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Moore's Law: A psychological explanation?

Many members of the tech-savvy public are familiar with "Moore's Law\, which has successfully predicted since the 1960s that, in approximate terms, costs for computing power would be cut in half over short periods of time, about every 18 months in retrospect.  Looking back, this formula works since the late 19th Century for various forms of computing hardware.

The original form of Moore's Law is very specific, but the important idea is that technologies may advance exponentially.

Why exponentially?

Exponentials are widespread in nature.  The meaning of an exponential trend is that a variable changes in proportion to its value.  Big things change quickly, small things change slowly.  An example is radioactive decay.  The number of decay events is proportional to the number of undecayed nuclei.  Over time, the decay rate goes down exponentially, measured as the 'half-life' of the sample.  Interestingly, the costs for available figures of merit for commodity technologies also tend to decrease exponentially.  This is true for hard drive capacity, camera resolution, and a host of other desiderata.

There is an equivalent law in cognitive psychology, called the "Weber-Fechner Law\".  It states that, for many variables relevant to sensing, perception, and cognition in humans, a 'just noticeable difference' in a variable is proportional to its baseline.  Telling whether one light is brighter than another depends on what the first light's brightness was.  Bright lights require a bigger change to notice a difference.  Dim lights admit smaller changes to be noticed.

When human consumers invest money in technologies like computing power, they are almost certainly subject to this perceptual ratio effect.  How much more would I pay to get better hardware?  What kind of advantage does better hardware give me in a competitive situation?  This should translate directly into investments on the part of producers to generate the next improvement.

The author's affiliation with The MITRE Corporation is provided for identification purposes only, and is not intended to convey or imply MITRE's concurrence with, or support for, the positions, opinions or viewpoints expressed by the author.

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