Science Porn

[vorlon13]

BTW, how do they know their pi calculation is correct?

Well agreeing with the prior record holder helps, but a completely separate technique can be used. There *is* a way of directly calculating the Nth digit of pi (without generating all the previous digits) but only in hex. Nobody to date has discovered a way of doing it for pi in base 10. So you just start checking digits out towards the end of the printout with a completely separate formula and you'll know if you're right or not.

(found that little gem on a math board a while back, cool factoid)

[vorlon13]

MU69 has a moon ?


Maybe . . .


https://www.nasa.gov/feature/does-new-ho...ave-a-moon

I am waiting for the first natural moon to have a natural moon of its own.

Not quite as definitive as we might like, but 'something' is going on around Rhea, a moon of Saturn.

The 'stains' are near the equator of Rhea and might be from de-orbited meter size boulders. Some Cassini instruments detected anomalies near Rhea, but the narrow angle camera didn't show any thing.

[polymath257]

Since 2016 Pi is known to more than 22*10^12 digits.

What I find to more mind destroying is the largest prime number:

23,249,425 digits. And it's divisible by nothing. Yeah I know.

Regarding Pi, will there come a time when people just give up for being a waste of time and resources. I mean it is indeed fascinating but isn't it rather futile?

Unlike the grueling 371 days that was needed for our previous computation of 10 trilllion digits, this time we were able to beat it in about 94 days.
 
The computation was interrupted 5 times - all due to hard drive errors. Furthermore, a bug was discovered in the software which had to be fixed before the computation could be continued.
 
Memory Statistics:

• 60.2 TiB of disk was needed to perform the computation.
  
• 9.20 TiB of disk was needed to store the compressed digit output.
  
• More disk space was needed to make backups of the checkpoints.
  

From here.

Very little of mathematical value is obtained from these calculations.

But they are very, very good tests of the entire computer system.

[Succubus]

What I find to more mind destroying is the largest prime number:

23,249,425 digits. And it's divisible by nothing. Yeah I know.

Regarding Pi, will there come a time when people just give up for being a waste of time and resources. I mean it is indeed fascinating but isn't it rather futile?


From here.

Very little of mathematical value is obtained from these calculations.

But they are very, very good tests of the entire computer system.

Thank you for addressing this but my question still stands, if we were to parallel all the world computers to give us the largest calculable number of Pi, then what will we gain. Will Pi ever be more than a curiosity?

[vorlon13]

There would be some interest in the distribution and frequency of the individual digits. Are the digits 0-9 evenly used or are there more 3s used, for instance ??

How many digits out do you have to go till you find 5 zeros in a row? 10? 100?

Carl Sagan's book Contact had some 'anomalies' turn up in the digits of pi, wouldn't hurt to check . . . .

[polymath257]

Very little of mathematical value is obtained from these calculations.

But they are very, very good tests of the entire computer system.

Thank you for addressing this but my question still stands, if we were to parallel all the world computers to give us the largest calculable number of Pi, then what will we gain. Will Pi ever be more than a curiosity?

Well, there is a concept of a 'normal number'. This is one where each sequence of digits occurs at the frequency you would expect from its length. So each digit occurs 1/10 of the time, each pair 1/100 of the time, etc.

The computer studies can give evidence for whether pi is normal or not. But they can't actually prove it either way. And it is an open question whether pi is normal or not.

[Sal]

There would be some interest in the distribution and frequency of the individual digits.  Are the digits 0-9 evenly used or are there more 3s used, for instance ??

How many digits out do you have to go till you find 5 zeros in a row?  10?  100?

Carl Sagan's book Contact had some 'anomalies' turn up in the digits of pi, wouldn't hurt to check . . . .

I remember that part, in the end of the book after Ellie had come back from the Machine.

I don't see how there could be anything hidden in the decimals of pi, exactly how would you compute that? If something like a series prime numbers in the decimals showed up after some nth progression in the decimals, then maybe we could conclude that, otherwise it's a transcendental number and there is no apparent signifying pattern to the decimals.

[vorlon13]

Might be interesting to turn something like the WMAP pattern recognition software lose on the digits of pi . . . .

(bwa ha ha ha ha !!!!)

[vorlon13]

FWIW, Don't have any proof, but statistically speaking, it would be profoundly unlikely for any of the outermost retinue of Jupiter's (or Saturn's for that manner) to not contain any binary objects or to have their own moons.

Seriously. We've found asteroids scooting by earth with moons, the outer most flock of Jupiter's satellites are captured asteroids, there's gotta be some moons of moons there, even if we haven't detected any yet.

[Fireball]

FWIW, Don't have any proof, but statistically speaking, it would be profoundly unlikely for any of the outermost retinue of Jupiter's (or Saturn's for that manner) to not contain any binary objects or to have their own moons.

Seriously.  We've found asteroids scooting by earth with moons, the outer most flock of Jupiter's satellites are captured asteroids, there's gotta be some moons of moons there, even if we haven't detected any yet.

Larger masses are going to jack those little satellites' orbits quite a bit. Still, the universe is big, and I, like you, wouldn't be surprised by little moons on bigger moons. Who said it? Little fleas have smaller fleas...? Too close to dinner and too lazy to look.