Thursday, November 27, 2008

The Ghost and The Machine

James Knight, the Network Norwich columnist, asked me the following question. Posted below it is my reply.

Do you think the cosmos is platonic just in the mathematical sense or in another way too? I'm just making sure that when we speak of the cosmos we are both using platonic in the same terms. How are you using it?

Hi James,

The following answer to your question impinges upon some issues that I have been pondering for years: in particular why is that in our culture the “irreducible intuitive” is so often pitted against the “reducibility of mechanism?” This theme I see in almost everything: from H. G. Well’s “The Time Machine” where the Eloi are pitted against Morlocks, through the Cartesian ghost in the machine and ‘left brain’ versus ‘right brain’ traits, to charismatic verses non-charismatic. This seemingly irreconcilable dichotomy has now consumed my theoretical deliberations for many years and constantly makes unexpected appearances in my writings (See this link for example ). Here is my attempt to address this issue. It is in fact a very pressing matter because for many years I have been very alienated from evangelicalism. I have put that down to a swing in mainstream evangelicalism toward ‘right brain’ faith expressions and this has become the de-facto version of Christianity in some quarters. There has, in my view, been a consequent loss in authenticity and this has threatened my faith. So, the stakes here are very, very high and I find myself defending my faith from other people with faith. Paradoxically I don’t find atheists anywhere near as threatening!

The short answer to the question is: I use the word ‘platonic’ to refer to the world of mathematical constructions and models. These constructions are explored with the likes of number theory, geometry, set theory, computational theory etc. The most salient feature of this world is its debatable ontological status; it seems to be a world of possibility rather than actuality. Many (if not all?) objects in the cosmos can be modeled using a subset of platonic mathematical constructions isomorphic with them. Cosmic objects are platonic in as much as they may be isomorphic with mathematical objects. A much longer answer is probably necessary when one realizes that there are some tough conundrums here.

At first sight the fundamentals of mathematics are disarmingly minimal, undemanding of an elaborate physics to host them. Take for example the Turing machine: it seems to ask for little more than two discrete sequences (the tape and procedural steps) and a state transition diagram (=software). From this simple model the whole of mathematics seems to open up. Many versions of material reality could host such a simple machine and its computational equivalents and therefore there seems no lack of clarity or mystery in trying to conceive mathematics: it is devoid of that ‘right brain’ mystique; it is, seemingly, the progeny of the ‘left brain’, a paragon of mechanism.

But the self-referencing intricacies and enigmas come in thick and fast once we get reflexive. For a start if we allow the Turing machine to analyse its own mathematics (meta-mathematics) up pops Gödel’s theorem and Turing’s halting theorem. Also there is this question: Is the concept of mathematics intelligible without at least a minimal physical world able to host the mechanical reifications of its computations? Is there truly an independent platonic world that mathematics inhabits irrespective of the existence of a material ontology? And where does the mind fit in all this? Is the activity of an apparently ‘mindless’ mechanism of elementals, such as we find, in a Turing machine, the essence of mathematics? Or does mathematics only exist by virtue of a preexisting mind that can conceive it?

Mathematics appears to transcend a particular material instantiation of its objects whether that instantiation is a Turing machine or some other model of computation. The objects of mathematics can in principle be instantiated on a variety of media ranging from Searle’s beer cans to silicon chips. Therefore the essence of mathematics is to be found over and above material instantiation. Mathematics is about abstraction from material reification; it is about classes of activity and pattern and these things are not necessarily tied to a particular substantive realization. Abstraction, class and pattern are intelligible only as pure concepts inside an up and running mental context which can then handle.

These are difficult issues, but for a theist their resolution is likely to be bound up with the concept of Divine Aseity (see also your concept of absolute reason) Like you I favour the view that mathematics betrays the a-priori and primary place of mind; chiefly God’s mind. The alternative view is that gritty material elementals are the primary a-priori ontology and constitute the foundation of the cosmos and mathematics. But elementalism has no chance of satisfying the requirement of self explanation as the following consideration suggests: what is the most elementary elemental we can imagine? It would be an entity that could be described with a single bit of information. But a single bit of information has no degree of freedom and no chance that it could contain computations complex enough to be construed as self explanation. A single bit of information would simply have to be accepted as a brute fact. Aseity is therefore not to be found in an elemental ontology; elementals are just too simple.

In the search for Aseity elementalisation leads to an ontological dead end because elementals have a lower limit complexity of one bit, a limit beyond which there is no further room for logical maneuvering that could resemble anything close to self explanation. In contrast complexity has no upper limit and hence if Aseity is to be found at all, it must reside at the high end of logical complexity, perhaps at infinite measures of complexity with some kind of reflexive self affirming properties, such as we find in your “there is one true fact” example.

Like you James I’m attracted to Berklian idealism and/or a phenomenological philosophy, because taking sentient complexity as the fundamental given seems to provide a better chance of solving the philosophical conundrums over the nature of the mathematical abstractions, self explanation, and consciousness. However, I can find no necessary objection to the idea that sentience, particularly Divine sentience, may be able to engage in some kind of mathematically reductive self description; but in doing so such description would be no more than sentience describing itself in terms of its own ontology; something similar happens when a programming language is used to write its own compiler. As you say “…..personality is not something that we can turn on itself and identify outside of the layering we put in. I think personality is too big for such isolated imputations.”, If I understand that correctly then yes, personality cannot be described with something beyond itself; but in the final analysis personality, particularly God’s personality, may be big enough to cope with its self description in terms of its own ‘substance’. So sentience is at once both reducible and irreducible. Reducible because it may be mathematically reducible, but irreducible in that it cannot be reduced to an ontology other than itself. This may help satisfy the twin but seemingly contradictory intuitions of the reducibility and irreducibility of sentience.

There is often distaste for the idea that somehow reductive descriptions of sentience are possible. This distaste may result because our self-conscious first person ontology, something which is very sacred to each of us, is trivialized if a reductive description of sentience is used as Trojan horse to smuggle in a profane materialist ontology. It is one thing to attempt a reductive description of sentience in terms of the cognitive artifacts of sentience, but it is entirely another to surreptitiously swap a first person ontology for an elemental materialist ontology whilst attempting to carry out this reduction. A descriptive reduction is an entirely different thing from an ontological reduction. In any case I would question the intelligibility of the whole notion of a gritty “material” cosmos “out there”: if I am right then the fundamental particles of the cosmos are not solid little quarks or strings but cognita. Quarks and strings demand a complex mathematical context to be intelligible. The philosophical problems in this area seem to result of an attempt to relate incommensurables; mind and matter. My own opinion is that one or the other has to go and since ‘material’ noumena are far less real than the first person experience it is the former that has to go.

I have always had grave doubts about the intelligibility of an ontology of “material” elementa pictured to be lurking out there somewhere beyond sentience. It is surely ironic that many Christians are at one with many atheists in picturing such a conception. It is ironic that the default Christian folk philosophy is that of a “materialism plus” ontology – that is, a basic off the peg materialist ontology is supplemented with a “spiritual world” of demons, sprites, angels and of course God himself, all of which haunt the interstices of our gritty earthly reality in the manner that the human “spirit” is supposed to haunt the human body: the ghost in the machine. This is of course Cartesian dualism. For theists dualism actually leads to a tripartite reality: 1. God. 2. The Spiritual World 3. Matter. It all smacks of the classical Gnostic view of particles of spirit somehow trapped in a profane material world, a world that owes its creation to a demiurge; after all, the feeling goes, how could a perfect spiritual God have anything to do with a world of grimy matter? In the light of this default philosophy it is no surprise that Christians across the board are so utterly alienated from their world and are retreating into the mysteries of the “right brain” and the mysteries of the inner self where the unaccountable machinations of intuition replace mechanism. There follows the great Christian cop out from having to account for itself by simply declaring “It’s all in the heart”. In its more extreme expressions salvation for the Christian Gnostic is an escape from the ‘evil’ material world through states of altered consciousness.

Christian dualists are never far from atheism; they hover on the abyss of atheism. If for some reason their concept of a haunted reality should betray them and they react against it, they find a profane materialism purged of sacredness ready to welcome them. And the betrayals do happen: crises in leadership, failure of their religious paradigm to materialize in the form prophecies, blessings, healings and revivals, and the whole creaking show patched up by a bullying authoritarian leadership, well versed in spiritual spin.

I don’t accept a three substance or even a two substance cosmos: I am striving for an integrated vision, not the horribly fragmented vision of contemporary Christian Gnosticism that has lead to the incompatibilities between heart and mind, right and left brain, intuitive Christians and analytical Christians. But an integrated one substance vision is not the same as pantheism. Ultimately what distinguishes substances apart is differences in logical configuration, and configuration is about pattern, abstraction and classification and therefore about mathematics and therefore about mind. And so a one substance vision when looked at more closely is capable of resolving itself into a multi-category, multi-substance vision.

There is, in fact, one very fundamental category division to be found in this one substance vision. We are patterns of mind stuff, but of an entirely different genus to God himself. We and our cosmic context seem to be in that part of the mathematical spectrum that counts as mere possibility: we are too simple as logical constructions to possess the property of Aseity. Our patterns of sentience have no necessary existence and it is this that distinguishes us sharply from the substance of Deity and Aseity. So in one sense the greater cosmos is composed of two very different substances: God, the sentience that necessarily exists, and everything else created ex-nihilo and sustained at His pleasure.

Monday, November 17, 2008

Heiddeggerian Artificial Intelligence Part 2

After reading Hubert L Dreyfus paper on Heiddeggerian Artificial Intelligence I was left with many impressions and thoughts, but amidst it all I had the feeling that he is onto something. Dreyfus is a philosopher and is thus inclined to speak in very general, abstract and impressionistic terms. Take this key comment by Dreyfus, for example:

Rather, acting is experienced as a steady flow of skillful activity in response to one's sense of the situation Part of that experience is a sense that when one's situation deviates from some optimal body-environment gestalt, one's activity takes one closer to that optimum and thereby relieves the "tension" of the deviation. One does not need to know what that optimum is in order to move towards it. One's body is simply solicited by the situation [the gradient of the situation’s reward] to lower the tension. Minimum tension is correlated with achieving an optimal grip.

I think I understand that: The goals one aims for are not literally envisaged by our minds but are implicit in that one is less aware of goals than how one is supposed to move toward them. The situations confronting us cause a response but not necessarily by way of an internalized model that allows us to envisage the goal of that response. However, if Dreyfus’ ideas are to be realized in hardware and software how does one reduce terms like “optimal body-environment gestalt”, “tension”, “soliciting” “optimal grip” to bits, bytes and “if then elses”?

From the outset I was immediately attracted to Dreyfus phenomenology: phenomenology is a philosophy founded in the realization that our experience of the world and our thoughts about it are to all intents and purposes the extent of our cosmos. This existential philosophy side steps the horrendously intractable Cartesian problem surrounding the ontological distinction (if any) of noumena and cognita by positing conscious cognition as the effective center of our cosmos. From Dreyfus phenomenology follows his starting observation:

[T] he meaningful objects ... among which we live are not a model of the world stored in our mind or brain; they are the world itself.

Dreyfus starting point makes for a huge economy in his version of AI: A complex model of the world does not need to be carried around in our heads when in fact our experience of that world, delivered to our brains by our senses, will probably serve far better: all we are asked to do is to react to that perceived model and not to exhaustively envisage it. The real world is in effect our 'core memory' and we are but the depository of the neural 'algorithm' that tells as how to react to the contents of that 'memory' as we move around our world. In particular, if the world itself is our model then we don’t have to internalize a model of how it reacts to our actions. In principle our actions could have vast and ramifying effects on the rest of the world and a comprehensive internal model of reality would have to include the logic required to model these knock on effects; the problem of trying to somehow cater for the possibility of these escalating effects is called the “frame problem”.

Dreyfus looks to be a fairly abrasive character and uses general terms that can be very slippery. It is easy to misinterpret him and anyone who tries to use Dreyfus' ideas and turn them into something workable is probably taking a similar risk to those who attempt to articulate the meaning of the Holy Trinity and open themselves up to charges of heresy. Dreyfus is a hard task master. He is AI's prophet of doom and as is the prerogative of prophets of the infinitely complex he tends to work apophatically; that is, he is much clearer about what human intelligence is not, rather than what it actually is. Perhaps this is a good thing because there has been so much hype and over optimism in AI that it cries out for a judgmental preacher. It is very difficult to do justice to the infinitely complex and the scientific equivalent of charges of blasphemy and idolatry as humans attempt to create images of our their own selves reminds us not to be too complacent about progress in the face of simplistic and unrepresentative models. Did I just say ‘model’? Aren’t they the things that Dreyfus says we shouldn’t be using?

My own guess is that human intelligence solves the frame problem in a plurality of ways. The ‘absorbed coping’ that Dreyfus talks about may well be found in intelligent organisms like ourselves; his view is that such organisms are dynamic systems coupled to their environment via stimuli which are not processed using representations and models, but these stimuli succeed in ‘soliciting’ the right responses without the use of representations and models. It is likely that humans have inherited this computationally economic modus operandi. And yet it seems to me that humans also appear to model the world computationally in the internal Cartesian sense: Humans can and do reflect on ‘external systems’ and can anticipate their behavior without coming into contact with them and being prompted by them. However, often this reflection may make use of pencil and paper jottings and various external contrivances that help prompt thinking, thus betraying the roots of human intelligence in organisms coupled dynamically to their environment. If the human mind does do symbolic modeling it may not actually be very good at it as a standalone system.

There is one other characteristic of the human mind suggesting that “Dreyfus is right but....”. In a connectionist model of the mind, everything is connected to everything else through pathways that may be no longer than ~ Log(N), where N is the number of neurons in the brain. Thus when attention is focused on one activity like say language translation, the whole of the mind’s accumulated connectionist experience is never far away in access terms and thus the whole domain of an individuals experience can be brought to bear on a problem. The mind has the potential to use the widest frame available to it and there may be no artificial frame or relevance boundary arbitarily drawn within the domain of one’s experience. In short the human mind may not even attempt to solve the frame and relevance problems and instead throws all its knowledge resources at the situations it meets. Learning never stops and the human mind is therefore always placing contexts within new contexts. Problem solving truly is an open ended activity.

Human intelligence uses three modus operandi:
1. Heiddeggerian: Human intelligence uses the world itself as its own model.
2. Modelling: Human intelligence has a mental facility to model, but that facility betrays an inheritance from 'Heiddeggerian' organisms by making frequent use of 'external' world contrivances such as pencil and paper.
3. Isotropy: Human intelligence, via connectionism, does not attempt to impose any a-priori limitations on what knowledge resources are relevant to a situation. That is, it doesn't attempt to solve the frame problem.

Wednesday, November 12, 2008

Heideggerian Artificial Intelligence

Here is a link to a paper on Artificial Intelligence sent to me by Stuart. I’m still absorbing the contents of this paper, but in the meantime here are a few lines of hot mail conversation that I had with Stuart whilst I was still reading this paper.

Timothy says:
I’m hoping to do a blog entry on it (the paper)
Stuart says:
Yes. It is an interesting paper
Timothy says:
Stuart says:
Better towards the end when he discusses Freeman(?)'s stuff

Timothy says:
I'm on that bit now
Stuart says:
Yeah. AI has been a bit of a failure. Which is why the phenomenological perspective in HCI and AI has been very important
Timothy says:
I agree. AI was even starting to look a failure as far back as the seventies. In the 60s I swallowed the message that we would have HAL machines by the end of the millennium, but then I has only 14
Stuart says:
Haha. Yes. You can be forgiven. I think Dreyfus is a bit harsh but unfortunately he's right
Timothy says:
Looks like it (Editors note: well, we shall see!)
Stuart says:
Even simple things like computer vision end up facing the solve-all-AI problem. Divide-and-conquer research strategy doesn't work. And perhaps we can argue that this is present in other disciplines
Timothy says:
Yes everything taps into a myriad associations. Similar with language translation: you can't translate everything without an enormous cultural knowledge.
Stuart says:
Well indeed

I must admit that Stuart’s comment about the divide and conquer strategy failing gave me a slight attack of the jitters: Does it mean that an incremental evolution can’t evolve intelligence in a piece meal, step by step fashion? ID here we come? In fact what of our own ability to solve problems given that we have a limited quantum of intelligence? It may well be true that certain problems are insoluble given a limited 'step size' whether that step size is limited by random walk or by human capabilities. However whether or not it is possible to solve any problems at all depends on the existence or otherwise of those “isobaric” lines of functionality conjectured to run continuously through morphospace. In the case of biological evolution those lines must be lines of self sustaining (=stable) funtionality.