happy Pi Day!

[stathmk]

If memorizing Pi to thousands of digits doesn’t sound like comedians impersonating cult members, then here’s a hilarious video of a Pie cult!: https://www.youtube.com/watch?v=0vsqqoGrTeo. I laughed at it & it reminds me of Monty Python. I think I showed it to a local museum before Pi Day in 2010.

Originally Posted by jasong

The number is over 20 terabytes of information. Most people couldn't even store it on their available hardware. It is unbelievably huge.

And, yet, after about 10 digits or so, the precision is about as much as most people will ever need. I think at one point someone calculated the number of digits needed to calculate the circumference of the known universe to the width of a hydrogen atom, if we were capable of that type of precision, and it was only a few tens of digits, I don't remember the exact number.

Jasong, that’s over 20 TB, but watch this for about a minute about a coin-sized disc that could hold 360 TB: https://www.youtube.com/watch?v=xE0AYH9dwj4&t=02m03s . I can infer that one particular year when it gets to 360 TB of Pi, then possibly Pi will be archived on a coin-sized disc like that.

This is deep & pretty much off topic. I can imagine that one decade at funerals that people will be buried with a 360 TB disc copy with details & videos of their personal lives, DNA ancestry, computer files, & etc if it’s indestructible up to 1,000 degrees C. I do know a fair amount about the Red Indians & about 800 of The Incans were buried with Quipu ( https://en.wikipedia.org/wiki/Quipu ), which nobody can translate. So it’s theorized that it has details about their personal lives since they were buried with them. That’s the closest analogy that I can think of to being remembered forever.

[retina]

Originally Posted by jasong

The number is over 20 terabytes of information.

Decimal digits can be stored more efficiently than one digit per byte. Actually it would be best IMO to store the binary output and convert to decimal on demand when required. Or alternatively, if computers get fast enough then just compute the digits on-demand, that would only require the storage of the algorithm.

[Mysticial]

Originally Posted by retina

Decimal digits can be stored more efficiently than one digit per byte. Actually it would be best IMO to store the binary output and convert to decimal on demand when required. Or alternatively, if computers get fast enough then just compute the digits on-demand, that would only require the storage of the algorithm.

Author of y-cruncher here:

The compression that I'm using for decimal digits is 19 digits per 8 bytes. Admittedly, 3 digits/10 bits is better and more efficient to convert from. But maintaining 8-byte (64-bit integer) alignment is easier to implement since it uses the same format for storing compressed digits in other bases.

Also, a radix conversion of all the digits from binary to decimal requires 10% of the computation cost and the same memory cost as the full computation of Pi. Even worse, it requires the same communication-bound disk-swapping FFT logic. So you're not really gaining much by saving the binary digits and not the decimal digits if you want the latter.

[retina]

Originally Posted by Mysticial

Author of y-cruncher here:

The compression that I'm using for decimal digits is 19 digits per 8 bytes. Admittedly, 3 digits/10 bits is better and more efficient to convert from. But maintaining 8-byte (64-bit integer) alignment is easier to implement since it uses the same format for storing compressed digits in other bases.

Also, a radix conversion of all the digits from binary to decimal requires 10% of the computation cost and the same memory cost as the full computation of Pi. Even worse, it requires the same communication-bound disk-swapping FFT logic. So you're not really gaining much by saving the binary digits and not the decimal digits if you want the latter.

Okay, thanks for the clarification. But I wasn't really being serious about the on-demand stuff I spoke about, obviously that would require resources equivalent to the original computation. I thought my last sentence made it clear that I wasn't really advocating it. I just wanted people to think more deeply about things rather than simply accepting that 22T digits requires an equivalent 22T bytes to store.

[Mysticial]

Originally Posted by retina

Okay, thanks for the clarification. But I wasn't really being serious about the on-demand stuff I spoke about, obviously that would require resources equivalent to the original computation. I thought my last sentence made it clear that I wasn't really advocating it. I just wanted people to think more deeply about things rather than simply accepting that 22T digits requires an equivalent 22T bytes to store.

Actually, the on-demand thing is best the way to go - if the computation fits in memory. You can get the first billion digits in a couple minutes on a quad-core Haswell. That'll beat 4 MB/s download speed.

The real problem with downloading digits is finding a suitable place to get them from. Back when I was in college, we had unlimited fast internet. So I was able to seed some torrents for the first 5 trillion digits. But I can't do that anymore. The torrents were popular enough to sustain itself for another year or so before they finally died.

[Uncwilly]

355
-----
113

7 digits of accuracy for 6 digits of expression.
I figured the easiest way to remember this is it has 2 each of the first 3 odds with 3's on the ends and the others in pairs.

[Dubslow]

https://twitter.com/Rockies/status/841717552795418624

[ewmayer]

For those of us whose Pi-memorization ambitions are more modest, an NC reader gives a useful 30-digit mnemonic.

[ewmayer]

Was thinking along the lines of easy mnemonics, and clearly wordlength-in--poetic-phrase is one way to go, but one which is quite inefficient in terms of chars-needed. Better would be one-char-per-decimal-digit, which likely approaches the chars-per-digit compactness of the best rational approximations, but adds easy-to-remember-ness.

So here is a modified-phonepad mnemonic for Pi, using that the first occurrence of 0 is in the 33rd place, based on the following number-to-letter-range mapping:
1:abc
2:def
3:ghi
4:jkl
5:mno
6:pqr
7:stu
8:vwx
9:yz
0:as-is [unneeded in first 32 places]

Based on that, here is the selection table, with my letter choices in the rightmost column:

3	ghi	h
1	abc	a
4	jkl	l
1	abc	a
5	mno	n
9	yz	y
2	def	f
6	pqr	r
5	mno	o
3	ghi	g
5	mno	o
8	vwx	x
9	yz	y
7	stu	u
9	yz	z
3	ghi	i
2	def	f
3	ghi	i
8	vwx	x
4	jkl	k
6	pqr	r
2	def	e
6	pqr	p
4	jkl	j
3	ghi	i
3	ghi	g
8	vwx	w
3	ghi	h
2	def	e
7	stu	t	[8 vwx for proper 30-digit rounding]

[continued: 9502884197169399375105820974944592307816406286208998628034825342117068...]

We assume the user knows where the decimal point is, and may insert blanks and punctuation ad libitum. Thus, the easy-to-remember nonsense-phrase 'hal any frog oxy uzi fix' gives 19 digits - more than enough for a double-precision-constant init - and appending the nonsense-word/phrase 'krep jig whet' gives 30 digits, truncated-round. (...'krep jig whew' gives proper 30-digit rounding.)

[stathmk]

Ewmayer, I didn’t think about 1 for abc, 2 for def, & so on. I don’t know Greek or Japanese. About 10 years ago, I saw a web site where I thought that it’s made by a man who types perfect English & also knows modern Greek. He said that there’s a modern Greek poem to memorize Pi. Greeks also have Cyrillic crossword puzzles. He didn’t notice or didn’t care to mention that the Japanese man who memorized over 100,000 Pi digits wrote a Japanese poem or story to remember Pi.

[Uncwilly]

Originally Posted by ewmayer

Was thinking along the lines of easy mnemonics, and clearly wordlength-in--poetic-phrase is one way to go, but one which is quite inefficient in terms of chars-needed.

We assume the user knows where the decimal point is, and may insert blanks and punctuation ad libitum. Thus, the easy-to-remember nonsense-phrase 'hal any frog oxy uzi fix' gives 19 digits - more than enough for a double-precision-constant init - and appending the nonsense-word/phrase 'krep jig whet' gives 30 digits, truncated-round. (...'krep jig whew' gives proper 30-digit rounding.)

I would suggest the following would be about the practical extent of this:
H. Alan y frog oxy