Re: Other than physics

[Peter Schoch <pschoch@NAC.NET>]

I like the revisions that hve been mentioned, except for the continual
references to "sketching".  I presume that everyone here could take 10
minutes and perform the necessary calculations in a spreadsheet, and use
it to graph it as well.  That way you get all the accuracy you want, and
any amount graphical extension.

If you want a more "robust" way to graph it and do the calculations, use
Mathcad.  It's a Pre-CalcII question, almost straight out of a textbook
on math -- y'know, the ones that are notorious for trying to write
"application" problems, but are always atrocious at it!

Peter Schoch

brian whatcott wrote:
> At 23:43 5/29/99 -0400, Greg Darakjian wrote:
> > Hello:
> >
> > A student of mine asked me to help her out with the following problem.
> > Would somebody care to provide an answer ?
> >
> > "Linguists study the changes in word usage in a language over time.  They
> > find that words disappear from a language according to an exponential model
> > W(x) = e raised to the power -0.75 x where W(x) represents the percent of
> > words remaining in a language after 'x' thousand years (ignoring the addition
> > of new words.)
> > Formulate a visual presentation to estimate the dates for the disappearance
> > of 25%, 50%, 75%,and 100% of today's language.  Suppose a word fell into
> > disuse this year.  In what year would it have originated ?   List any words
> > that have disappeared from our language in the last 100 years.  Estimate the
> > time of their origin."
> >
> > Thanks.
> > Greg Darakjian
>
> A person might choose to sketch a graph of word extinction with time,
> using x = 1,2,3 etc kiloyears.
> One could thereby estimate a time for a surviving vocabulary of
> 75, 50, 25% etc.
>    One expects the tail to proceed until the last of 140,000 (?) words
> has turned over, which might need about 17 half-lives, about as many
>  millennia.
>     One could suppose that when a word has survived to a time when
> 50% of words have been replaced, it is then likely to succumb - for this
> assumption, its half-life of about a millennium would be subtracted from
>  todays date for its putative birth.  (I'm sure people can see that
> this is taking a rather deterministic view of individual probabilities.)
>
>     To list words that have disappeared from the language is to revive
> them to the flush of life. Perhaps a more rational objective is to list
> some words that are archaic - with the implication that they no longer
> find common usage: the Old English plural pronoun "Ye" is now
> effectively replaced by "You" I imagine, like its singular
> buddy, "Thou."
>
> I expect the physicist(?) who posed this problem about linguists meant
>  to have the expression W(x) = exp(-0.75*x) represent fractional survival
> of a vocabulary for time x in kiloyears, rather than percent survival.
>
> A numerate person might essay a more accurate value for the vocabulary's
> half-life, in the usual way:
> 0.5 = exp(-0.75.x)
> ln 0.5 = -0.75.x
> x = -ln(0.5)/(0.75) = 0.924 kiloyears.
>
> brian whatcott <inet@intellisys.net>
> Altus OK