Dear List, I ended my last note highlighting that Bits are strongly local and their organization is arbitrary.
The “word” in my last post is the binary word, such as “1010” and not “THIS.” The latter is more complex than the former, although they both depend upon an arbitrary organization. It may not seem that way to you but this is merely because we are familiar with conventions that enable us to apprehend, to perceive or “feel,” a particular organization. An 8bit or a 64bit word is equally arbitrary and has little locality, except that which is useful for engineering, not science. On BIT Locality So a weaker view of Bit Locality concerns the width of organization and, necessarily because we are dealing with Bits, the step-wise nature of their transformation. But let me point out that stated at its most dramatic nothing varies, the world can be said to transforms. It moves from one distinct state to another. But there is no “returning” to a prior state, there can be no variable state. These are simply ways to speak about the world. Clearly we can dig a hole in the ground and place a stone in it. Between us we may call this hole a “Bit.” We may agree that when there is a stone in the hole its value is 1 and when there is no stone its value is 0. We may dig a second hole at your house and we can do the same. We can agree to combine the two such that were a stone in each hole the value can be said to be “11” and when not the value can be said to be “00.” We may also speak about the value “10.” To increase our confidence, perhaps, we may pay a grandchild to stand by the hole and shout out whether or not there is a stone in the hole. By this means we may eventually build a computing system, grandchildren shattered all over the neighborhood. But this organization has little locality, it does not “scale,” and it is not sustainable. Children tire, holes eventually fill and stones break. And, this is especially challenging, each time a stone is placed in the hole it is not, in fact, the same stone nor is it the same hole. Even though this will not be how it will seem to our grandchildren. The reuse of the stone and the hole is itself an arbitrary pragmatic. Automated information processing varies from this scenario only as a matter of degree. Reducing the problem to microelectronics enables us to put the machine into our pocket but it does not change the locality question nor does it make the states the same. Every state is, in fact, new. The illusion that it is otherwise is transitory. Now, obviously, engineers make best efforts to give us the impression that things are other than this. And, of course, I understand that for practical purposes we take the organization of machines to maintain repeatable states for practical purposes. Indeed, we depend upon this fragile pragmatism. The illusion is so pervasive that we call our time the Digital Age and we attempt to explain everything in terms of illusory Bits. We are enamored. On Step-wise Functions At the core of the Bit issue is a dualism that extends back to the start of the twentieth century. It is the dualism of “This” and “That,” “True” and “False.” It was brought to us largely by Bertrand Russell, his advocacy of Logicism and his celebrated authorship of the Principia Mathematica. Gödel showed us in 1931 that this system is necessarily inconsistent and even that the foundations of arithmetic based upon well considered but none-the-less arbitrary axioms, like those of Peano, could express no truth. I argue that the conventional axiomatic method is not well grounded and must be replaced by one that has greater rigor. I suggest one that is explicitly structuralist and covariant. It has to be admitted, of course, that despite these problems we have achieved remarkable success. But, again, we must shake off our love of this success in order to see how things are. Adoption of dualistic and strong bit-wise locality, arbitrary organization, and step-wise functions (due to Alan Turing and Alonzo Church) define the effective methods of modern computing. We have also finally accepted that the parallel processing of large-scale data is required. But this acceptance does not help us if we we are merely back to where I started 30 years ago. In fact, step-wise functions are deeply flawed. The result of a step-wise function is entirely unrelated to its former or subsequent value. In addition, the parallel execution of such a function suffers the long known problems of parallelism. Structure is hidden from such functions and is present only as a matter of fait or deception and must be enforced or imposed by engineering or mathematical artifice. I can hear many software engineers and applied mathematicians crying out in rebellion that this simply cannot be the case, but it is an imposition upon their minds that is involved and the truth of the matter has likely never occurred to them. Holomorphism and at once “Functors” I distinguish "step-wise functions” from “holomorphic functors.” True Holomorphism (a continuous and whole dynamic structure) is simply impossible for a computing machine to simulate. The "at once” geometric transformation of a structure may only be simulated by very fast machines using great electrical power burning and time consuming step-wise functions for only small cases - or many such small cases. We can and do fool ourselves into believing the magic by pointing at the movie or the game screen. But it is all artifice, a sham of Moore’s law, timing, and the miracle of theatre. There are important differences in the power profile of computing machines and biology, two important differences that despite the clever short cuts and mechanisms identified by Shannon and others demand that we accept that Turing computation, in all of its forms (including neural networks), is excluded from biophysics. These are the low power requirements of biology and the absence of hotspots. Hotspots occur in computing systems because of locality in their operation. There appears to be no such “hotspot" locality in biology. Alan Turing dismissed this lack of locality in his famous paper concerning Computing Machines And Intelligence. "I do not wish to give the impression that I think there is no mystery about consciousness. There is, for instance, something of a paradox connected with any attempt to localise it. But I do not think these mysteries necessarily need to be solved before we can answer the question with which we are concerned in this paper.” Alan Turing, 1950. By dismissing locality Turing excludes a role for biophysical sensation, what he calls “consciousness," in his mechanics. Of course, his paper concerned the vague notion of “intelligence” and this really is a separate question to that of sense. But I believe that if we are to build truly intelligent machines, machines with the strength of the uniquely human skill set - admittedly shrinking since the time of Turing, I am thinking of the things that are truly unique: easy general recognition, self-maintenance, reproduction and creativity, not chess, arithmetic etc… - then we must find a role for sensation, feeling or “experience” in our physical mechanics. I make a pragmatic argument that Turing computation is necessarily excluded from biophysics that runs along the following lines: The human brain dissipates 15Joules of power per second in a profile that is quite extraordinary. The power dissipation is uniform across the brain to within 1degree everywhere. There are no hotspots. Neurons and astrocytes work together to change blood flow, they change the brain’s structure. It has been widely predicted, although there is now a great deal of push back from the neuroscience community, that the human brain can be simulated in a machine with 10^18 operations (of some kind), the fabled “Exascale” machine. Let us ignore the architecture of such a machine, and the hotspots, and simply consider the numbers. If a brain possessed this much computing power it would require 94eV per operation. Although estimates vary widely, projections for the Exascale machine, with designs that are close to physical limits, are 60MegaWatts, a reasonably sized power station sufficient to power a moderately sized city. Biology has the locality problem solved, the Exascale machine does not. Plus biology has the advantage of being able to function effectively on a couple of burritos and a few cups of coffee per day. Allosteric Conformance The absence of locality in biophysics, generally refers to the variety of biophysical conformances called Allostery. This is defined as "a fundamental process by which ligand binding to a protein alters its activity at a distant site.” The truth is that biophysicists are still mystified by this effect, despite putting their best foot forward to provide an explanation is conventional terms. See, for example, the latest edition of Essential Cell Biology, 4th Edition. This absence of locality in biology defies Information Theory. If, however, we listen to Brit Cruise closely we discover that he makes many assumptions concerning locality despite the fact that he mentions the Bit as the foundation of information theory. He fails, as do most information theory presentations, to mention locality and existent structure as a consideration. We speak about data structure, certainly, but data structure is not an existential structure. Its various implementations are no less arbitrary than the word. If I confront a Tiger alone on the path I feel the entire experience at once across my physical structure. My apprehension is bound intimately with my responses. There is no time for reasoned thinking. I stand or run as one entity, fully coordinated, no part of me is standing still while the rest of me is running. This is not merely a matter of software, it is one of structure. At the end of the day only holomorphic functors can describe biophysical sense and actions, allosteric conformances, and it is only the binding of these as hyperfunctors that they can describe my sense and response at all scales. Shapes and Shaping At its simplest, information in biophysics involves shapes and shaping. These shapes are cell receptors and motor functions, changed and bound by genetic mechanics in flexible closed structures (cells and membranes). We can describe these shapes at all levels of the organism with dynamic holomorphic functors. These describe the shapes upon the surface of cells, be they receptor clusters or motor functions. These are sensitized by a necessary new basis. A universal that is across all flexible closed structure and is responsible for the associated range of sensation, allosteric shaping and coordination across these structures. I have one more piece to add, expanding information science into its proper domain. My apologies for the delay between posts. I am still in recovery and in addition to the problems with the FIS server last week my Thyroid crashed (the consequence of radiation treatment last year) leaving me feeling pretty ill. Regards, Steven -- Dr. Steven Ericsson-Zenith, Los Gatos, California. +1-650-308-8611 http://iase.info
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