– Alan Turing in a letter to Mrs Morcom
Turing’s quest for the spirit
Heartbroken by the untimely death of his boyfriend Christopher Morcom, the young Alan Turing set out to investigate the distinction between the material mechanism of the body and the spirit or mind.
Christopher died in February of 1930 of bovine tuberculosis, an illness which he had contracted years earlier from tainted milk. Deeply affected by the loss, Alan became obsessed with unravelling the nature of consciousness, its structure and its origins. As his conversations with Mrs. Morcom reveal, he longed to understand what had become of Christopher, of that essential aspect of him: mind.
Alan Turing’s investigations of the distinction between the discarded mechanism of the body, and the spirit or mind which is reborn after finding a new body 'sooner or later' (within forty-nine days, according to traditional Buddhist belief) led him to formulate a simple, logically complete and philosophically coherent definition of ‘mechanism’.
That simple archetypal ‘mechanism’, which can completely simulate the behavior of all other mechanisms and physical systems - including all computers, no matter how complicated - is known as the Turing Machine.
Because of its simplicity, the Turing Machine demonstrates the fundamental capabilities and limitations of all physical systems in a clearly recognisable form. Turing's machine enables philosophers to develop a clear demarcation between 'mechanism' and 'spirit'.
|"If the mind is not the brain..."|
Significance of the Turing Machine for Buddhism
The most significant intellectual challenge to Buddhism in the modern world is ‘Materialism’: the belief that the mind is nothing but a product of matter, so that when the mechanism of the body ceases to exist, so does the mind. There are of course other challenges to Buddhism in the modern world, such as evangelical Christianity and jihadism, but they can hardly be classed as intellectual!
Buddhism is founded upon the Four Seals of Dharma, four philosophical statements of which the fourth states that the mind is non-physical and can transcend biological existence. Obviously materialism contradicts this foundation of Buddhist belief.
As described elsewhere, it is surprisingly difficult to get a definition of materialism based on the concept of matter, because it is difficult to get a coherent definition of matter as a ‘thing in itself’, totally disentangled from the mind of the observer. For this reason, the philosophical view formerly known as ‘Materialism’, or ‘Physicalism’ (or even more archaically as ‘Naturalism’) is nowadays expressed as the Computational Theory of Mind, otherwise known as ‘Computationalism’.
The Computational Theory of Mind grew up in the 1950’s, when computers were being hyped as ‘Electronic Brains’ and their potentials were seen as limitless, including the ability to simulate all human mental processes. However, the computational theory was soon found to have at least two serious limitations:
(1) The limitation of Aboutness
The computational theory of mind could not account for ‘aboutness’ (technically known as ‘intentionality’). A computer operates on character strings, whose meaning is inaccessible to a machine.
|The number 11|
For example, a computer carries no internal reference to what the character string ‘elf’ is about. It could refer to the number eleven in German, or one of Santa’s helpers in English, but the computer neither knows nor cares, and has no mechanism for knowing or caring.
Readers familiar with high level programming languages such as FORTRAN or BASIC may protest that the variable names used in their program statements do have meaning. This is true only in so far as they have meaning for the programmer, but they have no meaning for the machine. For example, the statements used to describe the requirements for carpet laying and the theatrical success of a musical comedy about Hitler seem to have very different meanings...
(i) IF RoomLength * RoomWidth > CarpetArea THEN NeedMoreCarpet = TRUE
(ii) IF Audience * TicketPrice > HireOfVenue THEN AvoidedBankruptcy = TRUE
But both statements have all their meaning stripped out during compilation into the binary strings that can be used by computers, and end up as exactly the same logical and arithmetic operations on the same anonymous memory locations. This is the fundamental difference between a mind actively cognising and a machine passively representing an object.
(2) The limitation of Qualitative Experience.
Computers can only process logical, structural and numeric quantities. They can neither experience nor react to internal qualitative mental states such as pleasure or pain, nor experience the redness of red or the smell of flowers (though they can record the wavelength of light and molecular structures of scents)
The reasons why these limitations are fundamental, and indeed fatal, to computationalism (and hence materialism) becomes apparent once we examine the structure of the Turing machine in the light of Buddhist philosophical theory and meditational practice, but first we need to understand the working of the Turing machine in greater detail. Fortunately there are only four components:
So what is a Turing Machine?
A Turing Machine is not primarily a physical device (although physical demonstrations have been constructed) . Its primary purpose is as a thought-experiment, or a precisely defined simple mathematical object, whose precision and simplicity produce a rigorous definition of the fundamental behavior of all mechanical devices and physical systems.
A Turing machine consists of just two main components:
(i) A tape of characters, which may be limited to just 1’s and 0’s.
(ii) A table of actions, which instructs the machine what to do with each character.
There are also two minor components:
(iii) A read/write head, which simply transfers symbols from the tape to the table and vice versa,
(iv) A register that holds the numeric identifier for the machine’s current state.
The tape consists of a string of characters. These are sometimes imprecisely described as 'symbols', but this is rather confusing in that symbols often make reference to something beyond themselves (they exhibit 'derived intentionality' or evoke a qualitative state of mind.) It is important to remember that the characters on the tape, like the string ‘elf’, carry no intrinsic meaning.
The precise definition of the marks on the tape is that they are characters drawn from a defined alphabet, where the term ‘alphabet’ is used in a rather technical sense of a restricted set of characters, such as the 26 characters of the Latin alphabet, the 33 characters of Russian alphabet, the four characters of the DNA alphabet, or the two characters of the binary alphabet. The size of the alphabet makes no difference to the capabilities of the Turing Machine, since all characters are capable of being encoded as binary.
The table consists of five columns, with as many rows of instructions as are needed to do the job. The columns are:
1 The row's machine state identifier to be tested against the actual machine state.
2 The row's character to be tested against the current character as read from the tape.
3 The identifier of the new state to which the machine will change
4 The new character to be written to the tape.
5 An instruction to move the head one character right or left along the tape.
The machine works by going down the table checking each row until it finds a row where the state identifier corresponds to the machine’s current state as held in the register, and the character corresponds to the character under the head.
In accordance with the three remaining columns in that row, the machine then:
(i) changes the state of the register
(ii) moves the head
(iii) writes a new character on the tape
It then restarts the checking procedure from the top of the table.
- Computer equivalence of the Turing Machine
So it’s apparent why the Turing Machine isn’t a practical proposition for doing any useful tasks: the number of rows in the action table would become huge. Real computers condense the action table into a small set of instructions or ‘opcodes’. Nevertheless, the simple architecture of the Turing Machine can be mathematically proved to be completely functionally equivalent to any real-world computer.
Computer geeks will have spotted that the tape corresponds to the memory of a computer and the table to its program. The correspondence between tape and memory is direct and one-to-one, but the correspondence between the action table and a practical computer program is less direct and requires a different kind of architecture to keep the table in a manageable form.
- Physical equivalence of the Turing Machine
Not only can the Turing machine simulate any other kind of computer, it can simulate and predict the behaviour of any physical system, including any other type of machine.
The tape corresponds to datastructures (including two and three dimensional structures which can be represented by the linear memory array of any computer.)
The table corresponds to causal relationships, including formulae for physical and chemical laws.
So Alan Turing had well and truly defined ‘mechanism’, including biophysical mechanisms such as the body. We now turn our attention to the ‘spirit’ or mind.
- Mind equivalence of the Turing Machine?
- - Inability of the Turing machine to emulate mental designation
Buddhist philosophy states that the phenomena we experience depend upon three modes of ‘existential dependence’:
Causes - which correspond to the table
Structure - which corresponds to the tape
Mental designation or ‘aboutness’ - for which there is no equivalent structure in the Turing Machine! As mentioned earlier, the tape consists only of character strings, which in themselves are not ‘about’ anything.
Since mental designation is a fundamental and axiomatic aspect of reality, and cannot be reduced to either structure or causality, it follows that there are aspects of our experience of phenomena that are non-mechanistic and non-physical.
- - Inability of the Turing Machine to hold and manipulate qualitative states.
The Buddhist practice of Lamrim meditation uses procedural mental operations to generate qualitative states of mind. These qualitative mental feelings are known as 'qualia'. They are internal subjective mental states which are produced by guided thought procedures. However, the Turing machine does not possess any structure that could hold or experience such states, nor could any combination of instructions within the table generate such states even if there were something that could hold them.
The inability of the Turing machine to hold internal qualitative mental states is obvious. The only internal state it can have is the number in its register. Even if additional registers were added, they could only contain ‘alphabetic’ characters or state numbers, for there is nothing else in the machine and nothing else can get into the machine.
The inability to formulate any mechanical procedure to generate qualia was first described by the eminent Victorian physicist John Tyndall over 140 years ago:
"the passage from the physics of the brain to the corresponding facts of consciousness is unthinkable. Granted that a definite thought, and a definite molecular action in the brain occur simultaneously; we do not possess the intellectual organ, nor apparently any rudiment of the organ, which would enable us to pass, by a process of reasoning, from the one to the other. They appear together, but we do not know why. Were our minds and senses so expanded, strengthened, and illuminated, as to enable us to see and feel the very molecules of the brain; were we capable of following all their motions, all their groupings, all their electric discharges, if such there be; and were we intimately acquainted with the corresponding states of thought and feeling, we should be as far as ever from the solution of the problem, "How are these physical processes connected with the facts of consciousness?" The chasm between the two classes of phenomena would still remain intellectually impassable. Let the consciousness of love, for example, be associated with a right-handed spiral motion of the molecules of the brain, and the consciousness of hate with a left-handed spiral motion. We should then know, when we love, that the motion is in one direction, and, when we hate, that the motion is in the other; but the "Why?" would remain as unanswerable as before."
What Tyndall is basically saying, behind the rather flowery Victorian language, is an early recognition of the Hard Problem: that there is no logically describable physical mechanism that can get from quantitative physical inputs to qualitative experience.
So in following the Lamrim meditations, the mind is doing something that no machine could ever do.
The behavior of all machines, computers and physical systems is reducible without remainder to the operations of a Turing machine.
The behavior of the mind shows at least two functions - aboutness and qualitative experience - that cannot in principle be reduced to the operations of a Turing machine.
Therefore, there are some aspects of the mind that are non-mechanistic and non-physical.
- Sean Robsville
Refuting the computer theory of mind - and why it matters to Buddhists
Buddhism and Science
The Church-Turing-Deutsch Principle and Buddhist Philosophy
Buddhism and Mathematics
The Mind in Kadampa Buddhism
How things exist - according to Buddhism and Science
Intentionality ('Aboutness') and Mental Designation
Evolution, Emptiness and Delusions of the Darwinian Mind