## Zeno’s paradox, Moravec’s paradox and rethinking how we project forward in our planning 2

This is my second posting to a series on paradoxes, and both as philosophical constructs and as the concept of paradox is applied to business and technology contexts (see Part 1.)

I began this series in Part 1 with a brief discussion of an historically famous example: Zeno of Elea’s dichotomy paradox. And I used that as a working example in outlining two fundamental reasons as to why a seemingly empirically validatable scenario might be describable as encompassing an apparent paradox. To further connect that posting with this and as a basis for further discussion, I repeat them here:

1. A seeming paradox can arise when a logically consistent and formally valid line of reasoning is offered in description of an empirically observable circumstance, but where its underlying axiomatic assumptions are not applicable to the circumstances or conditions for which it is being applied.

2. Alternatively, a seeming paradox can arise and even when the application of its reasoning to a specific empirically observable circumstance would seem valid, when there are perhaps subtle and unobvious but still significant flaws or gaps in its underlying logic.

I continue this series and its overall discussion, turning to the modern proposed-paradox example of Moravec’s paradox, which I state here as follows:

• Higher level cognitive reasoning is computationally simple while seemingly much more basic and lower level skills of perception and sensory data analysis, balance, motion and timing are computationally very challenging.

• And this seems to be so counterintuitive as to appear to be starkly paradoxical.

I stated at the end of Part 1 that I would examine this proposed paradox in a manner that at least parallels my discussion of Zeno’s of Part 1. And I begin that by stating up-front that my discussion of this assertion will lead up to my proposing and stating a third basic mechanism by which a proposed paradox might fail. But first, let’s consider Moravec’s paradox and I add, the technology context in which it arose.

Historically, the electronic computer and electronic data processing and management began with the single central processing unit (CPU) and with that single point of data processing capability and activity supported by a system of data input and output devices, short-term and longer-term memory and data storage and so on. Parallel computing with first two and them more coordinately functioning processors in a single system, and then vast numbers of such processers came later. And the development of parallel processing systems in general and of massively parallel computing systems raised whole new technical problems, and both at the hardware and software levels.

To cite one of these software challenges, some data processing and computational problems are readily divisible into smaller problems that can be worked upon in parallel and in large part separately, with ongoing intermediate results accumulated and as necessary coordinated between. In this example “adjacent” parallel processed sub-problem outcomes would be used in and of themselves and also serve as updated boundary value input for continued work on “neighbor” calculations. Computer based weather forecasting, and wind tunnel data analysis that would go into the design of new aircraft are obvious examples of where this approach would apply, and of where massively parallel computing approaches would offer value that single CPU approaches could not match. Single processors would perform calculations relevant to small areas or volumes of space over time and their calculations would be meshed together to account for wider-ranging causal impact from adjacent data processing areas and beyond.

There are, on the other hand, computational and data processing problems that cannot be readily partitioned so as to make efficient use of parallel processing systems. Problems that involve following through upon and completing single, difficult to partition threads of logic, that do not divide into parallel-solvable sub-problems fit this pattern.

• Computational and data processing problems do not in general fit equally well into just any computer system’s architecture or design.

• Most problems that are amenable to algorithmic solutions approaches and certainly most complex problems that meet that basic requirement, are optimizable to at least specific categories of computer systems architecture. And pursuing a broad brushstroke partitioning of computational problems as to type here, some are more amenable to single massively powerful CPU resolution and some are more amenable to parallel processing and even massively parallel processing systems.

There is an assumption built into and underlying the Moravec’s paradox to the effect that the data processing driven challenges of higher level cognitive reasoning, and of perception and sensory data analysis, balance, motion and timing should be equally solvable independent of any computation-problem to computational-systems alignment considerations – and with the default computer architectures used following the pattern of what in computer technology is the best known and technologically most developed and advanced. It would make more sense to think of the first of the two problem types as set out above in my phrasing of Moravec’s paradox as constituting a set of computational problems that are more amenable to single CPU architectures, or at least simpler arrays of more powerful processing units that can individually process larger amounts of memory-provided data in any period of time, while the “lower level skills” cited there demand tremendously massively parallel processor arrays where each processor in those systems can be much less powerful individually – but where they can be incredibly powerful coordinately and collectively. As of this writing, parallel processing systems of sufficient scope and scale, and power are still being developed.

And at this point, I have to note that the development of brains and of neural networks in general followed a very different path than has been followed in developing newer and more powerful computer technology generations. Our artificial computers have evolved in large part around development and production of progressively more powerful single processors. Natural data processing and storage systems – neural networks and brains evolved along a very different path. There, evolution led to development of what amounted to simpler processor capability first, and then more advanced systems arose evolutionarily that could more effectively use that technology and its underlying genetic blueprints – by producing and interconnecting multiple and even vast numbers of proven simpler assemblies. So for biological systems, parallel processing of simpler computational elements came first and then development of more powerful single computational elements (e.g. counterparts to more powerful computer processing units) came later.

Our growing knowledge of how real-world biological neural networks and brains constructed of them work is still primitive as of this writing, but it is already sufficient to at least validate the basic outline descriptions offered above here. And this brings me to that third basic mechanism point that I said above, I would offer here as to how a seeming paradox might arise:

3. A seeming paradox can also arise when axiomatic assumptions are made that simply reflect the limitations of some current state of the art, and for the technology available, for current practices in using that technology, or both. And this can, among other things arise because of implicit assumptions that the particular path that technology is developed in historically could be the only one possible.

If we want to develop technologies that can perform the “lower level skills” of perception and sensory data analysis, balance, motion and timing, or I add comparable counterparts to them, simply advancing single massively capable CPU technology that is more familiar cannot suffice. And I add that simply building current power-demanding silicon technology parallel processing arrays will not suffice either, and no matter how massively scaled they can be made. This is where we will have to move beyond our as-of-this-writing still early “proof of principle” efforts in designing and building artificial neural nets – and with development of both massively powerful single processing unit capability and for massively parallel processing unit capability – and with real focus on the later.

When I challenged Zeno’s dichotomy paradox in Part 1 it was by arguing that this ancient assertion fit the pattern that I lay out in numbered Point 1 above. When I challenge Moravec’s paradox here it is by arguing that his assertion fits the pattern of my Point 3 as just stated, which yes – might be viewed as a variation of Point 2.

If this series were to end at this point and only consider these two asserted paradoxes, I would at least seemingly be trying to tie off this area of discussion in a neat and clearly stated package. But the complexities and I add “alternative simplicities” of the real world intrude. And I will at least begin to peel back the lid from over that in a next series installment. Meanwhile, you can find this and related postings at Ubiquitous Computing and Communications – everywhere all the time 2 and in my first Ubiquitous Computing and Communications directory page. I also include this in my Reexamining the Fundamentals directory as an entry to a new Section V: Rethinking Underlying Assumptions and Their Logic.

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