Douglas Hofstsadter laments in his preface to his sequel ("I am a strange loop"; ISL, 2007) to his much more famous "Gödel Escher Bach" (GEB, 1979) that for all its fame and prizes, including the Pulitzer prize, most people he meets didn't get the point of GEB. And no wonder, as those points flit by with great rapidity amidst a welter of puns, word games, abstruse code exercises, maddening repetition, dilatory dialogs, and wayward tangents.
But here they are (apologies for my lack of expertise ... please comment on any inaccuracies):
" The possibility of constructing, in a given system, an undecideable string via Gödel's self-reference method, depends on three basic conditions:
1. That the system should be rich enough so that all desired statements about numbers, whether true or false, can be expressed in it. ...
2. That all general recursive relations should be represented by formulas in the system. ...
3. That the axioms and typographical patterns defined byitsrules be recognizable bysome terminating decision procedure. ...
Satisfaction of these three conditions guarantees that any consistent system will be incomplete, because Gödel's construction is applicable.
The fascinating thing is that any such system [human thought and language are the obvious references] digs its own hole; the system's own richness brings about its own downfall. … [analogy to critical mass in physics and bomb-making] ... But beyond the critical mass, such a lump will undergo a chain reaction, and blow up. It seems that with formal systems there is an analogous critical point. Below that point, a system is 'harmless' and does not even approach defining arithmetical truth formally; but beyond the critical point, the system suddenly attains the capacity for self-reference, and thereby dooms itself to incompleteness."
All the references to Bach and Escher in GEB are really tangential examples of self-reference. It is Kurt Gödel's work that is the core of the book, as it is of ISL. Gödel made a critique of the Principia Mathematica (PM), by Alfred Whitehead and Bertrand Russell, which attempted to build a tightly closed system of axioms and logic that was both incapable of rendering false statements, and also comprehensive in its ability to found all relevant aspects of mathematics and logic. But Gödel showed that it was incomplete, which means that it could represent paradoxical statements that could not be either true or false. It did indeed found all mathematical logic on very uncontroversial axioms, but it developed (painfully) a language for all this that was so rich that it was impossible to keep within the bounds of truth alone.
Gödel's paradigmatic statement, constructed out of unspeakably complicated machinations of the PM tools (and which Russell never accepted were proper machinations) essentially created the statement "This statement is false". But Hofstadter admits that self-referencing paradox is not the only possible type of ambiguous, unresolvable statement Gödel created or suggested- there is an infinite zoo of them.
The point is that truly intelligent systems are open. They are not cognitively or computationally bound by their programming to tread around some threshing track time, and time, and time, again. They not only are responsive parts of their environment, but more importantly have the symbolic capacity to represent imagined realities, real realities, (and the self!), in such recursive, endlessly complicated ways that no theorem-bound system of cognitive computation can account for it. In this way we are endless, multilevel, strange, loops.
But there is one aspect of all this that is most odd, which is Hofstadter's focus on the self, which is prominent in both books, and especially, even gratingly, so, in the second. Much of his conceptual play concerns self-reference, which is enjoyably loopy. Many philosophers and thinkers generally seem to think self-consciousness the very height of consciousness itself. Perhaps even its definition. As Hofstadter says, "Just as we need out eyes in order to see, we need our 'I''s in order to be!". But I don't think that is the case, at least not consciously. Self consciousness certainly comes along in the package of cognitive complexity, once one is making models of everything conceivable about the world. But to me, the core of consciousness is far more basic- the sense of being, not of self. And the core of the sense of being is made up of the flow of sensations, especially pain and pleasure.
I frequently see squirrels from my window, playing, chasing, eating, hiding, calling, etc. They are especially interested in the bird feeder and have tried no end of strategems to get into it. They are clearly highly conscious beings, driven by pleasures and pains, just as we are. They wouldn't know what to do with a mirror, but nevertheless we immediately empathize with their desires and fears, clearly communicated and experienced by themselves. Their consciousness is not infinitely expansive by way of symbolic representation, as ours is, but nor is it negligible.
Hofstadter makes a special project of declaring that mosquitos have zero consciousness, thus sanctioning his frequent bloodthirsty murders, when he is otherwise a principled vegetarian. Why be a vegetarian if you are interested only in symbolically self-referential and unbounded forms of consciousness? Obviously something else is going on, which he jokingly names "hunekers"- small sub-units of consciousness, of which he assigns various amounts to animals and humans of various grades and states.
"Mosquitos, because of the initial impoverishment and the fixed non-extensibility of their symbol systems, are doomed to soullessness (oh, all right- maybe 0.00000001 huneker's worth of consciousness- just a hair above the level of a thermostat)."But don't mosquitos experience pain and pleasure? Their behavior clearly shows avoidance of danger, and eager seeking of sustenance and reproduction. We know that the biology of animals with nervous systems (not bacteria) organizes these motivations in an internal experience of pain and pleasure. Would Hofstadter compacently sit down to a session of pulling the legs and wings off of mosquitoes he has caught? I think not, because though we certainly don't know what is going on in those very tiny heads, if anything it is the integration of perception, pain, and pleasure in ways that must earn our empathy, and which amount to a level of consciousness radically beyond that of a thermostat.
Hofstadter adds in the analogy of a human knee reflex, saying that perhaps a mosquito's mind is at that level, which no one would claim is conscious. But the integrative work being done, and the whole point of the integration, is quite different in these cases, making it seem much more likely, to me at least, that the mosquito is working with a very tiny, but intensely felt, bit of consciousness. Indeed one might posit that there need not be any particular relation between the cognitive complexity of an animal's consciousness and the degree of its feelings. We know from human infants that feelings can be monumental, and consciousness of hurt (and pleasure) be extremely acute, with precious little cognition behind them. Do we therefore empathize with them less?
This leads to the more general issue of the relation between consciousness and its physical substrate. Despite the talk of "souls", Hofstadter is a thorough naturalist, steeped in the academic field of artificial intelligence. While he has shown much greater proclivities towards philosophy than programming, the basic stance is unchanged- consciousness is a case of enormously complicated computation with (in the human case) the infinitely rich symbol sets of language and whatever is knocking around internally in our mental apparatus. All of which all could conceivably happen on a silicon substrate, or one of orchestral instruments, or other forms, as long as they have the necessary properties of internal communication, logical inference, memory, etc.
For Hofstadter, consciousness is necessarily a high-level phenomenon. It depends on, but is not best characterized by, particular neurons, and certainly is not specifically associated with quantum phenomena, microtubules, or any of the other bizarre theories of mind / soul that various pseudo-theorists have come up with to bridge the so-called mind-body divide. Indeed he spends a great deal of time (in ISL) on consoling himself that his wife, who died unexpectedly and young, lives on precisely because some part of her high-level programming continues to function inside Hofstadter, insofar as he learned to see the world through her eyes, and through other remaining reflections of her consciousness. Nothing physical remains, but if the programming still happens, then the consciousness does as well.
I have my doubts about that proposition, again drawing on my preference for characterizing consciousness in terms of experience, feeling, and emotion, not symbology. But if one has been trained by one's wife, say, to thrill to certain types of music one hadn't appreciated before, then one could make the case in those terms as well.
The question is made more interesting in a long section (in ISL) where Hofstadter discusses a thought experiment of Daniel Dennett, as written about at great length by Derek Parfit. Suppose the Star Trek transporter really worked, and could de-materialize a person and send them via a (sparkling) light stream to be re-assembled on another location, say Mars. Suppose next that an improved version of this transporter were later devised that didn't have to destroy the originating person. A copy is faithfully made on Mars, but the Earth copy remains alive. Who would be the "real" person / soul? Imagine further that the transporter could send multiple copies anywhere it chose, perhaps depositing one copy on Mars, and another on the Moon, etc... What & who then?
Parfit reportedly mulls this over for a hundred pages and agonizes that there is no way to decide which is the "real" person. Hofstadter also makes remarkably heavy weather of the question, finally hinting that a reasonable way to regard it may be as a faithful doubling, where none of the clones have any priority, all are equivalent, and each goes on to an independent existence built on the structure and history of the original person. Well of course! In programming, this is called a "fork" where a program is replicated and both copies keep running in perpetuity, doing their own thing. No need to fret over soul-division or irreducible essences- if the physical brains and bodies are faithfully reproduced in all detail, then so are the minds in all respects. Each will carry on the prior consciousness and other internal processes, differing only by the occurrence of, and interaction with, subsequent events.
And one can extend this to other substrates, supposing that some means has been devised to replicate all the activity of a human brain from neurons into, say, silicon. Just making such an assumption assumes the answer, of course. But the real question is- at what level would the modelling have to be faithful in order to generate a replicated consciousness? Do all the atoms have to be modelled? Clearly not. The model Hofstadter and I share here is that the overall activity of the brain in its electrical activity and structure-to-structure communication constitutes consciousness. So it is the neurons the need to be modelled, and that perhaps only roughly, to recreate their communication flow and data storage. Generate enough of those elements that perceive, that condense and flag significant information, that tag everything inside and out with emotional valences, that remember all sorts of languages, and world events, and experiences, at explicit and implicit levels, that coordinate countless senses and processes, and we might just have some thing that has experiences.
- And dogs- are they conscious?
- J P Morgan, et al. Their practices were not just "shady", they were criminal fraud; signing false affidavits, scamming loan customers and investors alike, corrupting appraisers, LIBOR fixing, etc.
- Should atheists take an economic position?
- And do they have better morals?
- Another way the health-related free markets don't work. Big data is fundamentally incompatible with broad-based insurance.
- Two can play that game... "Last month, the U.S. raided an Afghan convoy carrying a Pakistani Taliban militant, Latif Mehusd, who the Afghan government was using to cultivate an alliance with the Pakistani Taliban."
- The Koch folks- apparently too embarrassed to stand up for their own beliefs.
- Unwritten institutions are often the most important- the long shadow of slavery & oppression.
- Cuddly capitalism- yes, it really works.
- Our infrastructure is unsightly and unsafe as well as decrepit. And underfunded.
- Bill Mitchell on why full employment shouldn't just happen for the sake of killing people.
- Quote of the week, from Paul Krugman:
"A society committed to the notion that government is always bad will have bad government. And it doesn’t have to be that way."
- And, on rentiers and interest rates:
"But right now we’re awash in excess savings with nowhere to go, and the marginal social value of a dollar of savings is negative. So real interest rates should be negative too, if they’re supposed to reflect social payoffs."
