Ark - where are you headed?

[Richard]

A complex number can be written in the form a + bi where a and b are real numbers (including 0) and i is the imaginary number i. Therefore a complex number contains two 'parts'; one that is real, and another part that is imaginary.

Complex numbers are often represented on a complex number plane (which looks very similar to a cartesian plane). On this  plane, the imaginary part of the complex number is measured by the vertical axis (on the cartesian plane, this is the y axis) and the real number part of  goes on the horizontal axis (where the 'x' values of coordinates normally go).

I think I prefer copper plates.

[kenlee]

Groupoid in algebra clothing
When building a house, we start with the construction of a scaffolding.  Eiffel Tower is an example of an almost pure scaffolding. Even if today it houses a dozen of restaurants, nevertheless it is largely open to the winds does not attract an average human being to stay there for long.

This makes a lot of sense to me (at least from the point of view of how I am interpreting it) since I would think that there would have to be a scaffolding before anything else. But I would think that the scaffolding and/or the groupoid would have to exist as a fact. Maybe the groupoid and/or the scaffolding is the first existing 'fact' and as such I would think that it would have to have both it's abstract and concrete representations.  Don't know if it's concrete representation (assuming that there is one) could be measured or detected with "pointer readings" but if this is the case then perhaps it can "kick back" and be detected? Just some more thoughts on this fwiw!

[Bluelamp]

Already at 2x2 complex matrices, barely removed from a single bit.  One can go to Hilbert spaces, Lie Algebra, and Clifford Algebra from here; that's like quantum physics, classical physics, and binary math.

http://en.wikipedia.org/wiki/Pauli_matrices

The Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian... In the language of quantum mechanics, hermitian matrices are observables, so the Pauli matrices span the space of observables of the 2-dimensional complex Hilbert space. In the context of Pauli's work,  is the observable corresponding to spin along the coordinate axis in R3.

The Pauli matrices (after multiplication by i to make them anti-hermitian), also generate transformations in the sense of Lie algebras: the matrices form... the Lie group of rotations of 3-dimensional space. Moreover, the algebra generated by the three matrices is isomorphic to the 3-dimensional Euclidean real Clifford Algebra.

[dant]

Interesting, I was reviewing The Wave: CH 24

...
We know without a shadow of a doubt that the megalith builders utilized advanced mathematics, geometry and astronomy. Numbers appear to be the language by which we can translate right-brain perception into useful left-brain action. This is why the mystical traditions are written in mathematical codes.

The original splitting of the unity into two is described mathematically as the cosmos contracting infinitely, leaving a void, and everything else. This contraction or split made Divine apperception possible. Using this divine principle of creation, Gottfried Leibniz developed binary arithmetic in the 1700s, and this is the basis of all of our computer communications today. Two figures, 0 and 1 can express everything in the cosmos.
...

[Richard]

Still with the binary, I was lying in the bath letting my mind wander and I thought up a mechanical binary adding machine (haven't tried a subtracting machine).

Excuse my diagrams....they're in 2D due my lack of skills. What we have are hollow columns down which we drop a wheel with a platform attached on top. To make it easier let's call it a bean.

(image of wheel platform) (how does one get images up here?)

So what we have in the next two pictures is a chute down which we can drop as many beans as we wish. What happens is that the first bean is captured by the hole underneath column 1. The next bean (2) rolls over the first bean, hits a button or trip wire or shorts a connection, causing the first bean to fall and is captured by the 2nd hole. The third bean falls into the first hole. We have dropped three beans and our tally of closed holes is three. We can send down as many beans as we want and this process will count correctly.

(first and second grid pics)

If we want to represent the number of beans by dropping them down the upright columns, the last picture shows we already have the number 10 (8 + 2) to which we want to add the number 6 (4 + 2). So we drop beans down the 4 and 2 columns. Bean c falls straight into the hole while bean d falls onto bean b, rolls to the left and over beans d and a causing them all to fall and is captured by hole 16. (10 + 6 = 16)

(last pic)

What I found interesting about this is how there is a meaningful mechanism to the binary system and we can start looking at the process from a conceptual basis. We can talk about "states" and "transitions".

In the last example, the first "state" is the state of "10". By adding the beans we see a transition take place until the state of "16" is reached. Each hole is also in a closed or open state and their state at any particular moment gives meaning to the whole system

We could also look at the holes and define an "energy" to each of them depending on their position in relation to each other. And this gives me the idea that the positions of orbits in an atom or maybe in a solar system have a particular "energy" depending on their relation to each other. I wouldn't know if they would be in a binary relationship or perhaps in a relationship built upon prime numbers.

An interesting side thought. If beans are added only from the right hand sloping column, each of the beans would be intimately involved with the transition, falling through the holes. If, however, we added a "64", the 'smaller' beans wouldn't know they had just become members of a larger group. Sort of like a larger business buying a smaller one without making any personnel or operational changes vs a merger.

I don't know if this will spark any ideas but it was fun for me.

[Megan]

...I don't know if this will spark any ideas but it was fun for me.

I think I understand the mechanism, but I guess I don't see what it is "for." It seems to be a composite of a binary counter and a binary adder, although not exactly because the input is all 1's and parts of the mechanism are not defined. Ordinary counters also involve states and transitions. "State" comes in when there is feedback that creates "storage." What is different here?

I had a computer science professor that was very interested in the topic of "energy of computing," decades ago, and he wasn't talking about the power consumed by server farms. Unfortunately, I still have no idea what he was talking about.

[Richard]

Hi Megan,

It seems to be a composite of a binary counter and a binary adder, although not exactly because the input is all 1's and parts of the mechanism are not defined.

I don't know if it's a combo of anything. Could well be.  If we write "10" in binary it would be 1010. The zeros are just placeholders and don't really do anything other than position the ones to give them their special meaning.

Ordinary counters also involve states and transitions. "State" comes in when there is feedback that creates "storage." What is different here?

I'm talking about a language with which I'm not familiar so if I misuse words like "state" please forgive me. I doubt though that there is much, if any, difference. I don't know if the state in ordinary counters is the same as what I'm referring to here. I'm looking at the machine as a whole which is always in a different state depending on where the beans lie and trying to connect it to the binary universe and perhaps to Ark's monads.

parts of the mechanism are not defined

I could explain how I see the full mechanism and let an engineer work out how best to put it together, but as I'm not planning on building one and am only using the idea for conceptual thinking I didn't think it necessary to go into infinite detail. (In one possibility the platform is hinged and off-center so when a bean lands on it, it tips the bean forward to the next hole ) The idea helps me "see" better. Numbers really don't do much for me - they don't "talk" to me.

I had a computer science professor that was very interested in the topic of "energy of computing," decades ago, and he wasn't talking about the power consumed by server farms. Unfortunately, I still have no idea what he was talking about.

LOL! - I don't blame you

I do think it could be really good way of introducing students to binary counting if nothing else.

[Megan]

...I don't know if it's a combo of anything. Could well be.  If we write "10" in binary it would be 1010. The zeros are just placeholders and don't really do anything other than position the ones to give them their special meaning.

It's the inputs where I don't see any zeroes. Just "beans."

I'm talking about a language with which I'm not familiar so if I misuse words like "state" please forgive me. I doubt though that there is much, if any, difference. I don't know if the state in ordinary counters is the same as what I'm referring to here. I'm looking at the machine as a whole which is always in a different state depending on where the beans lie and trying to connect it to the binary universe and perhaps to Ark's monads.

I think we're using "state" the same way. But you need some kind of storage latch in order to feed data into the system. That, in turn, involves introducing feedback. A simple RS latch looks like



A pulse to the S input sets it and a pulse to the R input resets it. The outputs feeding back to the opposite inputs are what allows it to retain state. A more complex type of latch can readily serve as a counter, or at least a chain of them can.

To add binary numbers you need a network of full adders, with the carry-out of each stage (bit position) feeding the carry-in of the next higher-order stage.



Oops, I've got to go to a meeting. But anyway, the two XOR symbols along the top of the diagram resemble Ark's groupoid example.

[Muxel]

Getting back to the math of the quaternion; the real number timelike Jungian 4th is actually a 0-vector scalar which means it's like an empty set, none of the bits (neither transformation nor static location), it's nothing which sounds very much like an STS definition (at its limit which one never gets to).   

Or, could it be a set containing a whole universe? (Set of all possible sets.) Sets within sets, so it never ends? Then a monad could be 1 of these "sets"?

What Biomiast said on "nano":

Considering what C's said about viruses and information fields aggregating matter, it seems to me whole life is created in such an act where information fields form membranes, organelles and proteins form an organism. So, an organism may be on macro scale, but its building blocks and interactions are on nanoscale.

Made me think, membranes = sets? We're made of membranes, which are themselves composed of membranes...and on and on...?

I've always thought of universes as points on a plane (or 3D space). So the real number loner could be a point, and the "imaginary vectors" indicate the position.

Or maybe universes aren't points but whole squiggly lines (= past present future). I dunno.

[Davida]

I’m surmising that MONAD is short for MONO meaning one + AD short for add the mysterious change and maybe ark’s reference to hamster (Monad) harnessed in wheel (Groupoid), toppling at one side and the other, flip flopping poor hamster in the Groupoid and all the transformations are happening simultaneously.

And since the transformations are known they are determined, or pre-determined depending on perspective or at least easily evaluated as a matrix.

What would a groupoid look like that would yield a third order matrix, would that just be adding another arrow another transformation and isn’t there a key.

And wouldn’t some patters yield a negative number or a positive and nothing at all.

Like 353 535 353 …. Pattern/cycle/wave for want of better   

{353}                 
{535} Comes to Nothing         
{353}

Anyway my wave will probably collapse upon receipt of new information… or maybe transform, hard to think inside the matrix, especially when I don’t have any real understanding of the magic of the mysterious matrix.. hope I’m not to much off.

Interesting remark earlier in this thread about system1.. automatic/pre-determined when programmed, I’m going to give my poor hamster a rest… (hamster is the heart, perhaps)… bed calls.

[forge]

I have just listened to a description of light wave dispersion observable on glass objects. Ernst Abbe's name came up naturally. Creator of super-precise optical lenses in the 19th century with Zeiss. Here is the part of his research i found most interesting:

The most surprising fact about Abbe's experiments is that when the first-order diffraction pattern is masked at the objective rear aperture, so that only the zero- and second-order diffraction patterns are transmitted, the image of the specimen appears with twice the spatial frequency, or with only half the spacing between the lines. In the absence of what is really the first-order diffraction pattern, the image is now generated by interference between the zero- and second-order diffraction patterns, the latter of which is masquerading as the first-order pattern. The observation proves that the waves making up the diffraction pattern at the aperture plane converge and interfere with each other in the image plane and generate the orthoscopic image.

http://micro.magnet.fsu.edu/optics/timeline/people/abbe.html

Now thinking about hints from the C's that current theories about electromagnetics and light phenomena and gravity ought be combined to get desired totally new results.

spatial frequency in optics:

An object- or image-plane irradiance distribution is composed of "spatial frequencies" in the same way that a time-domain electrical signal is composed of various frequencies: by means of a Fourier analysis. As seen in Fig. 1.3, a given profile across an irradiance distribution (object or image) is composed of constituent spatial frequencies. By taking a one-dimensional profile across a two-dimensional irradiance distribution, we obtain an irradiance-vs-position waveform, which can be Fourier decomposed in exactly the same manner as if the waveform was in the more familiar form of volts vs time. A Fourier decomposition answers the question of what frequencies are contained in the waveform in terms of spatial frequencies with units of cycles (cy) per unit distance, analogous to temporal frequencies in cy/s for a time-domain waveform. Typically for optical systems, the spatial frequency is in cy/mm.

An example of one basis function for the one-dimensional waveform of Fig. 1.3 is shown in Fig. 1.4. The spatial period X (crest-to-crest repetition distance) of the waveform can be inverted to find the x-domain spatial frequency denoted by ξ ≡ 1/X.

http://spie.org/x34301.xml

Now if waves making up the diffraction pattern at the aperture plane (A) actually converge interfere with each other (B) in the image plane and generate the orthoscopic image (C)

Can this not be used for Transdimensional atomic remolecularization? Teleportation of objects and living matter. Waves structure making up living matter must be discovered in order to copy their pattern (A) study how these electro-gravity-light-matter-waves converge with each other to make up objects and living matter (B) and generate the exact copied pattern at desired location - at desired multiplied quantities if possible (make thousand bacon slices from 1 bacon slice sample) - and generate the electro-gravity-light-matter-scopic physical imprint of sampled object (C) in 3rd Density.

Session 941116     November 16, 1994 F*** and Laura

about the expansion of the star being conducive to creation. Could you give us a little bit on that aspect?
A: Transdimensional atomic remolecularization.
Q: (L) What is remolecularization.
A: Being reassembled.
Q: (L) Reassembled from what to what?
A: Complex. Density collision.
Q: (L) Collision of one density with another. Which?
A: Learn 4 level assembly.
Q: (L) How?
A: Study.
Q: (L) Does this mean that this was a point in space time when pure energy could form around a framework of a thought pattern and thus become solid matter?
A: Close.
Q: (L) Is this transitioning of energy from higher densities into third density or solid matter kind of a traumatic event for universal energy?
A: Subjective.
Q: (L) Is it a form of death?
A: Death and birth are the same.
Q: (L) Was it a requirement to be on a planet with a dying star for this remolecularization to take place?
A: If 3rd density remolecularization.
Q: (L) So, for energy to go into 3rd density physical level... is energy moving down when it comes into 3rd level?
A: No. Upward.
Q: (L) What moves upward?
A: Molecules, atomic matter. Light is first density and unifies all densities.
Q: (L) Does that mean that by us moving from 3rd density into 4th density that we are getting farther away from unification with the source?
A: No. Light and darkness unify all densities. 

[kenlee]

Now if waves making up the diffraction pattern at the aperture plane (A) actually converge interfere with each other (B) in the image plane and generate the orthoscopic image (C)

Can this not be used for Transdimensional atomic remolecularization? Teleportation of objects and living matter. Waves structure making up living matter must be discovered in order to copy their pattern (A) study how these electro-gravity-light-matter-waves converge with each other to make up objects and living matter (B) and generate the exact copied pattern at desired location - at desired multiplied quantities if possible (make thousand bacon slices from 1 bacon slice sample) - and generate the electro-gravity-light-matter-scopic physical imprint of sampled object (C) in 3rd Density.

It might be that when you get down to it the basis of everything is just information although I'm not sure how this concept might fit in (if it fits at all) with the concept of the groupoid. But (if we take as an hypothesis) that matter is basically information then (hypothetically speaking) there is no reason to think that matter can't be disassembled and then reassembled/transmitted just as digital signals can be. The diffraction patterns you mentioned make me think of interference patterns which is I think the basis of holography.

Also, in the Gurdjieffian Cosmology you have three "rays," or Octaves of radiation. The 1st primary octave is between the Absolute and sun. The 2nd is between the sun and earth. The third is between the earth and moon. So if you look at each octave of radiation as being kinda like light rays then there might be some kind of interference pattern going on between the three "rays" and in some way this may transmit information resulting in (this being just one example) the generation of existing life forms on earth, or something like that. FWIW. 

[voyageur]

Knowing this thread speaks to mathematics and physics (which I don’t profess to know anything – but interested) and having read this thread a few times over, following some of the links posted too, including the esoteric properties you discuss Ark, this send me off looking up a few things, and as happened, went to Fulcanelli.

In your picture of the Groupoid, could not help thinking about interlocking gears with the central circle representing the influence over the others as it transforms their triad aspects. In reading out of Fulcanelli’s ‘The Dwellings of the Philosophers’, firstly on Algebra, this came up related to X (unknown quantity):

Furthermore, almost all meanings revealed by the sign X have a transcendent or mysterious value, and this fact is singular. In algebra, X is the unknown quantity; it is also the problem to be solved, the solution to be discovered; it is the Pythagorean sign of multiplication, and the element to cast out the nines in arithmetic; it is the popular symbol of mathematics in what concerns higher or abstract development. It characterizes that which, generally is excellent, useful, remarkable.

Secondly, in thinking about the Groupoid depiction you posted, chemistry came to mind, and in particular Fulcanneli’s words below. It is noted that in this case my thinking is that the central circle of the Groupoid, as it relates to the chemical description, is like X (what is the nature of the influence, how does it transform the others and is there something in the others that either does nothing or energetically changes its nature?).

Light --- rarified and spiritualized fire --- possesses the same chemical virtues and power as elementary crude fire. [whatever light is, in this case assigned it to the central circle 1] An experiment, with the object of synthetically creating hydrochloric acid (HCl) from its components, amply demonstrates it. If we put equal volumes of chlorine and hydrogen gas in a glass flask [circle 0,0 & circle 1,0], the two gases will keep their own individuality as long as the flask that contains them is kept in darkness. With some diffused light [circle 1], they progressively combine. But if we expose the vessel to direct solar rays, it explodes and shatters violently.

“exchange transformation” is denoted by 1.

Probably barking up the wrong tree here in thinking about chemical reactions and Groupoids, however, Fulcanelli discusses some unusual principles of triad interactions in many instances.

Hope to learn more.