Life and .618 (3)
Unified Understanding Needed
We need a unified understanding of log spirals, Fibonacci numbers and the Golden Angle- the particular unification we are seeking being the one expressed in plants. We also need to be able to measure curves which, as far as I know, can only be done by measuring squares and rectangles and relating these measurements to curves. In other words, we need to know the relationships in numbers of circles, spirals, rectangles and squares.
The Physical Idea - DNA and .618
Tproposition is that spiral forms in living Nature ultimarely flow from from the spiral form of DNA; and the presence in Nature of forms based on .618 flows from the presence in DNA of forms based on .618.
DNA is a form of spiral called a helix - the spiral one sees in a screw. But DNA does not spiral evenly about its center or pole as does a screw. The two sides of A DNA helix have their sugars and phosphates in reverse order - 3, 5 is joined to 5, 3. This causes the helix to turn unevenly about its pole, swinging out now to one side, now the other. The distance it swings out is .618 matched by .382. Thus there are two "notches" in the helix which recur every 34 Angstroms. They, like leaf phyllotaxy, are based on .618 and, I think, leaf phyllotaxy is based on them.
So this why I keep working on unifying log spirals, the Golden Angle and Fibonacci numbers - because these ideas can never be really tested without better ways of measuring spirals and without a better understanding of how spirals, Fibonacci numbers and the Golden Angle are all interrelated mathematically. Ultimately I believe that all the features that have been discovered about these forms and numbers will turn out to explain one or another feature of organic life.
So now I will post what I know so far about how these are united. Or I will as soon as I figure out how to post a picture since this blog's types don't include mathematical features.
We need a unified understanding of log spirals, Fibonacci numbers and the Golden Angle- the particular unification we are seeking being the one expressed in plants. We also need to be able to measure curves which, as far as I know, can only be done by measuring squares and rectangles and relating these measurements to curves. In other words, we need to know the relationships in numbers of circles, spirals, rectangles and squares.
The Physical Idea - DNA and .618
Tproposition is that spiral forms in living Nature ultimarely flow from from the spiral form of DNA; and the presence in Nature of forms based on .618 flows from the presence in DNA of forms based on .618.
DNA is a form of spiral called a helix - the spiral one sees in a screw. But DNA does not spiral evenly about its center or pole as does a screw. The two sides of A DNA helix have their sugars and phosphates in reverse order - 3, 5 is joined to 5, 3. This causes the helix to turn unevenly about its pole, swinging out now to one side, now the other. The distance it swings out is .618 matched by .382. Thus there are two "notches" in the helix which recur every 34 Angstroms. They, like leaf phyllotaxy, are based on .618 and, I think, leaf phyllotaxy is based on them.
So this why I keep working on unifying log spirals, the Golden Angle and Fibonacci numbers - because these ideas can never be really tested without better ways of measuring spirals and without a better understanding of how spirals, Fibonacci numbers and the Golden Angle are all interrelated mathematically. Ultimately I believe that all the features that have been discovered about these forms and numbers will turn out to explain one or another feature of organic life.
So now I will post what I know so far about how these are united. Or I will as soon as I figure out how to post a picture since this blog's types don't include mathematical features.
posted by wildswan at 12/16/2006 07:43:00 AM
0 Comments:
Post a Comment
<< Home