Turing’s quest for the spirit
Heartbroken by the untimely death of his boyhood sweetheart, the young Alan Turing set out
to investigate the distinction between the material
mechanism of the body and the spirit or mind.
Alan Turing's beloved Christopher Morcom 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.
"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 wrote in a letter to Christopher's mother
Alan Turing’s investigations of the distinction between the 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'.
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.
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
(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) writes a new character on the tape
(iii) moves the head
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 behavior 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 ‘intentionality’ - 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 fate of Alan Turing
Richard Dawkins in The God Delusion describes how Turing was
persecuted by evangelical bigots:
"In Aghanistan under the Taliban, the official punishment for
homosexuality was execution, by the tasteful method of burial alive under a wall pushed
over on top of the victim. The 'crime' itself being a private act, performed by consenting
adults who were doing nobody else any harm, we again have here the classic hallmark of
religious absolutism.
My own country has no right to be smug. Private homosexuality was a
criminal offence in Britain up until- astonishingly - 1967. In 1954 the British
mathematician Alan Turing, a candidate along with John von Neumann for the title of father
of the computer, committed suicide after being convicted of the criminal offence of
homosexual behaviour in private.
Admittedly Turing was not buried alive under a wall pushed over by a tank.
He was offered a choice between two years in prison (you can imagine how the other
prisoners would have treated him) and a course of hormone injections which could be siid
to amount to chemical castration, and would have caused him to grow breasts. His final,
private choice was an apple that he had injected with cyanide.
As the pivotal intellect in the breaking of the German Enigma codes,
Turing arguably made a greater contribution to defeating the Nazis than Eisenhower or
Churchill. Thanks to Turing and his 'Ultra' colleagues at Bletchley Park, Allied generals
in the field were consistently, over long periods of the war, privy to detailed German
plans before the German generals had time to implement them. After the war, when Turing's
role was no longer top secret, he should have been knighted and feted as a saviour of his
nation. Instead, this gentle, stammering, eccentric genius was destroyed, for a 'crime',
committed in private, which harmed nobody. Once again, the unmistakable trademark of the
faith-based moralizer is to care passionately about what other people do (or even think)
in private."
No wonder Buddhism seemed
so attractive to this gentle, vulnerable genius.
And lest we become complacent, murderous
homophobic religious bigotry is again stalking the cities of Britain,
Christian
versus Buddhist worldviews
