Forgive, has to do only tangentially with language but many wordaphiles are also into math

1. If population doubles in two generations, won't there be about 300 trillion of us (U.S.) in 20 generations or did I slip a decimal point

2. it took approximately 3 million years to reach the present world congestion (at 6 billion estimated to be overpopulated from 5 to 20 times). At the foregoing rate of growth what would world population be in another 3 million years

One of the reasons I am unable to make the calculation myself is that I need it to be expressed not in exponential terms but in in common digits (sepoctillions, quintillions, etc etc) that a typical calculator is simply not equipped to handle

Thanks all

Twenty generations means the population will double 10 times. Taking the current pop=300 mil, this new pop will be 300 * 2^10
(where 2^10 means 2 to the power of 10 = 1024). Approximating 2^10 as 1000, yields a new population of about 300 billion.




Assume we start out with 2 humans 3 million years ago. (That's not quite right, but it was a small population and the actual number would not affect the results drastically.) Assume generations are 20 years. This means there are G=150,000 population increases (generations) in 3 million years. Of course, "G" is too big a number for the population to double. No population with finite resources can increase exponentially. Populations are limited by resources, predation, disease, and in the case of humans, war. We need to find the factor to use that will get us to 6 billion from 2 in 150K generations.

2*K^(150000) = 6000000000

Using logs, we find K=1.000145491

The number we want is N=2*K^(2*150000) = 1.8e19
(The e in this case doesn't denote the base of the natural logs, but engineering notation)

1.8 x 10^19 = 18 x 10^18 = 18 quintillion

However, this assumes the K is constant, which is a very bad assumption.

There are too many unknown variables such as catastrophes on the one hand or polygamy on the other. If it were (on average) a simple doubling, the present population could have been reached in a mere 30 generations.

But it's not necessary to go back that far, all you have to do is to look at the more recent rate of growth of say the past few hundred years and extrapolate that forward. But then obviously at some point, something has to give. No way is there ever going to be gazillions of people on this planet. Eventually there has to be either a slowing of the growth by social engineering to a point of equilibrium or catastrophic collapses by destruction of the environment and loss of capacity to provide the essentials of life to the whole population.

Fal, thanks, I did slip a decimal place didn't I--actually three places. Thank you for that second computation and I'm sorry I I should have said "present" not "foregoing" so if it's no trouble could you repeat the calculation based on current growth rate, which is, contraceptives notwithstanding, much, much higher

Pook: Thank you also for that pertinent observation, which FAl also pointed out. Of course the figure is impossible to attain but it bolsters my contention as well as yours that we ought to be doing something before it's too late

Assuming once again that a generation is 20 years, we have 150,000 generations. The '2' denotes doubling, and the 300 mil is the starting population, we get:

N = 300e6 * 2^(150000) = 3e8 * 2^(10 * 15000)

The number is too big for my calculator, but we can play with it a little:

N = 3e8 * 1024^(15000)

I'm going to simplify, lose precision, and give you a lowball answer:

n = 3e8 * 1000^(15000) = 3e8 * (10^3)^(15000)
n = 3e8 * 10^(45000) = 3 * 10^45008

That's 3 followed by 45008 zeros - and this is a lowball answer.
Of course, the number is meaningless, as Pook pointed out. Just a sort of game, really.

Thank you guys most profusely. If you are interested, it might be instructive to perform the following calculation: Notwithstanding means of production and distribution of life support, suppose one person requires 100 sq ft of living space 10 ft high. If housing covered every square foot of the planet (supposing means of flotation and for heating and pumping oxygen to the top), to accommodate 3 x 10^45008 bodies how high would the resulting structire have to be. For instance, wouldn't it reach past the moon

At a certain altitude closer to the sun of course heating wouldn't be required

Take those numbers cum gano salis. I rushed through it. No time right now, but a few simplifying assumptions, a person occupies 1000 cubit feet. This is pretty cramped and does not include space for him to walk or exercise or what have you. The volume of a sphere is V=4/3 pi r^3. Say pi=3, so V ~ 4 r^3. The radius of Earth ~ 4000 miles, with approximately 5K feet in a mile, so the radius of Earth is about 2e7, or 20 million feet. Cubing this is 8e21.

We're looking for volume of new sphere - volume of old sphere = 3e45008 * 10^3, where old sphere is the Earth.

Sphere is not a bad approx, of course, though it's technically a 'geoid' or an 'oblate spheroid.' We'll also assume we'll build over the oceans, as well.

4 (R^3 - 8e21) = 3e45011
R^3 = .75e45011 - 8e21 = 75e45009 - 8e21
The 8e21 is minuscule with respect to the rest, but let's just get rid of the 9.
R^3 = 75e45000
R = (75e45000)^(1/3)
R = 4.2e15000 feet ~ 1.4e15000 meters.

For comparison, it takes, I think, 8 minutes for light to get to Earth from Sol. 8 minutes is 480 seconds (say 500 to make it simple) at 3e8 meters per second, so light travels about 1500e8m= 1.5e11m. Wikis says the distance is 149,597,870,691 meters. We are surprisingly close for so many simplifications. So this extends well past the sun, even the solar system, and probably the galaxy. Still, you should check the math on my earlier msg. The 3e45008 seems suspiciously high. I probably screwed something up.

This thread brings to mind an excerpt from Isaac Asimovs Foundation.

Gaal leaned out over the shoulder-high railing and bathed himself in all the panorama. He could not see the ground. It was lost in the ever increasing complexities of man-made structures. He could see no horizon other than that of metal against sky, stretching out to almost uniform grayness, and he knew it was so over all the land-surface of the planet.

Isaac Asimov had the fantastic knack of having a great imagination and being able to write.

Fal thank you most kindly for your efforts on my behalf, perhaps another math wizard will corroborate

olly, see post #10

http://www.wordwizard.com/phpbb3/viewtopic.php?f=16&t=19942&hilit=manhattan

Oops I see WS' link curtailer retained WW, and if this is a breach of protocol I apologize most profusely

I've been really busy these days (judging a swim meet tonight, among other things). If it's not too late when I get back, I'll take a few minutes and review the math in first post to see if anything obviously stupid sticks out. But I think almost any college student in the sciences or engineering should be able to critique it.

Fal alas alack, I for one can't as you must have inferred from my first calculation having missed the mark by 3 decimal places. Thank you again and I will be looking forward to your confirmation. In fact I'm saving the draft of a Letter to the Editor which if necessary I shall correct accordingly before submitting