For instance, despite what some neuroscientists may claim, and some gullible philosophers may believe, there is no complete mechanistic, algorithmic chain of causation from hitting your thumb with a hammer, to feeling the sensation of pain. The last step in the process is non-algorithmic and is not explainable without invoking the mind as fundamental, irreducible aspect of reality.
Another 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. In fact, the entire phenomenon of intentionality ('aboutness') does not seem amenable to an algorithmic explanation.
Other apparently nonalgorithmic phenomena are:
- Qualia 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.
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 mother of all algorithms
Although some superficial mental processes are algorithmic (for example performing mental arithmetic) there are more fundamental aspects of the mind that do not seem to be reducible to procedures, for example the processes that create algorithms.
Possibly one way forward in describing non-algorithmic phenomena is to describe what they are NOT.
For a start, they are without form. They cannot be described in terms of structure, nor of procedures (which can always be reduced to form in a flowchart). Taking an analogy from computer programming we can say they are NOT 'objects'.
An object is a structure (the term 'structure' includes datastructure), which may or may not have an associated procedure (the term 'procedure' includes mathematical and logical functions and algorithms).
All algorithms (and other procedures) 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.
Objects, in this context, include databases, buttons, boxes, forms, scrollbars and all the other paraphernalia of object-oriented programming. These objects consist of graphical structures (customisable to some extent by changing their properties) with associated algorithms, which are usually where the main customised functionality resides. This often takes the form of specially written code.
Outside the realms of computer programming, examples of objects are:
- Bicycle - mechanical structure but no algorithm.
- Wall calendar - physical structure and datastructure but no algorithm.
- Grandfather clock - mechanical structure, datastructure (clockface) and intrinsic algorithm (the adjustable pendulum length is the independent variable in the function determining the period of oscillation).
- Wind-up musical box - mechanical structure and algorithm as stored program (metal pegs on rotating drum).
- Solar system. Structure consists of one star, nine planets, a few dozen moons, and several thousand asteroids and comets. Algorithms are Newton's laws of motion (with a minor relativistic corrections for the planet Mercury).
All physical structures can be simulated as datastructures (CAD packages etc). All intrinsic algorithms can be expressed and implemented programmatically (eg desktop clocks and MIDI players as programmatic implementations of mechanical clocks and musical boxes). Therefore all physical objects can be simulated by computer programs.
If a computer program or algorithm is simpler than the system it describes, or the data set that it generates, then the system or data set is said to be 'algorithmically compressible'.
This concept of algorithmic simplicity/complexity can be extended from the realms of mathematics into physical systems. The complexity of a physical system is the length of the minimal algorithm than can simulate or describe it. Thus the orbits of the planets, which seemed so complex to the ancients, were shown by Newton to be algorithmically compressible into a few short equations.
Towards a science of consciousness?
Formless and non-algorithmic phenomena are, by their very nature, forever beyond the grasp of science. The scientific method (at least in the real sciences) consists of producing models constructed out of datastructures and algorithms, which are used to predict the behavior of the phenomena under investigation. Successful models are those with the greatest predictive accuracy and widest applicability.
Science may never be able to analyse such phenomena as semantics, qualia, consciousness and intentionality because these 'things' do not have any structure, either static or procedural. They do not have any conceptual 'nuts and bolts' for the dismantling tools of science to get a grip on, or to put it more technically, they have no isomorphism with Turing machines.
The phrase 'Science of Consciousness' may thus be a self-contradiction. For a more detailed discussion, see 'Refuting the computer theory of mind - and why it matters to Buddhists'.
- Sean Robsville
Mysterians, Mysterianism and the Mystery of the Mind
Buddhism versus Materialism
The Church-Turing-Deutsch Principle and Buddhist Philosophy