Sunday, 5 February 2012

The Church-Turing-Deutsch Principle and Buddhist Philosophy.

Alan Turing

The Church Turing Deutsch (CTD) principle states that a universal computing device can simulate every physical process.    

The principle appears to work fine when applied to purely physical systems, but it runs into some interesting problems when we try to extend it to simulating the mind.     If we assume that the CTD principle is universally applicable, then evidence suggests that aspects of the mind may lie outside the scope of physics.  

The Church Turing Deutsch principle is a wider and more general restatement of the 'Unreasonable Effectiveness' of mathematics in science and engineering.

Alonzo Church

The Church-Turing-Deutsch Thesis
To quote Michael Nielson 

'The Church-Turing-Deutsch (CTD)  Principle is a descendant of a famous idea known as the Church-Turing Thesis, taught to all computer scientists early in their degrees. I’ll talk later about the relationship between the Thesis and the Principle.

Just stating the CTD Principle makes it look deceptively obvious: Every physical process can be simulated by a universal computing device.
Most educated adults in the West today believe this Principle, whether they realize it or not.

We do not blink an eye to be told that a computer is being used to simulate a new aircraft, the explosion of a bomb, or even the creation of the Universe. The fact is, most people take it for granted that your standard desktop computer, given enough time and memory, can simulate pretty much any physical process.

Yet our ease with the CTD Principle is an ease brought by familiarity. One hundred years ago the statement would have been far more surprising, and, I suggest, even shocking to many people.

Viewed from the right angle, the CTD Principle still is shocking. All we have to do is look at it anew. How odd that there is a single physical system – albeit, an idealized system, with unbounded memory – which can be used to simulate any other system in the Universe... 

David Deutsch

Does the Church-Turing-Deutsch Principle apply to mind?
However, when we attempt to apply the CTD principle to the mind and mental processes (as some materialist philosophers have tried in the past) , we quickly come across a variety of limitations that lead us to question whether the mind is a physical entity at all.  

Of course Turing never intended his thesis to be an explanation of the mind,  and there is speculation that his friend Morcom’s death influenced Turing’s work on artificial intelligence, as he analysed the relationship between the material and the spiritual. 

Christopher Morcom

Limitations of Computer simulations
In order to compare the Church-Turing thesis with the Buddhist philosophical teachings of the three modes of existential dependence (Causal Relationships, Structural Relationships and Mental Designation), we first need to be more explicit about what we mean by a computer simulation.

A computer simulation consists of an algorithm or set of algorithms working on datastructures.  Translating to  Buddhist terminology, the algorithms correspond to causal relationships, and the datastructures correspond to physical structures ('mereology').

The third aspect of reality - mental designation or 'intentionality' - lies outside the scope of the Church-Turing-Deutsch principle, so the limitations of the CTD may tell us something about the mind.

Nonalgorithmic Phenomena
Computer simulations are, by their very nature, incapable of dealing with nonalgorithmic phenomena.

The great difficulty in talking about nonalgorithmic phenomena is that although we can say in general terms what they do, it is impossible by their very nature to describe how they do it. (If we could describe in a stepwise manner what was going on, then a phenomenon would be algorithmic!).

A typical example of a nonalgorithmic activity is assigning meaning to any object. For example, when is a chariot a heap of firewood? Or when is a car a pile of parts? (as discussed under sunyata). Many processes involving semantics, as distinct from syntax, appear to be non-algorithmic.

Other apparently nonalgorithmic phenomena are:

Qualia (singular 'quale') are internal, subjective, qualitative states such as the redness of red, aesthetic experiences of beauty and revulsion, pain, happiness, boredom, depression, elation, motivation, intention, the experience of understanding something for the first time, etc. Such states are subjective and private and are distinct from (though causally related to) physical and neural activities. Whether the causal relationship is one-way or two-way is open to debate.     The subject of qualia is closely linked to aesthetics.

- Freewill
Freewill is the ability to make conscious choices between options, which thus implies taking responsibility for one's actions. The assumption that sane citizens possess freewill is the basis for the rule of law in all civilised countries.

The Hard Problem
-The Hard Problem
It is hard to see how the mere enaction of a computation should give rise to an inner subjective life. 

'The 'Hard Problem' of consciousness is the problem of explaining how and why we have qualitative phenomenal experiences. David Chalmers contrasts this with the "easy problems" of explaining the ability to discriminate, integrate information, report mental states, focus attention, etc. Easy problems are easy because all that is required for their solution is to specify a mechanism that can perform the function. That is, their proposed solutions, regardless of how complex or poorly understood they may be, can be entirely consistent with the modern materialistic conception of natural phenomena. Chalmers claims that the problem of experience is distinct from this set, and he argues that the problem of experience will "persist even when the performance of all the relevant functions is explained".

The existence of a "hard problem" is controversial and has been disputed by some philosophers. Providing an answer to this question could lie in understanding the roles that physical processes play in creating consciousness and the extent to which these processes create our subjective qualities of experience.

Several questions about consciousness must be resolved in order to acquire a full understanding of it. These questions include, but are not limited to, whether being conscious could be wholly described in physical terms, such as the aggregation of neural processes in the brain. It follows that if consciousness cannot be explained exclusively by physical events in the brain, it must transcend the capabilities of physical systems and require an explanation of nonphysical means. For philosophers who assert that consciousness is nonphysical in nature, there remains a question about what outside of physical theory is required to explain consciousness.  - Wiki 


- Neuroplasticity and downward causation.
Neuroplasticity is essentially the reverse of the Hard Problem. In fact, it turns upside down the assumptions inherent in the previous statement: ‘this question could lie in understanding the roles that physical processes play in creating consciousness and the extent to which these processes create our subjective qualities of experience.‘  
Neuroplasticity seems to show that subjective qualitative awareness such as experienced during Buddhist meditation can actually produce ‘mind-over-matter’ effects on the structure of the brain.   Since the qualia of inner peace, universal compassion, and tranquillity have no known algorithms, it seems impossible to produce a computer model of this process, which has physical results, but no physical causes.

This form of causation, distinctive from physics, where mental/conscious agency exerts "downward" causal influence on brain plasticity and the various levels of brain functioning, has been studied by teams of neuroscientists and Buddhist meditators:

How thinking can change the brain
'The Dalai Lama, who had watched a brain operation during a visit to an American medical school over a decade earlier, asked the surgeons a startling question: Can the mind shape brain matter?

Over the years, he said, neuroscientists had explained to him that mental experiences reflect chemical and electrical changes in the brain. When electrical impulses zip through our visual cortex, for instance, we see; when neurochemicals course through the limbic system we feel.

But something had always bothered him about this explanation, the Dalai Lama said. Could it work the other way around? That is, in addition to the brain giving rise to thoughts and hopes and beliefs and emotions that add up to this thing we call the mind, maybe the mind also acts back on the brain to cause physical changes in the very matter that created it. If so, then pure thought would change the brain's activity, its circuits or even its structure.

One brain surgeon hardly paused. Physical states give rise to mental states, he asserted; 'downward' causation from the mental to the physical is not possible. The Dalai Lama let the matter drop. This wasn't the first time a man of science had dismissed the possibility that the mind can change the brain. But 'I thought then and still think that there is yet no scientific basis for such a categorical claim,' he later explained. 'I am interested in the extent to which the mind itself, and specific subtle thoughts, may have an influence upon the brain.'

The Dalai Lama had put his finger on an emerging revolution in brain research. In the last decade of the 20th century, neuroscientists overthrew the dogma that the adult brain can't change. To the contrary, its structure and activity can morph in response to experience, an ability called neuroplasticity. The discovery has led to promising new treatments for children with dyslexia and for stroke patients, among others.

But the brain changes that were discovered in the first rounds of the neuroplasticity revolution reflected input from the outside world. For instance, certain synthesized speech can alter the auditory cortex of dyslexic kids in a way that lets their brains hear previously garbled syllables; intensely practiced movements can alter the motor cortex of stroke patients and allow them to move once paralyzed arms or legs.

The kind of change the Dalai Lama asked about was different. It would come from inside. Something as intangible and insubstantial as a thought would rewire the brain. To the mandarins of neuroscience, the very idea seemed as likely as the wings of a butterfly leaving a dent on an armored tank…’ 

Buddhists build a better brain
'Participating in an eight-week mindfulness meditation program appears to make measurable changes in brain regions associated with memory, sense of self, empathy, and stress. In a study that will appear in the Jan. 30 issue of Psychiatry Research: Neuroimaging, a team led by Harvard-affiliated researchers at Massachusetts General Hospital (MGH) reported the results of their study, the first to document meditation-produced changes over time in the brain’s gray matter.

Although the practice of meditation is associated with a sense of peacefulness and physical relaxation, practitioners have long claimed that meditation also provides cognitive and psychological benefits that persist throughout the day,” says study senior author Sara Lazar of the MGH Psychiatric Neuroimaging Research Program and a Harvard Medical School instructor in psychology. “This study demonstrates that changes in brain structure may underlie some of these reported improvements and that people are not just feeling better because they are spending time relaxing.”

Previous studies from Lazar’s group and others found structural differences between the brains of experienced meditation practitioners and individuals with no history of meditation, observing thickening of the cerebral cortex in areas associated with attention and emotional integration. But those investigations could not document that those differences were actually produced by meditation.

For the current study, magnetic resonance (MR) images were taken of the brain structure of 16 study participants two weeks before and after they took part in the eight-week Mindfulness-Based Stress Reduction (MBSR) Program at the University of Massachusetts Center for Mindfulness. In addition to weekly meetings that included practice of mindfulness meditation — which focuses on nonjudgmental awareness of sensations, feelings, and state of mind — participants received audio recordings for guided meditation practice and were asked to keep track of how much time they practiced each day. A set of MR brain images was also taken of a control group of nonmeditators over a similar time interval.

Meditation group participants reported spending an average of 27 minutes each day practicing mindfulness exercises, and their responses to a mindfulness questionnaire indicated significant improvements compared with pre-participation responses. The analysis of MR images, which focused on areas where meditation-associated differences were seen in earlier studies, found increased gray-matter density in the hippocampus, known to be important for learning and memory, and in structures associated with self-awareness, compassion, and introspection.

Participant-reported reductions in stress also were correlated with decreased gray-matter density in the amygdala, which is known to play an important role in anxiety and stress. Although no change was seen in a self-awareness-associated structure called the insula, which had been identified in earlier studies, the authors suggest that longer-term meditation practice might be needed to produce changes in that area. None of these changes were seen in the control group, indicating that they had not resulted merely from the passage of time.

“It is fascinating to see the brain’s plasticity and that, by practicing meditation, we can play an active role in changing the brain and can increase our well-being and quality of life,” says Britta Hölzel, first author of the paper and a research fellow at MGH and Giessen University in Germany. “Other studies in different patient populations have shown that meditation can make significant improvements in a variety of symptoms, and we are now investigating the underlying mechanisms in the brain that facilitate this change.”

Mind and Meaning - Algorithms are not self-interpreting.
Something else, other than the ability to deal with non-algorithmic phenomena, is missing from attempts to apply the Church-Turing-Deutsch model to the mind.  All meaning is stripped out of an algorithm before it can be processed by a machine, an operation known as compilation.  For example, the following two statements reduce to exactly the same algorithm within the memory of a computer

(i) IF RoomLength * RoomWidth > CarpetArea THEN NeedMoreCarpet = TRUE

(ii) IF Audience * TicketPrice > HireOfVenue THEN AvoidedBankruptcy = TRUE

both, when compiled, will appear to the machine as an anonymous executable form such as
IF a*b > c THEN d=1

The algorithmic models for carpet laying and theatrical success are said to be 'isomorphic' - they both have the same form, though they are 'about' very different phenomena.   This 'aboutness' is called 'intentionality' by philosophers, and is something that minds can process and machines can't.

The computer will perform the same internal operations whether its consequences are a visit to the carpet store, or an embarrassing surplus in Max Bialystock’s bank account.

Audience * TicketPrice > HireOfVenue


John Searle's critique of Computationalism
This critique of the possibility of machine intelligence has been further developed by John Searle in the famous Chinese Room Argument, which claims to demonstrate that a computer cannot understand what it is doing or why.

So procedure and structure, no matter how programmed, or as implemented on any sort of physical machine, are inadequate to describe the capabilities of human mental processes. (See computationalism).

This limitation will not be solved by hardware improvements. No matter how many terabytes, gigaflops, neural nets or iterations of Moore's law we throw at the problem of producing artificial intelligence, the difficulties will remain insurmountable as long as the hardware is only capable of dealing with truth values which can be treated as binary or numeric, and as long as compilers strip out all meaning from the source code in order to produce machine code.

But what other computer architecture is there?.   Every computer is equivalent to a Turing machine, which is itself a state-transition table coupled to a tape of symbols, neither of which are capable of holding intrinsic meaning.

For a discussion of why the mind is a non-physical, fundamental aspect of the universe which is not derived from anything else, see Confronting Materialism and the Delusion of the Mechanical Mind.

Towards a definition of non-physical mind.
So we are beginning to see a definition of Mind emerging  from the limitations of the Church Turing Thesis.  The Mind is that which gives meaning and is ultimately formless and non-algorithmic.

Minds can perform algorithmic operations such as mental arithmetic (though remarkably poorly compared with machines), and are capable of perceiving structure, yet when both algorithms and structures are factored out of mental processes, there remains a non-algorithmic residuum, which is a clear formless awareness.   

This foundational ‘formless’ mind is without form itself, either as datastructures,  or as algorithmic operations expressed as structures such as state transition tables and flowcharts.

Nevertheless, the mind can grasp, comprehend and give meaning to such external structures, and also to structures of its own imaginative creation.

The mental faculty that creates algorithms in the mind of the scientist, analyst or programmer ('The Mother of all Algorithms') is probably itself partly ‘intuitive’ and  nonalgorithmic.


Was Alan Turing a Buddhist?
Despite his Anglican background, it's unlikely that Turing was a Christian, or would have been accepted by any church. He was persecuted mercilessly by Christians because he was gay, (there were no Muslims around in Britain at that time, or at least not enough to cause a problem)

The fact that he ranked along Churchill and Eisenhower as one of the people who had done most to defeat Hitler counted for nothing among the religious establishment, who wanted him either dead or castrated.     In 1954 they got what they wanted.

However, Alan Turing did seem to have sympathies with Buddhism.    In his biography of Turing,   Andrew Hodges refers to a letter he wrote to the mother of his deceased boyfriend:

'He fell in unrequited love with Christopher Morcom, a very talented youth in the school sixth form, and his longing for friendship brought him to communicate. A brief flowering of scientific collaboration perished when Morcom suddenly died in February 1930. Turing's correspondence with the dead boy's mother gives insight into the development of his ideas in the aftermath. He was concerned to believe the dead boy could still exist in spirit, and to reconcile such a belief with science. To this end he wrote for Mrs Morcom an essay, probably in 1932. It is the private writing of a twenty-year-old, and must be read as testament to background and not as a thesis upheld in public; nevertheless it is a key to Turing's future development.

'It used to be supposed in Science that if everything was known about the Universe at any particular moment then we can predict what it will be through all the future... More modern science however has come to the conclusion that when we are dealing with atoms and electrons we are quite unable to know the exact state of them; our instruments being made of atoms and electrons themselves. The conception then of being able to know the exact state of the universe then must really break down on the small scale. This means that the theory which held that as eclipses etc. are predestined so were all our actions breaks down too. We have a will which is able to determine the action of the atoms probably in a small portion of the brain, or possibly all over it. The rest of the body acts so as to amplify this...

In stating the classic paradox of physical determinism and freewill, Turing is influenced by Eddington's assertion that quantum mechanical physics ('more modern science') yields room for human will. Eddington asked how could 'this collection of ordinary atoms be a thinking machine?' and Turing tries to find some answer. His essay goes on to espouse belief in a spirit unconstrained by the body: 'when the body dies the 'mechanism' of the body, holding the spirit is gone and the spirit finds a new body sooner or later perhaps immediately.' 

- Sean Robsville




Anonymous said...

'when the body dies the 'mechanism' of the body, holding the spirit is gone and the spirit finds a new body sooner or later perhaps immediately.'

Alan Turing spoke these words when he was grieving for his lost boyfriend.

nonzero said...

1.) Non-computability: In formalizing the Church-Turing thesis, Turing did, echoing Godel, show that there are processes that are not computable without appeals to an oracle machine, and that oracle machine would be constrained by its own limitations, needing a 2nd order oracle machine, ad infinitum. This hypercomputation or super-turing computation is metamathematics, and really has no bearing on what is actually computable in the physical world unless you take the universe (or a subset of the universe centered on the phenomena being analyzed) to require infinite continuous precision analogous to the transfinite infinities of the real number line and higher infinities. Qualia and free-will are not non-algorithmic unless the brain relies on non-algorithmic physical processes, at least in part, which is a hypothesis Roger Penrose has proposed, but almost no one, not physicists, mathematicians, cognitive scientists, or neuroscientists, have been convinced of, and there are many arguments against Penrose's hypothesis that most scientists agree put Penrose on very shaky ground. Even if there are quantum mechanical effects taking place in the brain, that is just an exponential speedup of algorithms which can be simulated on classical computers (though may take longer than lifetime of universe to compute) and so, in that case, we'd need quantum computation to simulate efficiently in time. Thus far, there are no known uncomputable functions of the physical universe.

2.) Downward causation: Many reductionists don't like to talk about emergence or downward causation, I don't know why, but there are complex systems that can be usefully described as performing downward causation, it is just not of the ontological emergentist variety, but epistemological. It may be more useful to drop 'downward' or 'upward' and just view the system as a network without the baggage of directionality of causation. In this sense, the neuroplasticity of the brain is not some non-materialistic 'mind' influencing the matter of the brain, it is parts of the brain's network influencing other parts of the network, which cause the network to change on the whole. When you meditate, you purposefully inhibit the default mode network (among other things), and continual practice causes the default mode network to rewire and be less active , like flexing a muscle against a stressor, the body reacts and changes.

3.) John Searls's critique is of symbolic AI approaches ever being able to exhibit consciousness like humans (and other animals). He is still a materialist, but he thinks there is something special about biology that cannot be recreated using digital computers, but is ambiguous as to why. Again, most scientists agree with the simple critique against symbol manipulation programs being conscious, but simulating neural systems to enough of a degree on digital computers might very well create a conscious entity on par with humans (and animals).

nonzero said...

4.) The Hard Problem, ie qualia, is still not explainable in mechanistic terms, they are emergent internal subjective experiences of materialistic processes, and so qualia really is a very hard problem for scientists, unless, as recent prominent scientists like Christof Koch and others have admitted, panpsychism or some form of property dualism must be assumed. In this case, qualia is baked in to the universe on a fundamental level and subjective experience evolves as the material that embodies it evolves. This is much more parsimonious, and in my opinion, more wonderful and beautiful, than positing supernatural causes or unnecessary uncomputable phenomena occurring only in brains but no where else. I also think this view is very close to a Buddhist view of the cosmos.

5.) Meaning: Two computer programs that have different variable names and are interpreted by human users to mean different things may well decompose to the exact same binary code. How does meaning arise out of bits that don't carry meaning implicitly? Meaning is, again, evolved. If our universe, from big bang to my typing this comment is viewed as a computer program, you can view it all as bits from the outside without meaning, but from the inside, the meaning resides in the conscious edge of our evolved universe, I'm referring to us humans, we can't see the matrix as jumbles of code, our hardware that does the thinking comes preloaded with evolved meaning-making processes.

Sorry for the long comments, wanted to dump my thoughts quickly. Cheers!

nonzero said...


seanrobsville said...

@ nonzero
An alternative quantum mind/brain mechanism to Roger Penrose's microtubule theory is the 'Quantum Zeno effect' proposed by Henry Stapp: