Posts Tagged ‘fermat’s last theorem


Fermat’s Last Theorem–Extreme Sports for the Brain

I love exercising my brain. I don’t like health clubs or running, so the only

fermat's last theorem

350 years ago, in the margin of this text, Fermat claimed he could prove this theorem

way I get exercise is by thinking. To me, this is one of life’s traits that separates human from non-. Have you ever seen a dog sit quietly and think. No. He falls asleep.  Most animals hunt, play or sleep. Their critical problems–those that might cause their extinction, those that might make their life easier–are solved by evolution. They are replaced by a different species that adapts better to the environment.

Not true with the human species, Homo. When we aren’t hunting or playing, we are as likely to be thinking through a problem as sleeping. We have adapted to our environment as much through our own big brain’s problem solving abilities as by evolution’s incremental process of replacing one species with another.

Extreme sports for a thinker is solving unsolvable mathematical problems. And one of the most extreme is Fermat’s Last Theorem. It took 350 years and over 150 pages to solve the first time, making it a worthy exercise for the brilliant human brain.

In the novel I am currently working on, my antagonist sponsors a competition between a brilliant mathematical scientist and a unique problem solving AI to see which can come up with the solution to Fermat’s Last Theorem. Even for an eidetic mind, memorizing 150 pages of obtuse equations would be close to impossible. But if you know the logic that provides a blueprint for the solution, you could reproduce it. Continue reading ‘Fermat’s Last Theorem–Extreme Sports for the Brain’


Nazi Codes–Still Uncrackable

wheelEncryption is a fascinating field. Since WWII, when the Allies ability to break secret messages enciphered by the German Enigma Machines contributed substantially to the Allied war-winning intel, it has captured the minds of mathematicians and scientists alike. I’ve used several myself, based on:

  • musical codes (i.e., Morse Code Music)
  • Palindromes
  • Fibonacci Numbers and the Golden String

Up until January, 2006, there were still three uncracked Nazi Enigma messages intercepted in the North Atlantic in 1942. had no idea this was still uncracked. The M4 Project (named for the four rotor Enigma M4 used to encipher the messages), and later Enigma at Home, was created to use the power of home computers to break these last messages. The encrypted messages are:


Not unlike Fermat’s Last Theorem which was only just solved after 358 years of trying by Andrew Wiles of Princeton University in 1993.

Still trying to crack Nazi Enigma messages

Volunteers contribute spare computing cycles to crack old wartime ciphers
By Bob Brown

You can donate your spare PC processing power to dozens of cool volunteer computing projects simply by downloading some software. Enigma@home is the one that called me.

Enigma@home is based on the M4 Project, an effort spearheaded by German-born violinist and encryption enthusiast Stefan Krah. The M4 Project was designed to break three original messages generated by a famed electro-mechanical Enigma machine and intercepted in the North Atlantic in 1942. (The project gets its name from the four-rotor Enigma M4 machine presumed to be used by the Germans for enciphering the signals during wartime.) The project’s method for cracking the ciphers is described as “a mixture of brute force and a hill climbing algorithm.”

Slideshow: 12 cool ways to donate your spare PC processing cycles

Enigma@home provides access to the M4 Project using BOINC software for volunteer and grid computing. The project, which started in January of 2006, succeeded in breaking the first two messages within the first couple of months. Enigma@home is still working on message No. 3. As for why it’s such a tough one, Krah says there could be several reasons:

1. It could be a so-called Offizier message, part of which is doubly encrypted.

2. The message was badly intercepted and some letters are missing.

3. There are some messages that require the algorithm to be applied many times. This is pretty much what we are doing right now.

As for what sparked Krah’s interest in breaking ciphers, he says that in 2005 he started solving the challenge messages of Simon Singh’s Cipher Challenge – long after the actual challenge was over.

“The Enigma message in Singh’s challenge is in many ways relatively easy to break and subsequently I improved the algorithm so that real world messages could be broken. In summer of 2005, a publication by Geoff Sullivan and Frode Weierud helped to refine the algorithm further.(More about decoding)


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Discover the sizzle in science. It's not that stuff that's always for the smart kids. It's the need to know. The passion for understanding. The absolute belief that for every problem, there is a solution. The creative mind seeking truth in a world of mystery. The quest for the Holy Grail.

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Books I’m Reading

Great Science Books

Assembling California
Born On A Blue Day: Inside the Extraordinary Mind of an Autistic Savant
The Forest People
Geology Underfoot in Southern California
The Land's Wild Music: Encounters with Barry Lopez, Peter Matthiessen, Terry Tempest William, and James Galvin
My Life with the Chimpanzees
Naked Earth: The New Geophysics
Our Inner Ape: A Leading Primatologist Explains Why We Are Who We Are
The Runaway Brain: The Evolution of Human Uniqueness
Sand Rivers
The Singing Neanderthals: The Origins of Music, Language, Mind, and Body
The Tree Where Man Was Born
The Wildlife of Southern Africa: A Field Guide to the Animal and Plants of the Region
The Worlds of a Maasai Warrior: An Autobiography

Jacqui's favorite books »
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RSS Fact and Fiction about Early Man

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    author: GHR von Koenigswald name: Jacqui average rating: 4.00 book published: 1492 rating: 5 read at: 2014/10/04 date added: 2014/10/04 shelves: early-man review: Meeting Prehistoric Man by GHR Von Koenigswald is a journey throughout the world in discovery of early man as paleoanthropologists understood him during VonKoenigswald's time, circa 1950' […]
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  • The Unfolding of Language: An Evolutionary Tour of Mankind's Greatest Invention January 12, 2014
    author: Guy Deutscher name: Jacqui average rating: 4.17 book published: 2005 rating: 3 read at: date added: 2014/01/12 shelves: early-man, research review: Dr. Deutscher has done a scholarly, thorough discussion on the roots of language, but I believe he started too late in time. I'm of the persuasion that language involves more than the spoken word. I […]
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  • She Who remembers November 3, 2013
    author: Linda Lay Shuler name: Jacqui average rating: 4.00 book published: 1988 rating: 4 read at: date added: 2013/11/03 shelves: early-man review: […]
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  • The Runaway Brain: The Evolution Of Human Uniqueness July 25, 2011
    author: Christopher Wills name: Jacqui average rating: 4.15 book published: 1993 rating: 5 read at: date added: 2011/07/24 shelves: science, early-man review: In my lifelong effort to understand what makes us human, I long ago arrived at the lynchpin to that discussion: our brain. Even though bipedalism preceded big brains, and we couldn't be who we are […]
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  • The Origin Of Humankind July 25, 2011
    author: Richard E. Leakey name: Jacqui average rating: 3.97 book published: 1981 rating: 5 read at: date added: 2011/07/24 shelves: early-man, history review: If you're interested in man's roots, there are several authors you must read: Birute Galdikas Dian Fosse Donald Johanson GHR Von Koenigsman Glen Isaacs Jared Diamond Ian Tattersell Lev Vygots […]
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  • Lucy: the beginnings of humankind July 24, 2011
    author: Donald C. Johanson name: Jacqui average rating: 4.12 book published: 1981 rating: 5 read at: date added: 2011/07/24 shelves: early-man, science review: I read this book when I was writing a paleo-historic drama of the life of earliest man. My characters were Homo habilines, but they cohabited Africa with Australopithecines, so to understand the co-st […]
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  • Through a Window: My Thirty Years with the Chimpanzees of Gombe July 24, 2011
    author: Jane Goodall name: Jacqui average rating: 4.25 book published: 1990 rating: 5 read at: date added: 2011/07/24 shelves: early-man, science review: I have read every book that Jane Goodall wrote. She has an easy-going writing style that shares scientific principals easily with the layman. Probably because when she started, she was little more than a no […]
    Jane Goodall
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