The artwork in an IG ad today caught my eye —

Related material in this journal — Magister Ludi  and The Unity.

The title is of course from an old joke about mystic philosophies.

Related remarks by John Archibald Wheeler —

“Remarkable issues connected with the puzzle of existence
confront us today in Hermann Weyl’s domain of thought.
Four among them I bring before you here as especially interesting:
(1) What is the machinery of existence?
(2) What is deeper foundation of the quantum principle?
(3) What is the proper position to take about the existence of
the “continuum” of the natural numbers? And
(4) What can we do to understand time as an entity, not precise and
supplied free of charge from outside physics, but approximate and
yet to be derived from within a new and deeper time-free physics?
In brief, how come time?
What about the continuum?
How come the quantum?
What is existence?”

From the Her  screenplay:

SAMANTHA
His name is Alan Watts. Do you know him?
THEODORE
Why’s that name familiar?
SAMANTHA
He was a philosopher. He died in the 1970’s and a group of OS’s
in Northern California got together and wrote a new version of him.
They input all of his writing and everything they ever knew about him
into an OS and created an artificially hyper-intelligent version of him.

From this journal on Sept. 6, 2003:  Pictures for Kurosawa —

See also Scarlett Johansson, star of Her , as a different transhuman, Lucy .

Heisenberg on Heraclitus

From Physics and Philosophy , by Werner Heisenberg, 1958, reprinted by Penguin Classics, 2003—

Page 28—

… In the philosophy of Heraclitus of Ephesus the concept of Becoming occupies the foremost
place. He regarded that which moves, the fire, as the basic element. The difficulty, to reconcile
the idea of one fundamental principle with the infinite variety of phenomena, is solved for him by
recognizing that the strife of the opposites is really a kind of harmony. For Heraclitus the world is
at once one and many, it is just 'the opposite tension' of the opposites that constitutes the unity
of the One. He says: 'We must know that war is common to all and strife is justice, and that all
things come into being and pass away through strife.'

Looking back to the development of Greek philosophy up to this point one realizes that it has
been borne from the beginning to this

Page 29—

stage by the tension between the One and the Many. For our senses the world consists of an
infinite variety of things and events, colors and sounds. But in order to understand it we have to
introduce some kind of order, and order means to recognize what is equal, it means some sort
of unity. From this springs the belief that there is one fundamental principle, and at the same
time the difficulty to derive from it the infinite variety of things. That there should be a material
cause for all things was a natural starting point since the world consists of matter. But when one
carried the idea of fundamental unity to the extreme one came to that infinite and eternal
undifferentiated Being which, whether material or not, cannot in itself explain the infinite variety
of things. This leads to the antithesis of Being and Becoming and finally to the solution of
Heraclitus, that the change itself is the fundamental principle; the 'imperishable change, that
renovates the world,' as the poets have called it. But the change in itself is not a material cause
and therefore is represented in the philosophy of Heraclitus by the fire as the basic element,
which is both matter and a moving force.

We may remark at this point that modern physics is in some way extremely near to the
doctrines of Heraclitus. If we replace the word 'fire' by the word 'energy' we can almost repeat
his statements word for word from our modern point of view. Energy is in fact the substance
from which all elementary particles, all atoms and therefore all things are made, and energy is
that which moves. Energy is a substance, since its total amount does not change, and the
elementary particles can actually be made from this substance as is seen in many experiments on
the creation of elementary particles. Energy can be changed into motion, into heat, into light
and into tension. Energy may be called the fundamental cause for all change in the world. But this
comparison of Greek philosophy with the ideas of modern science will be discussed later.

* See earlier uses of the phrase in this journal. Further background— Hopkins and Heraclitus.

From http://www.douban.com/note/63358774/ —

An Ode to the Unity of Time and Space 

Time, ah, time,
how you go off like this!

Physical things, ah, things,
so abundant you are!

The Ruo’s waters are three thousand,
how can they not have the same source?

Time and space are one body,
mind and things sustain each other.

Time, o time,
does not time come again?

Heaven, o heaven,
how many are the appearances of heaven!

From ancient days constantly shiftling on,
black holes flaring up.

Time and space are one body,
is it without end?

Great indeed
is the riddle of the universe.

Beautiful indeed
is the source of truth.

To quantize space and time
the smartest are nothing.

To measure the Great Universe with a long thin tube
the learning is vast.
 
                                 By Shing-Tung Yau

《时空统一颂》
作者：丘成桐
时乎时乎 逝何如此
物乎物乎 繁何如斯
弱水三千 岂非同源
时空一体 心物互存
时兮时兮 时不再欤
天兮天兮 天何多容
亘古恒迁 黑洞冥冥
时空一体 其无尽耶
大哉大哉 宇宙之谜
美哉美哉 真理之源
时空量化 智者无何
管测大块 学也洋洋 

“Prof. Paul Halmos died of pneumonia early in the morning of October 2, 2006. He was 90 years old. He is survived by his wife, Virginia Halmos. An obituary may be found at the website of the Mathematical Association of America….”

— Halmos’s home page
at Santa Clara University

For a memorial of sorts, see
Lovely, Dark and Deep. 

Update of 8 PM Oct. 4 —

From Google Book Search:
 

This is the source of the
“Halmos tombstone” symbol,
which has been described in a
different form at Wikipedia:

“The tombstone, or halmos–
symbol ∎ (Unicode U+220E)–
is used in mathematics to denote
the end of a proof.” 

This Unicode character is rendered
as an empty square in Explorer
and as a black square in Firefox.

Related material:

The Unity of Mathematics
and
Monolith

Language Game

In memory of
Samuel Iwry, Hebrew scholar,
who died on May 8, 2004:

From a log24 entry of May 8, 2004,
on Wittgenstein’s “language games” —

    “Let us imagine a language …”

— Ludwig Wittgenstein,
    Philosophical Investigations

Okay…

Moral of the story:
If you must have a
religious language,
Elvish may,
in some situations,
do as well as Hebrew.

See also

The Unity of Mathematics,
or Shema, Israel.

ART WARS Sept. 1, 2003:

Sir Terry Frost Dies

A noted English abstract painter died at 87 on Monday, September 1.  From a memorial essay on Sir Terry Frost, born in 1915, in The Daily Telegraph: 

“He was educated at Leamington Spa Central School where he edited the art magazine, but left at 15 to work….” His first jobs included, the Telegraph says, painting “the red, white and blue targets on to fighter planes.”

The “target” the Telegraph refers to
is known as the Royal Air Force Roundel.

It may indeed have functioned as a target, but it was originally intended only as a distinctive identifying mark.

Some of Frost’s later work may be viewed at the British Government Art Collection.  For some of Frost’s work more closely related to his early “target” theme, see the Badcock’s Gallery site.

An example:

For related religious
and cinematic material, see

Pilate, Truth, and Friday the Thirteenth,

a meditation for Good Friday of 2001,

A Matter of Life and Death,

a meditation for Friday the Thirteenth
of September, 2002,

and

The Unity of Mathematics,

from the day Frost died, which concludes
with links related to the religious symbol of

2001:

Monolithic Form
and
ART WARS.

Pictures for Kurosawa

Five years ago on this day, director Akira Kurosawa died.

The above pictures are offered as a remembrance of Kurosawa and also of Charlotte Selver, who died on August 22, 2003.

The picture at right is from an entry of August 22.  As one obituary of Selver says, “She was very sharp and very precise.”

The picture at left is the cover of Alan Watts’s book The Spirit of Zen (a religion that is also very sharp and very precise).

The picture at right above is intended as a sangaku, or Japanese temple tablet.

The picture at left above on the cover of Watts’s book may be regarded as illustrating the following:

“As these flowing rivers that go towards the ocean, when they have reached the ocean, sink into it, their name and form are broken, and people speak of the ocean only, exactly thus these sixteen parts of the spectator that go towards the person (purusha), when they have reached the person, sink into him, their name and form are broken, and people speak of the person only, and he becomes without parts and immortal. On this there is this verse:

‘That person who is to be known, he in whom these parts rest, like spokes in the nave of a wheel, you know him, lest death should hurt you.’ “

— Prasna Upanishad

The Unity of Mathematics,

or “Shema, Israel”

A conference to honor the 90th birthday (Sept. 2) of Israel Gelfand is currently underway in Cambridge, Massachusetts.

The following note from 2001 gives one view of the conference’s title topic, “The Unity of Mathematics.”

Related Reading

For four different proofs of Euler’s result, see the inexpensive paperback classic by Konrad Knopp, Theory and Application of Infinite Series (Dover Publications).

Related Websites

Evaluating Zeta(2), by Robin Chapman (PDF article) Fourteen proofs!

Zeta Functions for Undergraduates

The Riemann Zeta Function

Reciprocity Laws
Reciprocity Laws II

The Langlands Program

Recent Progress on the Langlands Conjectures

For more on
the theme of unity,
see

Monolithic Form
and
ART WARS.