Ark - where are you headed?

[Guardian]

This report reviews what quantum physics and information theory have to tell us about the age-old question,

How come existence?

No escape is evident from four conclusions:

1. The world cannot be a giant machine, ruled by any preestablished continuum physical law.

2. There is no such thing at the microscopical level as space or time or spacetime continuum.

3. The familiar probability function or functional, and wave equation, of standard quantum theory provide mere continuum idealizations and by reason of this circumstance conceal the information theoretic source from which they derive.

4. No element in the description of physics shows itself as closer to primordial than the elementary quantum phenomenon, that is device-intermediated act of posing a yes-no physical question and eliciting an answer or, in brief, the elementary act of observer-participancy. Otherwise stated, every physical quantity, every it, derives its ultimate significance from bits, binary yes-or-no indications, a conclusion which we epitomize in the phrase, it from bit.

Hmmm I have the same thought about all 4 "conclusions". Just 'cause ya can't see it, doesn't mean it isn't there.

 

[Esote]

If you try to use a black hole equation on an electron you actually get a radius described by a complex not real number. Some gravity models (like Ark's) may be able to handle that in both a classical and quantum way. There are certainly models where the information for your next universe "now" state preexists.

Weizsäcker developed the theory of ur-alternatives (archetypal objects), publicized in his book Einheit der Natur (1971)[21] and further developed through the 1990s,[22][23] which axiomatically construct quantum physics from the distinction between empirically observable, binary alternatives. Weizsäcker used his theory, a form of digital physics, to derive the 3-dimensionality of space and to estimate the entropy of a proton falling into a black hole.

Simply put, is there a possibility (as you seem to be engaged in) that models of preexisting information and archetypal objects (ur-alternatives or monads) could have some true structure, not only a virtual one ?
I know I'm way below the surface of your practical research, and it's uncomfortable to grasp concepts like a complex not real number, the entropy of a proton falling into a black hole and so on.
I try to think pin (instead of spin), but so far I didn't reach any relief (may be messing around by trying to dot every i and cross every t ).
Only I'm glad "Some gravity models (like Ark's) may be able to handle that in both a classical and quantum way"...
Crossing the frontier beyond physics and bringing back a fundamental on and off (non) structural information, what a quest !!!
Thanks for sharing a it from bit of your knowledge

 

[ark]

Groupoid – an easy concept

As my atom of action, a fundamental MONAD, I take the simplest non-trivial groupoid. It is an easy concept, yet it requires some serious contemplation. It will take us a while to get used to it. I will discuss it, show it from several angles, talk about its "esoteric meaning" as well. So, prepare for some little pain, like when a nurse injects the needle into your body! But the pain will pass. And do not worry if you do not get it the first time. You will get it with your second or third pass!

As it was noticed by Alain Connes, even professional mathematicians despise groupoids. But, in fact, groupoids can be tamed easily, like hamsters. Let us see how it can be done on an example. In fact, as we will see this example will play an important role in our story. A groupoid consists of points and of arrows. Points represent the static aspect, arrows represent the dynamic aspect. Arrows connect points. It will be enough for us to concentrate on transformation groupoids. In this case each arrow represents a transformation of an underlying set. The simplest (but not too trivial) transformation groupoid can be depicted as follows:

(Try to imagine this picture in 3D, play with it in your imagination, see what comes out - I will come back to this subject later on)

We have two points. One denoted by 0, the other one by 1. We also have two transformations. The first one is the identity transformation, that transforms 0 into 0, and 1 into 1 – a “do nothing” transformation. The second transformation transforms 0 into “do nothing” transformation is also denoted by 0, the “exchange transformation” is denoted by 1. At first it may look confusing to denote points and transformations of point by the same symbols, but, in fact, such a notation, in this case, makes sense. If we think, for example, that there are only two integer numbers, one called “even” and denoted by 0, the other one called “odd” and denoted by 1, then even+even=even, even+odd=odd, and even+odd=odd. Or, in symbols: 0+0=0, 0+1=1, 1+0=1, 1+1=0 as in the binary modulo 2 calculus. Thus, for example, transformation 1 (odd) transforms the point 0 (even) in the same 1 (odd), etc. On our picture above the circle with and arrow, on the left, depicts the transformation 0 (“do nothing”) acting on the point 0. The arrow-circle on the right, depicts transformation 0 acting on the point 1 – it goes back to the point 1. The upper arrow of the central circle, denoted (0,1), represents transformation 1 acting on the point 0, while the lower arrow, denoted (1,1), depicts transformation 1 acting on the point 0 (and transforming it into 0).

 

[ark]

Simply put, is there a possibility (as you seem to be engaged in) that models of preexisting information and archetypal objects (ur-alternatives or monads) could have some true structure, not only a virtual one ?

I don't know. Good question. What is "real"? Something that kicks back when we kick it? Well, I think monads may be able to kick back. Only these kicks are rather weak.... In this sense a group of monads, or a whole army of them, may have more reality than just one.

 

[ark]

Just 'cause ya can't see it, doesn't mean it isn't there.

On the other hand not all we "see" IS there. Sometimes our senses and our mind deceive us, and we make a little cat into a huge lion.

 

[Esote]

What is "real"? Something that kicks back when we kick it? Well, I think monads may be able to kick back. Only these kicks are rather weak.... In this sense a group of monads, or a whole army of them, may have more reality than just one.

Just 'cause ya can't see it, doesn't mean it isn't there.

On the other hand not all we "see" IS there. Sometimes our senses and our mind deceive us, and we make a little cat into a huge lion.

May be we can understand something like there is a virtual information, for instance 1+1=0 or 3x2 is not 2x3 (as somehow stated in the previous posts) "crystallizing" in regard to the level of the observer's perception, like 1+1=2 or 3x2=2x3...

 

[mcb]

...If we think, for example, that there are only two integer numbers, one called “even” and denoted by 0, the other one called “odd” and denoted by 1, then even+even=even, even+odd=odd, and even+odd=odd...

It looks like an "exclusive OR" transformation. A difference detector: a "1" output means "different" and a "0" output means "same." Half of a "half adder."

...A groupoid consists of points and of arrows. Points represent the static aspect, arrows represent the dynamic aspect. Arrows connect points. It will be enough for us to concentrate on transformation groupoids...

"Static" meaning something like "values belonging to a domain" and "dynamic" meaning "operations?" So this diagram represents a particular transformation (sometimes called "exclusive OR")?

 

[Buddy]

...If we think, for example, that there are only two integer numbers, one called “even” and denoted by 0, the other one called “odd” and denoted by 1, then even+even=even, even+odd=odd, and even+odd=odd...

It looks like an "exclusive OR" transformation. A difference detector: a "1" output means "different" and a "0" output means "same." Half of a "half adder."

...A groupoid consists of points and of arrows. Points represent the static aspect, arrows represent the dynamic aspect. Arrows connect points. It will be enough for us to concentrate on transformation groupoids...

"Static" meaning something like "values belonging to a domain" and "dynamic" meaning "operations?" So this diagram represents a particular transformation (sometimes called "exclusive OR")?

That's a question that occurs to me also. Does "digital" physics start here? If so, the English way of precisely describing this relationship is very inefficient:

(0 OR 1) AND (NOT(0 AND 1))

...because the level below this requires inclusion. So, assuming the answer to Megan's question is "yes", is this 'unit of symmetry' the fundamental monad of which you originally asked?

 

[ark]

The possible esoteric meaning of the fundamental groupoid.

Sometimes a scientist is inspired by a philosophy, and a philosopher is inspired by mysticism. I think that there is nothing wrong with such a state of affairs as long as different modes of thinking are clearly separated in the mind of a thinking person. With this in mind let me take an excursion leading us beyond the rigorous way of a scientist, and also beyond the inquisitive way of a philosopher. Let us visit the distant past, let us go back to the Orphic cosmogonies.

According to Damascius (West, 1983) among the first-born gods (Protogenoi) there were two serpent deities: Khronos and Ananke. They were not corporal. Khronos was of a male character, Ananke (or Adrastea) of a female one, “her arms extended throughout the universe and touching its extremities.” Khronos stands for the static principle of “unaging time”, while Ananke represents the dynamic principle of “Inevitability” (or Compulsion, or Necessity).
The following quotation is from Damascios, a Neoplatonist who lived c. AD 500. […] (West, 1983)

"United with it was Ananke, being of the same nature, or Adrastea, incorporeal, her arms extended throughout the universe and touching its extremities. I think this stands for the third principle, occupying the place of essence, only he made it bisexual to symbolize the universal generative cause. And I assume that the theology in the Rhapsodies discarded the two first principles (together with the one before the two, that was left unspoken), and began from this third principle after the two, because this was the first that was expressible and acceptable to human ears. For this is the great Unaging Time that we found in it [sc. in the Rhapsodic Theogony], the father of Aither and Chaos. Indeed, in this theology too [sc. the Hieronyman], this Time, the serpent, has offspring, three in number: moist Aither (I quote), unbounded Chaos, and as a third, misty Darkness (Erebos) . . . Among these, he says, Time generated an egg this tradition too making it generated by Time, and born `among' these because it is from these that the third Intelligible triad is produced. What is this triad, then? The egg; the dyad of the two natures inside it (male and female), and the plurality of the various seeds between; and thirdly an incorporeal god with golden wings on his shoulders, bulls' heads growing upon his flanks, and on his head a monstrous serpent, presenting the appearance of all kinds of animal forms . "

Our fundamental groupoid has two points and two transformations.) 1 may well represent Khronos, the male principle, 0 can represent Ananke – the female one.. Then we have the central circle – the egg, or the Light. They form the triad, an Intelligible triad, as it is called by Damascios.

 

[ark]

That's a question that occurs to me also. Does "digital" physics start here? If so, the English way of precisely describing this relationship is very inefficient:

(0 OR 1) AND (NOT(0 AND 1))

...because the level below this requires inclusion. So, assuming the answer to Megan's question is "yes", is this 'unit of symmetry' the fundamental monad of which you originally asked?

I would prefer to stay with my original picture. Two static points and four arrows. Or: two static points, and two transformations: one "do nothing" and one "change the point to the other one". One passive, and one active. But still you have three loops - see the picture.

 

[Esote]

What a strange "incorporeal god" with so many appearances !
It looks like the realm of fundamentals is a (non) place to meet such weird beings or concepts.

Static Time and Dynamic Necessity... Straight coming from the Virtual (or Full Void) and generating the plurality of a world where time seems dynamic and where necessity is mechanical (static somehow).
A virtual information generating some strangely mirrored world ?

As it depends on the level of the observer's perception, it's little wonder that one would see a freaked god and another a non-trivial groupoïd (with a funny look also if you ask me) ;)

 

[John G]

Two static points and four arrows. Or: two static points, and two transformations: one "do nothing" and one "change the point to the other one". One passive, and one active. But still you have three loops - see the picture.

That's a very cool law of 3/Greek triad!!! Does it relate to a single bit, Cl(1), and a circle (Poincare disk) being representations of complex numbers/time/space? Is this groupoid a group also?

 

[StrangeCaptain]

Two static points and four arrows. Or: two static points, and two transformations: one "do nothing" and one "change the point to the other one". One passive, and one active. But still you have three loops - see the picture.

That's a very cool law of 3/Greek triad!!! Does it relate to a single bit, Cl(1), and a circle (Poincare disk) being representations of complex numbers/time/space? Is this groupoid a group also?

Not to get bogged down in details as I think Ark wants to focus on some fundamental ideas and not so much the math itself (but I could be wrong), a groupoid is a generalisation of a group. Thus, a group is a groupoid, but there are groupoids that are not groups. A groupoid G is a set that has a unary operation f : G -> G and a binary operation * : GxG -> G that IS NOT necessarily defined for every pair of elements from G. Probably the most immediate example of what I mean by an unary operation is the association of an element in G with its inverse.

So... Bluelamp... You have always seemed mathy, so I will say that the setting in which the notion of groupoid came about is category theory. You may have seen groupoids without knowing it in studying topology. The mathematically rigorous transition from general topology to algebraic topology (mapping a topological space to its fundamental group) is done via category theory one of whose notions is the groupoid. Category theory is a sort of math that allows us to map large collection of mathematical objects to another collection in a well defined manner. In the example above, we map a member of the collection of things called "topological spaces" (the collection is called a category) to the collection of things called "groupoids." The map that does this in a well defined way is called a functor. A good basic example of such a process is associating a group to the set of elements the group contains but without the group operations. This is a functor that maps an element from the category of groups to an element in the category of sets. Notice that there is a loss of information in this particular example as we go from groups to sets.

Not to derail the discussion, but for you Bluelamp and anyone else curious, this gives you some key words for any supplementary web searches that you might do... Cheers...

 

[dant]

Looks to me, that the groupoid diagram appears
as prime matter: water (H2O) :)

Anyway, I will just and wait until Ark provides more
material so as not to add to pure speculation.

 

[John G]

Thus, a group is a groupoid, but there are groupoids that are not groups. A groupoid G is a set that has a unary operation f : G -> G and a binary operation * : GxG -> G that IS NOT necessarily defined for every pair of elements from G. Probably the most immediate example of what I mean by an unary operation is the association of an element in G with its inverse.

So... Bluelamp... You have always seemed mathy, so I will say that the setting in which the notion of groupoid came about is category theory.

The test I've tried to use for group vs. groupoid is this one:

http://cornellmath.wordpress.com/2008/01/27/puzzles-groups-and-groupoids

Roughly speaking, a group is any collection of transformations of an object, subject to the following requirements:

1.If you compose two transformations (i.e. perform one and then the other), the result is also a transformation.
2.Any transformation can be undone by some other transformation.

Thus the multiples of 45 degree rotations for an octagon would be a group since any two rotations can be done as one (and you can undo your rotations) but a groupoid for one of those 4 x 4 square puzzles with one square missing where you try to move the pieces back to their original order is not a group since you can't always do the two transformations (blocked by a square).

But yes all groups are groupoids and if you are dealing with transformations that are trying to describe something that gets blocked or can't be undone (which kind of sounds arrow of time-like) then you can certainly call it all a groupoid even if some subsets of what you are doing are actual groups.

Category theory I've seen mentioned as the ultimate thing to do once you get all you can get out of lattice-like ideas but I haven't looked at it yet to see how much of it I can understand. What little I remember seeing almost reminded me of object oriented programming.