and what to say about descartes?
I came across this poem describing the way circles come together. They describe this as "kissing". I like Descartes even more, even if he is controversial!
The Kiss Precise
by Frederick Soddy
For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.
Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance from the center.
Though their intrigue left Euclid dumb
There's now no need for rule of thumb.
Since zero bend's a dead straight line
And concave bends have minus sign,
The sum of the squares of all four bends
Is half the square of their sum.
To spy out spherical affairs
An oscular surveyor
Might find the task laborious,
The sphere is much the gayer,
And now besides the pair of pairs
A fifth sphere in the kissing shares.
Yet, signs and zero as before,
For each to kiss the other four
The square of the sum of all five bends
Is thrice the sum of their squares.
In _Nature_, June 20, 1936
And on the subject of conservation and/or expenditures I found this to be related.
"'re-enchant'
"There is another world. But it is in this one."
–poet Paul Eluard
Over the past two centuries Western thinking has come to be dominated by the Cartesian worldview– one in which nature is reduced to a series of mechanized systems. This view, championed by French philosopher and mathemetician Rene Descartes, holds that the mind and body, Man and Nature, are distinctly separate from each other. According to this view, man is an observer of the cosmos instead of a participant in it.
Such thinking has obscured Nature's intrinsic unity– and its mystery. In his book, "The Reenchantment of the World" Morris Berman writes, "The view of nature which predominated the West down to the eve of the Scientific Revolution was that of an enchanted world. Rocks, trees, rivers and clouds were seen as wondrous, alive, and human beings felt at home in this environment. The cosmos, in short, was a place of belonging."
http://www.forestsforever.org/rrr.html
© Brad Perks PC Imagenetwork
Re-enchantment is about abandoning the false view that Nature is something that can be ultimately "figured out." It is about recognizing the inherent wonder of Nature, the mystery of life itself."
The Kiss Precise
by Frederick Soddy
For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.
Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance from the center.
Though their intrigue left Euclid dumb
There's now no need for rule of thumb.
Since zero bend's a dead straight line
And concave bends have minus sign,
The sum of the squares of all four bends
Is half the square of their sum.
To spy out spherical affairs
An oscular surveyor
Might find the task laborious,
The sphere is much the gayer,
And now besides the pair of pairs
A fifth sphere in the kissing shares.
Yet, signs and zero as before,
For each to kiss the other four
The square of the sum of all five bends
Is thrice the sum of their squares.
In _Nature_, June 20, 1936
And on the subject of conservation and/or expenditures I found this to be related.
"'re-enchant'
"There is another world. But it is in this one."
–poet Paul Eluard
Over the past two centuries Western thinking has come to be dominated by the Cartesian worldview– one in which nature is reduced to a series of mechanized systems. This view, championed by French philosopher and mathemetician Rene Descartes, holds that the mind and body, Man and Nature, are distinctly separate from each other. According to this view, man is an observer of the cosmos instead of a participant in it.
Such thinking has obscured Nature's intrinsic unity– and its mystery. In his book, "The Reenchantment of the World" Morris Berman writes, "The view of nature which predominated the West down to the eve of the Scientific Revolution was that of an enchanted world. Rocks, trees, rivers and clouds were seen as wondrous, alive, and human beings felt at home in this environment. The cosmos, in short, was a place of belonging."
http://www.forestsforever.org/rrr.html
© Brad Perks PC Imagenetwork
Re-enchantment is about abandoning the false view that Nature is something that can be ultimately "figured out." It is about recognizing the inherent wonder of Nature, the mystery of life itself."
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