(Updated 9/12/12)

Related reference:

http://www.kurzweilai.net/thinking-quantitatively-about-technological-progress)

**An Example of Extrapolation:**

**Overpopulation on Mars**

### Suppose we started a self-sustaining colony

### 100 colonists

### 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*

*Trajectories*

### Let’s apply the following to:

### a few ethics cases…

### We will see how…

** Trajectories of change**

### In the short term, change appears **linear**

### (what do the axes represent?)

### 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 often looks **exponential**

### Lightbulb example:

### you start with 1-2,

### but after a couple of years

### you’ve got a whole 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

(Could also slow, have halving time)

**Exponential curves explained**

### Suppose something doubles every 3 years

### Popular example:

### Computer chip complexity doubles every 2 years

### New value after *t* years is starting value *T* times 2^(t/3)

### *f*(*t*)=*T **2^(*t*/3)

### Why does this double every 3 years?

### It can work for

### Any factor of increase

### 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:

### Malthusian scenarios

### 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 shaped curve?**

### Think about quill pens, ball point pens, incandescent bulbs, compact fluorescents, etc., etc.

### What do you think of these curves?

### (Source: http://nextbigfuture.com/2010/08/white-led-lights-with-135-lumens-per.html, 9/5/10)

### How might this apply to technology-related ethics problems?

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