Since my May update I have made numerous small revisions to my book's draft "Introductory Remarks." These revisions are mainly derived from feedback on a related submission document to SuperComputing 2011 that comes from a chapter of the book on the Foundations of Computation.

In that submission to the Disruptive Technologies Program I propose a new computational paradigm for certain large scale parallel computing problems so the reviewers were all leading Computer Scientists. This work is not generally available but I did want to propagate some of the important elements of the review back into the Introductory Remarks.

The primary additions from the review relate to some relative comments with respect to Connectionism and Neural Networks.

Honestly, despite its popularity among Neuroscientists, I had dismissed Connectionism long ago and view Neural Networks as a failed technology founded upon a model that is naive and poorly informed.

However, several senior reviewers criticized my failure to mention it directly and, worse, suggested that I had not done adequate research because it was absent.

The truth is that during the late 1980s and early 1990s, before I embarked upon this work, I spent a lot of time with the Churchland work and with McClelland's "Distributed Parallel Processing" text and thought that we had all moved on from what had become a footnote in history :-) 

This was wrong of me and I should have included Connectionism in my review, at least to compare my model of distributed representation with the earlier work.

In short, the problem with Connectionism and Neural Networks is that they were founded before a lot of the more detailed evidence became available: they are naive, not founded upon a general theory, they deal with "brains" not organisms, and they ignore physical structure.

My decomposition arguments also hold. Neural Networks do not form a computational parallelism that makes a difference since the parallelism in Neural Networks can be removed (the node computations executed in sequence) without a discernible effect upon the results.

I have started to correct my deficit in the "Introductory Remarks" and, for historical completeness, will add a discussion of Connectionism in a new section of the book. This sort of evolution is why books should always be well reviewed before publication. It's why I publish drafts of my evolving work online.

Although I get few real review comments unless I pointedly ask someone to do it. I tend instead to hear only from people that either love the work and it has changed their entire view of the world (this is nice but not especially useful) or from crazy people that claim that I have stolen their ideas. So far it turns out that such people understand neither their own work nor mine, and precedence is easily established via the Archive.org record.

I also took the opportunity over the past day or two to refine the Introductory description of the model of memory and recognition. This is mostly word craft and clean up of late night bumbling, it is now a clearer technical introduction I hope. 

In a recent Foundations of Information Science posting (FIS) I attempted to clarify the scientific theory of "Truth." Here I restate and expand that argument. 

"Truth" is simply a way of speaking about existence, it is a way of speaking about the correspondence between the apprehension of statements and the way things are or, more generally, of experience and the way things are. 

"Justified true beliefs" are today, essentially, verifiable and fallible, not absolute. This is how we now characterize Plato's appeal to "justification." 

Therefore, even science that is not strictly correct can be said to be "true." Newton's laws are true to this extent, they do correspond to the way things are, they are verifiable and fallible. That we know the extent of their fallibility is beside the point. General Relativity is simply a closer approximation, and it is also verifiable and fallible. 

Can we say then that Newton's laws are "not true" on the basis of this? If we are rigorous about it, I don't think that we can. Clearly General Relativity can be said to be closer to the way things are because the statement of it provides a broader "explanation," a boarder identification of causes. But if we do so then we must accept that "truth" is simply a matter of degree, a measure of "certainty" in our statements.

In short, the notion of "truth" has become redundant, a metaphysical notion inherited from a time when the conception of "absolute truth" seemed viable and could be imparted by an ultimate authority. In fact there is no such authority and "truth" is a meaningless notion in science unless by it we refer to "certainty," a question of degree; and at that point the notion of "truth" is obsolete, our attachment to it emotional.

The nature of "Truth" is then what Rudolf Carnap would call a "psuedo-problem" in philosophy. Science necessarily abandons all hope of absolute truth and our use of the term and hand-wringing over the notion can be comfortably put aside.

Some controversy online over the claims of a proof that P != NP by Deolalikar of HP Labs. Here is the latest revision of the paper:

Vinay Deolalikar, P != NP 

Alasdair Urquhart's insightful response on FOM can be trusted:

http://www.cs.nyu.edu/pipermail/fom/2010-August/014981.html

A more metered response comes from Dick Lipton and Ken Regan:

Issues In The Proof That P≠NP 

I will read the paper but given the responses so far my expectations are low for this proof.

Is it true that P != NP? Harvey Friedman claims it is so. I've never been clear on the matter myself but in terms of the limits of current computational models the question is an important one. Note that I place emphasis on the word "current." A proof will be important in the development of future computational models if one can demonstrate why it is so in one case and not the other.

Here's a link to the guy, Stephen Cook, that got us into this mess:

Stephen Cook 

And here is a link to his paper that started it all:

The complexity of theorem-proving procedures

UPDATE:

Deolalikar responds to critics:

Deolalikar Responds To Issues About His P≠NP Proof

This posting by Richard Lipton provides some useful comments on a strategy for assessing proofs.

But no-one is buying into spending a lot of time on the question:

Harvey Friedman on FOM 

And now the ultimate indignity 

Trashed on TechCrunch

FINAL UPDATE:

Hopefully this is the last we will hear of it except in the annals of foolhardy Internet career moves:

Fatal Flaws in Deolalikar’s Proof?

This is a follow up note to my comments related to the prevalence of Pax genes in eye development.

I do not want to give the impression that I dismiss all phylogenetic trees. It seems obvious that in species at least, and across closely related species, such developments by mutation are easily traced. I am deliberately avoiding arbitrary categorization terms like "genus." 

So I do not argue that phylogenetic trees are of no use, they certainly are.

However, recall that for the man with a hammer every problem is a nail. The phylogenetic tree is such a hammer in the hands of naive genetic research.

In my view, the entire hierarchy of life on earth is unlikely to derive from a single common ancestor molecule. I do not think the case for the ancestor molecule can be justified. It's the over application of phylogenetic trees. I suspect that there are, in fact, multiple points of origin and also that these roots to life readily and spontaneously occur.

I will accept that it is plausible that the system is self-limiting; that once life begins conditions change sufficiently to prevent or limit subsequent spontaneous production.

So I accept phylogenetic trees as useful and interesting in species but I am committed to the view that there exist general laws, physical laws, that produce the mechanics of biology. As such then I expect to see similar mechanics occurring independently to produce common effects such as the development of eyes.

Nature is profoundly uniform and I would have been very surprised if the genes involved in the production of visual acuity in any species had been entirely different from our own.

I should add that without this insight the MrBayes program used in this study will draw spurious connections from the dataset. In short, the Bayesian analysis is, at best, misleading and in all likelihood false. This will be true for all applications of MrBayes when applied without the consideration of possible independent origins of similar genetic structures. In other words, monophyly is the inevitable consequence of the base assumption that similarity demonstrates it.

Here are some comments after spending some time with the paper:

"Flexibly deployed Pax genes in eye development at the early evolution of animals demonstrated by studies on a hydrozoan jellyfish"

http://www.pnas.org/content/early/2010/07/14/1008389107

By Hiroshi Suga et al. published in PNAS this past week.

This is very interesting work and uncovers very much the kind of empirical data that I have been looking for these past few years concerning these organisms, for reasons given in my earlier post on the subject (these organisms possess visual acuity but no brain). However, the conclusions as presented in the paper are weak.

My objection relates not to the work in particular but to the general competition between the notions of genetic conservation and evolutionary convergence.

It is really very common in nature, because of its startling uniformity, to find that the same sort of thing happens everywhere to produce any given result.

If we follow the logic presented in this paper on the subject then we are required to identify a common ancestor molecule from which the accident of earth bound biology follows. This opposes the view that it is possible to identify general laws, physical laws, by which biophysical entities broadly arise.

My bet is on the general laws. However, the data presented in this paper is inconclusive and may be interpreted to contribute as much to one argument as the other.

The following paper by Hiroshi Suga of Parc Cientifíc de Barcelona, work done at Universitat de Barcelona and Department of Cell Biology, Biozentrum, and Institute of Zoology, Pharmazentrum, University of Basel, et al. has just come to my attention.

As you know, I have a strong interest in evolutionary convergence and the structure of sensory organs and how they occur in nature. I have also been a keen follower and advocate of genetic research and other basic research that includes cubozoan jellyfish because of the apparent convergence for visual acuity.

These organisms are especially interesting because they have eyes and few neurons. That they do not have a brain but obviously "see" leads to interesting questions concerning our assumptions about vision processing in our species.

When I have reviewed this paper thoroughly I will post some detailed comments.

As it stands my view is that the presence of the Pax-6 gene across widely separated species does not necessarily mean that it is present as the product of conservation, but it is highly suggestive and this research may offer some new insight.

This insight could simply be that the uniformity of nature as it is seen in biophysics is even more startling than we at first suspect. That is, when the mechanics that produce particular sensory organs occurs it occurs in the same way everywhere. This is certainly what my theory suggests.

In this case conservation could be eliminated as the source of the common gene.

"Flexibly deployed Pax genes in eye development at the early evolution of animals demonstrated by studies on a hydrozoan jellyfish"
http://www.pnas.org/content/early/2010/07/14/1008389107