsequences of single digits, the zeros occur much more than 1/2 the time and ones occur much less than 1/2 the time or in two digits zero-zero occurs the vast majority of time instead of 1/4th and one-one occurs exactly once instead of 1/4th the time.
(Score: 2) by maxwell demon on Wednesday August 18 2021, @03:58PM (3 children)
OK, so I misunderstood “normal”, thank you for the explanation. However the point that irrational numbers are not necessarily pattern-free remains; indeed, it is even strengthened given that even normal numbers (which are always irrational) don't need to be pattern-free.
Is there a name for pattern-free numbers?
The Tao of math: The numbers you can count are not the real numbers.
(Score: 0) by Anonymous Coward on Thursday August 19 2021, @01:34AM (2 children)
Uncomputable numbers are numbers that cannot be generated to arbitrary precision using any program that will halt. By way of example, Pi is a computable number and Chaitin's Constant is not.
(Score: 2) by tangomargarine on Friday August 27 2021, @07:11AM (1 child)
So it sounds like this Chaitin Constant thing is a very elaborate way of saying "we have no fucking idea"?
Freakin' math majors, man. I don't even. Trying to read this Wikipedia article is making me go cross-eyed from the sheer density of terms they're throwing around in every sentence.
"Is that really true?" "I just spent the last hour telling you to think for yourself! Didn't you hear anything I said?"
(Score: 0) by Anonymous Coward on Sunday August 29 2021, @10:43AM
It's an elaborate way of saying "it is a fact about the universe that we know is impossible to know." In mankind's collective quest to discover the sum of all knowledge in the Universe, knowing what you cannot know can be the most important facts of all.
(Score: 3, Funny) by Rosco P. Coltrane on Wednesday August 18 2021, @04:17AM (6 children)
Nevermind the pattern. The real breakthrough is when they finally bump on the last digit. Wake me up when that happens. The "we found the xth kajillionth decimal" stories are kind of meh at this point...
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @05:22AM
pattern is 20 trllion pi in 62.8/3.14;
(Score: 2) by acid andy on Wednesday August 18 2021, @08:59AM (4 children)
Yeah that would be one of the best discoveries ever if they found a point in Pi where its just all zeroes from there on, for hundreds or even thousands of digits. It's not going to happen though.
Welcome to Edgeways. Words should apply in advance as spaces are highly limite—
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @03:14PM (3 children)
If pi is an infinite decimal with no pattern, then there will be sections that have hundreds or thousands of zeroes. If you take the decimal representation of the string of bytes that make up the Soylent database and concatenate them all into a string of digits, that is in there too. Your SSN is in there too, and even your cell phone number, passport number, and your Blockbuster account ID number, all strung together.
(Score: 2) by acid andy on Wednesday August 18 2021, @03:43PM (1 child)
Yes you could find all those things if the digits were truly random, but as stormwrym wrote:
I don't think anyone truly knows whether the statistical distribution of the digits of Pi will allow all such sequences to occur in some finite subset of Pi's digits.
I'm not even sure statistics are sufficient to answer such questions. The digits of Pi are deterministic and so at best pseudorandom.
Welcome to Edgeways. Words should apply in advance as spaces are highly limite—
(Score: 2) by FatPhil on Thursday August 19 2021, @12:56PM
Given what we know about the first few trillion digits of pi,
"""
the decision “π is not normal” has credibility
P(T_s≤42, s= 1,...,9274770297096, T_9274770297097>42) = (1−exp(−42/2))^9274770297096·exp(−42/2) = 4.3497×10^−3064
"""
thus one might say that predicate is "incredible".
the maths required to get to that conclusion isn't for the faint-hearted.
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @04:07PM
Good thing they used Linux to run the calculation then, since the hash numbers for known CSAM are in there too, and Apple would have reported them to the feds.
(Score: 4, Informative) by c0lo on Wednesday August 18 2021, @04:34AM (9 children)
Nanometer is such a big distance, try Planck lengths** (but stop short of seeking any plank length, it's useless, Bunnings is out of timber).
---
**
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 2) by maxwell demon on Wednesday August 18 2021, @05:28AM (6 children)
I'm pretty sure the universe is older than a second. :-)
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by c0lo on Wednesday August 18 2021, @05:40AM (5 children)
Ummm... yeah, you have a point (that needs a larger precision).
Another 19 digits. Let's be generous and make it 29, bringing the total digits to 256.
Or about 1024 bits. Which puts a hard limit to the physical usefulness for the bitness of a CPU in a computer. Or the number of bits to represent an integer used in physics computations.
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @07:15AM (4 children)
you have a point, but you forget that it's floating.
for most useful calculations (such as weather prediction) we need to be very careful with precision.
see "what every computer scientist should know about floating point arithmetic" (pdf file) http://pages.cs.wisc.edu/~david/courses/cs552/S12/handouts/goldberg-floating-point.pdf [wisc.edu]
(Score: 2) by c0lo on Wednesday August 18 2021, @07:32AM (3 children)
All quantified in Planck units, with mass converted into energy units.
Fixed precision, no floating decimal point representation. Integer arithmetic on 20Abits should suffice.
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @09:02AM (2 children)
I think you're half joking, but I'll continue anyway.
I was talking about evolution in time, and more generally numerical solutions of differential equations.
For such things you can't avoid real numbers, and some form of floating point is the reasonable option at present.
related: even if it makes sense to talk about quantized space-time, that doesn't mean that you can go from real analysis to discrete math as far as the evolution equations are concerned. and the experimental evidence so far points to continuous space-time anyway.
let's say that you are right, and space-time and matter and energy can all be discretized into a grid and minimal units of matter and energy.
the discrete math approach would be to allocate memory for each cell of the grid (or vertex or whatever), and then count how many units of matter/energy are present there. I am certain that if this was the case, you would need significantly more memory to allocate for the relevant integers, then you would need to decribe the continuous version of the system with floating point numbers. by "significant" I mean at least some power (probably 3rd or 4th power, due to space-time dimensionality). even if you use a sparse representation (you can always use a sparse representation for the floating point version too).
so you will not gain memory by going from floats to integers.
(Score: 2) by c0lo on Wednesday August 18 2021, @10:23AM
Well, I was sorta joking, but now seriously, I did not make a claim on the cost efficiency of using different representation of numbers in computer memory. I said only that:
* theoretically, you can choose a representation of the Universe that will make the "computer modelling" use integers only.
* 1024 bits fixed precision real numbers (i.e. integers) should be enough for everybody; i.e. sufficiency but nothing about optimality of the choice
You can't have a total representation of all the cells in the universe, there's not enough matter to use for memory. So, necessarily, we are talking about a tiny slice of the Universe to be modeled/approximated inside a computer; and yet, the Universe will still influence that slice in some ways that you don't and never will account in your model.
Besides, even the laws of interaction (between whatever parts you consider in your model) are "whatever we think is valid" and many of the "laws of nature" that we are using are valid within a quite strict set of assumptions, most of them only approximately met in reality.
One on top of the other, the accuracy of the predictions based on modelling (including differential equations) are going to be affected anyway. And this is in the nature of the "modelling" beast, no matter how you represent it.
Now, if you have enough "precision space, for the accuracy of the results, it won't matter if your representation is floating point or fixed-width real numbers (aka integers) - the inherent nature of modelling will guarantee limits in the accuracy.
Again, in the above, I'm not making any consideration on the optimality of one or another representation of the numbers.
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 2) by maxwell demon on Wednesday August 18 2021, @04:12PM
Floats *are* discrete. Indeed, each float is an integer multiple of a small value (if the floating point type supports denormalized values, that small value is the smallest denormalized value the type can store; otherwise the type cannot store that value); it's just that not all integer multiples of that value have a representation.
Indeed, for IEEE single precision floats, we have a mantissa of 23 bits, and an exponent of 8 bits, which means that all values it can exactly represent can also be represented by an integer with 256+23 = 279 bits. With double precision, you've got 11 bit exponent and 52 bit mantissa, therefore all double precision values could be represented by a 2100 bit integer. But then, you usually only need the higher precision, not the full exponent range of the double type. Therefore with 1024 bits you'd be able to store all relevant values with at least the same precision as with double precision floating points.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 3, Funny) by coolgopher on Wednesday August 18 2021, @05:40AM (1 child)
Bunnings "dried" timber is great if you want to study the warping in space over time however....
(Score: 3, Informative) by c0lo on Wednesday August 18 2021, @05:55AM
The study will only be valid for smooth universes, given bunnings has it available only in DAR.
Most of it is already warped, cupped or bowed to various degrees, so a Multiverse theory is testable. That is, if you can get to it outside a lockdown.
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: -1, Troll) by Anonymous Coward on Wednesday August 18 2021, @04:38AM (1 child)
> Calculating to this distance is really just a vanity project
No shit Einstein.
(Score: -1, Offtopic) by Anonymous Coward on Wednesday August 18 2021, @04:42AM
FTFY
(Score: 5, Insightful) by stormwyrm on Wednesday August 18 2021, @05:32AM (5 children)
Yes, there is a pattern. The formula they used to calculate it is the pattern. That such a formula exists says that the sequence of digits of π is not truly random. The definition of a random sequence (from Kolmogorov complexity) is one for which there exists no computer program shorter than the sequence itself that can be used to generate it. It isn't that hard to write a short program to calculate the digits of π.
What they likely really want to do with these digits is statistically analyse them. There are many really vexing questions about randomness that might conceivably get closer to being resolved by looking at such a huge sample. They could notice that if they got the digits in a certain numeric base there is a slight deviation from normality [wikipedia.org]. Or there might be other statistical biases that various tests on them might show.
Numquam ponenda est pluralitas sine necessitate.
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @09:46AM (4 children)
An interesting side effect of using Komogorov alone as your definition of randomness is that there are no random numbers.
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @04:17PM (3 children)
(Score: 0) by Anonymous Coward on Thursday August 19 2021, @01:48AM (2 children)
Sure there is, I'll just build a machine that will output a single 1 numeral and halt in the absence of input instructions. The input program (length == 0 symbols) is shorter than the output number (length >= 1 symbol). Cheating you say? No, because Kolmogorov was your only definition of randomness.
(Score: 1, Insightful) by Anonymous Coward on Thursday August 19 2021, @06:34AM (1 child)
(Score: 0) by Anonymous Coward on Thursday August 19 2021, @07:42AM
It is universal and can simulate any Turing machine running any program, it just has the behavior of spitting out a 1 with no input.
(Score: 2) by DannyB on Wednesday August 18 2021, @08:14PM
Yeah, they said that when IBM first calculated PI to 2,000 digits in the early daze of computers.
There can be only one cable TV Network: USABCNNBCBSyFy
(Score: 0, Offtopic) by Anonymous Coward on Wednesday August 18 2021, @03:53AM (4 children)
Pi sucks. Pizza better.
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @04:40AM
Yawn. Any time π is the topic, there'll be someone to interject a "Yummy" or "Yikes" kind of "joke". Pretty much the same with Uranus.
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @04:50AM (2 children)
Yes, but how do you calculate its circumfence and surface area?
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @04:54AM (1 child)
Keep out your fences from my circumference.
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @05:19AM
from the spoiler, it seems like diameter is same as the pie, of course that does not make the circumference the same nimer of pi's.
(Score: 3, Insightful) by Anonymous Coward on Wednesday August 18 2021, @05:52AM (3 children)
I like the comments on this post.
This is the way SN should be.
(Score: -1, Troll) by Anonymous Coward on Wednesday August 18 2021, @03:04PM
Oblig. fuck you
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @07:19PM
In Soviet Russia, pi eats YOU!
(Score: 2) by DannyB on Wednesday August 18 2021, @08:16PM
Biden isn't doing enough to protect us from sharks with lasers!
There can be only one cable TV Network: USABCNNBCBSyFy
(Score: 3, Informative) by rigrig on Wednesday August 18 2021, @08:58AM (4 children)
It's all a plot to distract you from the correct circle constant [tauday.com].
No one remembers the singer.
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @09:49AM
I did notice the significance of of the number of digits they calculated. We can all appreciate their attempt to bring glory to the one true constant.
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @07:27PM (2 children)
I know you are half-joking, but it's true.
Pi is a bullshit number. The real number you want is 2 * pi. Equations are simpler and it is easier to reason about.
Pi is defined as circumference / diameter. What the fuck? Diameter is not a fundamental circle property. That would instead be the RADIUS.
Tau is defined as circumference / radius.
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @10:08PM (1 child)
Oh, one of you guys had to show up.
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @10:52PM
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @12:42PM (3 children)
Everyone knows the TRUE circle constant is tau, or 2 * pi.
Somebody break out a calculator and multiply the university's answer by 2.
(Score: 2) by DannyB on Wednesday August 18 2021, @08:20PM (2 children)
Everybody also knows that when the positive (+) and negative (-) labels were assigned to the poles of a battery, they got it wrong. And so now we have negative grounds, but schematics and explanations of the principles of a circuit (popular electronics) are always explained as if current flows from positive to negative.
We're stuck with it.
Just like how the size of horse's rear ends are indirectly related to the distance between rails for US train system.
There can be only one cable TV Network: USABCNNBCBSyFy
(Score: 0) by Anonymous Coward on Wednesday August 18 2021, @09:32PM
The electric charge sign convention is not as completely wrong as pi.
It is true that in ordinary electric circuits, it's the electrons that carry the electric charge. However, inside batteries and plasmas, some of the moving charges (currents) are positive ions. Furthermore, the direction of the current really only matters for DC; it's a non-issue for AC.
(Score: 0) by Anonymous Coward on Thursday August 19 2021, @04:14AM
Once you get into semiconductors and other "exotic" components, that no longer holds true. Some can only be explained in terms of electron flow, some only work with conventional current made of positive charge carriers, and other require simultaneous consideration of both.