(To incorporate for next time: http://www.kurzweilai.net/thinking-quantitatively-about-technological-progress)
An Example of Extrapolation:
Overpopulation on Mars
Suppose we started a
What is your estimated
rate of increase per year?
What is the total population
capacity of Mars?
Earth surface area = 510,072,000 km^2
Earth land area = 148,940,000 km^2
Mars surface area = 144,798,500 km^2
(0.284 of Earth)
How long do you think it will take
for Mars to overpopulate?
We can check this using a spreadsheet!
Just have the rows represent successive years
Each year has x% more people than the previous
See how many years go by until overpopulation!
Making and Discuss Predictions with Trajectories
Method: Trajectories of change
. . . in the short term,
change appears linear
Last year you had 1 or 2 compact fluorescent bulbs
This year you will "probably have 1-2 more"
In the longer term,
change may looks
. . . you start with 1-2, but after a couple of years you've got a bunch
. . . change accelerates, in this case
. . . if you look at an exponential curve with a microscope, what does it look like?
. . . "Exponential": complicated word, tricky math, simple concept
. . . . . . goes up faster and faster
. . . . . . has a doubling time
Exponential curves explained
. . . Suppose something doubles every 3 years
. . . Popular example: computer CPU complexity doubles every 2 years
. . . new value after t years is original value v times 2^(t/3)
. . . f(t)=to * 2^(t/3)
. . . . . . where does the "doubles" appear?
. . . . . . where does the "every 3 years appear?
. . . . . . so it works for
any factor of increase and
any time constant
Longer term, things "level off": the S-curve
Also called "logistic curve"
Sort of "linear" early on
Then looks "exponential"
Then levels off
Justified by many, many diverse phenomena modelable as:
Constructal Theory scenarios
A. Bejan and S. Lorente, The constructal law origin of the logistics S curve, Journal of Applied Physics, vol. 110 (2011), 024901, www.constructal.org/en/art/S-curve.pdf.
Do you think an even longer-term view will look like a plateau curve?
Think about pencils, compact fluorescents, and college, etc., etc.
What do you think of these curves?
There are other view of trajectories...
Gartner Hype Cycle
How might this apply to some of our topics?
There is also the Technology Adoption Life Cycle