Date: Wed, 23 Sep 1998 16:54:20 -0500
From: Aaron Lynch <firstname.lastname@example.org>
Subject: Re: Hosts vs. Instances
At 12:24 PM 9/23/98 -0700, Tim Rhodes wrote:
>Aaron Lynch wrote:
>>The answer is that we cannot just compute conversion rates on an a priori
>>basis, even in cases were it is very tempting to do so. Peer to peer,
>>parent to child, and other modes of transmission still have to be measured.
>>As Bill points out, the mass media and famous players play an increased
>>role in recent decades, too.
>Indeed, it would seem that the number of exposures one has to a meme and the
>emotional associations linked with such exposure play a large roll
>determining whether or not the individual adopts the meme. Which brings me
>to a question about some of the terms and formulas in your paper, Aaron.
>You define the following terms for non-parental transmission of a meme:
>(BTW, if you have a preferred method of translating your terms to ASCII
>please let me know)
>"Y12(p,a) is the average annual net number of non-parental converts a meme-1
>host of age p makes per unit meme-2 host population-age density at age a in
>his society. B12(p,a) is the average annual net number of non-parental
>converts a meme-1 host of age p makes per percentage-year of meme-2 hosts of
>age a in his/her society."
>My questions is this: Knowing that the controlling factors governing
>conversion are related to number and type of exposures to a meme, rather
>than strictly the number of hosts of that meme in the present population, is
>the above a useful and descriptive approach? How do the above terms help us
>in any way to predict from knowledge of Y and B at t (time), instances of a
>meme (in a host or otherwise) that we might find at t+1?
>If this seasons hosts use TV to spread their memes, where last season they
>used word-of-mouth, your formulas loose any predictive value they may have
Time t is not an integer in those equations. Predictions are made using the
equations or computer models. All predictions of a host population at time
t = T being within a specified interval are contingent upon parameters
remaining within corresponding intervals, unless a periodic re-measurement
scheme is incorporated.
>Now you do go on to say:
>"Although emotional and cognitive receptivity factors are not readily
>conspicuous in equation 1 and equation 2, they are in fact represented. The
>reason is the K's, B's, and Y's are measures of successful meme transfer
>events. As such, they are composites of both the rates at which propagation
>is attempted and the rates at which it is cognitively and emotionally
>But as such they give us no information. In fact, the formulas seem to
>become tautological; well balanced with all the appropriate information
>filled in, but with no way of predicting how to fill in those terms at t+1
>without going back out and gathering the information anew for t+1.
Why are you talking about t+1? You cannot even assume from the model that
it will be applied for a whole year, nor can you assume that it will be
applied for less than a year. The model is far easier to use in phenomena
where propagation parameters are stable enough that they do not need
frequent re-measurement. The same thing with epidemiological models,
population genetic models, and so on.
>You also note:
>"The K's, B's, and Y's are each modeled as overall effective rates of meme
>transmission. The K's, for instance, do not indicate how many times a parent
>needs to repeat a message to her children before it is effectively learned.
>The B's, and Y's likewise do not reflect how many a message was voiced from
>hosts to a non-host before that non-host converted."
>I won't query you on the K term, it may or may not be useful to talk about
>parent-child conversion rates in these terms. I simply don't know.
>But for the non-parental terms it seems here that the need to link adoption
>rates to number of _hosts_, rather than _events_ of exposure, clouds the
>issue. In fact, the unwillingness to abandon the host-to-conversion-rate
>inter-relation would seem to send you down an overly complicated blind
>alley, as follows:
The proportionality to host populations works well in cases where total
exposure event rates are proportional to host populations or fractional
host populations (betas).
>"A more detailed model might therefore break down these parameters into the
>subfactors of transmissivity, a measure of how often each host attempts to
>transmit a meme, and receptivity, a measure of the likelihood each host to
>non-host transmission attempt has of actually imparting the meme to a new
>person. Much research has been done on how various components of receptivity
>affect the diffusion rates of innovations . Receptivity parameters can
>also be broken down to reflect different probabilities of meme acceptance on
>first, second, third, etc. exposure."
>Is all this necessary? At this point, doesn't Occam's Razor demand that we
>let loose of the ineffective hosts-to-conversion-rate assumption at this
>and approach the problem from an instance-of-meme-to-conversion-rate
The last question looks utterly confused, as there is a one to one
correspondence between host of a meme and instances of that meme.
If you have an idea for a better system of differential equations, then why
don't you write it up and submit it for publication?
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