Jim Taylor's Columns - 'Soft Edges' and 'Sharp Edges'

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Published on Saturday, March 14, 2020

In the beginning was pi

This coming Saturday is International Pi Day. No, that’s not a typographic error. Pi, not pie, regardless of flavour. Or maybe pi. Usually represented by π, a Greek letter that looks like a wobbly footstool.

            It’s on March 14, because if you write it as 3/14, or better yet as 3.14, you have the first three digits of pi. Correctly, pi is 3.141592 plus an endless series of further decimals, but for most purposes, 3.14 will suffice. 

            The ancient Greeks apparently worked with a fraction, 22-sevenths, which divides to 3.1428 in decimals – not quite precise, but close.

            But then, pi can never be precise. Mathematicians have calculated pi to 13.3 trillion decimal digits, and they’re firmly convinced that it will never – no, never – repeat a pattern. Which means that no matter how precisely they define pi, the next digit will be unpredictable. 

            So pi is at once a constant, and a variable. 

            And yet the universe could not exist without it. 

            Most of us know pi only in the formula for calculating the circumference of a circle – its diameter, which is twice the radius, multiplied by pi. Or, most commonly, 2πr. But it’s also essential for the area of a circle, for the volume of a sphere, for the surface area of a sphere. In fact, for anything that involves a curve around a fixed point -- a circle, an ellipse, a cone, a cyclic pattern…

            Which means that pi had to be there right at the beginning of the universe. Maybe even before. Planetary orbits, the spirals of galaxies, curves in the fabric of gravity, could not exist without pi. 

            Even Heisenberg’s famed Uncertainly Formula, which proves mathematically that you cannot be certain about anything, depends on the proven value of pi. 

            Like gravity, pi was not invented; it was discovered. It was there all along, when the first cave dweller scratched a circle on a rock wall with a scrap of charcoal. It was there when Egyptians sculpted a circular sun on a temple wall. It was there when the first engineer devised the first wheel and/or axle. 

            They didn’t have to know its decimal value. But in creating anything circular, they invoked pi. 

            Pi is as inflexible as the truth that one plus one equals two. And as necessary.

            In 1897, the Indiana General Assembly tried to legislate pi as three. No decimal points. Just three.

            It won’t work. Any wheel, traffic roundabout, soccer ball, or planetary orbit, based on π = 3.0 will have a gap in it, an unfinished space. You can pull the ends together, you can eliminate the empty space -- but only by reducing the radius. The relationship between radius and circumference will always be, and must always be, a factor of pi. 

            The circumference of a circle is one of the few places where the Bible can  be proved incorrect. In I Kings 7:23, an artisan named Hiram made a bronze bowl 10 cubits across, and the Bible asserts, “a line of 30 cubits would encircle it completely”. The length of a “cubit” is irrelevant – the formula would be the same for millimetres and for miles. 

            We can only assume sloppy measuring. 

            You don’t have to understand pi, and you don’t have to believe in pi, to live by it. It just is. 

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Copyright © 2020 by Jim Taylor. Non-profit use in congregations and study groups, and links from other blogs, welcomed; all other rights reserved.

                  To comment on this column, write jimt@quixotic.ca

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YOUR TURN

 

Last week’s column – in which I think I argued that it is nearly impossible for us to imagine situations that we haven’t, at least in part, experienced ourselves produced a wide variety of responses. 

 

Tom Watson responded to my comment about the inability of science, etc., to prove anything forever: “The notion that new factors appear to challenge existing theories remind me of something Northrup Frye said: ‘The function of an answer is to help formulate the next question.’”

 

Steve Roney took issue with that same contention, that “arguments based on reason and logic don’t prove anything either. If they could, science and philosophy would both have ground to a standstill centuries ago.”

            Steve wrote, “It seems to me that reason and logic can prove and have proven a lot of things. Think of mathematical proofs. Mathematics is nothing but proofs. And, of course, it has not ground to a halt.

            “Science too proves many things. This is a bit harder to see, because its proofs are negative. A scientific experiment tests a theory; if the experiment fails, the theory is falsified, disproven. 

            “Logic can similarly prove or disprove in philosophical terms. Arguments can be shown to be fallacious or self-contradictory; positively disproven. Conversely, a syllogism is a proof, given that the initial premises are accepted as correct.

            “So it seems to me that we know lots of things, based on reason and logic.

            “I think you are also being too pessimistic about the possibilities of empathy. Whenever we read a book, watch a movie, or listen to a story, we are imagining the experiences of someone else. If we were incapable of doing so, nobody would ever read fiction (or memoirs, or biographies) or go to movies.”

 

John Shaffer: Where was God at the time of the Halifax Explosion in 1917? 

            A few months ago I took a trip to the Maritime Provinces (when Hurricane Dorian hit) and learned about the 1917 Halifax Explosion in a museum there that covers the Great Halifax Explosion and the Titanic disaster in the same building.

            Over and over again, I wondered why I had never heard of the greatest explosion (man-made) prior to the explosions in Japan.  Why wasn't it mentioned to me somewhere in the history classes?  etc. etc.  I came to the conclusion that I never heard of it because it didn't happen in the United States.

 

Bill Rogers says he keep gathering new experiences: “In a few months I will be 90.  Every day is a new experience (because it's first time around) so every day is an unknown -- mostly welcome.  It's exciting to view the experiences of the younger, relate them to my reaction to the same thing at their age, and challenging my reaction now. Oh how I have grown!”

 

Jean Skillman also keeps learning new things: “I have started watching Amazon’s The Hunters, a story about a group of Jews who hunt Nazis. It is a tension between law and unlawful acts, but it is also the age-old tension of anti-Semitism and racism in human populations.  

            “It draws me in, because it is not my personal experience.  I am white, grew up Christian, and my -ism experience is that of being a woman. Like many films today,  Even though my personal experience is not of bloody violence, I know it exists here in Canada, and in many parts of the world. 

            “I am only part way through it,  so I don’t know what conclusions, if any, it will draw, and what it will ask of the viewer.  I think your view that we can only deal with our personal experience , yet we are prone to generalizing broadly from a limited perspective, relates to this film in particular.  My context of violence is mostly as an observer, an outsider, yet for the sake of justice, I believe my awareness of the contexts of violence is important. If we as a culture learn about anti-Semitism, listen to the voices, and then support the need for justice, then that is a positive response.

            “Of course, justice appears to be another theme in this film; should a community denied justice take it into their own hands?  Ideally, the culture supports justice for everyone,  but we seem to live still in times where justice is denied to the poor, to name just one group, to the illiterate, to the disabled and to racially defined groups.”

 

 

Marilyn Josefsson responded to the personal experience I related: “I feel for you and your wife.  It must be a terrible thing to have to see the continuing decline in her health, along with the knowledge that she will not recover.  Seeing the changes in a (formerly) close friend, when I moved back to my home city after many years living elsewhere, was heartbreaking.  She had developed Alzheimer's and no longer recognized me, and actually, at times, seemed to be afraid of me.

            “In each case, there seems so little that we can do to make things better. However, I do believe that your being with her gives her comfort and, I hope, a feeling that she is still loved.”  

 

Pat Graham didn’t write about my column, but wanted to assure me, “You have made a difference in my life and my friend’s.  You enabled me to get in touch with Vera [another reader] after about 32 years.  Within 10 minutes of emailing you to ask you to pass my address on to her, I had a lengthy letter from her.”

 

 

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Psalm paraphrase

 

I don’t like either of my paraphrases of Psalm 95, this week. So I’m going to skip the paraphrase this time. Sorry, but that’s how it is. 

 

For paraphrases of most of the psalms used by the Revised Common Lectionary, you can order my book Everyday Psalmsfrom Wood Lake Publishing, info@woodlake.com.

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TECHNICAL STUFF

 

If you want to comment on something, send a message directly to me, jimt@quixotic.ca.

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                  I write a second column each Sunday called Sharp Edges, which tends to be somewhat more cutting about social and justice issues. To sign up for Sharp Edges, write to me directly, jimt@quixotic.ca, or send a note to sharpedges-subscribe@lists.quixotic.ca

                  And for those of you who like poetry, please check my webpage .https://quixotic.ca/My-Poetry I posted some new poetic works there a few weeks ago.  If you’d like to receive notifications about new poems, write me at jimt@quixotic.ca,  or subscribe yourself to the list by sending a blank email (no message) to poetry-subscribe@lists.quixotic.ca (If it doesn’t work, please let me know.)

 

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PROMOTION STUFF

 

To use the links in this section, you’ll have to insert the necessary symbols. Some spam filters have blocked my posts because they’re suspicious of some of the web links.

                  Wayne Irwin's “Churchweb Canada,” an inexpensive service for any congregation wanting to develop a web presence, with free consultation. http://wwwDOTchurchwebcanadaDOTca He’s also relatively inexpensive!

                  I recommend Isabel Gibson’s thoughtful and well-written blog, wwwDOTtraditionaliconoclastDOTcom. She also has lots of beautiful photos. Especially of birds.

                  Tom Watson writes a weekly blog called “The View from Grandpa Tom’s Balcony” -- ruminations on various subjects, and feedback from Tom’s readers. Write him at tomwatsoATgmailDOTcom (NB that’s “watso” not “watson”)

 

ALVA WOOD’S ARCHIVE

                  I have acquired (don’t ask how) the complete archive of the late Alva Wood’s collection of satiric and sometimes wildly funny columns about a mythical village’s misadventures. I’ve put them on my website: http://quixotic.ca/Alva-Wood-Archive. You’re welcome to browse. No charge. (Although maybe if I charged a fee, more people would find the archive worth visiting.)

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Author: Jim Taylor

Categories: Soft Edges

Tags: mathematics, astronomy, value, pi

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