Somethings are worth your time, other things are BS

## Friday, February 27, 2009

### Exponential v. Geometric

Geometric what word better expresses how I feel Geometric or exponential? Let's take a look at Geometric: This is from Merriam Websters, the leader in finding word that best express your sentiment
Main Entry:
geo·met·ric
Pronunciation:
\ˌ-ə-ˈme-trik\
Variant(s):
or geo·met·ri·cal \-ˈme-tri-kəl\
Function:
Date:
14th century
1 a: of, relating to, or according to the methods or principles of geometry b: increasing in a geometric progression <geometric population growth>2capitalized : of or relating to a style of ancient Greek pottery characterized by geometric decorative motifs3 a: utilizing rectilinear or simple curvilinear motifs or outlines in design b: of or relating to art based on simple geometric shapes (as straight lines, circles, or squares) <geometric abstractions>

Ok looks good.

Main Entry:
ex·po·nen·tial
Pronunciation:
\ˌek-spə-ˈnen-chəl\
Function:
Date:
1704
1: of or relating to an exponent2: involving a variable in an exponent <10x is an exponential expression>3: expressible or approximately expressible by an exponential function ; especially : characterized by or being an extremely rapid increase (as in size or extent) exponential growth rate>

Hmm, something seems to be amiss here, well let's do the most obvious thing, consult the epistemic paragon, the only entity that makes Edmund Gettier squirm....yes wikipedia, the leader in finding things that best describe your disposition. So, let's see what wikipeida has to say:

# Exponential growth

The graph illustrates how exponential growth (green) surpasses both linear (red) and cubic (blue) growth

Exponential growth (including exponential decay) occurs when the growth rate of a mathematical function is proportional to the function's current value. In the case of a discrete domain of definition with equal intervals it is also called geometric growth or geometric decay (the function values form a geometric progression).

OK, So if one was to say "my tree is growing at an geometric rate" they would be saying something different than
"my tree is growing at an exponential rate" Right? Here's why....

# Geometric progression

Diagram showing the geometric series 1 + 1/2 + 1/4 + 1/8 + ... which converges to 2.

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2. The sum of the terms of a geometric progression is known as a geometric series.

Thus, the general form of a geometric sequence is

$a,\ ar,\ ar^2,\ ar^3,\ ar^4,\ \ldots" src="http://upload.wikimedia.org/math/1/5/b/15b1e5bc8f8e8c5e7d46fd177eb625d6.png">

and that of a geometric series is

$a + ar + ar^2 + ar^3 + ar^4 + \ldots" src="http://upload.wikimedia.org/math/4/5/c/45c5fc422b6c7b23ac159bcb6f52bf47.png">

WOW, this truly is mind-bottling; So, the only people who know, or care about the difference are those who care about using concise language, scientist, philosophers, statisticians, a-holes, and me.

So, for the sake of language can we just agree on saying " Like, really, really fast", or at least refrain from using the world geometric, unless one is deliberately using the term.

So, you must be wondering by now, Mike why are you getting your panties in a wad over this distinction? Well, I could not decide whether or not to report that the amount of followers to my blog is growing exponentially or geometrically ( if geometrically, it would be on accident) let me see how many followers I have.... oh 0. Let me check again just to make sure, I could be approaching the exponential curve.... no, still zero. I guess if I am going to stick to using concise language, I will never have any followers if I have 0.....This sucks, well I hope my following increases really, really, fast

OK, So next week- what is better tool for expressing your feelings, wikipedia or Merriam websters dictionary, and the difference between sentiment and disposition.