gone parabolic (UNCLASSIFIED)
Victor Steinbok
aardvark66 at GMAIL.COM
Thu Dec 2 22:26:49 UTC 2010
@Bill--Our disagreement is not in the general description, but in the
division of assets, so to speak. My calculations use the fact that the
stock price first reached 100 in the last week of April and that period
in question only goes back to the beginning of the year, not last
November. So the rise from 50 to 100 took only 4 months, not 6. After
that, the stock slowed down before picking up pace again. So it took
another 7 months to double again. So, if we use these benchmarks,
instead of the six-month split, we have essentially linear growth. The
article specifically refers to the period from January to December 1.
Other than that we appear to be splitting hairs. In reality, because of
the fairly clean data, both linear and exponential models would offer a
fairly good fit. But the graph lacks a basic feature of a classic
exponential model--if you connect the endpoints with a straight line,
most of the exponential data and all of the model would be below that
line. This is not the case here.
@Joel--the short answer is no. It is hyperbola that approaches a
straight line as you move away from center, not parabola. Quadratic
growth ALWAYS exceeds linear growth /eventually/, no matter what the
linear growth rate is. Exponential growth, on the other hand, ALWAYS
exceeds polynomial growth /eventually/, no matter what the degree of the
polynomial is. To put is simply, a parabolic curve is one of /constant
acceleration/, so it would be inaccurate to describe it as you did.
VS-)
On 12/2/2010 3:23 PM, Mullins, Bill AMRDEC wrote:
> Obviously, one could curve-fit the data to various functions and find
> the residuals and minimize them for various curves. But I don't think
> that is what you, the WSJ, or I am trying to do here . . .
>
> I see a graph that goes (more or less) from 50 to 100 in 6 months (11/09
> to 5/10) and from 100 to 200 in the next 6 months (5/10 to 11/10). If
> it were linear, it would be gaining $50 per 6 months, and would have
> gone from 100 to 150 from 5/10 to 11/10 -- that is what linear does.
>
> If it doubles every six months (which is what it appears to do: $50 to
> $100, then $100 to $200), then that is the definition of an exponential
> growth -- not linear.
>
> Am I misunderstanding what you are saying?
On 12/2/2010 4:35 PM, Joel S. Berson wrote:
> Isn't there something wrong in the first place of thinking of
> increasing curvature with a parabola? As the arms of a parabola move
> further away from the center, doesn't the curvature continually
> diminish and approach a straight line?
>
> The analogy of ever increasing values to a parabola seems to me
> instead the progression of the arms to infinity, as contrasted with
> the other conic section, the ellipse, which closes upon itself.
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