Future Consciousness

Some thoughts from Howard Gardner:

Five Minds for the Future

[T]he world of the future--with its ubiquitous search engines, robots, and other computational devices--will demand capacities that until now have been mere options. To meet this new world on its own terms, we should begin to cultivate these capacities now. (2)

In the future, we need a less ritualistic, more deeply internalized form of discipline. (41)

Perhaps, as educator Vartan Gregorian has suggested, we need a specialization in becoming a generalist. Such a specialization would target promising candidates and devote resources toward the enhancement of synthesizing capacities. (75)

Corporate visionary John Seely Brown has quipped that, in the world of tomorrow, people will say, "I create; therefore I am." (77)

If one wishes to raise individuals who are respectful of differences across groups, a special burden is accordingly placed on education in the social sciences, the human sciences, the arts and literature. (114)

I would like to live in a world characterized by "good work": work that is excellent, ethical, and engaging. (127)

[A]nyone who aims to cultivate these minds must have a concept of what it means to be successful and what it means to fail. (164)

Data Consciousness

Digital history may be overwritten, but it is never lost. Just as in language, the past is held etymologically in the present.

On Cloud Computing

Cloud computing relies upon virtual machines to meet the elastic demands of network processing. Need another server? Instantiate another virtual machine.

But a virtual machine is just a file, a file that contains every bit required to represent the main memory of an actual computer--an operating system, an application, and some data. Then, in the ultimate case of code-generation, a program branches to that file and immediately begins to behave as a separate computer, the computer defined by that file.

Similarly, a book is just a file. When the brain reads the text in that file, the interpreter that is the mind branches to the code in the file and executes it as though it is a separate mind, the mind defined by that book.

The question, then, is this:

What analogy exists in the virtual private cloud?

Pattern Recognition: Perfect Numbers and Binary Numerology

For several weeks, recently, I awoke each morning thinking of perfect numbers, that species of positive integer for which the sum of its positive factors equals the number itself. Naturally, I had heard of perfect numbers in college, and I knew of 6 and 28, but was unaware of any others. As I lay there each day, I wondered what 6 and 28--and their factors--had in common, and whether any other numbers shared that characteristic.

1+2+3=6

1+2+4+7+14=28

It soon became clear that, because both numbers were even, and, by definition, their factors had to include 1, there would have to be an odd number to offset the 1. Then I saw a possible relationship between powers of 2 and the largest odd number in the factor set, so I began thinking in powers of 2 and could readily see the beginnings of a pattern in my two knowns:

21*(20+21)=6	[1+2+3=6]
22*(20+21+22)=28	[1+2+4+7+14=28]

The European scholars of the last millennium
Have considered the Polynesians to be illiterate
And therefore intellectually inferior to Europeans
Because the Polynesians didn't have a written history
And used only a binary mathematics,
Or "congruence in modulo two."
The European scholars scoffed,
"The Polynesians can only count to two."

-- from "Numerology" in Synergetics by R. Buckminster Fuller

Unfortunately, two instances does not constitute a pattern. Since I could not readily think beyond 28 without pencil and paper, I began to search for a precedent, and realized I could produce a pattern if I could bend the usual definition of a perfect number just slightly, including the number itself in the special case of unity, i.e., the sum of the factors of 1. Now I had a pattern:

20*(20)=1	[1=1]
21*(20+21)=6	[1+2+3=6]
22*(20+21+22)=28	[1+2+4+7+14=28]

Since the Polynesians lived on the sea
And were naked,
Anything upon which they wrote
Could be washed overboard.
The Polynesians themselves
Often fell overboard.
They had no pockets
Nor any other means
Of retaining reminder devices
Or calculating and scribing instruments
Other than by rings
That could not slip off
From their fingers, ankles, wrists, and necks,
Or by comblike items
That were precariously
Tied into the hair on their heads
Or by rings piercing their ears and noses.
These sea people had to invent ways of calculating and communicating
Principally by brain-rememberable pattern images.
They accomplished their rememberable patterns in sound,
They remembered them in chants.
With day after day of time to spend at sea
They learned to sing and repeat these chants.
Using the successive bow-to-stern,
Canoe and dugout, stiffing ribs and thwarts
Or rafters of their great rafts
As re-minders of successive generations of ancestors,
They methodically and recitationally recalled
The experiences en-chantingly taught to them
As a successive-generation,
Oral relay system
Specifically identified with the paired ancestral parents,
Represented by each pair of ship's ribs or rafters.

-- from "Numerology" in Synergetics by R. Buckminster Fuller

Naturally, I expected to find the next perfect number in the next iteration of my pattern:

23*(20+21+22+23)=120

Unfortunately, the factors of 120 add up to 240--not perfect. Undaunted, I tried the next iteration:

24*(20+21+22+23+24)=496

I checked my work, and eureka; I had found it--the next perfect number! Certain I would live forever in the annals of mathematica, I googled "perfect numbers" just to be sure. And there in the SERP, I learned what I'm sure you already know: there are many known perfect numbers higher than 496; in fact, Euclid had discovered the first four perfect numbers using powers of 2 some 2300 years before me. C'est la vie...

As complex twentieth-century,
Electronically actuated computers
Have come into use,
Ever improving methodology
For gaining greater use advantage
Of the computers' capabilities,
As information storing,
Retrieving, and interprocessing devices,
Has induced reassessment
Of relative mathematical systems' efficiencies.
This in turn has induced
Scientific discovery
That binary computation
Or operation by "congruence in modulo two"
Is by far the most efficient and swift system
For dealing universally with complex computation.

-- from "Numerology" in Synergetics by R. Buckminster Fuller

But Euclid approached the problem from a different angle. Rather than looking at the factor set as a series of binary terms, Euclid looked for cases in which 2^p-1 was prime; then he would find the next perfect number in 2^p-1(2^p-1). The problem is, checking a number for prime is a great deal of work. That said, networked computers have taken us to amazing extremes; the largest prime known as of today has about 13 million decimal digits.

In this connection we recall that the Phoenicians
Also as sailor people
Were forced to keep their mercantile records
And recollections in sound patterns,
In contradistinction to tactile and visual scratching--
And that the Phoenicians to implement
Their world-around trading
Invented the Phoenician,
Or Phonetic, or word-sound alphabet,
With which to correlate and record graphically
The various sound patterns and pronunciations
Of the dialects they encountered
In their world-around trading.
And we suddenly realize
How brilliant and conceptually advanced
Were the Phoenicians' high-seas predecessors
The Polynesians,
For the latter had long centuries earlier
Discovered the binary system of mathematics
Whose "congruence in modulo two"
Provided unambiguous,
Yes-no; go--no go,
Cybernetic controls
Of the electronic circuitry
For the modern computer,
As it had for millenniums earlier
Functioned most efficiently
In storing and retrieving
All the special-case data
In the brains of the Polynesians
By their chanted programming
And their persistent retention
Of the specific but no-longer-comprehended
Sound pattern words and sequences
Taught by their successive
Go--no go, male-female pairs of ancestors.

-- from "Numerology" in Synergetics by R. Buckminster Fuller

So I think we need a more elegant approach to searching out perfect numbers, as well as primes. Rather than tying up a multitude of computers for months on end, laboriously crunching out the simplest of arithmetic routines, we need pattern recognition routines that can "see" the properties of a number, probably in its most basic state: binary. When we develop these routines, we will likely find that they do not "see" the patterns at all; instead, they will "hear" the rhythm of zeroes and ones, and "feel" their perfection or their primal nature.

But certain numbers
Such as prime numbers
Have their own cosmic integrity
And therefore ought to be integrally expressed.
What the numerologist does
is to add numerals horizontally (120 = 1 + 2 + 0 = 3)
Until they are all consolidated into one integer.
Numerologists have also assigned
To the letters of the alphabet
Corresponding numbers: A is one, B is two, C is three, etc.
Numerologists wishfully assume
That they can identify
Characteristics of people
By the residual integer
Derived from integrating
All of the integers,
(Which integers
They speak of as digits,
Identifying with the fingers of their hands,
That is, their fingers)
Corresponding to all the letters
In the individual's complete set of names.
Numerologists do not pretend to be scientific.
They are just fascinated
With correspondence of their key digits
With various happenstances of existence.
They have great fun
Identifying events and things
And assuming significant insights
Which from time to time
Seem well justified,
But what games numerologists
Chose to play with these tools
May or may not have been significant.
Possibly by coincidence, however,
And possibly because of number integrity itself
Some of the integer integrating results
Are found to correspond elegantly
With experimentally proven, physical laws
And have subsequently proven to be
Infinitely reliable.
Half a century ago I became interested in seeing
How numerologists played their games.
I found myself increasingly intrigued
And continually integrating digits.

-- from "Numerology" in Synergetics by R. Buckminster Fuller

So, applying Bucky's zeal for integrating integers to a sample of perfect numbers, we arrive at an astounding observation:

28 = 2 + 8 = 10; 1 + 0 = 1

496 = 4 + 9 + 6 = 19; 1 + 9 = 10; 1 + 0 = 1

8128 = 8 + 1 + 2 + 8 = 19; 1 + 9 = 10; 1 + 0 = 1

33,550,336 = 3 + 3 + 5 + 5 + 0 + 3 + 3 + 6 = 28; 2 + 8 = 10; 1 + 0 = 1 8,589,869,056 = 8 + 5 + 8 + 9 + 8 + 6 + 9 + 0 + 5 + 6 = 64; 6 + 4 = 10; 1 + 0 = 1 137,438,691,328 = 1 + 3 + 7 + 4 + 3 + 8 + 6 + 9 + 1 + 3 + 2 + 8 = 55; 5 + 5 = 10; 1 + 0 = 1 2,305,843,008,139,952,128 = 2 + 3 + 0 + 5 + 8 + 4 + 3 + 0 + 0 + 8 + 1 + 3 + 9 + 9 + 5 + 2 + 1 + 2 + 8 = 73; 7 + 3 = 10; 1 + 0 = 1

Integrating the integers of the first several multi-digit perfect numbers consistently yields 1, unity.  Coincidence? I doubt it. More likely, it is evidence of number integrity itself.