TL development by population?

[MasterGwydion]

Just out of curiosity, has anyone done the math and historical research to figure out the correlation between population and research speed?

For example, (these numbers will not be accurate since I am not using a curve for population. I am using a straight line. Someone with better math than I have can provide us with better numbers if they are inclined to do so. This was just a random thought I had this morning.)

TL-0 ends with a population of about 5 million.
TL-1 roughly 7,000 years and a population of about 400 million. 57,000 research points
TL-2 roughly 500 years and a population of about 1 billion. 2 million research points
TL-3 roughly 100 years and a population of about 1.6 billion. 16 million research points
TL-4 roughly 50 years and a population of about 1.9 billion. 38 million research points
TL-5 roughly 30 years and a population of about 5.3 billion. 176.7 million research points
TL-6 roughly 20 years and a population of about 6.9 billion. 345 million research points
TL-7 roughly 20 years and a population of about 9 billion. 450 million research points
TL-8 roughly 30 years and a population of about 10 billion. 333 million research points
Etc...

Take population divided by time for each TL and you get a rough number of "research points" for lack of a better term. This describes the amount of human effort that goes into moving from one TL to the next. For the whole of actual human history, the number of "research points" needed for each new TL increased. After actual human history it starts to decrease. It seems that how TL was originally structured up to the level of current human achievement works in a progressive manner in regard to time, TL, and population. After the current, real-world dates though, their execution falls apart and suddenly the amount of "research points" that you need goes down, not up. This seems to be an error in thinking and not looking at prior human development to envision future human development.

This post was thought up as it was being written, so please understand that I consider this more of a stream of consciousness type of thing than a fully thought out and considered type of thing.

 

[Condottiere]

Actual research and development budgets.

Research facilities.

Industrial base.

General demographic intelligence.

Apples.

Bath tubs.

 

[MasterGwydion]

Obviously this is a rough baseline and the math needs fixed, but this may be something that could be usable for worldbuilding and universe development. If it is kept simple enough. Human Baseline, then few simple up or down modifiers on Effect of Population and a few simple modifiers for Effect of Time. These could account for any racial, cultural, economic, religious effects, etc that could be added to describe almost any variation that your Universe/Empire/Planet/Civilization/Nation might need.

 

[Limpin Legin]

Just out of curiosity, has anyone done the math and historical research to figure out the correlation between population and research speed?

Technological Change and Population Growth | Encyclopedia.com

TECHNOLOGICAL CHANGE AND POPULATION GROWTHThe relationship between population growth and technological change has been debated since the end of the eighteenth century–a debate whose main configuration has proved remarkably persistent. Source for information on Technological Change and Population...

www.encyclopedia.com

Main Points (via Wikipedia):
Malthusianism is a theory that population growth is potentially exponential, according to the Malthusian growth model, while the growth of the food supply or other resources is linear, which eventually reduces living standards to the point of triggering a population decline.
In Boserup's theory, agricultural methods depend on the size of the population. In the Malthusian view, when food is not sufficient for everyone, the excess population will die. However, Boserup argued that in those times of pressure, people will find ways to increase the production of food by increasing workforce, machinery, fertilizers, etc.
Julian L. Simon argued that Malthusians systematically underplayed the importance of economies of scale and of agglomeration and the positive contribution of population pressure to technological innovation.

After the current, real-world dates though, their execution falls apart and suddenly the amount of "research points" that you need goes down, not up. This seems to be an error in thinking and not looking at prior human development to envision future human development.

Or it could mean your linear assumption is unfounded. For example, when quality of life reaches Utopia, then Population interest in Technological progress diminishes. Similarly, when there is technological reaction/revolution, the population becomes anti-progressive, and your "research points" would likely decrease. (eg. Industrial Revolution, Cybernetic revolution, etc.)

 

[MasterGwydion]

Technological Change and Population Growth | Encyclopedia.com

TECHNOLOGICAL CHANGE AND POPULATION GROWTHThe relationship between population growth and technological change has been debated since the end of the eighteenth century–a debate whose main configuration has proved remarkably persistent. Source for information on Technological Change and Population...

www.encyclopedia.com

Main Points (via Wikipedia):
Malthusianism is a theory that population growth is potentially exponential, according to the Malthusian growth model, while the growth of the food supply or other resources is linear, which eventually reduces living standards to the point of triggering a population decline.
In Boserup's theory, agricultural methods depend on the size of the population. In the Malthusian view, when food is not sufficient for everyone, the excess population will die. However, Boserup argued that in those times of pressure, people will find ways to increase the production of food by increasing workforce, machinery, fertilizers, etc.
Julian L. Simon argued that Malthusians systematically underplayed the importance of economies of scale and of agglomeration and the positive contribution of population pressure to technological innovation.

This is going to be a cool read.

Or it could mean your linear assumption is unfounded. For example, when quality of life reaches Utopia, then Population interest in Technological progress diminishes. Similarly, when there is technological reaction/revolution, the population becomes anti-progressive, and your "research points" would likely decrease. (eg. Industrial Revolution, Cybernetic revolution, etc.)

Actually, I said I did linear because I can't do the math to do it right. You are correct that population growth is compounding and my calculations are not. I would invite someone with better math skills to do it with the populations compounding over time, instead of the inaccurate linear method that I used. Then we could use their new numbers to extrapolate forward and find out roughly how isolated societies could grow. We'd have to keep it simple enough that people who create their own settings would find value in it, but in might be doable. It will obviously always be a rough approximation with several questionable assumptions built into it, but it still may be helpful for some.

 

[Condottiere]

And warfare.

A bunch of our ancestors got together, and came to the conclusion that hunting and gathering wasn't cutting it anymore; so they found a nice place along a river, and started trying to grow cereals, and simplify hunting by keeping the animals in a stable.

Every time they came across a problem, that presumably was existential to a particular individual person, or group, they tried stuff until something seemed to work.

At some point, they started noticing coincidences, and started studying them, especially in relation to their life.

Also, they needed protection from others.

And so, societies started to organize themselves, invent sophisticated economies, learned writing and arithmetic to keep track of stuff that they claimed belonged to them, and figured out better ways to get rich, and kill each other.

At some point, the guys on top needed a way to keep the people under them under control.

That's why they invented the internet.

 

[MasterGwydion]

And warfare.

A bunch of our ancestors got together, and came to the conclusion that hunting and gathering wasn't cutting it anymore; so they found a nice place along a river, and started trying to grow cereals, and simplify hunting by keeping the animals in a stable.

Every time they came across a problem, that presumably was existential to a particular individual person, or group, they tried stuff until something seemed to work.

At some point, they started noticing coincidences, and started studying them, especially in relation to their life.

Also, they needed protection from others.

And so, societies started to organize themselves, invent sophisticated economies, learned writing and arithmetic to keep track of stuff that they claimed belonged to them, and figured out better ways to get rich, and kill each other.

At some point, the guys on top needed a way to keep the people under them under control.

That's why they invented the internet.

So... more people more innovation?

 

[Condottiere]

No, I think's it's mo' problems, mo' problem solvers.

Modified by culture, knowledge dissemination, modifications.