Finding any 'pattern' might take a bit longer than the calculation.
Google calculates Pi to 100 trillion digits
Google has put its cloud to work calculating the value of Pi all the way out to 100 trillion digits, and claimed that's a world record for Picrunching. The ad giant and cloud contender has detailed the feat, revealing that the job ran for 157 days, 23 hours, 31 minutes and 7.651 seconds. A program called ycruncher by …
COMMENTS







Thursday 9th June 2022 12:58 GMT Howard Sway
Re: They'd get a shock...
There is only 1 configuration with all 0s possible. Any other SPECIFIC configuration would be equally probable, but it would be almost (but not quite) 100% probable that you would end up with one of the nonzero configurations.
This is why lottery winning numbers are in practice always a random distribution rather than a numeric sequence.

Thursday 9th June 2022 18:07 GMT Anonymous Coward
Re: lottery ... numbers are in practice always a random distribution rather than a numeric sequence
So you are saying I should quit playing 1,2,3,4,5,6 in the lottery?
Which is a bad sequence to pick. My states lottery once said that that was the most popular guessed numbers. So while it is just as possible as any other combination in a 6 number lottery. The fun of winning millions will go down a bit when you find out you have to share it with a few thousand other people.


Friday 10th June 2022 11:08 GMT John Robson
Re: lottery ... numbers are in practice always a random distribution rather than a numeric sequence
So why not pick numbers above 30/31, so that those using dates don't scavenge from the pot before the jackpot is determined.
PS  I haven't done any statistical analysis of the distribution of chosen numbers.

Friday 10th June 2022 16:23 GMT John Brown (no body)
Re: lottery ... numbers are in practice always a random distribution rather than a numeric sequence
Yes, that is true. When choosing numbers, people tend to go for "familiar" numbers, often birthdays. There has been quite a bit of "research" into the "best" numbers to pick for a lottery. Since, as stated, any one combination is a likely as any other, clearly the best numbers to choose are those least likely to be chosen by other players such that if you do win the jackpot, you minimise the chances of having to share with others. Of course, all that "research" might be negated by the fact it exists and now people know about it. On the other hand, "human nature" :)

Saturday 11th June 2022 11:56 GMT CommanderGalaxian
Re: lottery ... numbers are in practice always a random distribution rather than a numeric sequence
"PS  I haven't done any statistical analysis of the distribution of chosen numbers."
That's ok. Somebody else has.
tl;dr version  pick the least popular numbers.
http://news.bbc.co.uk/1/hi/sci/tech/240734.stm



Friday 10th June 2022 16:47 GMT Anonymous Coward
Re: lottery ... numbers are in practice always a random distribution rather than a numeric sequence
I heard of a local guy who always played the same number sequence, and he always bought multiple tickets with the same numbers for a given drawing. His explanation was that way when he won he would get multiple shares if the prize was split.
I confess that I find myself unable to craft a rational counter to his argument.




Thursday 9th June 2022 17:32 GMT Anonymous Coward
Re: They'd get a shock...
Pi's NOT random, it's just not a simply repeating pattern, so the digits have their own statistical distributions. One of the reasons you don't seed crypto with Pi instead of an RNG.
The other gent pinned a better estimate based on previous work, as they either had the paper close at hand or a much better memory than I do.
Interestingly, this relates on one of the things this kind of run can shed light on, the statistical distributions, which do have some value in other fields.
That hand having a large chunk of noncompressible* data.
(yes, smartypants, technically you can "compress" the thing by storing the formula and recalculating it, in 123 days with nontrivial budget, power, and storage footprint)
That said, other than fully recalculating it, is there an intermediary format that would be faster to calculate but smaller to store? That would be an interesting read, at least for nights that I wanted to mentally confounded for hours and wake up at 3 in a puddle of drool.


Saturday 18th June 2022 06:14 GMT Contrex
Re: They'd get a shock...
My number theory is a bit shaky, but I didn't think there could be any 'last' digits of pi (that is, it is conjectured that pi goes on for ever, or, if you prefer, that you can continue the expansion indefinitely). I did read a scifi story once, that if I recall correctly, involved God hiding a message in the digits that would only be found when an intelligent race developed a certain level of computing hardware. At the time I thought this was quite a silly idea (I still do).




Thursday 9th June 2022 19:05 GMT Yet Another Anonymous coward
Re: They'd get a shock...
>Therefore, it's likely to include the telephone number and social security number of almost everyone on the planet?
Possibly not.
There are irrational numbers that go on for ever and contain a random distribution of digits  so all possible sequences exist. And another class that go on for ever but aren't random. (Can't remember what they are called)
AFAIK we haven't proved which type Pi is.



Friday 10th June 2022 01:16 GMT Bill Gray
Re: They'd get a shock...
Not sure why you're getting downvotes. Your basic idea is right, with the minor quibble that 100 trillion = 10^{14}, not 10^{15}. (As a Yank, I will leave it to other commentards to quibble about long vs. short trillions.)
In a sequence of that length, any given string of fourteen digits (fourteen zeroes, or 12345678901234, etc.) has a probability of almost exactly 1/e = 36.8% of appearing zero or one times. The probability of n occurrences of the string is 1/(e * n!). So, an 18.4% chance of two occurrences, 6.1% of three occurrences, and so on.






Thursday 9th June 2022 19:14 GMT Alan Brown
Re: spot the difference
you may jest but I've seen rounding errors in serious astrophysics work throw results completely out the window
The funny part is that it got picked up because "The new 64bit systems are giving wrong answers"  as it turned out the old 32bit systems weren't right either, just different. If you're evolving stars and galaxies don't use your intermediate results as imputs for the next calculations unless you _really_ understand what compounded rounding achieves

Friday 10th June 2022 01:23 GMT Bill Gray
Re: spot the difference
Not exactly astrophysics, but some old code I modified for artificial satellite orbits had a value of π given to enough places for a 32bit float, but not for a 64bit one.
https://projectpluto.com/sat_code.htm#pi_prec
"...The primary purpose of the Data statement is to give names
to constants; instead of referring to π as 3.141592653589793
at every appearance, the variable Pi can be given that value
with a Data statement and used instead of the longer form of
the constant. This also simplifies modifying the program,
should the value of π change."
 Fortran manual for Xerox Computers



Saturday 11th June 2022 02:34 GMT Bill Gray
Re: spot the difference
Dunno much about the Sinclair Scientific beyond what's described at the (very interesting and impressive) simulator for it. The case shows 3.14159, as you describe, but it looks as if you could only enter it as 3.1416.





Thursday 9th June 2022 12:27 GMT Richard Tobin
Re: spot the difference
Somewhat surprisingly, it turns out to be possibly to compute the Nth digit of pi much more cheaply than computing all the first N digits. This was used to verify the last few digits, making it very implausible that there was a bug in the calculation.
For more information google "BaileyBorweinPlouffe".






Thursday 9th June 2022 15:31 GMT Charlie Clark
Number theory makes it clear that it is neither paradoxical nor trivial: there's more than one infinity. Also, as it is known that Pi itself is nonrepeating, it's also not possible for Pi to contain Pi. You could, I suppose, think about what's the greatest precision ("314") that can be repeated but even if you find that Pi to 1000 digits (or more) is repeated, it won't really help either because the repetition itself is random and in a scale so great as to be practically useless.
But calculating Pi and other irrational numbers to nth digits turns out to have other uses.
Is this one yours?


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Thursday 9th June 2022 10:08 GMT Danny 2
Measurement creep
In the early eighties my TI82 calculated pi instantly, 3.1416926. Press of a button, no faff.
I realise there's been inflation since then.
My last love claimed to have memorised the first 102 digits, and she did recite those once but beyond the first eight digits she could have just been making it up  as could this computer. She put me off pi, I'm into tao now.


Thursday 9th June 2022 10:34 GMT Primus Secundus Tertius
Re: Measurement creep
"Calculators often lie..."
I have a test for calculators, spreadsheets, etc.
x = 355/113  PI() = 2.667E07 on my calculator. So the six most significant digits have been lost.
Then 1/x = 3749531.309, which is seriously wrong.
Excel yields 3748629.088.
An old Quattro Pro also yields 3748629.088
Windows 7 calculator: 3748629.093
An online 30digit calculator yields 3748629.093


Friday 10th June 2022 01:42 GMT Bill Gray
Re: Measurement creep
My 10" Versalog slide rule says 355/113 = 3.145, or close to that.
(I had to get my reading glasses out to see the numbers. The intersection on the Venn diagram of people who know how to use a siide rule and the people young enough to do so without reading glasses is probably just about empty.)

Friday 10th June 2022 16:43 GMT John Brown (no body)
Re: Measurement creep
I'm 60 this year and slide rules were still available but calculators with "scientific" in the name and function had just reached schoolboy prices, so I never did get or learn to use a "slipstick".
My first was a Sinclair something or other. White, with red LED display and two AAA batteries. They were still banned in exams at the time though!

Saturday 11th June 2022 02:43 GMT Bill Gray
Re: Measurement creep
I'm 57, and used a slide rule a bit (not much) in my early teens. Not sure what happened to it. I now have two of my grandfather's slide rules (pocket versions with not many functions) and recently picked up the Versalog at a thrift shop. Basic calculations are quite straightforward; developing the facility to tackle anything really complicated would probably take more practice than I'm apt to invest. Definitely an elegant computing instrument for a more... civilized age.



Thursday 9th June 2022 20:58 GMT nagyeger
Re: Measurement creep
Probably cheating:
$ bc l
scale=1000
pi=a(1)*4
x = 355/113  pi
1/x
3748629.0926628157868016244511646880974354889954070036234564032865454604793222886800140518816206836356898079757856583284769379701126839058362003772355496229770758776797063438635191977660363361658744058103117300160461407276837111486330913977530873701252813424084198400481405092339036142808124539709683599867051286776490510626222882018048540955721785108550715843278070987656589966381686938060800983246562587555490962488193999331001490603484545747242535590070139275682350221862811047078534288326502531238107419444664984567094661646407825083581568369435126109673237667122066542690481175490950780594741574076038648703833149716962300481919871324782090295149305449951761504107916830115926158948469898610910327249791290301794755871665455486720582729977835980177289213718137555499355392288048490060629138647289009508061564131833621484607268993002381032691514552359573669279876404364535066753777868985530913238716219930154570781566614631309790422382386201404931585554783220139580948786727209918542548521348819205030972



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Friday 10th June 2022 11:55 GMT Richard Cranium
Re: Measurement creep
When I was at school I learnt a mnemonic for the first 30 digits:
Now I, even I, would celebrate
In rhymes inapt, the great
Immortal Syracusan, rivaled nevermore,
Who in his wondrous lore,
Passed on before,
Left men his guidance
How to circles mensurate.
But it's been utterly no use to me in the ensuing 50 years  well maybe occasionally to show off (to those who give a damn, so not many!)


Thursday 9th June 2022 10:23 GMT Rasczak
Google can't count
For a team claiming a feat in the mathematical world, you would think that they would check what numbers they are claiming. 1 Trillion is 10 to the 18th power, or a million, million, million. Google seem to have calculated to 100 million, million, or in real mathematical terms, 100 billion.
I know that the world seems to have tried to dumb down counting, and popular media counts a 1000 million as a billion these days, but in true maths it is not, and to try and claim 100 Trillion in this context is disingenuous at least, if not downright fraudulent.

Thursday 9th June 2022 13:00 GMT IanCutress
Re: Google can't count
Sorry sir, but what you call 'real mathematics' is what the rest of the world calls 'old english', and hasn't been taught in schools for over 30 years. Signed by someone who went to school 30 years ago, wasn't taught it then, spends a career in engineering where it isn't used as you claim, and has had to correct the old about it for 30 years.

Thursday 9th June 2022 13:21 GMT GlenP
Re: Google can't count
My goto reference, Mathematics  From The Birth of Numbers, from 1997 states that a billion is 1 million million, except in the US where it's 1 thousand million as they based theirs on an older French system than the rest of the world.
From my recollection however that was already outofdate for the UK when written. It was that way when I was at school, up to about 40 years ago but popular culture (ie US TV) probably started to bring about the change around then.
For the record no true mathematician would risk the confusion and I don't recall terms above 1 million ever being used during my degree, even a million probably only occurred in loose discussions in stats.

Thursday 9th June 2022 17:11 GMT brainwrong
Re: Google can't count, nor can most of world
"states that a billion is 1 million million"
The long form of these numbers is logical =>
1 billion is a contraction of bimillion, a million million.
1 trillion is a contraction of trimillion, a million million million.
nmillion=10^(6n), simple.
Instead people use the nonsensical billion=10^(3*3), because it makes things sound bigger than they are.
The other thing that's stupid is using the ratio of the circumference to the diameter. Using the ratio of the circumference to the radius makes much more sense mathematically, and would remove oddball factors of 2 from many equations.

Friday 10th June 2022 09:06 GMT Charlie Clark
Re: Google can't count, nor can most of world
Mathematically your correct. What we observe linguistically is literally inflation due to the vulgar use of scientiffic terms, particularly when talking about things like the US budget or debt. Most people don't care about precision, and couldn't explain it anyway, they just want to be able to compare different numbers.

Friday 10th June 2022 16:52 GMT John Brown (no body)
Re: Google can't count, nor can most of world
If you watch any US documentaries, anything involving mass or weight that is engineering rather than science based, everything is in pounds. They rarely use tons/tonnes. There seems to be a fascination with bigger numbers so use smaller units to get those bigger, more impressive sounding numbers. The everyday people end up using those same methods because that's what TV has impressed on them for so many years.
"OMG! That 70,000 THOUSAND POUND truck SMASHED over the bridge", sounds, to TV producers, far more impressive than "That 35 ton truck bumped the guardrail of the bridge"



Thursday 9th June 2022 18:14 GMT Auntie Dix
Google Causing Trouble Again
Once again, for all of the circles in my life, I am going to have to doublecheck their circumferences and diameters. That is going to take years.
This is almost as bad as the ImperialtoMetric madness of the 70s. How did that end? Expensively, for every American guy owns not just one set of wrenches, drivers, etc., but two incompatible collections. No American can gauge easily copier enlargements, because nearly no one here uses A4 and the like; the misspent paper has sustained our timber industry for a century.
So, let's just stick to 22/7 for pi, which, whether calculated by hand or device, seems to be a simple, rational choice for a boring, irrational number.

Friday 10th June 2022 12:21 GMT Richard Cranium
The power of π
My maths teacher (nickname Bong IIRC), with a reputation for enjoying his food, bounced into class one day and declared:
"This is my favourite power of pi" and scribbled on the blackboard.
π^{t}
before proudly declaring to a bunch of confused teenagers:
"I like raising pie to the teeth!"
I expect the reception here will be a similar to that he received many decades ago.
Somehow The Register seems to have conveniently obtained his photo for me to to use as an icon