This should all be quantifiable. The controls (with parameters), the inputs, and the output (even if it is just a periodic real function). If it is open-ended, give a case with a specific set of inputs. If I want to tell you how to make Krispy Kreme glazed donuts, I can specify an algorithm for making them with a specific list of ingredients, etc..

Even in ANN models, you can have any number of possible inputs, but this doesn’t stop people from giving helpful and simple examples with, say four inputs to a single neuron, and describing how the output relates to the inputs.

Bob respondes: Well, let’s say a Quad Net device (or a neuron) is a like a Krispy Kreme factory that produces doughnuts (or beeps or action potentials). Different kinds of stuff are inputs and the list of possible ingredients is open-ended. The controls are more important. Learn enough about the controls to get a production line going with any convenient ingredients and then you can work out the variations. Inputs are non-specific to the question of function.

The output of any Quad Net device is the same — it goes “beep-beep-beep” — but, in large devices, the beeps are organized into patterns in space and time. It’s the patterns that are important, not the individual beeper. Patterns go in and patterns come out and patterns drive the going ins and the coming outs. There is no “transfer function” - changes in beep patterns are based on in inputs and controls and depend on particular configurations of parts and particular operating values of variables. There is baseline operation that can be changed by various means and the particular means depend on the circumstances.

Quad Nets are the mother of all “block diagrams.” Quad Net constructions are working block diagrams. A Quad Net spatial block (e.g., a Flat Quad Net shaped into a CQN or TQN) is activated and the activated block turns into a device. A Quad Net device embodies a working block in a block diagram. Hookups between QN devices embody lines in block diagrams. Each device transfers patterns to other devices and/or controls transfers between devices. Devices are hooked together into tiled assemblies; and, further, tiled assemblies are hooked together into nested tiled assemblies; and then nested tiled assemblies are hooked to each other. There are also hookups between devices in one tiled assembly and the entirety of a second tiled assembly, including all the devices in the second tiled assembly. Activities in different tiled assemblies resonate with one another and generate new possibilities. The resonating patterns are based on Critical Point principles that operate “the same” at every scale and on every level. When multiple possible pulse patterns and multiple possible block diagrams are co-existing together and changing continually into one another, then you’ve got
Shimmering - the Critical condition that precedes selection of and relaxation into one particular pattern or diagram. Quad Nets support this kind of activity that is different from that supported by devices that transform inputs into outputs.

bob kovsky (rlk “at” sonic.net)

Exactly! But also it would be good to fill out in more detail the input-output transform being implemented by an individual element: a drawing that specifies the inputs, outputs, and the transform between the two. In particular, does it take in real numbers as inputs and output real numbers? That kind of thing. For block diagrams, the systems people first clearly delineate what each block is doing (e.g., addition, multiplication), and then analyze how these blocks work when they are all hooked together.

Comparing the proposed alternative with the actual paper, it is the chicken-egg question. Which comes first, the organism acting purposefully or an individual elemental device producing shifting patterns of pulses? The question is especially difficult in the alternative proposal, where it is necessary to navigate a transition from individual time patterns in elemental devices to collective space patterns in Quad Net constructions. Supposing you can build a chicken up from an egg, sometimes it is better to start with the chicken and focus on the egg-producing system.

The design of the paper is grounded in the foundational concept of tiling. In Quad Nets, tiling is universal, primal and ideal and occurs in space, time and activity. The paper shows many and various tiled constructions. The purpose of elemental devices is to participate collectively in a tiled construction, not to model a neuron or to conform to a technology like computers. A tiled construction has character, however tediously reproduced. As stated at the outset of section 2, we are not in a mechanical system that starts with an empty void into which atom-like devices are introduced and assembled into systems according to a molecular principle. Rather, we are in the interior of something like a physical material with a particular collective character that is an actual starting point for what is going on. The details of a graph in section 4 are only secondary and other graphs would produce the same results if used in Quad Net constructions.

The present organization of the paper is also based on an approach that emphasizes biological and neuroscience models above engineering models. Quad Net constructions are “mesoscopic,” using a word that appears in a title of a book by Prof. Walter J. Freeman (link to online book on the quadnets website) and that denotes something in the middle between macroscopic organism models (e.g., stimulus-response) and microscopic neuronal models. In addition, an image of Quad Net material being fabricated during extrusion in a manufacturing plant suggests an answer to the question posed in Edelman’s Neural Darwinism, p. 75, “How does a one-dimensional genetic code specify a three-dimensional animal” and the suggested Quad Net answer resonates with the biological answer Edelman provides. It is reasonable to suppose that the path of Quad Net constructions resembles growth of brains in biological environments, with initial crude constructions providing points of attachment for later, more refined constructions. It is not reasonable to suppose that building a computer (or a neural network system) looks like growing a brain.

The same can be said of cellular automata, but the rules governing the behavior of individual cells is quite explicable. My main point is, that as a sociological fact, few people will read or understand your theory unless you take what you call the ‘atomic-molecular’ approach. Nobody will make it to section 4, and words/images are just not enough. Take a look at any introductory book on artificial neural networks to see a better way. (E.g., Neural Network Design, by Hagan).

Thanks for continuing the dialogue. Your posts (and that of Mike S) make clear a preference for an “atomic-molecular” approach where, first, elementary units are fully defined, then elementary units are hooked together with simple rules and, finally, desired activities occur as a consequence of the systemic organization of the units. This is a traditional approach that is used in mechanics (adding forces), chemistry, propositional logic and computers. I can structure such an approach for Quad Nets — e.g., using Images 40 and 46 for the activity of a single, isolated elemental device. These Images have the form of graphs and could be expressed, e.g., as sawtooth functions. However, my attempts to express the activity of a Quad Net in a mathematical formulation show no benefit. More, this approach misses a major point of the Quad Net model, namely that the different forms of activity are collective and, sometimes, you can’t tell just by looking at one elemental device which of several phases is being maintained. My approach, apparently imperfectly expressed, is to identify the collective activities as primal and individual activities as representative. This presents the material in a different order from that of an atomic-molecular approach. Hence, the “atomic” models appear in section 4 and the collective constructions in sections 2 and 3