Buddhism, mind, mathematics
'...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...'
Artificial Intelligence (AI)
'...Computationalism or philosophical AI, (sometimes also known as Strong AI), which is the view that all human mental activities are reducible to algorithms, and could therefore be implemented on a computer...'
'...The internal states, inputs and outputs of an automaton have no inherent meaning. Any meaning (semantics) must be assigned from outside the system...'
'It has often been remarked by physicists and chemists that the universe is very sensitively tuned to allow life to exist. If certain physical and chemical constants were just a fraction out from their observed values, life could never have arisen.'
'One interesting aspect of emergent phenomena is the different causal and organisational relationships which appear at different levels of investigation. For example, ecology emerges out of biology, which emerges out of chemistry, which emerges out of physics, which emerges out of mathematics, which emerges out of the mind contemplating the empty set. Each level of investigation has its own explanatory relationships, yet if we check carefully there is no 'added extra' coming from the side of the objects. (Everything is algorithmically compressible without remainder, there are no mysterious ingredients added as we progress from lower levels to higher levels).'
Empty set - the origins of number
'...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. Numbers are therefore fundamentally devoid of inherent 'Platonic' existence..'
'The description of the root mind as 'formless' doesn't just refer to its non-material nature, but it emphasises that it is unlimited, non-mechanistic and totally free from any structure or topology. . In Buddhist psychology the root mind is non-physical and non-algorithmic. The mind cannot be understood in terms of circuit diagrams and flowcharts. It is pure awareness.'
'...The version of materialism prevalent nowadays is more accurately known as physicalism. Physicalism has grown out of advances during the second half of the twentieth century in the fields of genetics, evolution and computer technology. Modern physicalism takes as its subject matter DNA codes, computer instruction sets and datastructures, rather than the bouncing billiard balls of the nineteenth and early twentieth century materialists..'
Mathematics - Its unreasonable effectiveness 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.
Metaphysics and metamathematics
'Metaphysics means, literally, 'beyond physics'. Metaphysics deals with phenomena which are either more basic than physics, or beyond the reach of physical methods of analysis and understanding.'
'The great difficulty in talking about non-algorithmic phenomena is that although we can say what it is in general terms that 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 we could write a computer program
to perform the task).'
Basically, what quantum theory says is that fundamental particles are empty of inherent existence and exist in an undefined state of potentialities. They have no existence 'from their own side' and do not become 'real' until a mind interacts with them and gives them meaning.
'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.'
Spooky action at a distance (EPR Paradox)
'One of the most vivid illustrations of the interactions of the mind of the observer with a quantum system is given by EPR - the 'Einstein Podolsky Rosen Paradox', or 'Spooky action at a distance' as it is sometimes known. The experimental evidence seems to show that the observer's mind goes to its object unobstructedly and instantaneously.'
- Sean Robsville
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?