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.