A no frills flight over the English Channel
Today, Austrian daredevil Felix Baumgartner jumped from an airplane 30,000 feet over England--and landed in France 14 minutes later. According to the BBC, "He wore only an aerodynamic jumpsuit with a 6-foot (1.8-metre) carbon fin strapped to his back, an oxygen tank from which to breathe, and a parachute to land." His speed peaked at 220 miles per hour, and the initial temperature at the jump point was 40 degrees below 0 (Celsius). Watch the video.
Thursday, July 31, 2003
Wednesday, July 30, 2003
Remember ideas futures?
Robert Hanson, the guy who came up with the notion of "ideas futures," is back; this time he's interested in setting up a futures market in terror and assasination. Too bad the research program got killed by demagogic congressmen.
Robert Hanson, the guy who came up with the notion of "ideas futures," is back; this time he's interested in setting up a futures market in terror and assasination. Too bad the research program got killed by demagogic congressmen.
Thursday, July 24, 2003
Friday, July 18, 2003
Monday, July 14, 2003
Friday, July 11, 2003
The secret of the Vitruvian man
(Found this interesting website)
Here's an interesting discovery in the famous Vitruvian Man (c. 1492) by Leonardo da Vinci, which was named after the Roman architect Vitruvius. The secret concerns a geometric algorithm in human form. In this unity, Leonardo saw the solution to the problem known as squaring the circle.Leonardo's man is an algorithm!
Squaring the circle is an ancient geometrical problem whereby of a pair of compasses and a ruler are used in an attempt to construct a circle and square of equal area. In the 19th century it was proven beyond doubt that this is not possible in a finite number of constructional steps. Solutions do exist in infinite numbers of steps, however.
The algorithm in the Vitruvian Man is based on an approach involving a continuation into infinity.
For the first time, the reconstruction of the algorithm provides an insight into the unique and bold image of man which Leonardo da Vinci has bequeathed to us in the form of this mystery.
The Vitruvian Man may not be the sole mystery of this type.
You can now witness the unfolding of the mystery with the aid of computer animations.
The Vitruvian Man shows a man represented as a double figure.
The drawing conveys movement via the double depiction of the limbs. The figure with horizontally extended arms and closed legs describes a square. The figure with arms stretched to head height and open legs forms a circle. The navel is the centre of this circle.
Leonardo thus framed the double figure with a flush-fitting circle and square. He took this idea from a treatise by the Roman architect Vitruvius.In the text on the configuration, Leonardo summarizes Vitruvius's ideas.
In this context he refers to the proportions (as fractions) of the depicted man.
Throughout his life, Leonardo sought solutions to the problem of squaring the circle. He even planned a treatise in which he intended to present his proposed solutions. Although the text on the drawing makes no specific mention of squaring the circle, the question nevertheless arises as to whether this work is not connected with this problem in some way.
Leonardo's mathematical studies and the very presence of the circle and square provide sufficient grounds for considering this possibility.
It is possible to measure the circle and the square in Leonardo's Vitruvian Man. No-one appears to have done this before us.
The area ratio of circle to square is approx. 1.16. As can be seen with the naked eye, the circle is larger than
the square.
The decisive step towards discerning the mathematical core of the Vitruvian Man involves adding a supplementary element to each of the two objects of unequal area, circle and square.
The square is supplemented by a circle of equal area to the square.
The circle is supplemented by a square of equal area to the circle.
Instead of a square and a circle with a slightly larger area, we thus now have two pairs of equal area, each consisting of a circle and square, whereby one pair is slightly larger than the other.
After adding these two supplementary elements 'on spec', one is surprised to establish that the drawing had already indicated the new circle.The middle fingers of the horizontal arms mark this circle in the same way as the middle fingers of the upward-stretched arms indicate the large circle.
At the base of the figure´s neck, Leonardo has drawn a line with two thick end points. The extensions of this line meet the points of intersection of circle and square on the left- and right-hand sides.
At first sight, only the high degree of symmetry which the sheet displays in all planes suggests that the second square is part of the 'plot'.However, the drawing provides sufficient direct evidence that this supplementary square is most certainly part of the concept of the Vitruvian Man.
The drawing shows how to construct the large equal-area pair consisting of circle and square. The starting point for this construction is the small pair consisting of circle and square.
1. The large circle is constructed first of all.To this end, the centre is also determined (the navel).The two arm movements illustrate how one is to proceed from the starting pair of circle and square to the large circle. These movements correspond to two construction circles, whose centres Leonardo has included in the drawing:
They are the two end points of the line at the base of the neck.
2. Now the large square is constructed.It is produced by two straight lines. These begin at the bottom corners of the existing square and pass through the centre of the previously produced circle (the navel). Higher up, the lines intersect the path of the large circle.
The level of these points of intersection is to be regarded as the edge length of the new square.
All the constructional steps for the algorithm are to be seen here once again. Starting from one pair of equal area, the construction leads to another pair of equal area (within the bounds of drawing accuracy). This second pair is slightly larger.
Of course, this discovery is not sufficient to qualify as a proposal for squaring the circle, as the result required to this end - a pair of equal area consisting of circle and square - constitutes the initial input for the construction.
This input is implied in the form of the figure with the horizontal arms.
But what happens if one begins this construction on the basis of an initial pair of unequal area?
The circle of the initial pair selected here has a smaller area than
the square. The lateral points of intersection are thus lower than in the original proportional study. Aligning a figure on the basis of this pair produces different proportions to those of the original.
The construction is then carried out on this basis.
A figure is then aligned once again on the basis of the resultant pair. It corresponds more closely to the original, because the area ratio has improved.
This effect can be intensified by repeating the construction on the basis of each new pair. The process is continued in this way to produce a sequence of pairs.
Whatever the appearance of the initial pair may be, the pairs of the sequence which is based on this initial pair always approach an area ratio of 1.00037.
This is an excellent squaring value which bears up admirably to comparison with any other corresponding values.
In theory, this method is intended for continuation into infinity, but after only a few generations the area ratio remains at the above-stated value.
This state is referred to as convergence.
Leonardo's Vitruvian Man as a drawing shows the method in a state of convergence by means of two successive pairs.
He draws the square of one of these pairs, and the circle of the other.The state of convergence makes the double figure´s harmonious proportions possible. This convergence is at once the rule and the result of the anthropomorphic algorithm.
Leonardo's knowledge in the fields of planimetry, anatomy and the philosophy of nature merges to produce a unique trans-disciplinary observation on the human condition:
Leonardo sees mankind as the representative of a principle of creation whose rules are ultimately dictated by mathematics.
The Vitruvian Man serves Leonardo as exemplary evidence of a genuine unity of mathematics and nature..
(Found this interesting website)
Here's an interesting discovery in the famous Vitruvian Man (c. 1492) by Leonardo da Vinci, which was named after the Roman architect Vitruvius. The secret concerns a geometric algorithm in human form. In this unity, Leonardo saw the solution to the problem known as squaring the circle.Leonardo's man is an algorithm!
Squaring the circle is an ancient geometrical problem whereby of a pair of compasses and a ruler are used in an attempt to construct a circle and square of equal area. In the 19th century it was proven beyond doubt that this is not possible in a finite number of constructional steps. Solutions do exist in infinite numbers of steps, however.
The algorithm in the Vitruvian Man is based on an approach involving a continuation into infinity.
For the first time, the reconstruction of the algorithm provides an insight into the unique and bold image of man which Leonardo da Vinci has bequeathed to us in the form of this mystery.
The Vitruvian Man may not be the sole mystery of this type.
You can now witness the unfolding of the mystery with the aid of computer animations.
The Vitruvian Man shows a man represented as a double figure.
The drawing conveys movement via the double depiction of the limbs. The figure with horizontally extended arms and closed legs describes a square. The figure with arms stretched to head height and open legs forms a circle. The navel is the centre of this circle.
Leonardo thus framed the double figure with a flush-fitting circle and square. He took this idea from a treatise by the Roman architect Vitruvius.In the text on the configuration, Leonardo summarizes Vitruvius's ideas.
In this context he refers to the proportions (as fractions) of the depicted man.
Throughout his life, Leonardo sought solutions to the problem of squaring the circle. He even planned a treatise in which he intended to present his proposed solutions. Although the text on the drawing makes no specific mention of squaring the circle, the question nevertheless arises as to whether this work is not connected with this problem in some way.
Leonardo's mathematical studies and the very presence of the circle and square provide sufficient grounds for considering this possibility.
It is possible to measure the circle and the square in Leonardo's Vitruvian Man. No-one appears to have done this before us.
The area ratio of circle to square is approx. 1.16. As can be seen with the naked eye, the circle is larger than
the square.
The decisive step towards discerning the mathematical core of the Vitruvian Man involves adding a supplementary element to each of the two objects of unequal area, circle and square.
The square is supplemented by a circle of equal area to the square.
The circle is supplemented by a square of equal area to the circle.
Instead of a square and a circle with a slightly larger area, we thus now have two pairs of equal area, each consisting of a circle and square, whereby one pair is slightly larger than the other.
After adding these two supplementary elements 'on spec', one is surprised to establish that the drawing had already indicated the new circle.The middle fingers of the horizontal arms mark this circle in the same way as the middle fingers of the upward-stretched arms indicate the large circle.
At the base of the figure´s neck, Leonardo has drawn a line with two thick end points. The extensions of this line meet the points of intersection of circle and square on the left- and right-hand sides.
At first sight, only the high degree of symmetry which the sheet displays in all planes suggests that the second square is part of the 'plot'.However, the drawing provides sufficient direct evidence that this supplementary square is most certainly part of the concept of the Vitruvian Man.
The drawing shows how to construct the large equal-area pair consisting of circle and square. The starting point for this construction is the small pair consisting of circle and square.
1. The large circle is constructed first of all.To this end, the centre is also determined (the navel).The two arm movements illustrate how one is to proceed from the starting pair of circle and square to the large circle. These movements correspond to two construction circles, whose centres Leonardo has included in the drawing:
They are the two end points of the line at the base of the neck.
2. Now the large square is constructed.It is produced by two straight lines. These begin at the bottom corners of the existing square and pass through the centre of the previously produced circle (the navel). Higher up, the lines intersect the path of the large circle.
The level of these points of intersection is to be regarded as the edge length of the new square.
All the constructional steps for the algorithm are to be seen here once again. Starting from one pair of equal area, the construction leads to another pair of equal area (within the bounds of drawing accuracy). This second pair is slightly larger.
Of course, this discovery is not sufficient to qualify as a proposal for squaring the circle, as the result required to this end - a pair of equal area consisting of circle and square - constitutes the initial input for the construction.
This input is implied in the form of the figure with the horizontal arms.
But what happens if one begins this construction on the basis of an initial pair of unequal area?
The circle of the initial pair selected here has a smaller area than
the square. The lateral points of intersection are thus lower than in the original proportional study. Aligning a figure on the basis of this pair produces different proportions to those of the original.
The construction is then carried out on this basis.
A figure is then aligned once again on the basis of the resultant pair. It corresponds more closely to the original, because the area ratio has improved.
This effect can be intensified by repeating the construction on the basis of each new pair. The process is continued in this way to produce a sequence of pairs.
Whatever the appearance of the initial pair may be, the pairs of the sequence which is based on this initial pair always approach an area ratio of 1.00037.
This is an excellent squaring value which bears up admirably to comparison with any other corresponding values.
In theory, this method is intended for continuation into infinity, but after only a few generations the area ratio remains at the above-stated value.
This state is referred to as convergence.
Leonardo's Vitruvian Man as a drawing shows the method in a state of convergence by means of two successive pairs.
He draws the square of one of these pairs, and the circle of the other.The state of convergence makes the double figure´s harmonious proportions possible. This convergence is at once the rule and the result of the anthropomorphic algorithm.
Leonardo's knowledge in the fields of planimetry, anatomy and the philosophy of nature merges to produce a unique trans-disciplinary observation on the human condition:
Leonardo sees mankind as the representative of a principle of creation whose rules are ultimately dictated by mathematics.
The Vitruvian Man serves Leonardo as exemplary evidence of a genuine unity of mathematics and nature..
Tuesday, July 08, 2003
Monday, July 07, 2003
A question came to me via email about the bodyscissor and it had this nice link... It works all right, heheh
I suppose this was inevitable
MSNBC has fired Michael Savage for "anti-gay comments:"
MSNBC has fired Michael Savage for "anti-gay comments:"
"Oh, you're one of the sodomites," Savage said. "You should only get AIDS and die, you pig. How's that? Why don't you see if you can sue me, you pig. You got nothing better than to put me down, you piece of garbage. You have got nothing to do today, go eat a sausage and choke on it."
. . . He asked for another phone caller who "didn't have a nice night in the bathhouse who's angry at me today."
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