geometric progress

[foofighter]

i heard a show talk about a certain technology developing in geometric progress, as opposed to exponential. i'm assuming this is rather slow progression, however what exactly is geometric progress, and how does it compare to exponential and linear progress? thanks

[iNow]

i heard a show talk about a certain technology developing in geometric progress, as opposed to exponential. i'm assuming this is rather slow progression, however what exactly is geometric progress, and how does it compare to exponential and linear progress? thanks

I'm not a mathemagician, but I'll share what I think. Be sure to check this data before relying on it.

 

Linear growth is steady, increasing by the same amount with each step... like grains of sand dropping from top to bottom in an hourglass... grain by grain by grain.

 

Exponential growth implies that with each step, the growth becomes greater... like population. More people are born, more people to have children, even more people born from them, even more children... and the process repeats at an ever increasing rate.

 

Geometric growth is where you multiply the preceding term by a common ratio... I think interest on a bank account may be an example, since the principle is multiplied by a common percentage (like 5%).

 

See wiki for some clarity:

 

http://en.wikipedia.org/wiki/Geometric_series

[bascule]

i heard a show talk about a certain technology developing in geometric progress, as opposed to exponential. i'm assuming this is rather slow progression, however what exactly is geometric progress, and how does it compare to exponential and linear progress? thanks

 

Anyone's guess as to the rate of change is merely of conjecture. I'm of the school that the rate of change is accelerating, or that is to say the speed at which change occurs is increasing. But again, this is only an opinion.

 

Furthermore, it's not as if this is happening across the board. Many areas of society are stagnant.

[foofighter]

the article was talking about anti-matter production

[Sisyphus]

Geometric growth is where you multiply the preceding term by a common ratio... I think interest on a bank account may be an example, since the principle is multiplied by a common percentage (like 5%).

 

That would be exponential growth.

[iNow]

That would be exponential growth.

 

Is it possible that it could be both... that there is overlap in definition/use?

[Sisyphus]

Is it possible that it could be both... that there is overlap in definition/use?

 

Yes, actually, and sorry if I came off curt before. A geometric series is an example of exponential growth. Specifically, it is discrete exponential growth, as opposed to a continuous function, say.

 

What this guy probably meant to say was arithmetic growth, which is neither linear nor exponential. The rate of growth is increasing, but at a linear (or at least non-exponential) rate.

 

For example:

 

Linear

 

1 (+1) 2 (+1) 3 (+1) 4...

 

Arithmetic

 

1 (+1) 2 (+2) 4 (+3) 7 (+4) 11 (+5) 16....

 

Geometric

 

1 (x2) 2 (x2) 4 (x2) 8 (x2) 16 (x2) 32...

[iNow]

Yes, actually, and sorry if I came off curt before.

No worries at all, mate. Thank you also for the fine explanation above.