Saturday, October 15, 2011

Population Weighted History

In Pharyngula article Humanity’s recent surge, PZ discusses a chart from The Economist. The chart deals with population and growth rate on the same time scale by century. 

The article got me wondering how the data would look if you plotted it along a population weighted year (PWYr) time scale. 
(NOTE:  this idea seems quite simple and obvious, so I suspect someone has done this before, but I could not find it.).

So what is a PWYr?
A PWYr is a measure of time based on the number of years lived collectively by a population over some long time scale (i.e. where population is changing dramatically). It turns out that a PWYr is equal average population over a reference period. A table of PWYr shift the years such that it creates a corresponding date within the reference period that assumes a constant population over that period.

So whats good about it?
The interesting thing is that change especially for technology, knowledge, and research driven endeavors like economics, science, longevity, communication, etc. should be at least in part proportional to the number of people living.  In other words, for any society, the more people there are, the more that can contribute to change, and so the faster the change appears.  I came up with the notion of a PWYr a few years ago and always thought it would be an interesting way to watch change over the centuries.


So what does it look like?
To see what a Population Weighted Year looks like, I used World population data from Wikipedia to calculate roughly how many years lived over each of the population intervals.  I then summed the total years lived and divided by the total period covered to get the average population, which is also the number of years lived in a population weighted year.  When I took the period from 0 CE to 2010, I get:
1 PWYr (0-2010) = 603,902 years lived
From there is is simple to calculate the equivalent date in PWYrs for each interval which I have calculated in Table 1. You may ask Why 0 to 2010? I was trying to look at the time line from roughly to day and so 2010 was the closest date to today.

Table 1: Calendar year vs Population weighted Year (PWYr) based on the average population (603902890) from year 0 to 2010. Therefore, 1 PWYr is equivalent to 603,902,890 years lived by the world population. The data came from Wikipedia World Population Estimates article.
Year
Estimate Population*
Population Weighted Year (PWYr)
-8000
5000000**
-2020
0
300000000
0
1000
310000000
505
1250
400000000
652
1500
500000000
838
1800
978000000
1179
1850
1262000000
1271
1900
1650000000
1392
1930
2070000000
1483
1950
2529346000
1559
1960
3023358000
1605
1970
3685777000
1660
1980
4437609000
1727
1990
5290452000
1808
2000
6115367000
1902
2010
6908688000
2010
*UN Department of Economic and Social Affairs (2008)
**Population for 8000 BCE is from Population Reference Bureau (1973–2008)



A couple of the things to note from Table one:
1. The early Roman empire is about halfway (remember this is to say years lived) between today and the earliest civilizations.
2. In 0 CE it was about 2 calendar years for every PWYr while today is about 10 PWYr for every 1 calendar year.

So with PWYr table in hand I went back to the economics graph shown above and tried to see if I could plot it on a PWYr Scale. So doing my best to count pixels and color values I tried to recreate the data. Since PWYr is inherently proportional to population I figured that what I needed from the graph is only the ratio between the economic output and the population. I also assumed the 21st century was just till today and assumed equivalent to 2010. Figure 2 is my plot of the data for the Economic Output as a percentage of output per percentage of population versus the equivalent PWYr for the average calender year for the period listed (i.e. going from points right to left they a for calendar year 2005, 1950, 1850, 1750, 1650, 1550, 1350, 1150, 950, 50).
Figure 2: Economic Output vs Population Weighted Year
My first reaction was WOW, that's interesting. 
I had wondered if there would be any pattern but if this represents anything real it looks like that the growth rate of output took a significant step around the late 19th early 20th century.. maybe the event that triggered it, is the singularity equivalent to the big bang...maybe not. Admittedly this data is real rough and if we looked at it on a finer detail especially for the 20th and 21st centuries it is likely to tell as very difference story. I hope somebody posts the supporting data in more detail.


History in a PWYr perspective
As I said above I originally thought of this as an interesting way of looking at the history and so created a table of various technological events and calculated their corresponding on PWYr time scale (Table 2).  Note the dates for the events are most taken from various technology timeline mostly on Wikipedia and I make no claim as to their accuracy.  I also tried to color code different types of data (key at top).

Table 2: 
PWYr For Various Historic Events (mostly technological). Original dates taken mostly from Wikipedia and linear interpreted from PWYr table. Note PWYr is based on a 0-2010 reference period


Historic
General Technology
Astronomy
Physics
Biology


Year
Historic Events
PWYr
9500 BCE
First building phase of the temple complex at Göbekli Tepe
2031 BCE
8000 BCE
First agriculture in Eygpt
2020 BCE
8000 BCE
First Wine
2020 BCE
5600 BCE
First writing -the Dispilio Tablet,
1414 BCE
5400 BCE
Otzi the Iceman lived
1338 BCE
2620 BCE
Earliest known Egyptian pyramids
663 BCE
2500 BCE
Stonehenge
631BCE
1211 BCE
The Great Pyramid of Giza
331BCE
320 BCE
Aristotle
81BCE
200 BCE
Archimedes
51BCE
27 BCE
Julius Caesar starts his rule over Ancient Rome
7 BCE
850
China: Invention of gunpowder
429
1220
Robert Grosseteste: rudimentals of the scientific method (see also: Roger Bacon)
634
1327
William of Ockham: Occam's Razor
709
1440
Gutenberg: Printing press
794
1543
Copernicus: heliocentric model
884
1609
Johannes Kepler: first two laws of planetary motion
955
1686
Newton: Laws of motion, law of universal gravitation, basis for classical physics
1037
1761
Mikhail Lomonosov: discovery of the atmosphere of Venus
1122
1843
James Prescott Joule: Law of Conservation of energy (First law of thermodynamics)
1258
1857
Johann Carl Fuhlrott & Hermann Schaaffhausen discover Neanderthal
1288
1859
Charles Darwin: Origin of Species
1293
1903
Wright Brother:s First powered flight
1400
1915
Albert Einstein: theory of general relativity
1450
1927
Charles Lindbergh becomes the first person to fly solo across the Atlantic Ocean 19927/1473
1473
1927
Heisenberg uncertainty principle
1473
1945
First atomic bomb (Trinity)
1576
1953
Crick and Watson: helical structure of DNA, basis for molecular biology
1572
1954
The first silicon transistor
1576
1957
USSR: First artificial satellite to be put into Earth's orbit
1590
1964
Detection of CMBR providing experimental evidence for the Big Bang
1626
1969
First Humans on the Moon
1654
1976
Viking landed on Mars
1699
1977
Classify archaea as a new, separate domain of life
1706
1977
First successfully mass marketed personal computer was the Commodore PET
1706
1985
Voyager makes visit Neptune
1766
1996
First cloned mammal: Dolly the sheep
1863
1998
Discover the cosmic acceleration in observations of Type Ia supernovae providing the first evidence for a non-zero cosmological constant.
1883
1999
First extrasolar planet definitely discovered
1890
2001
Compete Human genome mapped
1913
2008
1 billion PC computers world wide
1988
2010
Genetic code of Neanderthal and other archaic found in humans
2010


What is the significant of this, don't really know other than it gives a much more leisurely pace to technology. There are some very interesting progressions but I'll let you find your own.


1 comment:

  1. You forgot invention of the decimal system man. It is probably more important than Otzi or Caesar's rule ....

    ReplyDelete