Message-Id: <3.0.1.32.19980924170820.00cfd2bc@popmail.mcs.net>
Date: Thu, 24 Sep 1998 17:08:20 -0500
To: memetics@mmu.ac.uk
From: Aaron Lynch <aaron@mcs.net>
Subject: Re: Hosts vs. Instances
In-Reply-To: <000f01bde7f1$361f56c0$33a1bfce@lil--elvis>
At 12:25 PM 9/24/98 -0700, Tim Rhodes wrote:
>Aaron wrote:
>
>>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.
>
>Yes, as you write in your paper:
>
>"In general, propagation parameters can be measured over the duration of the
>time interval being modeled, as can the initial host populations of the
>memes under study. If the propagation parameters remain in some specified
>interval, then the final host population plus or minus a calculable error
>margin should be measured at the end of that interval. A host population
>measurement outside those error margins would then falsify the model being
>used for the specific memes under study."
>
>So, if I understand you correctly, this model is only applicable to cases
>where the propagation parameters (your K, B and Y terms) remain constant (or
>close to it) and not for all memes generally.
>
>Is this a correct reading of what you've said?
Yes, that is much of what I meant by calling it a "fairly idealized" model.
Any model based on a small system of differential equations applied to
something as complex as society will have similar exceptions. To get around
such difficulties will in general require more parameters and a more
complex model. I discuss some of the directions that more elaborate models
can take, but leave details to future papers.
>>Why are you talking about t+1?
>
>Sorry, I seem to have made the mistake of assuming that an accurate model
>memetic activity would be one in which the model had predictive power
>applicable to real world events, not just computer simulations. One that
>makes predictions about future events which can then be falisified by the
>data.
The assumptions implied by the above paragraph are false and unsupported.
>>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.
>
>I have made no such assumption. By "t+1" I simply meant "a unit of time in
>the future." I was not implying how long that unit should be. I assumed
>you were aware of the convention of f(t) and f'(t) = f(t+1).
>
>>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.
>
>Yes, but we are not modelling populations or disease. We are modeling
>memes, and as such our models must be able to apply to memes.
There are plenty of mathematical generalities that apply as well to
non-memetic models. If I point out that something such as stable parameters
making models easier to use in memetics, my remark is not in any way
negated by pointing out that it applies to other kinds of models as well.
My model applies to memes, even if I occasionally make remarks that apply
more generally.
>
>>>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
>>>point
>>>and approach the problem from an instance-of-meme-to-conversion-rate
>>>viewpoint instead?
>>
>>The last question looks utterly confused, as there is a one to one
>>correspondence between host of a meme and instances of that meme.
>
>This is not the case, although I see the confusion. By "instances of a
>meme" I was refering to instances of _exposure_ to the physical
>manifesations of a meme (meme-seeds, proxi-memes, artifacts, husks, whatever
>term you wish to use). In your paper you note that, "The B's, and Y's
>likewise do not reflect how many (times) a message was voiced from hosts to
>a non-host before that non-host converted." By "instances of a meme" I
>meant to refer to your "messages being voiced."
>
>Sorry, I forgot that we are not using the term "meme" in the same way.
>
>But, I think you will agree, there is NO one-to-one correspondence between
>the number of hosts of a meme and the number of instances of _exposure to_
>that meme. And that was my point.
That is more clear. Thank you. My model does not require or imply a one to
one correspondence between the number of hosts of a meme and the number of
instances of exposure to the meme. Rates of exposure are modeled as
depending on numbers of hosts and numbers of non-hosts in a manner that
cannot be described as simple one to one correspondence.
>For in your paper you state:
>
>" The overall theory would conceivably be falsified by refuting its premises
>or the logic and mathematics based on those premises."
>
>If a) adoption rates are known to correspond to instances of exposure to a
>meme (as shown by diffusion studies), and
>b) there is no one to one correspondence between hosts of a meme and
>instances of exposure to a meme, then
>c) any discussion of adoption rates linked to number of hosts in a
>population rather than instances of exposure must be logically incorrect.
>
>Is that somewhat clearer now?
It is clear, but your conclusion is unwarranted because modeling adoption
rates in terms of host and non-host populations does not require the one to
one correspondences mentioned in line b.
>>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?
>
>How did I know you were going to say that?!? (I must be psychic!)
>
>Yes, Aaron, I had written up a system of equations over a year and a half
>ago. (I have shared them with Gatherer, Brodie, and others for feedback.)
>They were very similar to yours, and led me down that same path you have
>taken. It soon became apparent to me that the most crucial term in all the
>equations was the term which governed an individuals likelyhood to adopt a
>meme from the environment into his internal meme-set. (This term was
>labeled R-sub-x in my equations--the x representing the meme in question.)
>
>Because I ran up against a wall where the importance of understanding and
>expanding this term became necessary in order to continue with any of the
>equations, I was forced to set the problem aside and seek more information
>on controlling factors which govern the choice to adopt. I believe
>diffusion studies shed some light into this area, but have not completed my
>research into them enough as of yet, to be sure. Ideally, I would prefer to
>have some emperical data to work from in this regard. The diffusion
>research seems the closest to that I have come across thus far. (Although I
>am open to suggestions!)
>
>And to be completely honest with you, Aaron, as an unpublished former
>college drop-out with an interest in memetics, the prospect of trying to get
>my work excepted in a forum such as this, after witnessing all the academic
>prejudices displayed by those such as you, is truly less than inspiring to
>me at the moment.
>
>-Tim Rhodes
>
Tim, I have not even known whether or not you graduated college, or had a
doctorate, let alone shown you prejudice over it. Nor did I show prejudice
against Richard Brodie in early 1994, when I sent him my 1991 Journal of
Ideas article. That paper contains virtually the same set of equations
given in my 1998 JoM-EMIT article. I would have sent the paper to you, too,
had I known of your interest back then.
Nevertheless, it will be difficult for me to consider your mathematical
modeling ideas without seeing your equations. If you do not yet feel like
taking the kind of criticism that I have been getting, then why don't you
put your equations on the web, and announce the URL? A variety of works in
progress have been offered for commentary on the memetics list, and this
can be a useful stage in preparing a paper for journal submission.
--Aaron Lynch
http://www.mcs.net/~aaron/thoughtcontagion.html
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