Pi is approximate

[Nick Thompson]

Peggy,

As the former english major on the list, struggling to understand
mathematics, I hasten to say,

pi is NOT approximate.  pi is precise.  Draw a perfect semi-circle of unit
radius and the diameter will be pi EVERY time.  

What is approximate is our capacity to represent the ratio between a
semi-circle's circumference and its radius by holding our fingers in the
air.   No matter how many fingers we care to hold up we will wish we had
more fingers.  

Now the real mathematicians will correct me.

Nick



Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])

> [Original Message]
> From: <[hidden email]>
> To: <[hidden email]>
> Date: 8/26/2008 10:02:02 AM
> Subject: Friam Digest, Vol 62, Issue 24
>
> Send Friam mailing list submissions to
> [hidden email]
>
> To subscribe or unsubscribe via the World Wide Web, visit
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> When replying, please edit your Subject line so it is more specific
> than "Re: Contents of Friam digest..."
>
>
> Today's Topics:
>
>    1. Thing one and Thing two (peggy miller)
>    2. Re: Thing one and Thing two (Phil Henshaw)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Mon, 25 Aug 2008 11:18:11 -0600
> From: "peggy miller" <[hidden email]>
> Subject: [FRIAM] Thing one and Thing two
> To: [hidden email]
> Message-ID:
> <[hidden email]>
> Content-Type: text/plain; charset="iso-8859-1"
>
> *Thing One:* Having read the book *Complexity* recently (I know -- late to
> the game) I wondered if Chris Langton's Edge of Chaos, Lambda point

arguing
> a point at which life began/begins, could have a similar counter point at
> which life ends -- and if so, has that been modeled somehow? Meaning, has
> that scientific evaluation been put out there in such a way it could help
> formulate the context where we might cause all life to end?
>
> (by the way, hi, I am Peggy Miller, new to the group, like reading your
> different questions and ideas, had a couple that might not be pertinent,
but

> figured I would fling them out to you ... I am a writer, and include
> scientific concepts in my novels, and am worried about global warming,
> population levels, and general global depletion of resources; live in
> Missoula, Montana.)
>
> *Thing Two: *
> **
> reading *A New Kind of Science,*  I wondered whether since pi is an
> approximate, 3.1416, then does that mean a circle is never perfect?
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>
> ------------------------------
>
> Message: 2
> Date: Mon, 25 Aug 2008 21:30:55 -0400
> From: "Phil Henshaw" <[hidden email]>
> Subject: Re: [FRIAM] Thing one and Thing two
> To: "'The Friday Morning Applied Complexity Coffee Group'"
> <[hidden email]>
> Message-ID: <007601c9071b$630cbb60$29263220$@com>
> Content-Type: text/plain; charset="us-ascii"
>
> Yes, there's a good way to connect beginning and ending.    It's as a
> organized series of questions applicable to any circumstance where change

is
> conserved.   It's based on the emergent continuities of beginning and
> ending, that require accumulation, and that the accumulations need to
change
> sign at the turning points.    It's an exploratory method, that might
result
> in individualized representations if complex systems, but exploratory
rather
> than deterministic models since the latter would require representing
> environments and that doesn't seem possible.  
>
>  
>
> Exploration gives you a window into the emergence of the behavioral
systems
> that do it.    It uses the fact that the best model of reality is reality
> itself.  Since we don't have the formulas the alternative is watching
> closely and asking good questions about things that are developing their
own
> formulas, as evidenced in the emergence of continuity in how they change.
> It's ass backwards of how everyone wants the world to follow our
> instructions.  but works.    
>
>  
>
> When all life as we know it ends, I presume it would be the sun exploding
or
> other cosmic coincidence.    I don't think life could extinguish life
> entirely.    There is some suggestion that a number of the great collapses
> in the number of species were systemic collapses of the life system as a
> whole, though.   I have not read anything good as to how, just some
evidence
> that extinction rates sometimes accelerate to a collapse, not just subside
> after a shock.     We're bringing one of those about at the moment, aren't
> we, precipitating some kind of grand collapse of the living systems that
we

> found here?
>
>  
>
> On pi,  Ideal circles are quite ideal I think.    You can fill in new
> imaginary points on an imaginary plane wherever you want and to whatever
> precision you want, just by specification.    It's only real circles that
> have to deal with being made by unruly physical stuff like hand crafts or
> computers that are always going to be a little bumpy...  ;-)
>
>  
>
> Phil
>
>  
>
> From: [hidden email] [mailto:[hidden email]] On

Behalf

> Of peggy miller
> Sent: Monday, August 25, 2008 1:18 PM
> To: [hidden email]
> Subject: [FRIAM] Thing one and Thing two
>
>  
>
> Thing One: Having read the book Complexity recently (I know -- late to the
> game) I wondered if Chris Langton's Edge of Chaos, Lambda point arguing a
> point at which life began/begins, could have a similar counter point at
> which life ends -- and if so, has that been modeled somehow? Meaning, has
> that scientific evaluation been put out there in such a way it could help
> formulate the context where we might cause all life to end?
>
>  
>
> (by the way, hi, I am Peggy Miller, new to the group, like reading your
> different questions and ideas, had a couple that might not be pertinent,

but

> figured I would fling them out to you ... I am a writer, and include
> scientific concepts in my novels, and am worried about global warming,
> population levels, and general global depletion of resources; live in
> Missoula, Montana.)
>
>  
>
> Thing Two:
>
>  
>
> reading A New Kind of Science,  I wondered whether since pi is an
> approximate, 3.1416, then does that mean a circle is never perfect?
>
> -------------- next part --------------
> An HTML attachment was scrubbed...
> URL:

http://redfish.com/pipermail/friam_redfish.com/attachments/20080825/f6a715c9
/attachment-0001.html

>
> ------------------------------
>
> _______________________________________________
> Friam mailing list
> [hidden email]
> http://redfish.com/mailman/listinfo/friam_redfish.com
>
>
> End of Friam Digest, Vol 62, Issue 24
> *************************************

============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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[John Kennison]

I think Nick said it well, except, perhaps, for the fingers. Expressed in another way, it is impossible to have a perfect circle in which both the diameter and the circumference are a whole number of inches (or of any other unit of distance, such as kilometers or light years). Since pi is the ratio of the circumference to the diameter, we can never represent that ratio by holding up a number of fingers for the circumference and a different number of fingers for the diameter, no matter how many fingers we have. A number, such as pi, with this property of not being a ratio of whole numbers, is called an irrational number In every (perfect) circle. Either the diameter or the circumference will be irrational.


On 8/26/08 12:15 PM, "Nicholas Thompson" <[hidden email]> wrote:

Peggy,

As the former english major on the list, struggling to understand
mathematics, I hasten to say,

pi is NOT approximate.  pi is precise.  Draw a perfect semi-circle of unit
radius and the diameter will be pi EVERY time.

What is approximate is our capacity to represent the ratio between a
semi-circle's circumference and its radius by holding our fingers in the
air.   No matter how many fingers we care to hold up we will wish we had
more fingers.

Now the real mathematicians will correct me.

Nick



Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])




> [Original Message]
> From: <[hidden email]>
> To: <[hidden email]>
> Date: 8/26/2008 10:02:02 AM
> Subject: Friam Digest, Vol 62, Issue 24
>
> Send Friam mailing list submissions to
>       [hidden email]
>
> To subscribe or unsubscribe via the World Wide Web, visit
>       http://redfish.com/mailman/listinfo/friam_redfish.com
> or, via email, send a message with subject or body 'help' to
>       [hidden email]
>
> You can reach the person managing the list at
>       [hidden email]
>
> When replying, please edit your Subject line so it is more specific
> than "Re: Contents of Friam digest..."
>
>
> Today's Topics:
>
>    1. Thing one and Thing two (peggy miller)
>    2. Re: Thing one and Thing two (Phil Henshaw)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Mon, 25 Aug 2008 11:18:11 -0600
> From: "peggy miller" <[hidden email]>
> Subject: [FRIAM] Thing one and Thing two
> To: [hidden email]
> Message-ID:
>       <[hidden email]>
> Content-Type: text/plain; charset="iso-8859-1"
>
> *Thing One:* Having read the book *Complexity* recently (I know -- late to
> the game) I wondered if Chris Langton's Edge of Chaos, Lambda point
arguing
> a point at which life began/begins, could have a similar counter point at
> which life ends -- and if so, has that been modeled somehow? Meaning, has
> that scientific evaluation been put out there in such a way it could help
> formulate the context where we might cause all life to end?
>
> (by the way, hi, I am Peggy Miller, new to the group, like reading your
> different questions and ideas, had a couple that might not be pertinent,
but
> figured I would fling them out to you ... I am a writer, and include
> scientific concepts in my novels, and am worried about global warming,
> population levels, and general global depletion of resources; live in
> Missoula, Montana.)
>
> *Thing Two: *
> **
> reading *A New Kind of Science,*  I wondered whether since pi is an
> approximate, 3.1416, then does that mean a circle is never perfect?
> -------------- next part --------------
> An HTML attachment was scrubbed...
> URL:
http://redfish.com/pipermail/friam_redfish.com/attachments/20080825/aa9d514f
/attachment-0001.html
>
> ------------------------------
>
> Message: 2
> Date: Mon, 25 Aug 2008 21:30:55 -0400
> From: "Phil Henshaw" <[hidden email]>
> Subject: Re: [FRIAM] Thing one and Thing two
> To: "'The Friday Morning Applied Complexity Coffee Group'"
>       <[hidden email]>
> Message-ID: <007601c9071b$630cbb60$29263220$@com>
> Content-Type: text/plain; charset="us-ascii"
>
> Yes, there's a good way to connect beginning and ending.    It's as a
> organized series of questions applicable to any circumstance where change
is
> conserved.   It's based on the emergent continuities of beginning and
> ending, that require accumulation, and that the accumulations need to
change
> sign at the turning points.    It's an exploratory method, that might
result
> in individualized representations if complex systems, but exploratory
rather
> than deterministic models since the latter would require representing
> environments and that doesn't seem possible.
>
>
>
> Exploration gives you a window into the emergence of the behavioral
systems
> that do it.    It uses the fact that the best model of reality is reality
> itself.  Since we don't have the formulas the alternative is watching
> closely and asking good questions about things that are developing their
own
> formulas, as evidenced in the emergence of continuity in how they change.
> It's ass backwards of how everyone wants the world to follow our
> instructions.  but works.
>
>
>
> When all life as we know it ends, I presume it would be the sun exploding
or
> other cosmic coincidence.    I don't think life could extinguish life
> entirely.    There is some suggestion that a number of the great collapses
> in the number of species were systemic collapses of the life system as a
> whole, though.   I have not read anything good as to how, just some
evidence
> that extinction rates sometimes accelerate to a collapse, not just subside
> after a shock.     We're bringing one of those about at the moment, aren't
> we, precipitating some kind of grand collapse of the living systems that
we
> found here?
>
>
>
> On pi,  Ideal circles are quite ideal I think.    You can fill in new
> imaginary points on an imaginary plane wherever you want and to whatever
> precision you want, just by specification.    It's only real circles that
> have to deal with being made by unruly physical stuff like hand crafts or
> computers that are always going to be a little bumpy...  ;-)
>
>
>
> Phil
>
>
>
> From: [hidden email] [[hidden email] On
Behalf
> Of peggy miller
> Sent: Monday, August 25, 2008 1:18 PM
> To: [hidden email]
> Subject: [FRIAM] Thing one and Thing two
>
>
>
> Thing One: Having read the book Complexity recently (I know -- late to the
> game) I wondered if Chris Langton's Edge of Chaos, Lambda point arguing a
> point at which life began/begins, could have a similar counter point at
> which life ends -- and if so, has that been modeled somehow? Meaning, has
> that scientific evaluation been put out there in such a way it could help
> formulate the context where we might cause all life to end?
>
>
>
> (by the way, hi, I am Peggy Miller, new to the group, like reading your
> different questions and ideas, had a couple that might not be pertinent,
but
> figured I would fling them out to you ... I am a writer, and include
> scientific concepts in my novels, and am worried about global warming,
> population levels, and general global depletion of resources; live in
> Missoula, Montana.)
>
>
>
> Thing Two:
>
>
>
> reading A New Kind of Science,  I wondered whether since pi is an
> approximate, 3.1416, then does that mean a circle is never perfect?
>
> -------------- next part --------------
> An HTML attachment was scrubbed...
> URL:
http://redfish.com/pipermail/friam_redfish.com/attachments/20080825/f6a715c9
/attachment-0001.html
>
> ------------------------------
>
> _______________________________________________
> Friam mailing list
> [hidden email]
> http://redfish.com/mailman/listinfo/friam_redfish.com
>
>
> End of Friam Digest, Vol 62, Issue 24
> *************************************



============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

[James Steiner]

On Tue, Aug 26, 2008 at 12:49 PM, John F. Kennison <[hidden email]> wrote:
> In every (perfect) circle. Either the diameter
> or the circumference will be irrational.

Said the Diameter: I am 12
Said the Circumference: I am a cute fuzzy bunny! Wakka wakka!

~~James

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

[Paul Paryski]

Interesting.  I assume that a circle as an idea or perhaps as a mathematical construct is perfect, but not as it exists in the physical universe.  Please, mathematicians and scientists, correct my ignorance gained as an historian and in the UN, which of course does often move in circles.  Paul


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============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org