[D-G] Concepts seen as functions

Cain, Prof. Jeffrey P. CainJ at sacredheart.edu
Thu Apr 28 17:42:55 PDT 2011

Dear Malgosia--

Thank you so much for taking the time to meticulously and clearly answer my rather ill-formed questions.  Your explanation makes perfect sense to me, especially the very telling balances you draw between intensive and extensive, actual and virtual, limited and unlimited speeds. I see now that the terms I thought were fairly exclusively mathematical can be thought of in other contexts (again perhaps an artifact of my inexperience in scientific and mathematical discourse). I am familiar with the scientific / thermodynamic meaning of "intensive," and it seems to me that what you say adheres quite definitely to my understanding of it.

I am, ultimately, grateful for having learned so much in a brief space of time.  And no worries, you haven't discouraged me from trying to learn calculus.  I'll definitely continue with it--it seems to me that D&G had a profound understanding of mathematics, and that there is a certain baseline knowledge of the subject one ought to try to attain in order to read them with some degree of precision. I've been keeping it quiet around the English department though--my colleagues might consider that I'd taken leave of my senses if they knew what I was doing :-)

Thanks again,

Jeffrey P. Cain, Ph.D.
Chair, Department of English HC221A
Sacred Heart University
Fairfield, Connecticut 06825

Office Hours Spring 2011: Mondays 12:00-2:00; Wednesdays 12:00-2:00; Fridays 11:30-12:15
From: deleuze-guattari-bounces at lists.driftline.org [deleuze-guattari-bounces at lists.driftline.org] on behalf of malgosia askanas [ma at panix.com]
Sent: Thursday, April 28, 2011 7:41 PM
To: deleuze-guattari at lists.driftline.org
Subject: Re: [D-G] Concepts seen as functions

Dear Jeff,

I wouldn't dream of discouraging you from a study of calculus, but to
me it seems that the passage you quote from WiP doesn't call upon any
special knowledge of calculus, or mathematics in general.  I think
that "limit" here does not have any specialized mathematical sense,
but just refers to restricting something, setting limits upon it -
and that "something", in this case, is the virtual.  As for
"abscissa", I think that the important point here is that in the
virtual there is no external "clock", or standard, which "clocks" the
variation of the differential elements (i.e. those elements whose
differences are responsible for the continuous variation within the
given virtual domain).  The differential elements thus form what D&G
call "intensive ordinates" - their variations don't depend on
anything extraneous, and neither are there any internal dependencies
between the differential elements (that's why they all form
"ordinates" and there is no "abscissa", i.e. no variable on which
they are all considered to be dependent).  They vary freely,
continuously and unrestrictedly.  For example, the gradations of the
phonemes in the Idea (or virtuality) of Language would not be
restricted by considerations of discernability by ear,
pronounciability, etc.

Science, on the other hand, imposes limits on the virtual in more
ways than one, if only through its stringent methodological
requirements: that it be based on experiment, that the experimental
results be reproducible, that the theoretical results have a close
connection to the experimental and be formulated according to certain
standards of shared intelligibility, and so on.  And since the
language in which it expresses its results is the language of
functions, the first step of any scientific project is to choose the
variables under study - the variables whose changes express the
natural phenomena under study, and whose functional dependencies the
study will pertain to.  And every scientific project has to limit
itself to studying the given phenomena under a certain set of
conditions - which, in turn, sets limits on the possible values which
the variables can range over.  So: the first two components of every
scientific function - i.e. the first two functives, to use D&G's
language - are the limit (or limits) and the variable (i.e. the
choice of variables).  It is these two components that constitute the
scientific plane as a plane of reference.  And why is "the variable"
an "abscissa of speeds"?  I think it is because the introduction of
these two components (or perhaps even just the choice of variables,
qua potential functives and with their limits) sets a "clock" (like a
sampling rate, but in a more profound sense) to the free variations
within the virtual - the "sampling" will only take place according to
certain methods, and only on certain terms, at certain "speeds" of
thought, according to a certain experimental protocol, etc.  So if
the variation of the virtual is described as taking place intensively
and "at infinite speeds", then the scientific actualization is
achieved by slowing down the virtual to speeds dictated extensively,
by the methods of science, which thus effectuate an "abscissa".

These are just the general lines along which I would tease that
passage, and perhaps completely off.


At 6:42 PM +0000 4/28/11, Cain, Prof. Jeffrey P. wrote:
>RV, thanks for the interesting comments.  I do understand, I think,
>a reasonable part of this issue with regard to
>schizoanalysis--though I will never claim to have any of D&G's
>concepts completely or even mostly exhausted, especially not
>schizoanalysis. But the part of _What is Philosophy?_ that has
>always seemed a bit vague to me (and I blame it on my own lack of
>mathematical sophistication, not Deleuze and Guattari), is Part Two,
>Section Five, "Functives and Concepts."  Specifically, the English
>translation says that "the first functives are the limit and the
>variable and reference is a relationship between the values of the
>variable, or, more profoundly, the relationship of the variable, as
>abscissa of speeds, with the limit" (118-119).
>I'd be gratified to resolve a gnawing question about how this
>relates to differential calculus, the limit theory, the asymptote,
>mathematical functions, etc; particularly since D&G do make remarks
>elsewhere that implicate the calculus. Perhaps an unfocused but
>well-intentioned question would be: "how is schizoanalysis like
>differential calculus?" But I already sense that it isn't formulated
>rigorously.  Again, I assume this is my own ignorance--I can say
>that I've been working fairly hard on my math for the last couple of
>months, have arranged to audit a calculus class and am definitely
>trying to get there by myself. (My Ph.D. is in English!) But it
>occurred to me earlier today that someone on the list might have a
>complete understanding from a mathematical point of view.  Just
>thought I'd clarify my reasons for writing.
>"Abscissa," by the way, seems to be a somewhat outdated word in
>English--I understand it as simply the term one plots on the x or
>horizontal axis of a Cartesian grid. My pre-calculus book doesn't
>use the term, so I'm also wondering whether it has any other meaning
>for D&G.
>Thanks again, RV, for your very kind help.
>Jeffrey P. Cain, Ph.D.
>Chair, Department of English HC221A
>Sacred Heart University
>Fairfield, Connecticut 06825
>Office Hours Spring 2011: Mondays 12:00-2:00; Wednesdays 12:00-2:00;
>Fridays 11:30-12:15
>From: deleuze-guattari-bounces at lists.driftline.org
>[deleuze-guattari-bounces at lists.driftline.org] on behalf of
>saphiregnauld [saphi.regnauld at numericable.fr]
>Sent: Thursday, April 28, 2011 1:37 PM
>To: deleuze-guattari at lists.driftline.org
>Subject: Re: [D-G] Concepts seen as functions
>  dear all
>  according to D+G and at least in french "concepts" are not "functifs"
>and will never be..
>Concepts are able to mobilize the movement whereas  functifs are said to
>immobilize the movement in order to build a  true equation..   This is
>one the worst D+G idea : concepts are only for philo and science is left
>with  second order ideas which are called  functifs.
>  The basis of this is in "cartographies schizoanalytiques" by G (alone)
>when he dismisses neuro sciences  and wants to promote schizio analysis
>(in the french edition it is page 47 to 51)
>  " notre souci principal est de developper un cadre conceptuel qui
>prémunisse la schizo A contre toute tentation de s'abandonner à l'idéal
>de scientificité qui prévaut ordinairement dans le domaine "psy"  "..
>which in english is something like :
>"our main  aim is to develop a conceptual framework which may prevent
>schizo A to be leaning toward the idealistic scientist model which
>usualy dominate the "psy" field..."
>  Good idea , absolutely great idea for the "psy" field. But the problem
>is that other sciences do not fit with this local epistemic model. For
>so called "natural sciences" such as geology or physical geography or
>ecology.. there is no need to separate the concept (which ables the mind
>to move) and the functif which stops the minds and reduces it to a set
>of neuronal interactions.
>There no mind in natural sciences.. and this difference between self
>concious minds and incouncious minds does mean anything.
>  So D+G should not have taken the model of neuro science vs schizo A as
>a universal model of the relation between science and philosophy..
>Hopelessly this is not a main topic in the excellent book about Deleuze
>and space..
>  Anyhow
>  it is of the most tricky aspect of D+G work and working about it is a
>difficult task.. You have to get back to the early book on Hume and to
>all the difficults relations between D and G at the end of their lives
>(see Dosse's book) .
>  See, above all,  A Sauvagnargues'  mega excellent book on "empirisme
>transcendantal" (in french) and some papers in in Chimères..
>  amicalement  RV
>    malgosia askanas a écrit :
>>  Dear All,
>>  When D&G, in WiP, refer to the view that concepts are functions, are
>>  they referring to Frege, or is there an earlier philosophical
>>  tradition that proposes this view of concepts?  I recently chanced
>  > upon a text that claimed the latter, but now I cannot locate it
>>  again.  Your help will be much appreciated.
>>  -m
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