http://www-groups.dcs.st-and.ac.uk/~histor...atosthenes.html

....a man whose accomplishments in many different areas are remembered today not only as historically important but, remarkably in many cases, still providing a basis for modern scientific methods....

duplication of the cube

One of the classic problems of Greek mathematics was to find a ruler and compass construction for the cube root of 2. This was called duplicating the cube

This is sometimes called the Delian problem from the story that the oracle at Delphi demanded that this construction be performed to stop a plague.

The other classic problems were squaring the circle and trisecting an angle.

.....Eratosthenes made a surprisingly accurate measurement of the circumference of the Earth. Details were given in his treatise On the measurement of the Earth which is now lost. However, some details of these calculations appear in works by other authors such as Cleomedes, Theon of Smyrna and Strabo. Eratosthenes compared the noon shadow at midsummer between Syene (now Aswan on the Nile in Egypt) and Alexandria. He assumed that the sun was so far away that its rays were essentially parallel, and then with a knowledge of the distance between Syene and Alexandria, he gave the length of the circumference of the Earth as 250,000 stadia.....

Yes, I know the formula: The circumference of the Earth is equal to the distance from the well to Alexandria times 360 degrees divided by 7.5 degrees.

2400 * 360 / 7.5 = 500

The distance to Alexandria (500) is equal to the circumference of the earth (24000) times 360 (angle of a full circle) divided by 7.5 (angle between the well and Alexandria).

By the way, every mathematical expression in shorthand notation can be expressed equivalently as an English sentence. For example:

A = pi * r^2

The area of a circle is equal to pi times the radius squared.

or

The length of the hypotenuse of a right triangle is equal to the square root of the sum of the squares of the other two sides.

These expressions can also be equivalently expressed as binary strings. The set of all ideas maps directly to the set of all binary strings.

Binary strings? How so?

34587435432578989000009098765578899

or

011011110000011010111010010001111001

is an expression?

The Myth of the Machine – The Pentagon of Power ( ? ) – Lewis Mumford

At every point in development, the concrete, the empirical, and the historical on the one hand and the abstract, the mathematical and the analytical on the other, have both been necessary for forming an adequate picture of reality.

Types of business personalities: finders, collectors, fabricators, manipulators, etc.

Every man is a dabbler, if not a master in all knowledge. Every man is a divine, a physician, and a lawyer to himself, as well as a counsellor to his neighbours.

16th century mechanistic conversion of society – purely mechanical forms were superimposed upon every manifestation of life, thereby suppressing many of the most essential characteristics of organisms, personalities, and human communities.

16th century depersonalized world picture – mechanical activity and interests took precedence over more human concerns.

Copernicus, Kepler, Galileo, Descartes, Leibnitz, Newton were the driving forces in this transformation. Also note Boyle, Maxwell and Planck.

Marxist historians see feudalism as a universal historical stage through which all societies must pass before the emergence of capitalism.

Whereas many of the older ideologies of life had mistakenly accepted a static, earth centred world, with only the most limited possibilities of change, mostly of a cyclical or apocalyptic order, the new ideology fostered an intense interest in space, time, motion, in their widest cosmic setting, not the settings in which organisms actually function in their earthly habitat, intermingled with other organisms, pursuing their own further life potentialities.

Abstract motion took possession of Western mind. the rotation of the earth, the majestic geometric path of the planets, the swing of the pendulum, the arc described by hurtling projectiles, the exact motions of clockwork, and the rotations of watch wheels.

Speed shortens time, time was money, and money was power.

Farther and farther, faster and faster, became identified with human progress.

Metaphors and analogies derived from the machine were applied shrewdly, if coarsely, to organisms in order to reduce life to its quantitative mechanical and chemical components. This seemed an infallible method of eliminating the ultimate mystery of life itself.

Western man’s views of the new world – the geographic new world, with the Sun as the centre of the universe, the mechanical new world, and historical time, which released man from the grasp of his unconscious past, with its buried traumas and its futile repetition of attested errors.

The human figure as a mechanized automaton – that which is self-moving, self-acting machine; a mechanical contrivance, which imitates the arbitrary or voluntary motions of living beings; a person who acts mechanically.

Mechanization of the world picture.

Most aspects of our lives are immersed in the language of mathematics.

We are divided on so many issues, we add insult to injury, we seek the roots of our existence, and the powers to control and differentiate information as we integrate many aspects of our experiences. How many times do we get things out of proportion or factor in false assumptions? We set ourselves numerous tasks and seek common denominators for categorisation. [spot the 'mathematical' terms in that].

You missed differentiate, integrate and false. And we both missed 'true' which is unforgiveable!

True, although I did stop momentarily over differentiate and false. I don't know though about integrate.

The rate of change in the useage of integration has transformed my opinion about its value.

integration has been the key to multiculturalism. differentiation leads to disharmony. there is no room in modern society for individualism, unless you have the money to pay for it, or are good at mathematics.

Like the movie, "The Matrix"?

Not quite. "The Matrix" used human brains for experiencing the simulation.

Express something in a binary code then Rick, just as an example.

110 in binary is the number six.

A point in space has three number coordinates. These can be expressed in binary. Three points in space denote a triangle (nine binary numbers).

A JPEG image file consists of n bytes. Each byte is eight bits. The JPEG image is stored as binary. And so on for all things that can be known. Every book, picture, concept, etc.

So, this of course is possible only if we still believe in the old doctrine of a mathematical paradigm, where each particle of matter is broken down into the single point of geometrical proportion of a circle of matter. What happens when we break beyond this micro cosmic point, and delve into such theories like string theory which postulates that a string/wave like element is the fumdamental force that drives matter, nature and the cosmos?

Are these dimensions of reality binary?

the letter 'A' converts to '01000001' in binary.

You are misunderstanding me again. I am not saying that "all things are number" as Pythagoras did. I am only saying that all ideas can be "expressed" as numbers.

So, for example, how would the idea 'idea' be expressed in binary?

A certain number sequence for each letter that is stringed together to form the whole?

Very simply. Take my definition of "idea," expressed in English, and take the ASCII value for each character in that expression, and string them together as a binary string.

The whole definition and not the word?

Does that make it universal, so that all languges can be coded under the one binary system?

Just ideas!

A 24 inch by 24 inch box is expessed in one binary code no matter the language it is expressed in?

Interesting indeed.

There is a fine mathematical distinction between "unbounded" and "infinite"!

Unbounded means that you can keep adding new ones as you please. Infinite means a correspondence between the items in the set and the (infinite) numbers.

So if we are itemizing the coding systems, they seem to be unlimited, but we can't yet prove they're infinite! We must be mathematically precise, mustn't we?

It's the only way, is it not?

Absolutely. Apply critical thinking at every opportunity.

Most matter in the universe is not conscious. Consciousness is a special rarity, which is known to occur on only one planet in all creation.

just got me thinking about expanded consciousness. what comes after that?

maths will describe consciousness then?

so conscious activity can be predicted?

so some mathematician could work out what i'm thinking....now....and tomorrow?

1. Nothing.

2. No.

3. No.

4. No.

There is no known level of consciousness beyond the sixth one.

Math and other expressions of ideas are not capable of describing all that exists, especially consciousness.

The future can't be predicted (as is shown by chaos theory).

Mathematicians in particular have no clue about human beings.

ha, ha ! mathematicians are not human beings then?

I was always taught to plan ahead. Shawn wishes to draw attention to and stimulate activities to enable expanded consciousness. so, planning ahead, i want to imagine what the subsequent step is and how to describe it. humbly, i hoped that a reductionist approach might shed some light. using mathematics, it would at least avoid having to do some lab experiments in the meantime. (before you say it, I know the one about the mathematician's lab being inside their head).

logic is not a 'thing' that can be conscious. Information cannot 'come alive'. AI will always be A, and will evermore be a product of a programmer who can decide what is I. The code of this I, as formulated by the programmer, is fed into the AI device in order to elicit mechanical action that pleases the programmer or other 'metalanguage-capable' entities. This code can always be formulated in terms of binary strings given the appropriate construction of the AI device.

I am assuming that 'intelligence' is the ability to choose action that satisfies need. To me, the phrase 'artificial intelligence' simply means that the chooser has the ability to satisfy need via an 'artificial' (anthropogenic) extension of himself (like a robot). The 'intelligence' has not been placed into the robot, only the intelligently chosen behaviors. The robot is not intelligent, it is simply a device that acts according to its design as chosen by its intelligent designer. Without an intelligent designer assisting it, the robot's ability to acquire novel 'intelligent' behaviors that lie outside its pre-existing range of possibilities can be no better than chance.

Further, by my way of defining things, the term 'artificial consciousness' would be misleading. At best, I can say 'artificially initiated consciousness', but this consciousness, after being initiated, would evolve according to its own needs and cease to be 'artificial'.

Good post Dan, and it leads me to ask for your opinion on useage of the words artificial and natural.

Do human acts come under the meaning of natural or artificial?

I presume them to be natural because I presume humans to be natural.

But are the products we produce natural?
If you take a website as an example - it does not occur naturally.
Does natural mean 'without the touch of mans hand'?

From Rick at http://teamster.usc.edu/~fixture/Robotics/...phy/philo.html:

"....Consciousness can be defined as what it's like to be aware. One theory holds that all multi-celled animals (worms, etc., on up) have consciousness,4 and I think it's true. Certainly, if you have ever fished with worms, you know they don't like being pierced with the hook, and will squirm like hell to avoid it. Most philosophers will concede that the higher animals like cats and dogs can feel ....."


1. Self awareness or more? Conditions such as autism suggest that self awarness but not awareness of others can occur.
2. Even bacteria will translocate from an injurious environment. "Feel" needs defining better in this statement.
3. Interesting that you specifically mention animals. I have always wondered how we should view plants (that can be organised in very complex and sophisticated ways - for example they have complex eukaryotic cells, similar to our own, and for "natural" ecosystems are essential for the maintenance of other organisms). We assume that they do not have consciousness or intelligence, perhaps rightly so. But higher plants are often displayed at similar latitudes to animals on taxonomical/evolutionary charts, again perhaps rightly so. Life and intelligence (or even consciousness) are not one and the same, and the abscence of consciousness should not imply inferiority. As yet we have no evidence that conscious organisms will survive through eternity any better than ones lacking it; indeed we might expect the opposite according to how well we manage our place in the natural world. So, a question: is consciousness a requirement for sustained life in the universe? Big question!