"The problem is growing geometrically..." Say WHUT?

[BiggJawn]

Teaser for an "All Things Considered" segment on computer hacking this evening. They had a sound bite from some law-enforcement type saying "The problem is growing GEOMETRICALLY..."

You don't suppose he really wanted to say "exponentially", do you?

Yogi Beara does it, it's cute, Some cop spokesman says it on network radio, and nobody catches it, that's SAD....

[truthspeaker]

1. Maybe he meant geometrically

I think his understanding of the mathematical terms might be greater than yours. I'd explain it, but all I remember is geometric growth is faster than linear growth but slower than exponential growth. 11th grade was a long time ago.

[priller]

2. I don't think I've ever heard of growing "geometrically" before

I mean, you can have a linear growth chart, or you can have your line curving upwards (exponential), but what's a geometric line?

[Art_from_Ark]

4. Compounded bank interest (fixed rate)

would be an example of geometric growth

[SerpentX]

3. They meant exponential.

"Trigonometric growth" might make a little sense, if you were describing an oscillating function, but you wouldn't actually call it that.

[muriel_volestrangler]

5. a valid mathematical term

an 'arithmetic' series is n, n+m, n+2m, n+3m, etc.
eg 4,6,8,10,12,14,...
a 'geometric' series is a, a*r, a*r*r, a*r*r*r, ...
eg 4,8,16,32,64,...

[SerpentX]

14. When was the last time you used the term "arithmatic growth"?

[muriel_volestrangler]

16. Probably when discussing Malthus

see http://www.mtholyoke.edu/courses/jmorrow/malthus.html . Malthus wasn't actually right about food production growing only arithmetically, but the contrast between arithmetic and geometric growth can be seen in his theory.

Another possibility, as a poster above said, is when discussing bank interest. If you leave your interest in your savings account, you get geometric growth; if you transfer it to a checking account with no interest, you get arithmetic growth.

[gWbush is Mabus]

6. support EDUCATION!!!

in American public schools

[Rex]

7. You have to think in terms of cyberspace

nodes, networks, etc.

[kiahzero]

8. Geometric growth is a valid mathematical term

http://216.239.37.104/search?q=cache:B_DzDP8-ALcJ:www-biology.ucsd.edu/classes/bieb102.WI04/BIEB102/Lecture4.pdf+%22geometric+growth%22&hl=en&ie=UTF-8

Geometric growth -> Discrete measurement of time
Exponential growth -> Continuous measurement of time

Since the police would be doing measurements on a period basis (incidents per week or per month, or something similar), they would be using discrete measurement of time; hence, geometric growth is accurate.

[AZCat]

9. Yes, but

It doesn't have to do with the measurement- it has to do with the 'event' and whether it occurs discretely (like a coin flip) or continuously (like heat transfer through a wall).

Events that are discrete can be modelled as continuous if the resolution is high enough, i.e. there are many events in a given period of time.

Population growth is discrete, but since there are so many of us, and we 'breed' and die so frequently, exponential growth is an acceptable model.

[kiahzero]

10. Not really

If you are determining continuous growth, you're integrating with respect to t, time, rather than x, or count, or whatever your dependant variable is. It is the time that is continuous, not the event.

A quote from the paper that I sourced above (I would have preferred a site talking about exponential growth and geometric growth, but you cope with what you've got):

Population biologists trying to predict future population growth take different approaches to the mathematics. The first approach, "discrete time", as the name suggests, divides time into discrete chunks or intervals and forms equations that describe the growth of the population from one time interval to the next. This method produces equations for population growth called difference equations; an example is the opening equation of this chapter. The other approach considers time as a continuous variable and uses the calculus of differential equations to perform smooth continuous projections over time.

On Edit: One other thing - the events we're discussing here are discrete. If you were to look at a detailed graph of hacking attempts over time, it would be discontinuous - periods with dx/dt = 0 when there are no attempts, and a moment where dx/dt is undefined when the actual attempt is logged. Hence, you have lots of little straight lines that aren't attached to one another.

[AZCat]

11. I am confused

Are you agreeing with me?

Note: If you need references, I don't know of any on the web, but I have lots of non-electronic sources. Books I am currently using for class:

"Mathematical Statistics and Data Analysis (2nd Ed.)"
- John Rice

"Stochastic Processes (2nd. Ed)"
- Sheldon M. Ross

The second one is a bit wonky, but Ross has another book out that goes more into detail (I don't have that one).

[kiahzero]

12. Somewhat agreeing with you

My point was this:
You could do it that way, but it makes more sense to integrate / sum over time, since that's the independant variable.

If we do it your way, it's still discrete, since the events are not continuous.

So, either way, it's still geometric growth. As for the sources, I'm really not that interest. Comp. Sci gives me all the stupid number theory crap that I'll ever need.

[BiggJawn]

13. Hey, everybody!

So what are the chances of somebody from the FBI who got put on a "Cyber-Crime Task Force" knowing enough mathematics to diferentiate between "Geometric" and "Exponential" growth?

I say slim and none, and the guy was guilty of a "Yogi-ism".

Now I'm feeling like an uneducated boob for not knowing more geometry.

[carpetbagger]

15. I think it is actually geometric growth.

Like the old shampoo commercial, except instead of telling two friends about the shampoo, you're telling two friends about g3n3r1c v1a8ra, which you can't even spell right.