To integrate into the following: technology adoption life cycle; Gartner hype cycle
Making and Discuss Predictions with Trajectories
Let's apply the following to:
. . . Topics of your choice
or, as other examples -
. . . Cars of the future
. . . Going to college in the future
. . . The lowly(?) pencil
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 looks exponential
. . . 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
Do you think an even longer-term view will look like a plateau curve?
Think about pencils, compact fluorescents, and college, etc., etc.