Discussion:  All Topics 
Topic:  The L curve 
Related Item:  http://mathforum.org/mathtools/tool/18781/ 
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Subject:  RE: The L curve 
Author:  David Chandler 
Date:  May 13 2005 
> out [the only interatcion], but to what purpose? It merely shows a
> couple with a stack of bills at their feet to show the relative
> size. However, all is stated in text, and since I learned to read
> at an early age, I don't really need the graph. The fact that only
> a very few are very very rich is understandable. Only that many
> know how to accumulate and to retain their wealth, and only that
> many need to.
I am the author of the www.lcurve.org web site. I want to respond to this
comment in two parts. First: "...but to what purpose? It merely....since I
learned to read at an early age, I don't really need the graph."
Comprehension of big numbers is difficult for nonmathematicians, for an
interesting reason, actually. Consider the numbers:
1,000
1,000,000
1,000,000,000
The visual appearance of the numbers in place value notation makes them look
like starsteps. The lengths of the numbers are in arithmetic progression, but
the values of the numbers are in geometric progression. (...a sort of a
logarithmic transformation!) This makes it easy to do computation on huge
numbers, but it means you have to make a conscious effort to understand the
intuitive significance of the numbers. It also means that people who don't work
with numbers all the time have to be constantly reminded of the significance of
adding a zero (or three) to the end of a whole number. As I mentioned on the
supporting web page (on Millions and Billions), over the years on pretests in my
community college astronomy classes, I have found that 85% of adults walking in
off the street do not know how many millions there are in a billion. This has
implications for their understanding of social issues involving big numbers (be
it population, economy, pollution, growth, etc.).
The second thing I want to respond to is the idea that all the graph shows is
the proportion of people who "know how to accumulate and to retain their
wealth." The graph shows a fact of life in the US economy. The cause of that
fact is not immediately obvious. My own analysis is that the economy is a
stacked deck, where those with wealth have disproportionate political power to
tailor the rules to favor those with wealth. Whether this analysis, or the more
libertarian analysis (that this is what happens when people have freedom to make
their own choices) is correct is something that the graph by itself can't
answer. On the other hand, until people are empowered to understand big numbers
they are locked out of the discussion.
By the way, I did not submit this site to start a political argument. I was
invited to submit the site. I recognize its political content, but the
relevance is that mathematical understanding is important to informed
participation in the political process.
 
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