The Nature of Consciousness

Piero Scaruffi

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These are excerpts and elaborations from my book "The Nature of Consciousness"

The Measure Space

The British computer scientist Pat Hayes (“Naive Physics Manifesto “, 1978) introduced the "measure space" for a physical quantity (length, weight, date, temperature, etc.). A measure space is simply a space in which an ordering relationship holds. Measurement spaces are usually conceived as discrete spaces, even if the quantities they measure are in theory continuous.  In common use, things like birth dates, temperatures, distances, heights and weights are always rounded.

For example, the height of a person is usually measured in whole centimeters (or inches), and omitting the millimeters, and it can be safely assumed that only heights over one meter and less than two meters are possible. This means that the measure space for people’s height is the set of natural numbers from 100 (centimeters) to 200 (centimeters). The measure space for driving speed can reasonably be assumed to be the set of numbers from 0 to 160 (kilometers per hour). The measure space for a shirt’s size is sometimes limited to four values: small, medium, large, very large. The measure space for jeans’ size is a (very limited) set of  pairs of natural numbers. The measure space for the age of a person is the set of natural numbers from 1 to 130. The measure space for the date of an historical event is the set of integer numbers from -3,000 (roughly the time when writing was invented) to the number of the year we live in.  And so forth.

A measure space is a discrete representation of a continuous space that takes into account only the significant values that determine boundaries of behavior.

Hayes' program was more ambitious than just measurement spaces. Hayes set out to write down in the language of Predicate Logic everything that we take for granted about the world, all of our common-sense knowledge about physical objects. For example, we know that water is contained in something and that, if it overflows, it will run out, but it will not run upward. We know that wood floats in water but iron sinks. We know that a heavy object placed on top of a light object may crush it. We know that an object will not move if placed on a table, but it will fall if pushed beyond the edge. This is what Hayes called "Naïve Physics" and it is the physics that we employ in our daily lives.


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