Thursday, January 31, 2013

Diorama with Mermaid and Seashells **

As promised,  I got it together,  but the wind blew it all over the place when I was taking the photo.
I was  a bit frazzled,  so it is as it is.  One day things might be more perfect....

Please see May 25, 2010  post "Instructions for Making a Model of a Seashell". 
There is  a lot of information in the early pages of this blog. 
 More work will be done in future to perfect the spiral at the tip of seashells.
22/8/2014-   recent work is perfecting this tip of the spiral!  Getting better.
*** The mermaid was drawn by 10 year old Paris and she gave me permission to use it.  I mentioned her in a previous mermaid post,   and I have more mermaids to add asap.

The Vedic Connection

Very early on in this blog I was guessing that the origins of the Fibonacci Series is the Ancient Vedic Age.  A world wide Sanskrit speaking Culture.  A Korean website describing dolmens all over the world brings amazing clues.  And  ,  I think it is,  has historical.  Many other websites are in accord with this idea.  Jain mathematics.  You can even find info on You Tube.

Again it is late at night now and the essays must wait till another time.
 I think I will update this page when I am better organised.

I am keen to publish Diorama with mermaids and seashells,  on the next post!

 Update 23/8/2013

S.Goonatilake writes that “the Fibonacci Series was known, independently of the West, in Indian Mathematics.  Attributed in part to Pingala 200 BC,  then Virahanka about 700 AD, Gopala 1135 AD and Hemachandra 1150 AD.”

Wikipedia mentions -  Vedas 3000 BC,  ended 500 BC.

Rishis were seers.

Aryabhatta,  famous for the Vedic discovery of zero.    “Om has its origin in the unmanifest.  Oldest references are not in the Rig Veda but in Upanishads.”     Seven Books about Phi by Jain108 of Mullumbimby Northern New South Wales, Australia…..secret codes in the Gayatri Mantra…16 mathematical sutras….workshops offer learning Rapid Mental Calculation…he has a good diagram of the computational pattern of the sunflower seeds  and a perfect image of a splash droplet……Lo Shu magic square of 9….The Multidimensional Powers of Phi…psi….learn the secrets of Nature.

“From Natural Numbers to Numbers and Curves in Nature” by AKMallik,  Professor of Mechanical Engineering at Indian Institute of Technology, Kanpur.,34-40   I am not sure if access is possible directly from my blog.  I mention this report because sometimes one never finds the same work again.  This is from Resonance, Vol 9, No 9, pp 29-37, 2004   He has equations for double spiral sunflower,  plus a very Vedic approach, I am  guessing.

Searching  Internet -  shows many more websites on this topic.

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. 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



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.
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.  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  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.
“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   “How Lantern Slides Revolutionised Education”,  a Protein Story by Maria Popova. 
It came from

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. 
“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.

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 where I found his epitaph.  Others are And’ve-never-heard-of-alan-turing
What was Cleverbot? Did he/it pass the Turing Test?
See    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.”
** 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 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.  

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.
1.   Konrad Wolfram of Wolfram Research Europe makes computer software for maths.
(     (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.
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 search…….Fantastic.
-------------------that was a lot;   typed on Word and copied, pasted.


Phi Furthermore.

It came to me with a jolt one morning
that if Phi to minus Powers has an Equation related to the Fibonacci series,
then it must follow that Phi to plus Powers would have a similar Equation.

Just by looking at the following Tables one can see
that Phi to the Power n is related to the half Fibonacci Series!


Next I related the Powers of Phi to the Half Fibonacci numbers:-
 The ratio is 0.947217 or very close to this....
I decided to calculate the other way, to be more in line with the minus powes equation:-
The ratio is inverse to above, that is 1.055727
For a while I thought it was really close, that last one----7881193 but it was equiv to 7811356
(not 78811......!).   Must be honest...not exact,     but awfully close-  only 70000 out!  but at those huge numbers I'd have to study it further---  this is all I have the energy to do.
Correction 6/2/2013----the error was one of simple transcribing---
I recalculated 0.5278639 x 14930352,  =  7881193.8
and that is almost exactly equal-  only 0.1 difference from phi to power 33!
You get a different result if you use 0.52786395, or 0.527864 or 0.52786
I used the result one gets on the calculator ie 0.5278639
We could do the same calculations all over the Fibonacci Series but if the number is larger than 8 digits we are unable to use calculator-  we need to do long manual multiplications.
What it all means, I have no idea.  From my reading on the Fibonacci series there may be an application in space travel or consciousness;  see  and fibonacci.  there is an excellent picture of the brain.
There is  an article in
  that  is, "Torsion:  The Key to a Theory of Everything - including Consciousness"  by BrendanDMurphy.
from Myshkin to Einstein to Nassim Haramein. 
This is the track I'm on.  Torsion is part of it.  Psi and Phi. 

Continuing from last posts...

I need to clarify the work done  recently.  Sorry the ink is not dark enough.
Equations, equations.  Patterns.  Often spookily exact;  sometimes almost equal but not quite.

1.0837212      this was the ratio consistently revealed
when dividing the minus power Phi times 10 to power 7,  and the closest "Fibonacci number"
This belongs to earlier posts;  more info that needs to be explained.
I should know by now not to use biro in these Tables,
 but no way am I going to rewrite it all;  hands have some RSI pain....
If you are interested, click on the image and it might be better visible.
This is all a work in progress, warts and all.  I still live without electricity, so this posh motel is my work place when I can organise it.

Monday, January 7, 2013

Planck and Phi

Please take a look at this.  Never again can anyone say that the Fibonacci Series is just "flim flam".


One can use "control and +"  to further enlarge,
then "control and _" to return to size.

Table 1:  Plus Powers of Phi.  **notice column 3!

Table 2:  Minus Powers of Phi

Remember the Cosmic Ouroborus of a recent post?
10 to the Power minus 33 cm is the smallest length,  the Planck length.

Table 2 shows  Phi   ie 1.6180340  (from the Fibonacci Series),
calculated for Powers to minus numbers.
***Phi to the power minus 33 is 0.0000001,
***Phi to the power minus 34 is zero

Phi to the Power 1 is 1.618034
Phi to the Power 0 is 1
Phi to the Power -1 is 0.618034,  etc... all the way to -33 power...
This is what happens between 1 and 0.

I guess this limit is due to 8 digit calculator.
I wonder what a supercomputer might do.

You can also see how the calculations
almost follow the Fibonacci Series
(x 10 to power minus 7)
from F34 and continuing on back to F1.

They are exact at 0.0000001, 0.0000002, 0.0000003, 0.0000005, 0.0000008....
That is what alerted me when I saw this.  I was amazed and excited!

The calculations correlate with the Fibonacci series,  true to a ratio of 1.08372.

Table 3:  Ratios:  Digits for Minus Powers of Phi, to the closest Fibonacci Number


"The Whole Bang Lot"

More data, on angles and Phi(s).

Angles for Giza Pyramid

The photo above was taken in bright sunlight, but such greyishness!
I wonder is it because of particles in the atmosphere from chemtrails (photo below)?
I feel mighty uneasy about what is happening-  sometimes there are up to 5 aircraft at it, all day,  often every day;  I've noticed them last year!  Oh dear.


Angles for Sunflowers

Angles for Fibonacci Series, 137.5 degrees

this one began as 2.5 degrees, but I must have been tired and it looks more like 30 degrees!  At least it shows a trend.