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To Infinity And Beyond

The Maor Visit

 

September 30, 2014

Mathematics

Written for Canadian Community News by Mike Sterling

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Photos by  Sandy Lindsay

Finished Sculpture and Computer model made by Mike Sterling shown from approximately the same viewpoint.  It was necessary to "fly" around the sculpture before it was made to see how it would look.  Every link is represented.  The process from conception to completion took 18 months.

Double Helix from below.  Eli Maor understood that the chain paths form a geodesic of an invisible cylinder.


To Infinity and Beyond

The essence of the Eli and Dalia Maor visit to Southampton is captured wonderfully by Sandy Lindsay's article (see link below}

Featured People  Renowned author & mathematician visits Southampton Read More

I'd like to add to the unusual story.

I am an avid reader of science and mathematical books.  Some are easy to read, others not.  For some of them it takes many months to squeeze the secrets out.

I have hundreds of such books and I've read them all or tried to do so.  I found Eli Maor's books some time ago and ordered and read them as they came out.

His writing is crystal clear.  He never obscures.  He helps the reader understand the beauty and never destroys the mystery.

On a trip to Nova Scotia ten years ago, I read one of his books "e-The Story of a Number" and was convinced that I should read everything he ever wrote. 

I read the book a number of times and it inspired me to design a musical instrument and now another.  The insight came from a short chapter about a hypothetical meeting of Bach and one of the Bernoulli family.  It was about music and was the only piece of fiction ever written by Maor.  He did it to reveal concepts that few know.

Eli is one of the leading experts on the relationship of Music and Art to Mathematics.  He is a historian of mathematics and a PhD mathematician.  I wanted to get in touch with him to thank him for his enrichment of my life.  I've never done that with any other author.

Try as I might I could not reach him.  He and his wife spend part of their year in Israel, part in Chicago and are busy with family and their work.  Their schedule is busier still with their research trips and eclipse chasing.  In the field of astronomy he wrote a book about the transit of Venus.

I understood not being able to get in touch with him. He is a best selling author for the prestigious Princeton University Press.  It's impossible to handle each and every piece of fan mail and still have a life and time to work.  There are a surprising number of people world-wide who love the subject and search for the best authors.

Finally, last year,  I sent a note and a number of things I'm interested in to his editor.  Somehow the editor saw some merit in forwarding my information on to Eli. Maybe it's a routine procedure. A few days later Eli contacted me directly.  I was surprised.  No, I was shocked.

Eli told me that he receives hundreds of letters and emails and has to limit his attention to them.  Something in the few things I sent him sparked his interest and he contacted me.

He asked permission to send some of my thoughts and designs on to an artist friend, Eugen Jost, who collaborated with Eli on the book 'Beautiful Geometry' and Eli has widened that distribution subsequently to include others. 

He then said he and his wife wished to visit me.  I was puzzled. Am I up to this visit by a famous mathematician/author?  I was not confident.  A trip from Israel/Chicago is not around the corner after all.

As the visit neared I became very nervous.  What would interest him?  How could I structure his time?

When he arrived I gave Eli and his wife Dalia a gift of a design that I had done that had to do with a concept called "The Theorem of Pappus". 

Now Pappus has quite a few theorems attributed to him by name, but this one is special. It's a beautiful dual theorem and the whole area that it encompasses is little known and rarely taught.  Eli knew it and had written about the general subject.

As soon as he saw it, he understood.  I could show it to 10,000 people and not have anyone see beneath the geometric beauty, but he did. The shape is not startling, but it holds a secret. He saw the duality immediately.  In the Theorem of Pappus you can interchange the words point and line and the theorem still holds.  He smiled broadly.  Well, that's a good start, I thought.

Our time at the Museum went quickly.  I wanted to centre the visit there because it's a grand place and I could muster bits and pieces of things I'm interested in for them to see. He and Dalia were relaxed, I was less so.

As we walked around the gardens, he would ask me questions about things and say "Do you know the formula for that"  I responded with the formula.  That's a good first step, I thought.  Do you know the history behind it?  I did, luckily.  Of course nature is full of mathematics from a visual standpoint.

He even examined a man hole cover that I had designed with 12 sides.  He's interested in finding more 17 sided figures called heptadecagons that have been constructed rarely in the history of the world.

 

Click the orange arrow to read the second column

I kick myself for not doing 17 sides.  I did 12 to mimic the number of sides of the lens room on Chantry Island.  A heptadecagon is much more exotic.  The number is prime and is a twin prime along with 19.  I had studied twin primes to some depth.

It dawned on me that he saw what others do not see.  He sees beneath the surface and knows the relationship of objects one to another and he sees the world as a wonder. 

The world is written about best in terms of mathematics.  Words bind the hidden concepts by the mathematics that embody them  It's a way of thinking and expressing oneself with precision.  Eli, does just that.

His world view is vibrant and different from ours.  It's like he has x-ray vision of a special type.  He sees through the haze of reality into the essence. 

I think he was pleased to have his questions answered.  I felt much like a student of his that he was gently testing to see if I was ready for an upcoming qualifying exam.

He was happiest to see how some of his books are aged by my repeated reading.  He said to Dalia: " ... come see how much Mike has used this book!  Look at it!"

Everyone else would see a tattered abused book with binding broken, but he saw immediately that I was indeed an avid reader.  What better proof is there?

He urged me to publish what I've discovered.    It's not an easy task for me.  There is not a natural fit with publication paths.  It was grand of him to suggest it, however.

Eli has another book that is complete, but is just entering the publishing process.  His books are peer reviewed so he just does not slap something together for quick publication.  The latest book will not be in my hands for 18 months.

He and Dalia are wonderful story tellers.  She was the youngest Sergeant Major in the armed forces of Israel.  That's something!  I must question her on that.

And there is more!  They chase eclipse events together and try to visit historic places where something happened that is part of one of his proposed or past books.  Yes, mathematics and science have a mysterious history and he captures much of it even the cultural side.

Dalia proofs all his books for clarity and he will not let a sentence pass that Dalia has not approved for understanding.  She is the holder of his torch of light.

Precise thought is at the heart of his writing.  Before anyone can write we have to have a thought.  He is a great story teller. He spins thoughts into charming stories.  He thinks and tries to convey his thoughts without obscuring them.

I asked him about one of his books called "To Infinity and Beyond".  He wrote the book before Buzz Lightyear used that phrase.  I hear those workds coming from a Buzz doll every day along with "Buzz Lightyear here, I come in peace."  Grandchildren love Buzz.  I do too!

He responded that Toy Story may have stolen the line, but he did too.  He once had a telescope that had a reference on it that said  " ... from 25 meters To Infinity and Beyond"  It's a great book title and a wonderful mantra for Buzz Lightyear.

They are a great couple of depth and scope. The combination of their talents is powerful.  In their presence you can feel their intensity and joy.

He told me about being taught mathematics and science by his Grandfather from an old text from the 1890s. 

His Grandfather and parents escaped Nazi Germany to Israel before death camps silenced the innocents.  Their 'exodus' took place in 1936 and 1939.  He recalls vividly his grandfather playing the violin.  Eli's words evoke images and they surface as new thoughts in others.  Much credit is due the grandfather.

Will it be possible to lure Eli and Dalia back to Southampton?  He could give a wonderful talk or a series of talks.  Since he is such an avid astronomer, we could combine his talk with a series of maybe four lectures, mathematics, music, art and astronomy.

He would be perfect for Perimeter Institute's public outreach lecture series too.

Until then, I want to see if I can accomplish a few things that he inspired and encouraged.  Until then "To Infinity and Beyond" 

The Sculpture Renewal under a mantle of snow.

This is one of the images that attracted the attention of Eli Maor

Eli Maor autographs one of his books.  A cutout model of the proposed Bernoulli Involute is in the background.  We discussed the beautiful properties of classic shapes.

Eli and Dalia Maor liked the shape of the Bernoulli.  The centre morphs the log spiral shape into a shell that halves its distance to the origin with every turn.  This is how the 12 tone scale works in music. 



To obtain one or more of Eli's books go to www.amazon.com and type in Eli Maor in the search box and you will be on the first leg of an adventure.



 

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