Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss

Does the octillionth digit of pi exist?

90 views
Skip to first unread message

calvin

unread,
Mar 13, 2012, 10:33:50 PM3/13/12
to
If so, in what sense does it exist?

quasi

unread,
Mar 13, 2012, 10:44:19 PM3/13/12
to
On Tue, 13 Mar 2012 19:33:50 -0700 (PDT), calvin
<cri...@windstream.net> wrote:

>If so, in what sense does it exist?

In the sense that if you change the value of Pi in the
octillionth place (leaving all other digits unchanged), the
new number could be too small by as much as one octillionth.

quasi

quasi

unread,
Mar 13, 2012, 10:48:13 PM3/13/12
to
Oops. I meant:

It could be too small by as much as 9 octillionths.

quasi

Richard Henry

unread,
Mar 13, 2012, 10:50:31 PM3/13/12
to
On Tuesday, March 13, 2012 7:33:50 PM UTC-7, calvin wrote:
> If so, in what sense does it exist?

It's a 3

quasi

unread,
Mar 13, 2012, 10:57:26 PM3/13/12
to
Ugh, I'll get it right:

It could be too small or too large by as much as 9
octillionths.

quasi

Tonico

unread,
Mar 13, 2012, 11:12:51 PM3/13/12
to
On Mar 14, 4:33 am, calvin <cri...@windstream.net> wrote:
> If so, in what sense does it exist?



In the sense that given enough time, energy and will (of someone
checking stuff), a computer can calculate it in a rather easy, though
probably lengthy, way.

Tonio

calvin

unread,
Mar 13, 2012, 11:36:44 PM3/13/12
to
Yes to most of the above, but is there an octillionth
digit in some sense right now, before the work is done
to compute it (and thus for one to be in a position to
alter it)?

calvin

unread,
Mar 13, 2012, 11:45:13 PM3/13/12
to
To be more clear (hopefully), I'm thinking
maybe the digit has only potential existence,
and wondering if there is a mathematical
concept of potential existence?

quasi

unread,
Mar 13, 2012, 11:50:49 PM3/13/12
to
On Tue, 13 Mar 2012 20:45:13 -0700 (PDT), calvin
<cri...@windstream.net> wrote:

>On Tuesday, March 13, 2012 11:36:44 PM UTC-4, calvin wrote:
>> Yes to most of the above,

There is no above -- you need to quote the message you are
replying to.

>> but is there an octillionth
>> digit in some sense right now, before the work is done
>> to compute it (and thus for one to be in a position to
>> alter it)?
>
>To be more clear (hopefully), I'm thinking
>maybe the digit has only potential existence,
>and wondering if there is a mathematical
>concept of potential existence?

It can be proved that the value is uniquely determined, thus
whenever it's computed it will always come out the same.

Also, there are methods to compute a given digit of Pi
without computing all the prior ones.

quasi

calvin

unread,
Mar 14, 2012, 12:40:11 AM3/14/12
to qu...@null.set
On Tuesday, March 13, 2012 11:50:49 PM UTC-4, quasi wrote:
> On Tue, 13 Mar 2012 20:45:13 -0700 (PDT), calvin wrote:
> > On Tuesday, March 13, 2012 11:36:44 PM UTC-4, calvin wrote:
> > > Yes to most of the above,
>
> There is no above -- you need to quote the message you are
> replying to.
> ...

By 'the above' I meant all previous posts.

Tonico

unread,
Mar 14, 2012, 12:46:46 AM3/14/12
to
Well, in the sense you seem to be talking that digit has as potential
an existence as the existence of a shark in the Pacific Ocean UNTIL
you see one there, or as potential as the existence of a city called
Minsk until you visit it, or...

By rather basic calculus we know we can have sequences or series that
can approach the value of pi as accurately as we want, say...within
10^(-227) of the value of pi, which is way more accurate than what you
want, an approximation that thus will give us the octillionth
(whatever that is...is it like an 8 with 12 zeroes after it?) digit of
the decimal expansion of pi.

Tonio

Hauke Reddmann

unread,
Mar 14, 2012, 5:49:25 AM3/14/12
to
Tonico <Toni...@yahoo.com> wrote:

> In the sense that given enough time, energy and will (of someone
> checking stuff), a computer can calculate it in a rather easy, though
> probably lengthy, way.

HA! But now assume we don't take the octillionth (much too
small :-) but, say, the googolplexth number and our universe isn't
large enough to provide with the time, space and energy needed
for calculating it. Also, replace pi (much too orderly, we might
find a way to shortcut the calculation) by "the value of the
mid cell of the 110 cellular automaton at the googolplexth iteration"
or something incompressible like that, so the only way to
calculate is actually running it. Does it still exist?
--
Hauke Reddmann <:-EX8 fc3...@uni-hamburg.de
Out on deck the dawn arrived
Your grey sweater oversized
The rooftops glimmered before our eyes

Bill Taylor

unread,
Mar 14, 2012, 7:22:12 AM3/14/12
to
> but is there an octillionth
> digit in some sense right now, before the work is done
> to compute it

Yes.

Next question please.

Bill Taylor

unread,
Mar 14, 2012, 7:21:02 AM3/14/12
to
> Does the octillionth digit of pi exist?

Yes.

> If so, in what sense does it exist?

In the same sense that 42 exists.


Bill Taylor

unread,
Mar 14, 2012, 7:23:32 AM3/14/12
to
> HA! But now assume we don't take the octillionth (much too
> small :-) but, say, the googolplexth number and our universe isn't
> large enough to provide with the time, space and energy needed
> for calculating it. Also, replace pi (much too orderly, we might
> find a way to shortcut the calculation) by "the value of the
> mid cell of the 110 cellular automaton at the googolplexth iteration"
> or something incompressible like that, so the only way to
> calculate is actually running it. Does it still exist?

Yes.

I see we're getting the easy ones first.

Tonico

unread,
Mar 14, 2012, 7:29:22 AM3/14/12
to
On Mar 14, 11:49 am, Hauke Reddmann <fc3a...@uni-hamburg.de> wrote:
> Tonico <Tonic...@yahoo.com> wrote:
> > In the sense that given enough time, energy and will (of someone
> > checking stuff), a computer can calculate it in a rather easy, though
> > probably lengthy, way.
>
> HA! But now assume we don't take the octillionth (much too
> small :-) but, say, the googolplexth number and our universe isn't
> large enough to provide with the time, space and energy needed
> for calculating it. Also, replace pi (much too orderly, we might
> find a way to shortcut the calculation) by "the value of the
> mid cell of the 110 cellular automaton at the googolplexth iteration"
> or something incompressible like that, so the only way to
> calculate is actually running it. Does it still exist?
> --


**** Yes, and assuming all that mess of googolplexth, mid cellular
automaton iteration and etc. can be translated into one definite
ordinal, we can then even find out what it is.

Tonio


> Hauke Reddmann <:-EX8    fc3a...@uni-hamburg.de

JEmebius

unread,
Mar 14, 2012, 10:32:14 AM3/14/12
to
See Wikipedia: http://en.wikipedia.org/wiki/42_(number)

42: the answer to end all answers.

42: the universal final answer to all questions, sensible and nonsensical, clever and stupid, wise
and foolish, to-the-point and vague. Four dimensions is enough.

"42" turns up everywhere, even in weird math-physical theories, like the hollow-earth theory
mentioned at http://jemebius.home.xs4all.nl/HollowEarth.htm .


Enjoy! - Johan E. Mebius

calvin

unread,
Mar 14, 2012, 11:15:34 AM3/14/12
to
On Wednesday, March 14, 2012 12:46:46 AM UTC-4, Tonico wrote:
> ... octillionth
> (whatever that is...is it like an 8 with 12 zeroes after it?) ...

1 with 27 zeros after it (10^27)

The progression is thousand, million, billion, trillion,
quadrillion, quintillion, sextillion, septillion,
octillion, ...

Herman Rubin

unread,
Mar 14, 2012, 11:35:03 AM3/14/12
to
No, that is much too large a change. One octillionth
would be one in the 27th place.

It could be too small or too large by as much as 9
divided by 10 to the octillionth power.

> quasi


--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558

Ross A. Finlayson

unread,
Mar 14, 2012, 11:38:37 AM3/14/12
to
Yeah of course it does. I have heard that Bailey, Bourwein, and
Plouffe discovered a function that gives you whatever digit of pi you
want without computing all the ones in the middle, a digit extraction
algorithm. This contrasts with a spigot algorithm that returns one
then the next etcetera. So you can find the function and put 8e12 in
it. You might find it easier to put in 16^21 than 10^21.

Frederick Williams

unread,
Mar 14, 2012, 12:27:29 PM3/14/12
to
calvin wrote:

Does the octillionth digit of pi exist? If all of these exist, then it
certainly does:

'0', '1', '2', '3', '4', '5', '6', '7', '8', '9'.

> If so, in what sense does it exist?

In the same sense as any other physical thing does.

--
The next few little actual people come from any much larger number of
different POSSIBLE perspectives.

George Green, aka GEORGE GREEN

Aatu Koskensilta

unread,
Mar 14, 2012, 12:28:47 PM3/14/12
to
Frederick Williams <freddyw...@btinternet.com> writes:

> calvin wrote:
>
> Does the octillionth digit of pi exist? If all of these exist, then it
> certainly does:
>
> '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'.
>
>> If so, in what sense does it exist?
>
> In the same sense as any other physical thing does.

You think digits are physical things?

--
Aatu Koskensilta (aatu.kos...@uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen."
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

Frederick Williams

unread,
Mar 14, 2012, 1:13:09 PM3/14/12
to
Aatu Koskensilta wrote:
>
> Frederick Williams <freddyw...@btinternet.com> writes:
>
> > calvin wrote:
> >
> > Does the octillionth digit of pi exist? If all of these exist, then it
> > certainly does:
> >
> > '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'.
> >
> >> If so, in what sense does it exist?
> >
> > In the same sense as any other physical thing does.
>
> You think digits are physical things?

Yes.

Martin Shobe

unread,
Mar 14, 2012, 1:49:06 PM3/14/12
to
Or 1 with 48 zeros after it. It depends on whether it's the long or
short version.

Martin Shobe

1treePetrifiedForestLane

unread,
Mar 14, 2012, 4:16:09 PM3/14/12
to
> Yes.
digits are physical manifestations of number; for instance,
what is the canonical digit for base-one accounting?

incidentally, the algorithm to get any digit works,
only in binary; you can bet ont the result with a coin.

konyberg

unread,
Mar 14, 2012, 4:55:09 PM3/14/12
to
So if you haven't been on the North Pole or any other position on Earth. this spesific posision doesn't exist?

KON

konyberg

unread,
Mar 14, 2012, 4:57:46 PM3/14/12
to
This was meant for the opener of the tread.

Transfer Principle

unread,
Mar 14, 2012, 4:59:24 PM3/14/12
to
On Mar 13, 7:33 pm, calvin <cri...@windstream.net> wrote:
> If so, in what sense does [the octillionth digit of pi] exist?

In classical analysis, the nth digit of pi exists for every
natural number n -- although we may never find out what it is
due to insufficient memory.

> Yes to most of the above, but is there an octillionth
> digit in some sense right now, before the work is done
> to compute it (and thus for one to be in a position to
> alter it)?

There is an algorithm to find the nth binary digit (Plouffe)
but I'm not sure about decimal.

Happy Pi Day, calvin! This is being posted to sci.math at
3/14 1:59 (i.e., Pi Moment) Pacific Daylight Time.

Transfer Principle

unread,
Mar 14, 2012, 4:59:33 PM3/14/12
to
Or 9/(10^octillion) = 9/10^10^27 (assuming USA notation).

Happy Pi Day, quasi!

Ross A. Finlayson

unread,
Mar 14, 2012, 5:43:33 PM3/14/12
to
On Mar 14, 9:28 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> Frederick Williams <freddywilli...@btinternet.com> writes:
> > calvin wrote:
>
> > Does the octillionth digit of pi exist?  If all of these exist, then it
> > certainly does:
>
> >  '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'.
>
> >> If so, in what sense does it exist?
>
> > In the same sense as any other physical thing does.
>
>   You think digits are physical things?
>
> --
> Aatu Koskensilta (aatu.koskensi...@uta.fi)
>
> "Wovon man nicht sprechen kann, darüber muss man schweigen."
>   - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

It exists however much you use it. As a thing it is that thing.
Physical things? Numbers maybe. For example you could label each,
immutable thing and then have plain order statistics on them, the
arrangement would be a physical object. Then as far as is concern,
the outcome is of those numbers. Along with units they represent
interchange.

The Platonists might have them be real objects in their immutability
here 1 + 1 = 2. Dare I say, Ken: 2 + 2 = 4.

I was reading you the other day, it was pretty good, basically you
went forward with the constructive argument. Aatu.

Michael Stemper

unread,
Mar 14, 2012, 5:44:02 PM3/14/12
to
In article <efc94382-388c-4132...@x5g2000pbl.googlegroups.com>, "Ross A. Finlayson" <ross.fi...@gmail.com> writes:
>On Mar 14, 8:15=A0am, calvin <cri...@windstream.net> wrote:
>> On Wednesday, March 14, 2012 12:46:46 AM UTC-4, Tonico wrote:

>> > ... octillionth
>> > (whatever that is...is it like an 8 with 12 zeroes after it?) ...
>>
>> 1 with 27 zeros after it (10^27)
>>
>> The progression is thousand, million, billion, trillion,
>> quadrillion, quintillion, sextillion, septillion,
>> octillion, ...
>
>Yeah of course it does. I have heard that Bailey, Bourwein, and
>Plouffe discovered a function that gives you whatever digit of pi you
>want without computing all the ones in the middle, a digit extraction
>algorithm.

Do any of those exist for decimal representations?

--
Michael F. Stemper
#include <Standard_Disclaimer>
"Writing about jazz is like dancing about architecture" - Thelonious Monk

Ross A. Finlayson

unread,
Mar 14, 2012, 5:47:07 PM3/14/12
to
On Mar 14, 2:44 pm, mstem...@walkabout.empros.com (Michael Stemper)
wrote:
Yeah sure last I heard.

Ross A. Finlayson

unread,
Mar 14, 2012, 5:58:26 PM3/14/12
to
On Mar 14, 2:47 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com>
wrote:
> Yeah sure last I heard.- Hide quoted text -
>
> - Show quoted text -

I have not even verified the first ten thousand values or understand
the machinery of the algorithm, just having seen the formula(e), of
the Bailey Bourwein Plouffe pi digit algorithm.

However, I recommend looking into Plouffe's , he wrote me one time
after I pestered him, or maybe for him it wasn't a bother, Plouffe has
a huge web site with much more about it.

As I recall.

1treePetrifiedForestLane

unread,
Mar 14, 2012, 10:01:26 PM3/14/12
to
*what* position doesn't exist?

porky_...@my-deja.com

unread,
Mar 14, 2012, 10:34:40 PM3/14/12
to
On Mar 13, 10:33 pm, calvin <cri...@windstream.net> wrote:
> If so, in what sense does it exist?

In exactly the same sense the first digit of pi exists.

And while we're at it, Happy Pi Day to everyone!

Frederick Williams

unread,
Mar 15, 2012, 11:53:33 AM3/15/12
to
1treePetrifiedForestLane wrote:
>
> > Yes.
> digits are physical manifestations of number;

That's what I thought. I very nearly replied "Yes of course." rather
than just "Yes."

Bill Taylor

unread,
Mar 15, 2012, 10:04:49 PM3/15/12
to
> > digits are physical manifestations of number;

You can define your terms that way if you want,
but it is not so very helpful.

It is better to allow digits as being abstract objects,
of character type rather than numeral or number type,
(should these distinctions ever be relevant).

Then what is a physical manifestation of such a thing
is what it has always been - a bunch of ink grains or
lit phosphors, outlining an instance of the standard
representation of a character, numeral or number.

No wonder we mathies don't want to bother with
physicality, especially in this trivial sense!

-- Blustering Bill

** "The point of philosophy is to start with something
** so simple as not to seem worth stating, and to end with
** something so paradoxical that no one will believe it."

Frederick Williams

unread,
Mar 16, 2012, 7:39:01 AM3/16/12
to
Bill Taylor wrote:
>
> > > digits are physical manifestations of number;
>
> You can define your terms that way if you want,
> but it is not so very helpful.
>
> It is better to allow digits as being abstract objects,
> of character type rather than numeral or number type,
> (should these distinctions ever be relevant).
>
> Then what is a physical manifestation of such a thing
> is what it has always been - a bunch of ink grains or
> lit phosphors, outlining an instance of the standard
> representation of a character, numeral or number.
>
> No wonder we mathies don't want to bother with
> physicality, especially in this trivial sense!

That's a good point. Now GET OUT! Oh, and leave the cash box behind
laddie.

Hauke Reddmann

unread,
Mar 17, 2012, 2:00:17 PM3/17/12
to
Tonico <Toni...@yahoo.com> wrote:
> On Mar 14, 11:49�am, Hauke Reddmann <fc3a...@uni-hamburg.de> wrote:
>> Tonico <Tonic...@yahoo.com> wrote:
>> > In the sense that given enough time, energy and will (of someone
>> > checking stuff), a computer can calculate it in a rather easy, though
>> > probably lengthy, way.
>>
>> HA! But now assume we don't take the octillionth (much too
>> small :-) but, say, the googolplexth number and our universe isn't
>> large enough to provide with the time, space and energy needed
>> for calculating it. Also, replace pi (much too orderly, we might
>> find a way to shortcut the calculation) by "the value of the
>> mid cell of the 110 cellular automaton at the googolplexth iteration"
>> or something incompressible like that, so the only way to
>> calculate is actually running it. Does it still exist?
>> --


> **** Yes, and assuming all that mess of googolplexth, mid cellular
> automaton iteration and etc. can be translated into one definite
> ordinal, we can then even find out what it is.

Sorry for the mess, but I had to avoid that there is a way
cheating around the question. In any case, I agree: suppose
the number foobar is not computable in universe A but in
universe B which happens to be a bit larger...so foobar exists
not in A but in B??...only a intuitionist on crack could
agree to that. (I'm a platonist.)
--
Hauke Reddmann <:-EX8 fc3...@uni-hamburg.de

1treePetrifiedForestLane

unread,
Mar 20, 2012, 2:02:17 PM3/20/12
to
Universe is always & only unit, although
diverse within itself.

Bill Taylor

unread,
Mar 21, 2012, 2:39:47 AM3/21/12
to
On Mar 21, 7:02 am, 1treePetrifiedForestLane <Space...@hotmail.com>
wrote:

> Universe is always & only unit, although
> diverse within itself.

Atom.

Michael Stemper

unread,
Mar 21, 2012, 8:56:58 AM3/21/12
to
In article <29cd9f2f-61dd-475c...@oq7g2000pbb.googlegroups.com>, Bill Taylor <wfc.t...@gmail.com> writes:
Totality.

--
Michael F. Stemper
#include <Standard_Disclaimer>
If this is our corporate opinion, you will be billed for it.

Frederick Williams

unread,
Mar 21, 2012, 1:20:52 PM3/21/12
to
1treePetrifiedForestLane wrote:
>
> Universe is always & only unit, although
> diverse within itself.

"Far away is close at hand in images of elsewhere."

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

1treePetrifiedForestLane

unread,
Mar 23, 2012, 3:29:16 PM3/23/12
to
only if it really wants to.

jgharston

unread,
Mar 23, 2012, 7:38:40 PM3/23/12
to
You haven't specified what base you want.
In base pi, the octillionth digit is 0.

JGH

Phil Carmody

unread,
Mar 25, 2012, 8:30:16 AM3/25/12
to
quasi <qu...@null.set> writes:
> On Tue, 13 Mar 2012 21:48:13 -0500, quasi <qu...@null.set> wrote:
>
> >On Tue, 13 Mar 2012 21:44:19 -0500, quasi <qu...@null.set> wrote:
> >
> >>On Tue, 13 Mar 2012 19:33:50 -0700 (PDT), calvin
> >><cri...@windstream.net> wrote:
> >>
> >>>If so, in what sense does it exist?
> >>
> >>In the sense that if you change the value of Pi in the
> >>octillionth place (leaving all other digits unchanged), the
> >>new number could be too small by as much as one octillionth.
> >
> >Oops. I meant:
> >
> >It could be too small by as much as 9 octillionths.
>
> Ugh, I'll get it right:
>
> It could be too small or too large by as much as 9
> octillionths.

Your iterative approach to posting does not appear to be
convergent.

If you were to change Pi in the tenth place, would
pi be different by as much as 9 tenths?

Phil
--
> I'd argue that there is much evidence for the existence of a God.
Pics or it didn't happen.
-- Tom (/. uid 822)

quasi

unread,
Mar 25, 2012, 9:47:12 AM3/25/12
to
On 25 Mar 2012 15:30:16 +0300, Phil Carmody
<thefatphi...@yahoo.co.uk> wrote:

>quasi <qu...@null.set> writes:
>> On Tue, 13 Mar 2012 21:48:13 -0500, quasi <qu...@null.set> wrote:
>>
>> >On Tue, 13 Mar 2012 21:44:19 -0500, quasi <qu...@null.set> wrote:
>> >
>> >>On Tue, 13 Mar 2012 19:33:50 -0700 (PDT), calvin
>> >><cri...@windstream.net> wrote:
>> >>
>> >>>If so, in what sense does it exist?
>> >>
>> >>In the sense that if you change the value of Pi in the
>> >>octillionth place (leaving all other digits unchanged), the
>> >>new number could be too small by as much as one octillionth.
>> >
>> >Oops. I meant:
>> >
>> >It could be too small by as much as 9 octillionths.
>>
>> Ugh, I'll get it right:
>>
>> It could be too small or too large by as much as 9
>> octillionths.
>
>Your iterative approach to posting does not appear to be
>convergent.
>
>If you were to change Pi in the tenth place, would
>pi be different by as much as 9 tenths?

Umm ...

My error was corrected by others about a week ago.

quasi

Phil Carmody

unread,
Mar 26, 2012, 3:47:53 PM3/26/12
to
Between the kooks, the google groups users, and those using
anonymisers, a lot of people get killfiled.

Be thankful I didn't correct you three times.
0 new messages