Economy in embodied utterances by Matthew Stone

This is in Goldstein, L. (2013). Brevity. Oxford: Oxford University Press. Accessed 22 June 2017.

I like this because it brings questions about intentions and enactive type ideas right together.

3 Intentions and the principles of collaboration
While this account of intentions suggests how speakers might convey information
more economically by recognizing opportunities to overload their communicative
intentions, the account offers important insights into the limits of brevity as well.
Communicative intentions are prototypically collaborative. In communication,
interlocutors use utterances to contribute propositions to conversation, and thereby
to address and resolve open questions, as part of a joint process of inquiry. This
section argues that collaborative intentions generally, and communicative intentions
in particular, are subject to constraints of COHERENCE that limit how tightly
overloaded they can be.
Researchers such as Cohen & Levesque (1991) have argued that intentions
have a distinctive role to play in the deliberations of agents that work together,
because teamwork requires agents to coordinate with one another (Lewis 1969). p. 152

We can point to pervasive analogies between teamwork as it applies in a
cooperative conversation, and teamwork in pursuit of shared practical goals. Let’s
start with understanding. To understand your teammates’ actions, you have to
recognize the intentions with which they act. These intentions involve commitments
not only to action, but also to relevant facts about the circumstances in which the
action is being carried out and about the contributions which the action is going to
make. Recognizing an intention is a process of explanatory inference that can start
from background information about the agent’s action, knowledge, preferences and
goals, but that can also make assumptions to fill in new information about the agent
as well. Reasoning about preferences is particularly important when agents maintain
an open-ended collaborative relationship with one another (Cadilhac, Asher,
Benamara & Lascarides 2011).
Imagine, for example, you are part of a team that’s catering a party. You see
one of your colleagues carrying a full tray of drinks towards a closed door. You
probably conclude that your colleague intends to distribute the drinks to party-goers
in the next room. You’ve used what you already know about your colleague’s
beliefs: you see your colleague moving, you see the full drinks, and it’s obvious that
your colleague is moving purposefully and is aware of the surroundings. You’ve also
used what you already know about your shared goals: drinks must be distributed if
the party is to be a success. At the same time, you’ve made additional assumptions.
Perhaps you were previously unaware that the next room was open to guests, or that
it even existed. But given the intentions you’ve recognized, your colleague must
know about these guests and have the particular goal of serving them.
It’s crucial that intention recognition gives you this new understanding of your
colleague and the ongoing activity. You’ll need it to track the state of the
collaboration and to plan your own contributions to it. Your engagement with each
other means that your colleague’s continued action, like carrying the drinks here,
provides the shared evidence you need to keep coordinating, and relieves you of the
need to explicitly discuss each step of progress in the task. Thomason, Stone &
DeVault (2006) explore this reasoning in more detail. They argue that collaborative
reasoning always involves a shared presumption that team members act
cooperatively and are engaged in tracking each other’s contributions. This recalls
the famous Cooperative Principle and Maxims of Grice (1975), of course.
To use language collaboratively, agents need to recognize the intentions
behind utterances in much the same way p. 153


Contemporary Art and Anthropology

Schneider, A. and Wright, C. (eds) (2005). Contemporary Art and Anthropology (English Ed edition). Oxford: Berg Publishers.
An interesting book! I enjoy the worry about ambiguity (art tends to rather seek it out, after all) and points about visual anthropology.
2018-05-07 15.26.122018-05-07 15.24.522018-05-07-15-24-43.jpg2018-05-07-15-25-46.jpg2018-05-07 15.25.46

How to write mathematics


A major objection to laying down criteria for the excellence of an exposition is that the effectiveness of an expository effect depends so heavily on the knowledge and experience of the reader. A clean and exquisitely precise demonstration to one reader is a bore to another who has seen the like elsewhere. The same reader can find one part tediously clear and another part mystifying even though the author believed he gave both parts equally detailed treatment. (Steenrod, 1973)

He advises the division of the formal/logical mathematical part, and informal/introductory/metamathematical part. Some, he says, might say, “Show me the mathematics, I’ll supply my own philosophy” p. 2 but he advises supplying some gloss nonetheless.

“He must strive throughout to describe his own attitudes towards the various parts of the subject, and also such other views as he regards valid, but all such material must be labelled as distinct from the formal structure so that a reader can omit and skim such parts as are not to his taste. P. 2

Expects formal to come before informal.

Case for introduction:

“The fact that a reader forgets the introduction is no objection if the introduction helps him grasp the formal structure more quickly. At stake here is the question of how a student learns best. The first of two contending procedures is to ask him to examine first the lumber, bricks, and small structural members out of which the building is to be made, then to make subassemblies, and finally to erect the building from these. The second procedure is first to describe the building roughly but globally and provide a framework for viewing it, and then examine the construction of the building in detail. The first procedure would appeal to a student with a leisurely attitude who enjoys successive revelations. The second procedure, which I espouse, has the advantage that motivation is present at every stage; the student knows where each item belongs when he examines it. The second procedure can be elaborated by inserting between the first rough scan and the final detailed examination a series of scannings revealing successively finer details. P. 11-2

For example, Dunford and Schwartz make no attempt to entice readers to study their book, they do not say at the start what linear operators are about nor why they are important. The reasons for this omission are undoubtedly that their book is a reference work and text for a well-known standard field, and every mathematical education already includes much about linear operators; a sales-promotion job is unnecessary. One consequence of this omission is that they give no overall picture of the results that they obtain; I would like to have had such a review for study, and I suspect that some students of their book would have found it useful. P. 11-2


Writing mathematics is like“writing biology, writing a novel, or writing directions for assembling a harpsichord” p. 20

Halmos advises to write as though addressing someone and mentions mind reading p. 22-3 He estimates the longevity of a paper vs. a book: book 25 years, paper 5. p. 22

Bad notation can make good exposition bad and bad exposition worse; ad hoc decisions about notation, made mid-sentence in the heat of composition, are almost certain to result in bad notation.

Good notation has a kind of alphabetical harmony and avoids dissonance. Example: either ax+by or a1x1 +a2x2 if preferable to ax1 +bx2. Or: if you must use Σ for an index set, make sure you don’t run into PσΣ aσ. Along the same lines: perhaps most readers wouldn’t notice that you used |z| < ε at the top of the page and z ε U at the bottom, but that’s the sort of near dissonance that causes a vague non-localized feeling of malaise. The remedy is easy and is getting more and more nearly universally accepted: ∈ is reserved for membership and ε for ad hoc use.

Mathematics has access to potentially infinite alphabet (e.g. x, x’, x’’, x’’’, . . .), but, in practice, only a small finite fragment of it is usable. One reason is that a human being’s ability to distinguish between symbols is very much more limited than his ability to conceive of new ones; another reason is the bad habit of freezing letters. Some old-fashioned analysts would speak of “xyz-space”, meaning, I think, 3-dimensional Euclidean space, plus the convention that a point of that space shall always be denoted by “(x, y, z)”. This is bad: if “freezes” x, and y, and z, i.e., prohibits their use in another context, and, at the same time, it makes it impossible (or, in any case, inconsistent) to use, say, “(a, b, c)” when “(x, y, z)” has been temporarily exhausted. Modern versions of the custom exist, and are no better. Examples: matrices with “property L” — a frozen and unsuggestive designation.

There are other awkward and unhelpful ways to use letters: “CW complexes” and “CCR groups” are examples. A related curiosity that is probably the upper bound of using letters in an unusable way occurs in Lefschetz [6]. There xpi is a chain of dimension p (the subscript is just and index), whereas xip is a co-chain of dimension p (and the superscript is an index). Question: what is x23?

As history progresses, more and more symbols get frozen. The standard examples are e, i and π, and, of course, 0, 1, 2, 3, . . . (Who would dare write “Let 6 be a group.”?) A few other letters are almost frozen: many readers would fell offended if “n” were used for a complex number, “ε” for a positive integer, and “z” for a topological space. (A mathematician’s nightmare is a sequence nε that tends to 0 as ε becomes infinite.

Sometimes a proposition can be so obvious that it needn’t even be called obvious and still the sentence that announces it is bad exposition, bad because it makes for confusion, misdirection, delay. I mean something like this: “If R is a commutative semisimple ring with unit and if x and y are in R, then x2−y2 = (x−y)(x+y).” The alert reader will ask himself what semisimplicity and a unit have to do with what he had always thought was obvious. Irrelevant assumptions wantonly dragged in, incorrect emphasis, or even just the absence of correct emphasis can wreak havoc. P. 34

p. 34-5 advice on stating theorems—briefly as possible, irrelevancies excluded.

If you have defined something, or stated something, or proved something in Chapter 1, and if in Chapter 2 you want to treat a parallel theory or a more general one, it is a big help to the reader if you use the same words in the same order for as long as possible, and then, with a proper roll of drums, emphasize the difference. P. 35

The symbolism of formal logic is indispensable in the discussion of the logic of mathematics, but used as a means of transmitting ideas from one mortal to another it becomes a cumbersome code. P. 38 Generally avoid symbols. P. 40


He addresses himself to colleagues and coworkers whose knowledge of the subject and interest in his contribution can be taken for granted. He may be as brief and concise as he wishes and omit history, background and motivation for his work. However, even here it might be worthwhile to consider that by adding a little background information one might widen the audience from the close circle of specialists on the subject to a much more extended group of interested mathematicians…. While writing the paper, the author should envisage the reader who has taken the paper to a place without a library and who is willing to believe a few facts on the say-so of the author, but also wishes to understand what he means. P. 50


Rethinking the mathematical paper

On Wednesday I gave a talk at my university’s Postgraduate Research Forum, and took the opportunity to test out an activity I’d been mulling over. The idea was to get groups of people to work with a very short mathematical paper and find ways to restructure and lay the content out. This is a development from a previous idea.


The paper I used was this, a three-page paper by Mowaffaq Hajja. A_Very_Short_and_Simple_Proof_of_The_Most_ElementaIMG_0190

The results were quite interesting. The first group chose to make the main diagram in physical form, and then, interested by the arrowhead shape, folded a page of the paper to match.

IMG_0208The second set about organising the paper such that references to diagrams were placed next to the diagrams themselves, also using colour-coding and string to make such links more explicit. The string links themselves made another triangle. They also highlighted an interestingly emotive moment in the text.


The third group decided to reorganise the narrative of the paper, so that the history of the problem was given first, and the narrative progressed from there. They also placed the references as they occurred in the text.IMG_0222IMG_0224IMG_0230