Revision as of 18:14, 6 May 2017

Thoughts

Philip Johnson-Laird is an academic who sits at the intersection of philosophy and psychology. He studies cognition and the inner workings of the brain. My first exposure to his work came through his book "Mental Models," which I used when writing my dissertation to help articulate what, exactly, a model is, and understanding what models can and cannot do.

This book is particularly apt, given the recent resurgence in machine learning and artificial intelligence. When the book was originally published in 1988, the idea of a neural network was still undergoing development, and many foundational ideas are discussed here. That the book is not written like a computer scientist who is teaching how to do X in Y, or assume the reader will be able to follow graduate-level linear algebra concepts, but rather like a cognitive scientist carefully devising an experiment to devise the mechanisms of the brain.

The organization of the book is in six parts, each focusing equally on aspects of how our brains work, and how that can be replicated through computation.

Part 1, Computation and the Mind, starts by talking about the concept of computability, what it means to compute something, and how we might replicate some of the computing functions of the brain. It answers some basic questions that any non-expert would have, like how do you study the mind?

The remaining parts each focus on a particular aspect of our mental machinery:

Part 2: Vision

Part 3: Learning, Memory, and Action

Part 4: Cogitation

Part 5: Communication

Part 6: The Conscious and Unconscious Mind

Notes

Part 1: Computation and the Mind

Since Descartes, theorists have assumed that there is no problem in understanding how machines work. Indeed, Lord kelvin, the eminent Victorian physicist, even turned this argument around, and wrote in a letter to a colleague: "I can never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model I can understand it. As long as I cannot make a mechanical model all the way through I cannot understand.
p. 24

On the Meaning of Symbols

Any system of external symbols, such as numerals or an alphabet, is capable of symbolizing many different domains. Thus, the binary numeral 1100 can stand for many things. It may stand for the number twelve, for the letter Z as in morse code, or for a particular person, artifact, 3d shape, region of the earth's surface, or many other entities, Numerals are potent because they are each distinct from one another, and there is a simple structural recipe for constructing an unlimited supply of them.
Even if a domain contains a potentially infinite number of entities, then a numerical system can be used to symbolize it provided that there is some way to relate the numerals to what they signify. The simplest link is an arbitrary pairing of each symbol to one referent, and each referent o one symbol, as in a numerical code for the rooms of a hotel. A symbol may be well formed, e.g., the Roman numeral XII, but fail to designate anything (no room with number 13). Rather than arbitrary pairings, it is usually convenient to have some principles for assigning interpretations to symbols. These principles may be a matter of rules, conventions or habits. If symbols are assembled out of primitives according to structural rules, then the structure of the symbol may, or may not, be relevant to its interpretation. A Roman numeral has a structure that is relevant to its interpretation as a number. A pile of sand in an hourglass has a structure that is not relevant to its interpretation as an interval of time - only the volume of sand matters.
p. 31-32

Computability and Mental Processes

Computers work in a very different way from Turing machines: their memories are not just one-dimensional tapes, and they have a much richer set of basic operations. But a computer program is analogous to a particular Turing machine, and the computer is analogous to a univerasal machine because it can execute any program that is written in an appropriate code. Anything that can be computed by a digital computer cna be computed by a Turing machine.
Not everything, however, can be computed. There are many problems that can be stated but that have no computable solution. It is impossible, for example, to design a universal machine that determines whether any arbitrarily selected Turing machine, given some arbitrarily selected data, will come to halt or go on computing for ever. Hence, there is not test guaranteed to decide whether or not a problem has a computable solution.
p. 51

There are three morals to be drawn for cognitive science.
First, since there is an infinity of different programs for carrying out any computable task, observations of human performance can never eliminate all but the correct theory...
Second, if a theory of mental processes turns out to be equivalent in power to a universal machine, then it will be difficult to refute.
Third, theories of the mind should be expressed in a form that can be modeled in a computer program. A theory may fail to satisfy this criterion for several reasons: it may be radically incomplete; it may rely on a process that is not computable; it may be inconsistent, incoherent, or, like a mystical doctrine, take so much for granted that it is understood only by its adherents. These flaws are not always obvious. Students of the mind do not always know that they do not know what they are talking about. The surest way to find out is o try to devise a computer program that models the theory. A working computer model places a minimal reliance on intuition;: the theory it embodies may be false, but at least it is coherent, and does not assume too much. Computer programs model the interactions of fundamental particles, the mechanisms of molecular biology, and the economy of the country. The rest of the book is devoted to computable theories of the human mind.
p. 52

Part Two: Vision

The Visual Image

Consider three beliefs about vision:

The eye is like a television camera - you point it at a scene, it registers the scene, and it projects the image inside your head.
Vision is impossible. Different arrangements of things can produce the same image, so the brain does not know what particular arrangement you are looking at.
Vision is easy for brain to do, but hard for us to understand.

Three different levels of explanation are needed:

Theory of what is computed
Theory of how the system carries out computations
Theory of underlying neurophysiology (the "hardware")

Three stages of vision:

Vision stage 1: grayscale images (brightness value for pixels)
Vision stage 2: changes in intensity (gradients between pixels)
Vision stage 3: the primal sketch

Locating Gradients in Intensity

Gray-level array has certain amounts of noise - random fluctuations. How to differentiate between small scale changes and large scale changes?

Simple technique for reducing noise is to replace each value in the array by its local average - applying a 2D filter to smooth changes in the intensity.

Let's talk more about this filtering concept.

A crude local averaging stencil would just be an even weighted average of neighboring points:

$\frac{\Delta x}{3} \left( x_{i-1} + x_{i} + x_{i+1} \right)$

More generally - the left hand rule, right hand rule, midpoint rule approximate the function between two points as a constant (1 unknown), requires 1 point

The trapezoid rule approximates the function between two points as a line (2 unknowns, slope and intercept) and requires 2 points

Can get increasingly better stencils by using things like Simpson's Rule, approximates function over an interval with a quadratic (3 unknowns, 3 coefficients) and requires 3 points

$\frac{\Delta x}{2} \left( \frac{1}{3} x_{i-1} + \frac{4}{3} x_{i} + \frac{1}{3} x_{i+1} \right)$

Applying a filter and removing local irregularities reveals large scale changes. Another way to think about this: the SPECTRAL content of the image shifts to being larger scale changes.

Flags

The Computer and the Mind: Difference between revisions

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