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> The use of Math on the Path, Using math as a tool for self discovery
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post Apr 27, 2005, 06:20 PM
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Is science more than philosophy?
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post Apr 27, 2005, 06:22 PM
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physical science was originally known as natural philosophy
http://www.friesian.com/hist-2.htm
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post Apr 27, 2005, 06:23 PM
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Yes, but math has been around alot longer than either.
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post Apr 27, 2005, 06:24 PM
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really?
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post Apr 27, 2005, 06:26 PM
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Really!
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post Apr 27, 2005, 06:26 PM
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who sez?
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post Apr 27, 2005, 06:27 PM
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And art even longer than that.
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post Apr 27, 2005, 06:33 PM
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QUOTE (Dan @ Apr 27, 09:26 PM)
who sez?

It is our history man, it is how we evolved.

One step, two step, three step, four

Baby steps, crawl, walk, run, jump (quantum), leap (quantum).

It is the natural progression and evolution of thought.

Can you imagine how overwhelming it would have been for our ancient/prehistoric
ancestors if they were given all branches of the knowledge tree to climb at once?
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post Apr 27, 2005, 06:38 PM
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So, is science the path?

I've personally, synthesized it into my philosophy of and on the nature of absolute and ultimate reality.

Along with psychology, mathematics, cosmology, and etc., etc.
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post Apr 27, 2005, 06:40 PM
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QUOTE (Dan @ Apr 27, 09:22 PM)
physical science was originally known as natural philosophy
http://www.friesian.com/hist-2.htm

Which part is of interest that you are citing here?
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post Apr 27, 2005, 06:48 PM
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QUOTE (Trip like I do @ Apr 27, 06:33 PM)
QUOTE (Dan @ Apr 27, 09:26 PM)
who sez?

It is our history man, it is how we evolved.

what I mean is, what is your source for this claim?
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post Apr 28, 2005, 08:19 AM
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QUOTE (Unknown @ Apr 27, 06:33 PM)
philosophy deals in quality, math does not

Any philosophy that can be taught (communicated) is expressed as symbols. Mathematics is merely a formalization of symbolic expression. Qualities can be symbollically expressed, and therefore those expressions are in essence the same as mathematics. The set of all ideas maps directly to the set of all strings.
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post Apr 28, 2005, 09:53 AM
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'quality' is in the metalanguage
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post Apr 28, 2005, 02:14 PM
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"Quale" is too.
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post Apr 28, 2005, 03:27 PM
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QUOTE (Hey Hey @ Apr 26, 03:38 PM)
QUOTE (Rick @ Apr 26, 07:54 PM)

Mathematics is a formal language describing the number, shape, and place aspects of reality.

better if it was "..... and place aspects of what we think is reality."

.... and what we currently know.
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post Apr 28, 2005, 03:37 PM
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QUOTE (Dakota @ Apr 26, 07:56 PM)
.....An "irreplacable" and real way of expressing and presenting discoveries/inventions of the mind.....


Maybe not irreplacable, but it would be a beneficial attribute incorporated into your personality. The mechanical aspect of reality.
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post Apr 28, 2005, 03:42 PM
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Fennema

Try to minimize the constraining effects of sex role on cognitive functioning.

There is a preference for males to be in active games and past-times concerned with skills and mastery of objects.

There is a preference for females for play in which they practice skills related to mastery over people and interpersonal relations.

While males favour achievement in the traditionally highly valued areas of intellectual expertise and leadership skills, females are considered more likely to aim for excellence in areas congruent with their traditional role, that is, areas that require social skills.

Thus mathematics stereotyping as a male domain has often been used to explain females’ lower performance and participation in post compulsory mathematics courses.

Components of general intelligence include numerical, verbal, and spatial skills.

Spatial skills are related to mathematical achievement.

Spatial skills are diverse such as mentally rotating a cube or reorienting oneself in relation to a fixed object.

Spatial visualization includes mentally manipulating all or part of an object.

Performance involving the reproduction and/or combination of spatial information at the internal level.

Involve complicated, multi-step manipulations of spatially presented information.

Space structuring, females left, males right.
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post Apr 28, 2005, 03:51 PM
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Technics and Civilization (1963) – Lewis Mumford

18th century automation, step from naturalism to mechanisms.

The next move is to remove the organic symbol entirely.

Mechanization and regimentation have been projected and embodied in organized forms, which now dominate every aspect of our existence.

Surrendering to the machine.

Three phases of the machine and civilization: 1. The first wave came in the 10th century in an effort to achieve order and power by purely external means, turned away from the momentous moral and social difficulties that it had neither confronted nor solved. 2. The second wave came in the 18th century, where external regimentation and internal resistance went hand in hand. 3. Modern day.

The characteristic properties of emerging order – its patterns, its planes, its angles of polarization, and its colours.

Can one, in the process of crystallization, remove the turbid residues left behind by our earlier forms of thought?

Machines have developed out of a complex of non-organic agents for converting energy, for performing work, for enlarging the mechanical or sensory capacities of the human body, or for reducing to a measurable order and regularity the processes of life.

The tool lends itself to manipulation, the machine to automatic action.

The Universe as ordered by God.

No two cultures live conceptually in the same time and space.

Kant “Time and space are categories of the mind.”
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post Apr 29, 2005, 02:18 PM
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QUOTE (Trip like I do @ Apr 28, 06:37 PM)
QUOTE (Dakota @ Apr 26, 07:56 PM)
.....An "irreplacable" and real way of expressing and presenting discoveries/inventions of the mind.....


Maybe not irreplacable, but it would be a beneficial attribute incorporated into your personality. The mechanical aspect of reality.

Eratosphenes had connected shadow and time in the 3rd century B.C. to demonstrate that the earth was round and to calculate its circumference.

Without the use of a single scientific instrument, using his powers of observation alone, he noted that the sun shone directly upon the deep surface of a well at noon on the summer solstice in Syrene, Egypt.

Learning that the sun's zenith cast a slight shadow of 7*30' at the same moment, 500 hundred miles north at Alexandria, Eratoshenes deuced the spherical nature of the earth and calculated its approximate circumference to within 3000 miles.

This fantastic achievement regarding the shape of space was possible because Eratosphenes understood how shadows reveal time.
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post Apr 29, 2005, 02:24 PM
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I think in this case, the shadow revealed shape, and measurement of the distance between the well and Alexandrea revealed the size.
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post Apr 29, 2005, 02:25 PM
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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....
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post Apr 29, 2005, 02:27 PM
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QUOTE (Rick @ Apr 29, 05:24 PM)
I think in this case, the shadow revealed shape, and measurement of the distance between the well and Alexandrea revealed the size.

Do you know the formula?

If not, can you express what you just said in a mathematical formula?
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post Apr 29, 2005, 02:36 PM
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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.
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post Apr 29, 2005, 02:39 PM
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.....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.....

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post Apr 29, 2005, 03:04 PM
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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.
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post Apr 29, 2005, 03:09 PM
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QUOTE (Rick @ Apr 29, 06:04 PM)
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.

Prove it in number, not in words!
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post Apr 29, 2005, 03:27 PM
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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).
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post Apr 29, 2005, 03:30 PM
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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.
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post Apr 29, 2005, 04:44 PM
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Binary strings? How so?
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post Apr 30, 2005, 04:45 AM
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34587435432578989000009098765578899

or

011011110000011010111010010001111001

is an expression?
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