Trajectories of the Future

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
















Example:

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




Lightbulb example:


. . . 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.