[FRIAM] PM-2017-MethodologicalBehaviorismCausalChainsandCausalForks(1).pdf

Thu Feb 11 10:37:38 EST 2021

I thought this is where you were going, but if you can cause trouble, so can we!

-----Original Message-----
From: Friam <friam-bounces at redfish.com> On Behalf Of David Eric Smith
Sent: Thursday, February 11, 2021 5:32 AM
To: The Friday Morning Applied Complexity Coffee Group <friam at redfish.com>
Subject: Re: [FRIAM] PM-2017-MethodologicalBehaviorismCausalChainsandCausalForks(1).pdf

Nick,

There is a character to this conversation like many in this list.  There is a thing you do by instinct, which drives me batty and makes me want to call you an Analytical Philosopher and other such insults.  Like anything done by instinct (think of Trump’s instinct for instigation), it is surprisingly difficult to try to characterize didactically.

I think the core issue is this (for me):  Each of these terms — screening off, Currying, partitioning of variance — developed within a language in the service of _doing something_.  The thing that makes me want to call you an analytical philosopher is your penchant for insisting on ignoring the context in _doing_ where the term was given to you, treating it as if the whole meaning of something should be carried in the form of its expressions, and then calling the surface expression a metaphor when it isn’t self-interpreting.  I shouldn’t criticize; that is in some sense the essence of the Hilbert program, of Montague Grammar, or of any systematic study of forms: to ask how much of the sense of a thing is mirrored in the form of its expressions.  The default is that you seem to insist on treating everything as if _all_ of the meaning should be carried in form, whereas my expectation is that very little will be carried in form and most in context.  Hence your insistence on taking every sentence out of any context where it makes sense, and insisting on imposing it on a context where it seems non-sequitur (to “madly squeeze a right-hand foot into a left-hand shoe").  

Jon’s emails are helpful (and Glen’s), because they take this exercise seriously, and show that one can get away with a surprising amount of it.  I guess this is where Fields medals come from.

But this is why I introduced Currying in response to your Ham and Eggs; it was only slightly teasing you, but more my opinion that, in _totally and willfully ignoring_ the context for causal inference that Frank gave you, you had moved into another context where Currying was the natural language and Screening Off not the natural one.  So, of course, in response to that, you did what you do, and ignored the context where Currying arises, to jump to Partitioning of Variance.

Let me acknowledge that Jon’s logical renderings show how far one can get away with such things.  All good.  

Then, let me try to back-fill what makes the contexts different, so that I try to build more of that _into_ the forms of the expressions, so that the poor “definitions” of Screening Off or Currying will not have to stand so much on their own.

1. Screening Off:  I think of this as having arisen for a class of problems like updating of a set of variables that live on a network.  Think of coins spread on a table that may be head or tail, with threads telling which coins “affect” which other coins.  Then have some procedure to filp some of the coins, with probabilities that depend on the current state of the other coins to which they are connected in the network.  (The case I described is an instance of a Boolean Network.  One could generalize to many others while keeping its essential spirit.)

Here is what such cases have in common.  The network that tells which coins affect which others, and the algorithm for flipping coins based on the current states of other coins, are _given outside the state of the coins_.  The coins are _peers_ to each other.  They do not create the network; they do not impose the flipping rule; their job is very limited, to carry the _state_ of the system at any moment.

The notion of Screening Off comes from the act of “marking” a subset of the coins, to get at the sense in which their states may stand between the future states of some other focal coins you may wish to discuss, and the universe of other coins whose states you want to know if you can ignore.  But the “screening” part of Screening Off comes from the peer-status of any coin to any other coin, in context of a network that is provided to you as context.

To this you brought Having Ham and Eggs, as a kind of propositional expression that can go from truth values for ham and for eggs to truth values for the proposition, and you asked how some other propositional expression such as Having Eggs could be combined with the former.

HUH?

Where did the peer status of coins go?  Where did the externalness of the network and the flipping rule go?  Where did these new maps and operations come from?  None of that had been part of the _doing_ context in which the Screening Off expression was found helpful to organize thought.

2. Currying:  But, if we took the expression Having Ham and Eggs and asked whether it was familiar, and in what context it _had_ been found useful, we would recognize that it was at home in discussions of function application.  A function is a map from some domain that we call the inputs to some range that we call the outputs.  As Jon wrote:
(+) 2 5 = 7
can take a pair of numbers (2 and 5) and return a single number (7).
Currying is an operation that changes one kind of map to another kind of map, allowing us to do such things as change its domain or its range.  Hence, from (+) and (2) we can create a new map (+ 2) 5 = 7 which takes a single number (rather than a pair) as its input (5) and returns a single number (still) as its output (7).

Now the general habit in _calling_ something a function is to emphasize its role as a mapping — an activity that responds to inputs and delivers outputs.  The act is of interest; what the inputs and outputs are, or whether there is one or another algorithm relating them, can all be varied within the same notion _that_ a certain activity counts as “mapping”, and that the map is thus a function.  

To this, you branched to ANOVA which lives in the domain of regression in statistics.  Fair enough, and good as a case study.  (I am a heavily example-based thinker, so I have great sympathy for people who quickly look for examples.)  But additivity, or other properties of the _algorithm_ for relating outputs to inputs, is a separate matter of context from something’s _being_ a function.  To the extent that Currying was about converting one kind of function to another kind of function, that aspect of the abstraction gets lots in a kind of inattention blindness if one goes to asking whether projection of a regression onto a subset of coordinates is central to the dimensional reduction of functions (not general; it is the special feature that sets additivity apart among algorithms).  So it is not that projection might not be an instance of function transformation — that is okay — but that the awareness that what you are doing is _converting a map_ gets lost in focusing on the accidental features of a case.

But if we had chosen once again to shift contexts, we would have arrived at 

3. Partitioning of Variance: a property of statistical reductions through linear regression, which is quite at home in the doing-context of ANOVA, and useful there.

etc.

I don’t know if my above is at all helpful.  But I do think that contexts can be made explicit with a lot of work.  When these circles (circuses? Jamborees?) of confusion result, it often seems that they can be untangled by making explicit within descriptions, the contexts that before were not described.

Eric

> On Feb 10, 2021, at 4:08 PM, <thompnickson2 at gmail.com> <thompnickson2 at gmail.com> wrote:
> 
> All,
> 
> I guess, since nobody has responded to it, my attempt to analogize currying
> to partitioning of variance in an ANOVA is NOT apt.   Definitely a case of
> FRIWWMFTT. 
> 
> 
> 
> Nick
> 
> Nick Thompson
> ThompNickSon2 at gmail.com
> https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.e
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> 
> -----Original Message-----
> From: Friam <friam-bounces at redfish.com> On Behalf Of jon zingale
> Sent: Wednesday, February 10, 2021 2:54 PM
> To: friam at redfish.com
> Subject: Re: [FRIAM]
> PM-2017-MethodologicalBehaviorismCausalChainsandCausalForks(1).pdf
> 
> Ha! just posted on that point!
> 
> 
> 
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