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Quantified Technology

General

Quantified technology is possible with numbered inventions.

Certainly population is a quantity.   Also, time is a quantity which can be assessed numerically by years.    If population and time are numbers, can technology be quantified?   Is there a smallest, quantifiable unit of technology?  Technology on the surface seems difficult to put a number on.  I began this project with the creation of a list of the one hundred greatest inventions of all time.   The project then swelled to 200 inventions, then 500, now 2000 inventions.    Can each of these 2000 inventions represent a unit of technology?  If you accept that one invention can be viewed as a unit of technology, then quantified technology is possible.

2000 inventions represents all of technology history.

Perhaps the most famous example of quantified technology is Moore’s law

created by Gordon E. Moore in 1965 which states that the transistors on a semiconductor chip double every 2 years.  The corollary of Moore’s law states the cost of chip production halves every 2 years.    On the surface, the complexity of transistor and microchip manufacturing would not seem to likely follow such a simple numerical formula, but, nonetheless, Moore’s law has been largely accurate in predicting the development of transistors and their cost since 1969.  (See Figure 1).

Moore's law as example of technology quantified
Figure 1

At the risk of oversimplifying things too much, systems can have two simple common outcomes when graphed for 2 variables:  linear and exponential (logarithmic).   Linear outcomes exist in the natural world from Sir Isaac Newton’s famous equation for the second law of motion.  Force equals mass times acceleration.   F=ma.    Simply stated, force has a simple linear proportionality with both mass and acceleration.    As mass or acceleration increase, force goes up in a proportional fashion.  With technology, the same type of linear relationship exists with inventions and population.  Technology measures in inventions per 100 years.

Technology increases in direct proportion to time, that is, in a linear fashion.

A nearly straight line exists graphically with technology (1000 inventions) versus population (107 billion people since the beginning of human existence at 250,000 BCE).  This relationship is therefore linear, or directly proportional between inventions and population. (see Figure 2)

Linear relationship between quantified technology variables
Figure 2 – LINEAR RELATIONSHIP

EXPONENTIAL outcome can be demonstrated in the natural world by Albert Einstein’s famous equation:   energy is equal to mass times the speed of light squared.   E=mc2 .  The relationship between energy is linear with mass but exponential with the speed of light.  As mass increases linearly the energy increases in proportion to  the speed of light squared, an extremely large number.  With technology measured in inventions, technology are proportional to time squared, that is time x time. With inventions versus time, an exponential relationship exists.

As time increases then inventions increase exponentially.

  ( see Figure 3)   Since technology is proportional to population and technology is proportional to time squared, when taken together: 

Graph showing exponential relationship with quantified technology
Figure 3 – EXPONENTIAL RELATIONSHIP

This mathematical relationship between technology, population and time is the first truth of technology, TECHNOLOGY= POPULATION X (TIME)2

What does this mean?   So in human existence, large periods of time passed with small amounts of technology produced.   Then as time advances to the modern eras, a progressive increase in inventions occurs with each era.  Therefore, technology is accelerating and increasing exponentially with time.  

Other Examples of Quantified Technology

Several other examples of the logarithmic relationships with quantified technology exist: (from “Technological progress” Max Roser,  Hannah Richie 2020, Our World in Data.org)

  1. Moore’s law  -states the number of transistors on an integrated circuit doubles every 2 years (Gordon Moore in 1965) found to be largely true from 1969 -2019 and the cost per transistor decreases by 1/2 every 2 years.
  2. Butler’s law – data per optical fiber doubles every nine months
  3. Haitz’s law (Roland Haitz) states the exponential relationship between the LED light output per LED over time (flux/package) and decreasing cost/lumen over time from 1970 until 2010.
  4. Digital cameras – pixel number per dollar spent increased exponentially between 1994 and 2006.
  5. Clock speed of computer computation in computations per second doubles every 1.5 years from 1975-2009  measured in floating-point operations per second (FLOPS).
  6. Computer storage capacity increases exponentially with time.
  7. Computer storage cost decreases exponentially with time.
  8. Non-commercial flight distance record 1900-2006.
  9.  Human Genome sequencing decreasing cost 2008-2015

In summary, with quantified technology, powerful conclusions can be reached and predictions of future change are possible.