Synergetics: Explorations in the Geometry of Thinking

[Turtle]

Mmm-k, T. Check my understanding...

...

I guess he means like this:

bisected perpendicularly with axes AC, CD, and AD. The tetrahedron's triangular face ACD would then look like figure 100.1041. This makes 6 shapes. Doing the same with the other 3 faces of the tetrahedron should then make 6 x 4 = 24 shapes which I suppose are the "24 A quanta modules", but he doesn't really explain that in this chapter.

 

So, I guess I should take a detour into 913 now 'n figure out these moduli - is that the idea?

 

~modest :)

 

These books have chapters!?? :eek: :hyper: Anyway, nice drawings and on the last drawing, yes I believe those are the proper possible 6 divisions, and multiplying by the 4 faces gives the total of 24 A modules that make a regular tetrrahedron.

 

Fuller sent us to drawing 913.01 from §100.102, but did not 'assign' reading the text in the 913 section. Obviously once we're on the page it is hard not to read/see everything that's there, but in this case the drawing is the main thing that I think Fuller wanted to highlight.

 

Bucky will revisit the A module as we move along, as well as develop a number of other 'special' polyhedra, which he then uses in combinations as building blocks to piece together some of the other Platonic solids and other polyhedra.

[Turtle]

This reading covers pgs. 15 to 20 in the hardcover, and 3 of the pages have diagrams of some geometry of foldability. Longer than most readings so far, it is still only about 4 minutes long and it hangs together well. Moreover, this will bring us to the end of the Child As Explorer section. .:)

 

§100.320 - 100.63

 

Most of that reading is Bucky beating his world view drum. I get it already Buckster! I have printed out the diagrams and tomorrow I'll slice 'em up and fold 'em just to see for myself. In many regards the folding geometry here reminds me of the Penguin Book of Strange & Curious Geometry; interesting in & of itself, but not really tied to any particulars. :( What's a bull-headed reader to do. :doh: :hyper: B)

[Turtle]

Here's my models. Interesting to note that Bucky uses the phrase 'limit case' again; here to describe the foldability of the scalene right triangle.

100.412 The scalene right triangle is a limit case that folds into an almost-flat tetrahedron. (See Fig. 100.412. )

§ 100.412;pg 16,Synergetics 2

 

:singer: :hihi: :hihi:

 

[Turtle]

Well nows... 4 weeks since starting to read Synergetics and we finally come to the beginning. :)

 

Just so, today's 3 pages of new material gets us on our way with the definition of synergy and its relationship to the 'real' world. :phones:

 

;) §101.01-108.03; pgs.3-6 volume 1

[Turtle]

Reading and understanding Synergetics is like cooking & eating old fashioned oat meal. ;) :hyper: It takes a while to cook, but it sticks to the ribs, there's no simpler food, and you can't tell by looking at it that it's good for your heart. :hihi: Also, it tastes better with some honey & cream...maybe raisins or apricots if ya got 'em. :)

 

101.01 Synergy means behavior of whole systems unpredicted by the behavior of their parts taken separately.

 

Another generalized principle in the ol' lexicon. Tasty. :hihi: Please Sir, may I have sum more? :)

 

108.02 By conventional arithmetic, one triangle plus one triangle equals two triangles. But in association as left helix and right helix, they form a sixedged tetrahedron of four triangular faces. This illustrates an interference of two events impinging at both ends of their actions to give us something very fundamental: a tetrahedron, a system, a division of Universe into inside and outside. We get the two other triangles from the rest of the Universe because we are not out of this world. This is the complementation of the Universe that shows up time and again in the way structures are made and in the way crystals grow. As separate actions, the two actions and resultants were very unstable, but when associated as positive and negative helixes, they complement one another as a stable structure.

 

Mmmmmm....now here's stable on the table: >> Fig. 108.01

 

And now wash-up before the next meal.*

 

108.03 Our two triangles now add up as one plus one equals four. The two events make the tetrahedron the four-triangular-sided polyhedron. This is not a trick; this is the way atoms themselves behave. This is a demonstration of synergy. Just as the chemists found when they separated atoms out, or molecules out, of compounds, that the separate parts never explained the associated behaviors; there seemed to be "lost" energies. The lost energies were the lost synergetic interstabilizations.

 

*next reading: §109;pgs6-8

[Racoon]

Looks like Math becomes an Oragami lesson.

(referring to the monkey holding straws ready to be shaped)

 

:hyper:

[Turtle]

Looks like Math becomes an Oragami lesson.

(referring to the monkey holding straws ready to be shaped)

 

:)

 

That's sum of it fo show.

:)

Bucky,

and both me an' da monkey,

are after the structural limits

of oragami

and all dat jazz.

:hihi: ;)

:hyper:

[Turtle]

Reading Synergetics is like wading in a shallow creek...upstream...for a long time. :) Sometimes ya gotta go ashore for a smoke. :D :)

 

So the last section read, §109;pgs6-8, uses alloys to illustrate synergy in action, and the last sentence there is as good a summary as any.

We find the associated behaviors of various atoms complementing each other, so that we are not just talking about one thing and another one thing, but about a structural arrangement of the atoms in tetrahedral configurations.

 

Dont miss the drawing of nested tetrahedra forming cube. Here's a short video of my model: >> YouTube - nested tetrahedra form cube http://www.youtube.com/watch?v=2f6hvUuB4xk

 

Next reading is §110-117; pgs.8-10 volume1

[Turtle]

Quotables from the reading.

 

Synergy in Chemistry:

113.00 When we take two triangles and add one to the other to make the tetrahedron, we find that one plus one equals four. This is not just a geometrical trick; it is really the same principle that chemistry is using inasmuch as the tetrahedra represent the way that atoms cohere. Thus we discover synergy to be operative in a very important way in chemistry and in all the composition of the Universe. Universe as a whole is behaving in a way that is completely unpredicted by the behavior of any of its parts. Synergy reveals a grand strategy of dealing with the whole instead of the tactics of our conventional educational system, which starts with parts and elements, adding them together locally without really understanding the whole. ...

 

Synergy in Physics:

116.00 Physicists had predicated their grand strategies upon the experience of trying to make something like a perpetual motion machine. They found that all local machines always had friction, therefore energies were always going out of the system. They call that entropy: local systems were always losing energy to the rest of the Universe. When the physicists began to look at their total experience instead of at just one of their experiences, they found that while the energy may escape from one system, it does not go out of the Universe. It could only disassociate in one place by associating in another place. They found that this was experimentally true, and finally, by the mid-19th century, they dared to develop what they called the Law of Conservation of Energy, which said that no energy could be created and no energy could be lost. Energy is finite.

 

Nothing groundshaking there, rather more of giving concrete examples of synergy.

 

Next reading: :friday: §120.00-140.00;pgs10-12 volume1

[Turtle]

:)§120.00-140.00;pgs10-12 volume1

 

While short, these sections contain some ponderables worthy of pause. Herr Fuller spares no luminary from his pointed criticisms, and here he takes aim at the soft underbelly of Herr Newton. I have boldened the view Buckminstermeister wishes us to take.

 

120.01 Synergy is disclosed by the interattraction for one another of two or more separate objects. But any two masses will demonstrate that halving the distance between them will fourfold their attraction for each other. (Which is the way Newton might have said it, but did not.) He discovered the mathematical gain in attraction, but he stated it "inversely," which is awkward and nonspontaneously illuminating. The inverseness led him to speak in terms of progressive diminution of the attraction: as the distance away was multiplied by two, the attraction diminished by four; ergo, he could speak of it as "squared." The attraction of one mass for the other increases as the second power of the rate of increase of their proximity to one another: halve the distance and the interaction is fourfolded.

 

This is a reiteration too, of the earlier illustration Bucky gave us on the equivalence geometrically and countably between triangles/squares and tetrahedra/cubes. (Fig. 990.01)

 

Finishing the section, Bucky takes a poke at us all.

The thickness of a paper match superimposed on a 12-inch globe represents the point at which a rocket precesses into orbit, going from its 180-degree tendency to fall into its 90-degree orbital independence as an astronomical entity. This is the critical- behavior point at which it becomes an independent entity in Universe, a satellite. Small Earth satellites orbit at an altitude of only about 100 miles, which is only about 1/80th of the diameter of the Earth. This critical proximity event of transition from 180-degree to 90-degree independence is called precession. Mass attraction is also involved in precession, another member of the family of generalized principles. But scientists still have not the slightest idea why mass attraction occurs; they only know that it does. They do not know why. This requires admission of an utter a priori mystery within which the masses demonstrate their utterly mysterious attraction for one another. It appears that no single part of the Universe can predict the behavior of the whole. As we attain greater experience and opportunity to observe the synergetic effects of Universe, there is always a greater discernment of generalized principles. The discovery of a plurality of generalized principles permits the discovery of the synergetic effect of their complex interactions.

 

Will pick up with my own geometric thought-poking of §130.00 next post. :(

[Turtle]

Thought-poking of §130.00 :hyper: :)

 

I honestly do not have an intimate enough knowledge of the specifics in chemistry and physics involving entropy and precession to offer any opinion as to how Fuller's use, definition, and descriptions of the terms compares. Simply best then to make a concerted effort to learn what Bucky said. As this section is short and complexly fun-filled with words straight from the old horse's mouth, I quote it in its entirety. I have to note in particular though, that I have never seen the Moon's tidal lock with Earth described quite this way. Fascinating. :eek2: :moon: :hyper:

130.00 Precession and Entropy

 

130.01 Critical proximity occurs where there is angular transition from "falling back in" at 180-degree to 90-degree orbiting__which is precession. (Gravity may be described as "falling back in" at 180 degrees.) The quantity of energy that ceased to "fall in" is the system's entropy. Critical proximity is when it starts either "falling in" or going into orbit, which is the point where either entropy or antientropy begins.

 

131.00 An aggregate of "falling ins" is a body. What we call an object or an entity is always an aggregate of interattracted entities; it is never a solid. And the critical proximity transition from being an aggregate entity to being a plurality of separate entities is precession, which is a "peeling off" into orbit rather than falling back in to the original entity aggregate. This explains entropy intimately. It also explains intimately the apparent energy losses in chemical transformations, associations, disassociations and high-order element disintegration into a plurality of lower-order elements__and nothing is lost. Entity has become invisible. The switch is precessional.

 

132.00 The unprotected far side of the Moon has more craters of the "fallen-in" asteroids. Ergo, the far side weighs more than the near side, which is shielded by the Earth. The additional far-side weight of the Moon acts centrifugally to keep the weighted side always away from the Earth around which it orbits. Ergo, there is always one side, the same side, facing us. The Moon is always oriented toward us, like a ship that has its masts pointed inwardly toward us and its weighted keel away from us. This explains why the first photographs showed a greater number of craters on the far side of the Moon. The Earth acts as a shield. On Earth, the craters are not so concentrated because the Earth gets its cosmic fallout quite evenly. Earth's weight and massive pull are progressively increased to offset the Moon's farside weight increase and tendency otherwise to forsake Earth.

 

133.00 "Solids" are simply the fraternities of the "fallen-into-one-anothers."

 

Next reading: §140.00;pg12 volume 1

[Turtle]

§140.00;pg12 volume 1

 

Just to quote the crux and see another mention of Euler as well as a rule I don't know about, i.e. Gibbs' phase rule. I'll have a little side read on that. :naughty: :shrug:

141.00 There is a corollary of synergy known as the Principle of the Whole System, which states that the known behaviors of the whole plus the known behaviors of some of the parts may make possible discovery of the presence of other parts and their behaviors, kinetics, structures, and relative dimensionalities.

...

Euler's topology provides for the synergetic evaluation of any visual system of experiences, metaphysical or physical, and Willard Gibbs' phase rule provides synergetic evaluation of any tactile system.

 

Next reading is §150.00; pg13 volume1

[Turtle]

Well, at least we, -that is you, and me, and he- survived the great October purge. :) Bucky so evades classification that a move from Math & Physics to Philosophy is as easy as rolling over in bed. To whit, from our last reading, I quote the concluding paragraph:

 

153.00 Universe apparently is omnisynergetic. No single part of experience will ever be able to explain the behavior of the whole. The more experience one has, the more opportunity there is to discover the synergetic effects, such as to be able to discern a generalized principle, for instance. Then discovery of a plurality of generalized principles permits the discovery of the synergetic effects of their complex interactions. The synergetic metaphysical effect produced by the interaction of the known family of generalized principles is probably what is spoken of as wisdom.

 

Wisdom it is then. :) Off to get the experience of the next 3 minutes of reading in Synergetics: Explorations in the Geometry of Thinking. §161.00-164.00;pgs13-15 volume 1

[Turtle]

§161.00-164.00;pgs13-15 volume 1

 

In the above reading, Fuller expands the idea of synergies-of-synergies to generalized principles-of-genrealized principles. Strikes me as all rather fratal and I intend to have a look at any crossover between Fuller & Mandlebrot during their lives. :hihi:

 

The next reading finishes up §160.00 on Generalized Design Science Exploration. §165.00-174.00;pgs15-17 volume 1

I have read it and quote the final sentence:

174.00 The greatest and most enduring discoveries and inventions of humans on our planet are those of the scientist-artists, the name joined, or artist, or scientist. The name of artist or scientist, though often self-professed, can only be accredited to an individual by others who in retrospect discover the enduring quality of the symmetries with which the individual converted his conceptioning to the advantage of others, and realizations of increasing interadvantage in respect to survival__the gradual discovery of the function in Universe which humanity has been designed to fulfill.

 

I think the next vector is going to skip to volume 2 and another 'scenario', and I'll post the reading as soon as I figure out where it is. :eek_big: :eek:

[BLUE ELECTRIC MONKEY]

Hey,

This is quite interesting, all these weird concepts and definitions.

Did you know that Bucky F. used to go around with 3 clocks on his arm, so he could see the time in 3 places at once, usually:

the time from his departure point

the time of his now/here

the time of his destination

 

he also said he feels he lives on spaceship earth

 

this also seems to connect to my 2012 obsessions theory of 3 different cultures with beliefs about the end of the world, correlating to the beliefs about the end of the year and the end of the calender. time is relative in more than just Einstein's and Fuller's clocks.

Any one interested, check out

http://hypography.com/forums/strange-claims-forum/16290-all-the-truth-about-2012-a.html

This is a Synergetic Exploration of the numbers-and-theories of thinking-obsessions, covering the subject time after time, word by word, and sometimes with drawings, which we can also order in some way.

This is not so much in a Turtle Style and speed, but more like a Blue Monkey style and speed and electricity in the air.

 

[Turtle]

Hey,

This is quite interesting, all these weird concepts and definitions.

Did you know that Bucky F. used to go around with 3 clocks on his arm, so he could see the time in 3 places at once, usually:

the time from his departure point

the time of his now/here

the time of his destination

 

he also said he feels he lives on spaceship earth

 

this also seems to connect to my 2012 obsessions theory of 3 different cultures with beliefs about the end of the world, correlating to the beliefs about the end of the year and the end of the calender. time is relative in more than just Einstein's and Fuller's clocks.

 

:D [rhetorical question]All's fair in love & war eh Blue? [/rhetorical question] :D Anyway, here's the thread on Fuller himself and it's a better choice for your post than this specific study of Synergetics. Buckminster Fuller Thanks. :naughty:

[Turtle]

I think the next vector is going to skip to volume 2 and another 'scenario', and I'll post the reading as soon as I figure out where it is. :( :eek:

 

I got it partly right. The next 3 minute, 2 page reading is in volume 2, but not one of the 'scenarios'. Just so, here is the material: §180- Design Science and Human-Tolerance Limits; pgs 21&22 volume 2