Thursday, January 31, 2013

Mathematics at Large.


Have you noticed maths featuring more extensively on ABC Radio National 
and in books and magazines?

When I was in Queensland last October there was in the local library a copy of New Scientist which fell to my hands, and mind boggling is modern maths!  One thousand dimensions!  "The Algorithm that rules the world".  I shall work on the info that I noted down and publish it soon.  There is quite a lot to work with;  very fascinating.  Canada's Massey Lectures 2012 is on at the moment 8pm drat I missed it now it is 9pm...repeat is 3am.  I listened this morning 3am.  Big Bang etc.  www.abc.net.au/rn/Massey lecture.  Two more to go.  For copyright reasons there is no transcript.  One must buy the book.  I shall update this post accordingly asap.


Elaboration 7/7/2013

New Scientist, 11 August 2012.  Vol 215.  No. 2877.

“The Algorithm That Rules the World”  pp 32-37. By Dr Richard Elwes, visiting Fellow, University of Leeds,  author of “Maths 1001”.

He noted Historical:-

300BC Euclid

820 Al-Khwarzmu  Quadratic equations  x2

18th century  Leonhard Euler

1936 Alan Turing

1948 George Deutzig  Simplex algorithm

1957 John Backus IBM Fortran

1972 Klee and Minty USA  A hypercube in n dimensions has 2n corners.

 In 41 dimensions it has a trillion edges for the simplex algorithm to crawl along…

Dr Elwes notes a cube has 6 faces and 8 corners = 14.  Edges = 12.

This is the Rule for Polyhedrons.

A 4D Hypercube has 16 corners, 24 faces, 32 edges,  added to the number of 3D”facets” of the shape (8).

(***you can search Google Images for Hypercubes.)

-----------------one can buy the original article from http://www.newscientist.com

 

 

Fermat’s Last Theorem

BBC Radio.  In Our Time Programs with Melvin Bragg 

25 Oct 2012 (ABC Radio National 3/11/2012)

Diaphantus   a2 + b2 = c2,      3, 4, 5, are answers.  The Arabs translated this.

                      Xn + yn = zn        many people tried to solve it.

This is an excellent discussion between three mathematicians, re the story of this from 1637.  In 1995 the puzzle was finally solved by Britain’s Andrew Wiles.  One can read transcript of the entire program online.

***Dr Ron Knott was on this same program Nov 29, 2007.  Re Fibonacci Series.
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CBC Massey Lectures, with Neil Turok,  “The Universe Within Us will be the key to our future.  It is as if the evolutionary process has an anticipatory element”.
Neil Turock is Canada’s massey Lecturer for 2012.
http://www.cbc.ca/ideas  massey-lecture 2012
In lecture 1:  Galileo, Newton, David Hume, Adam Smith,
Faraday, Maxwell, Tate and Thompson,
Franklin, Gauss, Ampere, Einstein
Lecture 2 is most interesting:- Raphael’s “The School of Athens”.
Aristotle, Plato, Socrates.  Pythagoras, Anaximander whose teacher was Phthales,
Hypatia the first woman mathematician.  Heraclitus.  Archimedes.
I went to Google Images to view the painting.  It is a frescoe in the Vatican Stanza della Segnatura, commissioned by Pope Julius 2 who died in 1513. 
Michelangelo was painting the Sistine Chapel at around the same time.
Raphael was born March 1483 and died June 1520,  only 37 years old.
One can choose from many images and websites for discussion.  A good one is norfleet1941.tripod.com.  the author divides the picture into six groups-  sometimes there is doubt as to who is who…scholars differ….is it Hypatia, or  Duke of Urbino or Jesus?........
Raphael painted the architect Bramante as Archimedes (or Euclid?) drawing on the pavement with a compass (lower RHS), Diogenes is sprawled centre, in a one shouldered blue robe,  Plato is holding the Timaeus and pointing to heaven, Michelangelo with a mop of dark hair is portrayed possibly as Heraclitus or Democritus at lower middle.  Raphael has painted himself looking out at us – his is the calm face to the right of the work.  His friend Castiglioni invented a term for Raphael’s work –“sprezzatura”  which means “a certain nonchalance which conceals all artistry and makes whatever one says or does seem uncontrived and effortless”.   ……I quote these words because I like them so much, tho I worry about copyright…..there is so much lost in the world; it becomes ephemera…….
Later in the lectures:-  Friedmann, Krutkov 1920, Lemaitre, US Georg Genulf.
1962 first global satellite,  ….Apollo Moon Mission.
1900 Max Planck was the first to propose the quantum theory of light.
“The universe is almost unbelievably simple”
“The coming quantum revolution will supplant our current digital age”.
These are most wise and in depth historical scientific lectures.  I cannot write more.
One can buy the book “The Universe Within” from the House of Anansi Press, from cbc shop online or even from iTunes.
Neil Turock is Director of Canada’s Perimeter Centre Institute for Theoretical Physics, was previously Professor of Physics at Princeton University and was Chair of  Mathematical physics at Cambridge.
You can see and hear him on YouTube and on Ted Radio Hour Talks for NPR.
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“I Died For Beauty”,  Dorothy Winch and the Cultures of Science, by Marjorie Senechal.
Tells the story of a pioneering and controversial female mathematician who helped shed light on the molecular structure of proteins, was the first to receive a Doctor of Science from Oxford University.
This I found on http://www.brainpickings.org   “How Lantern Slides Revolutionised Education”,  a Protein Story by Maria Popova. 
It came from  motherjones.com/media/2011/12/maria-popova

In 1850 Lantern Slides were invented.  Beautiful models pictured.  1965 Dorothy stashed her slides on a high shelf.  New technology had made them redundant.  The slides were later discovered and the book was written. 
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“So Crazy It Might Work”,  on This American Life radio and transcript online.  
No. 450   originally 11/11/2011.  Also on ABC  Radio National.  With Ira Glass.
1644 monk Marin Marsenne was obsessed with prime numbers.  Book,  “The Man Who Loved Only Numbers” by Paul Hoffman.   267 – 1  was the famous formula to predict these.
In 1903 a mathematician Frank Nelson Cole, at a maths conference gave a talk.  He wrote down the Formula.  Then a number 21 digits long.  Then = a number 9 digits long x a number 12 digits long.     Silence.     Long Multiplication.  Result was – that number!
It had taken him 3 years of Sundays ie 156 days to prove he could factorise that number.
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Alan Turing
June 2012 marks 100 years since his birth.  He is credited with the invention of the modern computer.  His tragic death- suicide by cyanide poisoning- marked a life persecuted for his homosexuality.  He’d accepted treatment with female hormones as an alternative to prison in 1952. *
   His was a life of great achievement nonetheless.  There are endless stories online and in Wikipedia.  One such is http://www.incorrectpleasures.blogspot.com.au where I found his epitaph.  Others are jenorton.tumblr.com/post/8987599032/the-epitaph-of-alan-turing. And http://www.primemagazine.com/2010/learn/great-men-you’ve-never-heard-of-alan-turing
What was Cleverbot? Did he/it pass the Turing Test?
See www.abc.net.au/radionational/scienceshow/16jan2012    also 30May and 2June2012.
One has complete transcript you can read.  “In particular, one can account for the appearance of Fibonacci numbers in connection with fir cones” is a quote from him.  His 1952 paper was “The Chemical Basis of Morphogenesis”.  “Turing believed that chemicals, following simple math rules could account for all the diversity in nature.”
His Epitaph:-
“Hyperboloids of wondrous Light
Rolling for aye through Space and Time
Harbour those Waves which somehow Might
Play out God’s holy Pantomime.”
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** I find it such a pity – I believe the real reason for being gay is that in the mother’s womb the foetus might be exposed to non appropriate hormones (ie hormone disrupting chemicals, even oestrogens found in food!) at critical stages of development.  It can take only 1 part per billion as the critical dose. 
Just read “Our Stolen Future” by Theo Colborn, Dianne Dumanoski and John Peterson Myers.   Prof Fred vom Salk  does mouse experiments.  Many scientists are at work on this.  BPA in plastic  is related to breast and prostate cancers.  See http://www.ourstolenfuture.com and especially a recent article by Dr John P Myers.
There is also a YouTube video – 15 years on- certain chemicals interact with genes.  Suites of genes are being turned on and off all the time.
Dr Colborn wrote and I quote from memory, 
 “Genes are like the keys on a piano.  It is the hormones that play the tune”.   

  Strange how it has been ignored.  Even the New York Times declared war on the theory 21 March 1996!    There must be a way to do things better.  We must get rid of all hormone disrupting chemicals and go Green Chemistry.  It is happening.   My feeling is that many diseases are result of the poisoning of our earth-  insulin and obesity,  hormone disturbances of all kinds and severity.  
 
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The Algorithm
27/1/2013.   original broadcast was in March 2012.
can download audio or show transcript. 
Re Book “Nine Algorithms That Changed the Future” by John Mac Cormack
 ............
EDPod on ABC Radio   You can download the program as an MP3.  I just listened again.
http://www.abc.net.au/radionational/programs/edpod/the-future-of-maths/4413042
6Dec2012
1.   Konrad Wolfram of Wolfram Research Europe makes computer software for maths.
(http://www.wolfram.com/mathematica     (Just released is Mathematica 9.)
Song:  “Bye, bye, mathematical Pi…”
2.   Dr Keith Devlin, Exec Dir H-Star inst.  Stanford University
Today high school maths is 17th century….. – spreadsheets = Algebra = patterns of numbers.
3.   Laureate Professor Jonathan Borwein of School of Maths and Physical Sciences, University of Newcastle, NSW, Australia.
Data mining/simulation,   cursive exponentiality,  microparallelism (Google does it with info)
Gauss called mathematics the Queen of Science.   Maths is many languages.   Discover computer communication and collaborative skills.   The IBM Watson machine beat the Japanese at – chess?
Project Polymath of Tim Gowers = radical departure for the sciences.  Internet helps people anywhere do world class maths and physics.

4.   Prof Terence Tao  of Mathematics Dept, UCLA, was a child prodigy.  He won the Fields Medal which is the highest accolade in maths.  He is involved in the Polymath Project.   Another software is Maple.   He speaks very fast!
One can find info on Project Polymath in Wikipedia, etc.
by Jason Dyer written 25/3/2009 for the non mathematician.
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Lastly,  Salman Kahn of “One World Schoolhouse”.  Salman Kahn Academy.  2 million students per month.  Maths.   ( And every conceivable subject, it seems).  It is best to learn at home on video, then do the calculations at school.  Learn by teaching others. 
See him on YouTube,  on TED Radio Talks.  Radio interviews abc.net.au search…….Fantastic.
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-------------------that was a lot;   typed on Word and copied, pasted.






 

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