The slow, inevitable decay unto death

(2/18/07 - A little update has been added at the bottom...)

A few weeks ago there was a bit of a buzz amongst bloggers concerning this story by the BBC. It was reported that Dr. James Anderson, a computer science instructor at the University of Reading (UK), had constructed a technique for handling division-by-zero by inventing a new 'number' which he named nullity. Dr. Anderson claims that this is a revolutionary approach which will solve age-old problems faced by mathematicians and computer scientists.

Unfortunately, this idea is neither really new, nor does it solve any problem that wasn't already well understood. The BBC web page for the above story allows for reader comments, and Dr. Anderson was roundly hammered with over 1,000 comments, most of which were critical. For some nice discussions of why Dr. Anderson's idea are nonsense, you can see the critiques by Mark C. Chu-Carroll at Good Math, Bad Math and by Jason Rosenhouse at EvolutionBlog. Jason also has a nice follow-up post where he discusses the algebraic foundations behind division-by-zero and why it can't be explained away by inventing a new number.

Dr. Anderson isn't backing down, however. The BBC web page contains some follow-up links at which Dr. Anderson attempts to respond to the criticism. It also contains a link to Dr. Anderson's personal website, oddly named the Book of Paragon. At this website we find that the concept of nullity arose out of Dr. Anderson's work on his perspex machine, which he describes as follows:

The perspex can be understood in many ways. Mathematically, the perspex is a particular kind of matrix; concretely, it is simultaneously a physical shape, a physical motion, an artificial neuron, and an instruction for a machine that is more powerful than the Turing machine. In other words, a perspex is an instruction for a perspex machine that is more powerful than any theoretically possible digital computer.

A perusal of the web site finds that the rest of the content is painfully similar to this. In other words, Dr. Anderson is apparently a full-fledged crank. While this is certainly not uncommon to find on the internet, it is (I would hope) rare to find someone like this currently employed in an academic position.

When I see a story like this, it makes me wonder what I would do if I ever stumbled onto a proof that P ≠ NP. I'm not sure if I would be able to bring myself to publicize it. After all, such a proof would almost certainly fall in the "not even wrong" category, as attested to by all the foolhardy attempts at proofs listed on G.J. Woeginger's P-versus-NP page. In fact, it would probably be a sign that I needed to do some serious sanity-checking.

I mention all of this as a backdrop to main subject of this post. Dr. Anderson was an unknown in the world of theoretical computer science, and by now he has pretty much returned to that status. But what if the person in question was one of the luminaries of computer science, someone who had among his or her accolades been a recipient of the A.M. Turing Award?

When I received the January issue of the Communications of the ACM last month, I quickly skimmed through the contents to see if there were any theory-related articles (often there aren't), and was happy to see the Turing Lecture: Computing Versus Human Thinking by Peter Naur. Some background on Peter Naur can be found in the Turing Award press release, in this Wikipedia article, and on his web site.

Now, comparing computing and human thought is one of those tar pits that tends to reduce weaker souls to babbling inanities. But this was a Turing lecture, a chance for one of the masters to reflect on their life's work, so I eagerly started reading. (Unfortunately, this article appears to be available online only to ACM members. The article on the Naur web site, A Synapse-State Theory of Mental Life, looks like an earlier exposition of some of the same ideas.)

It doesn't take long before there are some oddly paranoid undertones in the article. In the introduction, describing how he has come to disagree with Turing's view of the human mind in terms of computation, Naur states:

Indeed, I have found that a large part of what is currently said about human thinking and about scientific and scholarly activity is false and harmful to our understanding. I realize that my presentation of some of these issues may be offensive to you. This I regret, but it cannot be avoided.

After describing his early work with compiler design and program development, he talks about how he turned his attention to human thinking:

In this context I had occasion to examine a number of newly published works on such topics as machine or artificial intelligence and cognitive science, by contributing reviews of works on such topics to the Computing Reviews [28-1985, 29-1985, 32-1988, 33-1989, 38-1993].

Through this reviewing activity I found confirmed time after time that present-day authors argue about mental life from totally defect, confused cognitivist notions, in terms such as ‘consciousness’, ‘knowledge’, ‘language’, ‘intelligence’, ‘concept’, that denote nothing clearly, and moreover that William James’s insight into human mental life as presented in his Principles of Psychology [5] is unknown. I gradually came to realize that the whole field of psychology, which supposedly is concerned with mental life, during the twentieth century has become entirely misguided into an ideological position such that only discussions that adopt the computer inspired form of description of mental life is accepted, while any other form, including the form developed by William James in his Psychology, is rejected as inadmissible and unpublishable. So as to clarify this extraordinary situation of psychology I engaged from 1986 into a series of studies.

Naur goes on to describe a book and several articles that came out of his research. However, he felt that his ideas were being suppressed, and he mentions an article, a book review, and a letter to the editor that were rejected for publication during the mid-1990s. As a result of the rejected letter to the editor (which was to the Communications of the ACM) he quit the ACM.

Naur next moved on to critiquing the work of philosophers on the subject of the mind:

Through these analyses I establish that what is said by philosophers about human mental life is void of empirical support. The overall conclusion of the work is that philosophy is an ideology of presumption, harmful to science and scholarship, while the descriptions by William James of mental life and by Otto Jespersen of the linguistic activity, although unsurpassed in their insight are unknown to philosophers.

Naur developed this work into a critique of contemporary psychology, apparently coming to the conclusion that little worthwhile has been done since the work of Williams James. He then began to look at the physiology of the nervous system, which led to his current thesis:

The work on the Anatomy [50-2005] gave me the occasion, in November 2003, to look closely at Charles Sherrington’s The Integrative Action of the Nervous System [54]. This immediately told me where in the nervous system one finds the plasticity that James states very clearly must be the neural ground of habits, to wit: in the synapses. And so the way was open to a neurophysiological description of the nervous system, which I have called the Synapse-State Theory [49-2004].

Finally, Naur is at the point in the article where he ready to describe the details of his synapse-state theory of the mind, based on work by William James and Charles Sherrington from the late 1800s and early 1900s. Having come this far, I hope you will not be disappointed if I do not attempt to critique Naur's ideas. (If you're really curious, the gist of the theory can be found in the A Synapse-State Theory of Mental Life article mentioned earlier.) It is not so much a question of being right or wrong so much as being simply irrelevant. His theory looks like something that might have appeared in print 30 years ago, which is not surprising given where his inspiration comes from. There is nothing present in the article to reflect advances made in the neurosciences over the past couple of decades.

Near the conclusion of the article Naur states:

I have tried to have these articles published in journals, so far without any success. The present presentation, when published in the Communications of the ACM, will in fact be the first presentation of the Synapse-State Theory of mental life to appear in a journal.

So I am clearly at the beginning of that twenty year period that it usually takes to have a scientific breakthrough accepted.

I'm not sure exactly what my point is in bringing all of this up, but I can't help finding it depressing. I don't think one should feel sorry for Naur. This article will quickly be forgotten, and Peter Naur will be remembered for the work he did earlier in his career, for which he received the A.M. Turing Award. No, I think the reason this seems so depressing is that it reminds me of my own aging and my gradual decline toward obsolescence and beyond.

Update:

I shouldn't make a habit out of adding updates to the bottom of my posts, but there were a few things I wanted to add. I originally started this post with the intention of critiquing Naur's article, but I quickly realized that would be pointless. The article appears to me, more than anything else, to be a chronicle of a twenty year descent into obsession. There are plenty of cranks on the Internet with half-baked theories about everything imaginable, but when someone who previously had a sharp mind turns into a crank, you can't help wondering if there is something organic at its root. It brings to mind John Nash (although I should emphasize that I'm not suggesting that Naur has any particular type of illness). But if I remember correctly, the Nobel award committee had some concerns about whether Nash would be well enough to receive the prize; I wonder if the ACM had any similar concerns about Naur?

I also have to wonder about the Communications of the ACM and their decision to publish the article. Presumably they felt obligated to publish it, as it was a Turing Lecture. Did anyone try to dissuade Naur from submitting the article as written? Or did they even consider it suspect? The Communications has a history of publishing wacky theory articles, so perhaps it didn't seem so odd to them.

I have to confess to being curious about what other people think about this. I haven't seen it mentioned on any of the theory blogs I read, perhaps out of disinterest or perhaps out of respect for Naur. I've seen the article mentioned in passing on a couple of blogs from the programming side of the aisle, and in those cases the sentiment was something along the lines of, "I'm not sure what to make of his theory, but why is he so angry?"

As for myself, as I mentioned earlier, it all just serves as a reminder of our inevitable mortality. I hope that if my mental faculties decline to the point where I can no longer craft a cogent argument, that I still have enough self-awareness to realize that fact.