Beach shot
Friday, December 22, 2006
Wednesday, November 30, 2005
There are many interesting propositions that were numbered VI.
One of these is Kurt Goedel's Incompleteness Theorem which can be interpreted to mean that when a system, such as the English language, is sufficiently advanced to say interesting things with it, particularly statements about itself, then it can also be used to make statements that are true statements but can't be proven (remembering that just because something can't be proven doesn't mean it doesn't exist).
Another is Euclid's Proposition VI from his The Elements, stating that If an angle of a triangle be bisected and the straight line cutting the angle cut the base also, the segments of the base will have the same ratio as the remaining sides of the triangle; and, if the segments of the base have the same ratio as the remaining sides of the triangle, the straight line joined from the vertex to the point of section will bisect the angle of the triangle.
Yet another is Newton's Proposition VI from Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy): That all bodies gravitate towards every planet; and that the weights of bodies towards any the same planet, at equal distances from the centre of the planet, are proportional to the quantities of matter which they severally contain.
And then there's vi.
I think there's something in that for all of us.
One of these is Kurt Goedel's Incompleteness Theorem which can be interpreted to mean that when a system, such as the English language, is sufficiently advanced to say interesting things with it, particularly statements about itself, then it can also be used to make statements that are true statements but can't be proven (remembering that just because something can't be proven doesn't mean it doesn't exist).
Another is Euclid's Proposition VI from his The Elements, stating that If an angle of a triangle be bisected and the straight line cutting the angle cut the base also, the segments of the base will have the same ratio as the remaining sides of the triangle; and, if the segments of the base have the same ratio as the remaining sides of the triangle, the straight line joined from the vertex to the point of section will bisect the angle of the triangle.
Yet another is Newton's Proposition VI from Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy): That all bodies gravitate towards every planet; and that the weights of bodies towards any the same planet, at equal distances from the centre of the planet, are proportional to the quantities of matter which they severally contain.
And then there's vi.
I think there's something in that for all of us.
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