| An algorithm is a sequential step-by-step procedure
involving calculations, comparisons and logical operations. It may involve branching
and selective execution of steps depending on the results of comparisons. All algorithms have associated datastructures, though these may be implicit
rather than explicitly declared. For example, even the simplest functions, such as
square root, have an implicit associated datastructure consisting of the paired dependent
and independent variables. In contrast, not all datastructures have associated procedures.
An algorithm's functionality must be definable in terms of mathematical or logical
operations, sequential and conditional execution of steps, and operations on
datastructures. All systems subject to the laws of physics can be simulated by algorithms.
Hence any system which cannot in principle be simulated by an algorithm must have a
non-physical component.
The ability to demonstrate any non-algorithmic function of the mind
would be evidence that some of the mind's activities have a non-physical basis. For more
detailed analyses, see:
Artificial Intelligence:
....'Algorithms do not contain within themselves any meaning. 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
Such considerations have led critics of computationalism to claim that algorithms can only
contain syntax, not semantics [SEARLE 1997]. Hence computers can never understand their
subject matter. All assignments of meaning to their inputs, internal states and outputs
have to be defined from outside the system.'...
'The unreasonable effectiveness
of mathematics in science and engineering
So we are left with something of a mystery. According to the physicalist worldview, the
mind (including mathematicians' minds) is an epiphenomenon of matter which has evolved
solely to ensure the survival of the selfish genes which code for it. Why should this
'top-level' phenomenon have such intimate access to the 'bottom level' phenomena such as
quantum physics? After all, the two levels are supposedly separated by less
well-understood (in some cases) explanatory layers such as evolutionary psychology,
neurology, cell biology, genetics, molecular biology, and chemistry.'
Generation of numbers by bootstrapping out of
the empty set
....'Numbers have causes - the algorithms that perform the operations on the
sets. Numbers have parts and aspects. The number 1 is defined as the set which contains
the empty set and so on. But in the final analysis the entire number system has been
generated by the play of mind on emptiness, in the complete absence of the need to refer
to any material thing, or things, which are being counted.'...
Materialism (Physicalism)
...'It is fairly obvious how Kadampa philosophy maps onto
physicalism. It agrees that things-in-themselves are unfindable and can only be
known by interdependence with other things. It agrees that the first of these ways of
interdependence is algorithmic - IF ... THEN... ELSE - cause and effect. It agrees that
the second way of interdependence is by analysis into structured information. However
it goes further by pointing out that physicalism is an inadequate explanation for
all phenomena. A third mode of interdependence - dependence on the mind
- is necessary to explain the phenomena of awareness.'...
Non-algorithmic phenomena
...'The great difficulty in talking about non-algorithmic 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
the phenomenon would be algorithmic).'..
Sunyata
...'Nagasena said this was because the chariot had no power to define itself from
its own side. Nor was there any ideal chariot form 'in the sky' which engaged and
disengaged with the timber at definite stages of assembly and disassembly. Milinda's mind
was the only thing that could make the distinction between vehicle and firewood. And there
were no logical rules, stepwise procedures or decision trees for Milinda to decide when to
cease imputing one thing and impute another.'...
Algorithms and datastructures of the mind
visualized in meditation
...'You'll become aware of the datastructures in your mind - the associations
or 'hyperlinks' which link all mental objects together. Then you'll become aware of
the algorithm - the automatic process which like a webcrawler follows all these
associations and presents them to your awareness. You don't (at present) control this
webcrawler. You will notice that the webcrawler has certain preferred types of links,
those that lead to objects of anger, fear or desire. It doesn't pay too much attention to
bland associations, and there's no family filter on what it dredges up. You have now begun
to understand the algorithms and datastructures of the mind/brain. What you still need to
experience is pure mind - the actual awareness which is viewing all the trivia which the
webcrawler is displaying to it....'
Qualitative subjective experience
...'The Buddhist does not doubt that the brain does some very sophisticated ordering of
its incoming nerve impulses into the datastructures which are the objects of knowledge.
But when all is said and done, those datastructures remain as objects. They are not
themselves knowledge, neither are they that which performs the function of knowing.'...
Sentient Beings
...'There is a Western school of philosophy known as dualism which claims that only humans
experience qualitative mental states, and animals are automata with no subjective
experiences, so it doesn't matter what you do to them. This view originates from the old
Christian dogma that humans are qualitatively different from all other animals
(because only humans have immortal souls). Dualism is not only contrary to Buddhist
teachings, but also to the modern scientific understanding of evolution.'...
- Sean Robsville
RATIONAL
BUDDHISM
If we regard Buddhism as a combination of a philosophy, psychology and religion, then how
much mileage can we get from the first two aspects before we have to start invoking
religious faith?
Christian
versus Buddhist worldviews |
