Economy in embodied utterances by Matthew Stone

Click to access brevity13.pdf

This is in Goldstein, L. (2013). Brevity. Oxford: Oxford University Press. http://capitadiscovery.co.uk/brighton-ac/items/1339856. 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
16
Economy
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.
17
Stone
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.

How to write mathematics

https://www.amazon.com/How-Write-Mathematics-Norman-Steenrod/dp/0821800558

Steenrod

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

Halmos

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 P_σ∈Σ a_σ. 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 x^p_i is a chain of dimension p (the subscript is just and index), whereas xⁱ_p 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 n_ε 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

Schiffer

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

 

Epistemic Vigilance by DAN SPERBER, FABRICE CL ́ EMENT, CHRISTOPHE HEINTZ, OLIVIER MASCARO, HUGO MERCIER, GLORIA ORIGGI AND DEIRDRE WILSON

Click to access Epistemic-Vigilance-published.pdf

Trust is obviously an essential aspect of human interaction (and also an old
philosophical topic—see Origgi, 2005, 2008). What is less obvious is the claim
that humans not only end up trusting one another much of the time, but are also
trustful and willing to believe one another to start with, and withdraw this basic
trust only in circumstances where they have special reasons to be mistrustful p. 361

The descriptive issue has recently been taken up in experimental psychology.
In particular, work by Daniel Gilbert and his colleagues seems to show that our
mental systems start by automatically accepting communicated information, before
examining it and possibly rejecting it (Gilbert et al., 1990; Gilbert et al., 1993).
This can be seen as weighing (from a descriptive rather than a normative point
of view) in favour of an anti-reductionist approach to testimonial knowledge. p. 362

When the communicator is producing a logical
argument, she typically intends her audience to accept the conclusion of this
argument not on her authority, but because it follows from the premises:
Conclusion of argument: p, q, therefore r (from already stated premises): While U[tterer]
intends that A[ddressee] should think that r, he does not expect (and so intend)
A to reach a belief that r on the basis of U’s intention that he should reach it.
The premises, not trust in U, are supposed to do the work (Grice, 1969/1989,
p. 107).

Despite the existence of such counter-examples, Grice thought he had compelling
reasons to retain this third-level intention in his analysis of ‘speaker’s meaning’. Sperber and Wilson, on the other hand, were analysing not ‘meaning’
but ‘communication’, and they argued that this involves a continuum of cases
between ‘meaning’ and ‘showing’ which makes the search for a sharp demarcation
otiose. In producing an explicit argument, for instance, the speaker both means and
shows that her conclusion follows from her premises. Although Grice’s discussion
of this example was inconclusive, it is relevant to the study of epistemic vigilance.
It underscores the contrast between cases where a speaker intends the addressee to
accept what she says because she is saying it, and those where she expects him to
accept what she says because he recognises it as sound.We will shortly elaborate on
this distinction between vigilance towards the source of communicated information
and vigilance towards its content.
Clearly, comprehension of the content communicated by an utterance is a
precondition for its acceptance. However, it does not follow that the two processes
occur sequentially. Indeed, it is generally assumed that considerations of acceptability
play a crucial role in the comprehension process itself. p. 367

What happens when the result of processing some new piece of information
in a context of existing beliefs is a contradiction? When the new information
was acquired through perception, it is quite generally sound to trust one’s own
perceptions more than one’s memory and to update one’s beliefs accordingly. p. 375

We would like to speculate, however, that reasoning in non-communicative
contexts is an extension of a basic component of the capacity for epistemic vigilance
towards communicated information, and that it typically involves an anticipatory
or imaginative communicative framing. p. 379

The institutional organisation of epistemic vigilance is nowhere more obvious than
in the sciences, where observational or theoretical claims are critically assessed via
social processes such as laboratory discussion, workshops, conferences, and peer
review in journals. The reliability of a journal is itself assessed through rankings,
and so on (Goldman, 1999).
Social mechanisms for vigilance towards the source and vigilance towards the
content interact in many ways. In judicial proceedings, for instance, the reputation
of the witness is scrutinised in order to strengthen or weaken her testimony. In the
sciences, peer review is meant to be purely content-oriented, but is influenced all
too often by the authors’ prior reputation (although blind reviewing is supposed to
suppress this influence), and the outcome of the reviewing process in turn affects
the authors’ reputation. Certification of expertise, as in the granting of a PhD,
generally involves multiple complex assessments from teachers and examiners, who
engage in discussion with the candidate and among themselves; these assessments
are compiled by educational institutions which eventually deliver a reputation label,
‘PhD’, for public consumption.
Here we can do no more than point to a p. 383

Audiences, Relevance, and Cognitive Environments CHRISTOPHER W. TINDALE (1992)

Cognitive environments are pretty important to my current work, because I’m thinking so much about how a communication is received by a mass audience, and the degree to which it can achieve relevance in dramatically more- or less-suited cognitive environments. This paper is a philosopher writing about relevance in a fairly loose way, though drawing upon Sperber and Wilson’s cognitive environment work.

The author distinguishes ‘in a provisional
way between premise-relevance (internal among the components of an argument),
topic-relevance (the relation of the argument to the topic or issue), and audience relevance. This last involves the relation of the information-content of
an argument, stated and assumed, to the framework of beliefs and commitments
that are likely to be held by the audience for which it is intended.’ p.177-8. This discussion focuses on the third.

In addition, where new ideas are being presented to an audience
and argued for, audience-relevance would require that as much as possible of the
information being given in support of those ideas be related to (relevant to)
assumptions which we know are manifest in that audience’s cognitive environment.
This must occur even when audiences are introduced to a new body of
information. When the Physics professor first confronts a freshman class he or
she expects that certain things are manifest to the class. One of these is the
professor’s own authority as a knowledgeable person, the recognition of which
serves as a warrant (in Blair’s sense) for the relevance of the information
disseminated. In addition to this, the professor assumes as manifest a set of facts
that is prerequisite for the level of study the class has reached, and tries to
introduce the new ideas in relation to those facts. The prerequisite facts include
those with which students are expected to be familiar, although individual
students may have gaps in their backgrounds that prevent them from grasping
the relevance of some of the professor’s remarks.3
What I have explained above is close to what Sperber and Wilson call
“contextual effect” (1986, pp. 108-109). Something has an effect on a context if
it modifies or improves a context. That is, in my terms, modifies what facts and
assumptions are manifest or implicates new facts or assumptions. As stated
before, these are mediate goals that we try to achieve in the process of attempting
to affect the actual thought processes of an audience. p. 183

 

Compression and Intelligence: Social Environments and Communication by Dowe, Hernandez-Orallo, Das

https://www.researchgate.net/publication/221328896_Compression_and_Intelligence_Social_Environments_and_Communication?enrichId=rgreq-a153919c4e1e79ad09e4306ce3b4edf2-XXX&enrichSource=Y292ZXJQYWdlOzIyMTMyODg5NjtBUzoxMDI4ODY5NTI0MDcwNTFAMTQwMTU0MTU2OTk1NQ%3D%3D&el=1_x_2&_esc=publicationCoverPdf

Abstract. Compression has been advocated as one of the principles
which pervades inductive inference and prediction – and, from there, it
has also been recurrent in definitions and tests of intelligence. However,
this connection is less explicit in new approaches to intelligence. In this
paper, we advocate that the notion of compression can appear again
in definitions and tests of intelligence through the concepts of `mind-
reading’ and `communication’ in the context of multi-agent systems and
social environments. Our main position is that two-part Minimum Mes-
sage Length (MML) compression is not only more natural and eective
for agents with limited resources, but it is also much more appropriate for
agents in (co-operative) social environments than one-part compression
schemes – particularly those using a posterior-weighted mixture of all
available models following Solomono’s theory of prediction. We think
that the realisation of these differences is important to avoid a naive
view of `intelligence as compression’ in favour of a better understanding
of how, why and where (one-part or two-part, lossless or lossy) compres-
sion is needed.

This is an interesting article about compression qua compression. This article http://lesswrong.com/lw/ite/mathematics_as_a_lossy_compression_algorithm_gone/ is a nice indication of the thinking that set me on this track.

Let us elaborate upon the points from the above paragraph with some ex-
amples. The creation of language is about developing a set of (hierarchical)
concepts for the purposes of concise description of the observed world and corre-
spondingly concise communication. Elaborating upon the ideas outlined in [25,
chap. 9] (and [2, footnote 128][4, sec. 7.2]), this can be thought of as a problem
of (hierarchical) intrinsic classication or (hierarchical) mixture modelling (or
clustering), where we might identify classes such as (e.g.) animal, vegetable, min-
eral, animal-dog, animal-cat, vegetable-carrot, vegetable-potato, vegetable-fruit,
mineral-metal, mineral-salt, animal-dog-labrador, animal-dog-collie, animal-dog-
labrador-black, animal-dog-labrador-golden, etc. Following these principles of
MML mixture modelling [26, 27, 29, 25] enables us to arrive at a single theory,
which is the rst part of an MML message and which describes the concepts or
classes. The data of all the various individual animals, vegetables and minerals
(or things) on the planet (such as their heights and weights, etc.) is encoded in
the second part of the message. Users of the language are free to communicate
the concepts from this single best MML theory.
Knowledge (and human knowledge especially) in a social environment is all
about this, about sharing models. And this shared knowledge makes co-operation
possible. For humans (elevated in knowledge), science is a type of knowledge
where we typically use one theory to explain the evidence, and not hundreds. p. 3

 

 

The Nature of Intuitive Thought by L. Järvilehto (2015)

© The Author(s) 2015
L. Järvilehto, The Nature and Function of Intuitive Thought and Decision Making,
SpringerBriefs in Well-Being and Quality of Life Research,
DOI 10.1007/978-3-319-18176-9_2 http://www.springer.com/gp/book/9783319181752

This is a book chapter I had a look at to think about what people mean when they talk about things being intuitive. I’ve been thinking a lot about how placement on a page or blackboard, writing style, colour etc. can make certain conclusions about the things being written feel intuitive, and what exactly that might mean. This chapter is a nice summary of the cognitive science on the topic.

There’s a lot of talk about System 1 and System 2, those being ‘in charge of autonomous and non-conscious cognition, and volitional and conscious cognition, respectively’ p. 23. These systems seem to be helpful way to think, albeit metaphorical:

The dual-system formulations of dual processing present a compelling picture of
how the mind works. As Evans and Frankish, among others, argue, these formulations
are, however, currently oversimplified. (Evans and Frankish 2009, p. vi).
According to Kahneman, the two systems are rather “characters in a story”—
abstractions used to make sense of how our cognition takes place. (Kahneman
2011, p. 19 ff.) He notes, “‘System 1 does X’ is a shortcut for ‘X occurs automatically.’
And ‘System 2 is mobilized to do Y’ is a shortcut for ‘arousal increases,
pupils dilate, attention is focused, and activity Y is performed.’” (Kahneman 2011,
p. 415). p. 28

Their relationship to working memory seems important:

One of the critical distinctions of the two types of processes is whether they
employ working memory. “In place of type 2 processes, we can talk of analytic
processes [that] are those which manipulate explicit representations through
working memory and exert conscious, volitional control on behavior” (Evans 2009,
p. 42). While the working memory is often likened to System 2, the two are not in
fact entirely the same:
Working memory does nothing on its own. It requires, at the very least, content. And this
content is supplied by a whole host of implicit cognitive systems. For example, the contents
of our consciousness include visual and other perceptual representations of the world,
extracted meanings of linguistic discourse, episodic memories, and retrieved beliefs of
relevance to the current context, and so on. So if there is a new mind, distinct from the old,
it does not operate entirely or even mostly by type 2 processes. On the contrary, it functions
mostly by type 1 processes. (Evans 2009, p. 37).
Type 2 processes need the constant application of working memory, such as in
calculating by using an algorithm, in evaluating various choices in decisionmaking,
or in practicing a new skill. p. 29

This is interesting because Cognitive Load Theory is based on working out how to reduce load on the working memory through design choices.

As
Engle points out, working memory is not just about memory, but rather using
attention to maintain or suppress information. He holds that working memory concerns
memory only indirectly, and that a greater capacity in working memory means a greater ability to control attention rather than a larger memory. (Engle 2002, p. 20.)

There’s a nice association between intuition and heuristics here, nice because relevance theory is so based in ideas about heuristics:

Gerd Gigerenzer presents a four-fold taxonomy for explaining intuitions.
According to Gigerenzer, gut feelings are produced by non-conscious rules of
thumb. These are, in turn, based on evolved capacities of the brain and environmental
structures.
Gut feelings are intuitions as experienced. They “appear quickly in consciousness,
we do not fully understand why we have them, but we are prepared to act on
them.” (Gigerenzer 2007, pp. 47–48.) The problem with the trustworthiness of gut
feelings is that many other things appear suddenly in our minds that bear a similar
clarity and that we feel like acting on, for example the urge to grab an extra dessert.
But not all such reactive System 1 behaviors are good for us.
Rules of thumb are, according to Gigerenzer, what produces gut feelings. These
are very simple heuristics that are triggered either by another thought or by an
environmental cue, for example the recognition heuristic, where a familiar brand
evokes positive feelings. (Gigerenzer 2007, pp. 47–48.) Evolved capacities are what
rules of thumb are constructed of. They include capacities such as the ability to
track objects or to recognize familiar brands. (Gigerenzer 2007, pp. 47–48.)
And finally, environmental structures determine whether a rule of thumb works
or not. The recognition heuristic may work well when picking up a can of soda or
even stocks, if it is directed towards trusted and well-known brands. (Gigerenzer
2007, pp. 47–48.) p. 41

Gary Klein has developed a similar position to Gigerenzer’s in his famous
decision-making research. In Klein’s recognition-primed decision making model,
decisions are made neither by a rational, conscious weighing scheme, nor by a fast
non-conscious calculation, but are based rather on quickly recognizing viable
strategies for action based on expertise. (Klein 1998.)
Like Gigerenzer’s, Klein’s idea is based on Herbert Simon’s conception of
intuition as recognition. According to Klein’s research, people do not in fact typically
make decisions by rationally evaluating choices. (Klein 1998, loc 202.)
Rather, a great majority pick up a choice that first comes to mind, mentally simulate
it, and if it seems to work, go with the first viable one, without ever considering
options. This decision-making scheme follows the strategy of satisficing, (accepting
the first viable option), made famous by Simon, in contrast to the more rational
strategy of optimizing, i.e. weighing all possible options and picking the one that
comes out on top as best. (Simon 1956.)
The difference between Gigerenzer’s and Klein’s positions is in that where
Gigerenzer assumes that gut feelings are produced by heuristics or rules of thumb
that are typical to all humans and produced by our environment, Klein’s idea of
recognition-priming is based on picking up much more individually complex
strategies of action based on prior experience and expertise.p. 42

The author works hard to distinguish ontogenetic from phylogenetic.

The gist here is that we generate a considerable amount of ontogenetic Type 1
processes, or habits, by exercise, deliberate practice and daily experience. p. 43

The author is also quite interested in situated mind ideas, and brings in questions of environment.

Martela and Saarinen delineate three principles of systems intelligence. First, we
must see our environment as a system we are embedded in. Second, we need to
understand that intelligent behavior cannot be traced back only to the capacities of
an individual, but arise as features of the entire system in which the individuals
operate. And lastly, intelligent behavior is always relative to a context. (Martela and
Saarinen 2008, p. 196 ff.) p. 48

 

The Bridge Between Worlds: Relating Position and Disposition in the Mathematical Field by Lorenzo Lane

This is an excellent ethnography and well worth reading.

Lane discusses use of

1. Common and private space
2. Formal and informal spaces
3. Productive and relaxation space p. 143

By “socialising ideas” I simply mean that concepts become part of assemblages of people and things. Ideas become grounded in day to day life through their attachment to people. At the institute people speak of Sarah’s technique, Penelope’s data, Luke’s theorem, and use these names to act as handles for searching MathSciNet, Arxiv.org, or google scholar, for related material by which to trace the origins of the ideas. p. 178

Knowledge in mathematics is embodied. Individuals act as repositories of knowledge, and many researchers prefer to ask a question directly to an expert, in order to find out more about a problem or idea, rather than consulting written material. The oral transmission of knowledge in mathematics is a means through which information contained in publications can be expanded and summarised, so as to provide the key points, motivations and overall structures of proofs. Interviewees highlight the importance of asking experts about a problem, paper or approach, which can serve a number of purposes:
1. As a time-saving device.
2. As a means of acquiring interesting techniques and problems.
3. As a way of getting up to speed in an area.
4. As a means to socialise and share interests in mathematics.p. 179

N: So I’m not fast in oral communication. So I like to discuss maths with others, but at the level that is of motivation and general interests, questions. But when I want to think really deep, I need a pen, and I need some loneliness at some point to think through a question. When someone is watching me I am not so good at thinking in front of somebody. But I need communication and exchange about questions, in fact to be interested about a problem I need to understand why we should all care, as a community, about this question, not just “Oh it’s a hot problem – you should try this”.
IN: So you use people to get a problem and interrogate them to find out why the problem is interesting?
N: Yes I use people in that way, and also I see it as a cultural thing also. So I like to exchange, and see what the vision of mathematics we have…Doing maths with others is all about what questions we can work on between ourselves. It’s not just “Oh lets go to the blackboard and solve a problem”, it’s rather: “Oh have you heard of that, and look I can do this, describe some simple examples and so on”. At some point exchanging around this, and maybe having a small idea or small example, and then afterwards have more quiet and just think about the natural places where these ideas should sit. p. 179-80

Adrian notes that reading the formalised, published papers is sometimes not enough. Rather a “fluid” approach is necessary, by which an individual can question a person who is a “knowledge-repository” on specific questions related to a concept or proof, in order to “get the bare-bones” or the “gist” of an argument. This is an important task to undertake before a researcher decides to fully commit to investing time and mental energy in reading a given paper. The informal back-channels of questioning knowledge-repositories serves as a means of scoping out potential problems or useful concepts, narrowing down the search parameters needed for later literature reviews and google-scholar/ arxiv.org searches. p. 181

Before any presentation, such preparatory work takes place. Individuals will ask what they call their “stupid” or “silly” questions before face-to-face encounters, utilising close friends or colleagues, or else will use the question and answer site MathOverflow.com. Then when it comes to asking the expert, or giving an exposition, one does so effortlessly.
Such displays of effortlessness are important in showing that a researcher possesses “natural” ability within their field, and thus they are important in developing their reputation as a competent, rigorous, trustworthy researcher. In public, much of the hard work of learning is made invisible. Through downplaying the effort involved in understanding concepts, so individuals create distance between themselves and their audience. Some individuals, I am told, are perceived as “naturals”, “geniuses”, “gods” because of their effortless ability to perform and demonstrate their understanding of mathematics. When many such “naturals” talk in private between themselves, or when being interviewed, the struggles involved in grasping concepts are revealed. p. 183

This mathematical corpus forms part of the habitus: the system of scheme-resource sets which produce orientations and dispositions towards phenomena. The conceptual machinery that a mathematician acquires thus serves to produce a certain way of perceiving mathematical objects and spaces, and also generates dispositions by which they are able to confront problems within certain mathematical domains. Through becoming familiarised with certain techniques, objects, languages or papers, mathematicians furnish their habitus, and this, in turn, re-shapes the perceptual lenses by which they are able to perceive a problem. p. 209

J: So yes he told me to read this one article and said I would understand things. But it was not well written, it was something like 30 pages. He said “OK, so if you read it in the first year it will be good for you”. I said “30 pages in one year?…yes I can do that [laughs]”. But this was really hard. For every word you have to understand a lot of things. You can read that, that, that, that and you just get used to the different notions.
He had a lot of time for me, so I could just discuss about things, and he explained a lot of things to me. It’s easier to read when someone explains the story before. I mean you don’t have the details but you know where you’re going, and you just fill in the details when you read. p. 201

In order to “keep alive” within the mathematical landscape, a researcher has to adapt to their changing environments, and learn new languages by which to communicate with their colleagues. Over time, they need to learn new vocabularies and gain access to new ways of inhabiting and exploring the mathematical landscape. This process of developing a shared working vocabulary is not confined to the office, the institute, or the seminar room, but as the following conversation with Han and Bernie indicates, the process of building a shared knowledge base is continuous, happening throughout the working day:
H: This is very important: the word vocabulary. Because this vocabulary has built up not only through working one day a week, but this vocabulary has been created when going to take a drink, or when walking, or when talking about another subject. This vocabulary pops up in math, so it’s difficult to say. Every day there is new input into this vocabulary. It took us really one month to have a common vocabulary, but this vocabulary has become richer and richer with time.
B: But it was about one month, and we could speak to one another, and we knew what the other guy was talking about. But we did other things. During this month we were explaining and asking and saying “I do not understand could you explain in more detail?”
H: This is like what we said at lunch, he was speaking German and I was speaking in French… p/ 215

We shall see in the next section how, through the mastery of technique, the tools and language of mathematics are moved to the background of consciousness. The perception of the mathematical landscape becomes second nature, and the researcher learns to use their intuition. We shall explore the processes by which the language of mathematics becomes naturalised and backgrounded, so that working memory is freed up, in order to focus on the process of discovery, creativity, and assembly. Mathematics, we shall see, becomes a craft, and the mathematician is transformed into the bricoleur. p. 216

This role of the body is played out through the practices involved in constructing mathematical proofs. It is through manipulating material representations by assembling, selecting, sorting, ordering, tinkering and relating that the mathematician builds up the machinery of proof. p. 217

G: In the last 40 years I simply never spent a week without thinking about mathematics, a day yes, but not a week. It’s like ruminating you know, we’re like cows but what we eat is mathematics. It’s a long rumination. Some people work late at night, and usually the best are like that and I’m not one of the best. For me it’s like a long rumination, OK, mathematics is with you whatever you do. You can go and something else, of course, but it is always escorting you around. I was mentioning these notebooks, they are with me essentially always, and sometimes I don’t touch them for a week because nothing happens but they are with me anyhow, where ever I am. p. 218

N: I have mathematical notes but it’s still vague, when I write down, it’s still at the early stage and it’s really badly handwritten. It’s more like a collection of “Oh this can work like that” or else just sentences to myself. But I can show you this. So currently [flicks through notebooks] it’s a mixture of papers that I have printed, and notes like this where I’m working on some random walks in some spaces, and these are the random walks. These are the kinds of stuff that I write. This is really not that precise. And when it’s crystallised into being something special like this, you have a statement labelled lemma and you can see that there is no proof behind, because when I’m at the level of proof then I will start writing things down the paper. And you can see stuff like this, where we can relate these two theories and these are notes from a discussion with a colleague. Not very precise, but quite helpful. At some stage it’s written in the computer and at some stage I will just chuck these. Maybe I will take this same paper and write down something else on it. At some point when I’m thinking I just need to write something down to help me think. I don’t keep these notes. The notes I keep are already type-set.
In fact seeing it like this – only a very few people will it be meaningful for. I think what is interesting is to see that even if the paper has no picture, but I’ve wrote a picture for myself here… So one important thing in writing is to help the mind to concentrate. Sometimes it’s not important if it’s right. I explained this to a collaborator once: that I just need to write. It’s not strictly useful to write down, but it helps to think. And also the mathematician does not want to be naked in public. You don’t want to show that you were really dumb at some point. p. 220-1

Writing, as Nemo tells us, helps him concentrate, to reformulate and to re-figure concepts. Such thoughts start off as vague, but over time they are shaped into something much more concrete, “crystallising” into definitions or lemmas. Mathematical writing thus provides a physical scaffold for crafting ideas. For many researchers this scaffolding is a way of offloading certain processes from working memory, distributing memory onto an external storage device. p. 222

Gordon explains that the picture sketched out on the blackboard is more than just a depiction of an object, like in a photograph; rather it is an interpretation of an abstract concept which is given expression within a painting. The painting, depending on the skill of the artist, can encode within it a number of concepts (Gombrich 1977: 44). Understanding what information is encoded within an artwork depends on one’s understanding of the style and language of the artist. The act of sketching out objects thus is a means of condensing mathematical concepts into a visual short-hand, which provides a further scaffold for constructing complex arguments. Through condensing information into a visual format, arguments or concepts become subject to visual inspection and interrogation, which facilitates the process of pattern discovery and the synthesis of information, as p. 234

I’m not sure about all this talk of encoding and art, but there are some interesting things here.

J: I first draw pictures and then go and try to explain it in a mathematical way and I ask “what is this picture really trying to say”. That’s the really hard problem. It’s like: “OK I have to write every details…ahaha” How do I do this? SO it has to be a real proof so everybody says “yes this is true”…For me I like speaking with my hands. But then we have to write rigorously… But if you look at my drafts it’s like picture, picture, picture.

Oftentimes mathematicians begin by working with pictures, building up intuitions about objects through manipulating such pictures. It is only later on in the proof construction process that these physical intuitions are erased, as the pictures are abstracted away, in the formal process of “writing up”. In writing up much of the informal processes of experimentation, as well as the physical intuitions on which arguments are based, get written out of the end publication. However, in erasing pictures and examples from the published proofs, it can often become difficult for other mathematicians to follow a proof. p. 235-6

These modes of visualising mathematical reality are referred to as gaining “intuition”. This “intuition” is what we refer to here as a perceptual frame. This perceptual frame is built up over the course of one’s career as a mathematician, and comprises of the vocabulary of concepts that an individual has internalised within long-term memory. p. 240

I’m not sure I understand this part – what is being pictured? Sometimes it’s a thing seen as spatial. I guess I can understand ‘picturing’ a sort of perceptual or mental state, perhaps. But I’m not sure I’m clear that that’s what people are referring to.

But perhaps the most important aspect of visual representations is the fact that they simplify complex constructions into visual short-hands. They are able to condense complex information into symbols, signs and graphics, which represent complex processes and phenomena. Through simplification and condensation into two and three dimensional drawings or algebraic symbols, so the background structure of the construction becomes more apparent. p. 242

I think there might be more going on here. There’s a lot of structure added in when we write something out in notation and so on – I’m not sure it’s just simplification, I think we actually must add something in. There’s been some research that shows experts reading mathematics in structured, language-like ways: http://www.tandfonline.com/doi/abs/10.1080/09541440600709955 . Might turn out to be relevant.

Creating visual analogues to abstract mathematical constructions transforms concepts into perceptible objects. The visual representation approximates the structure of the mathematical construct, sharing with it certain characteristics. Visual representations in mathematics are used in similar ways to how metaphors are used in natural language. The visual representation bears certain resemblance to, or shares certain features with, the mathematical construct that it refers to. The visual representation thus acts as a schema for organising the abstract mathematical construct. Modifying the visual representation becomes analogous to transforming the mathematical construct in some way.

Visual representations serve as frames for viewing and organising the abstract, mathematical landscape. The visualisations are not the mathematical objects themselves, but merely approximations of these objects, projected into our physical reality. p. 242-3

This gets tricky…

Such ways of thinking about or translating mathematical concepts are called “tools” by mathematicians, and they provide a way of educating their perceptions into being able to perceive the mathematical landscape. p. 243

This is interesting! I love all the ‘tools’ stuff, but not the idea of them allowing you to perceive a pre-existing mathematical world.

I explore the field as a competitive field, in which individuals are motivated by gaining social capital, through making their knowledge visible and recognisable. Ideas, in order to be assimilated within the wider field, and constituted as capital, must be structured so as to fit certain socially valued characteristics. Knowledge therefore must be coordinated and related to existing bodies of knowledge, in order to be accepted and assimilated within the wider field. I explore this process of coordinating local frames of reference to global reference frames, and show how individuals shape their ideas so as to conform to certain standards and exemplars. p. 250

He discusses authority in the next chapter.

Artist as ethnographer

Click to access cpro2ZgGKfArtist_As_Ethnographer.pdf

http://csmt.uchicago.edu/annotations/fosterartist.htm

Hal Foster wrote something important about the artist as ethnographer.

• the subject is othered, and the researcher still has the power
• the ethnographer envies the artist’s reflexivity, while the artist envies the ethnographer’s access to an ‘other’ that has various properties attributed to it

“…this setup can promote a presumption of ethnographic authority as much as a questioning of it, an evasion of institutional critique as often as an elaboration of it.” p. 306

“…the artist, critic or historian projects his or her practice onto the field of another, where it is read not only as authentically indigenous but as innovatively political!” p. 307

As I’m a white western academic studying other white western academics, I suppose my subject is pretty close to where I am. I’m also endeavouring to de-other them, to dismantle this overly romanticised image that we have that takes mathematics to be so mysterious.

http://www.tandfonline.com/doi/pdf/10.1080/02560046.2013.855513

Arnd Schneider and Chris Wright (2006: 4) assert that ‘[a]nthropology’s iconophobia and self-imposed restriction of visual expression to text-based models needs to be overcome by a critical engagement with a range of material and sensual practices in the contemporary arts’. p. 460

Based on Hal Foster (1995):

•

Does this artist consider his/her site of artistic transformation as a site of political

transformation?

•

Does this artist locate the site of artistic transformation elsewhere, in the field

of the other (with the cultural other, the oppressed postcolonial, subaltern or

subcultural)?

•

Does this artist use ‘alterity’ as a primary point of subversion of dominant

culture?

•

Is this artist perceived as socially/culturally other and has s/he thus limited or

automatic access to transformative alterity?

•

Can we accuse the artist of ‘ideological patronage’?

•

Does this artist use ‘alterity’ as a primary point of subversion of dominant

culture?

Does the artist work with sited communities with the motives of political

engagement and institutional transgression, only in part to have this work recoded

by its sponsors as social outreach, economic development, public relations?

•

Is this artist constructing outsiderness, detracted from a politics of here and now?

•

Is this work a pseudo-ethnographic report, a disguised travelogue from the world

art market?

•

Is this artist othering the self or selving the other?

Based on Andrew Irving (2006: 14):

•

Can this artist be criticised for underlying assumptions of misplaced

temporalisation

whereby non-Western practices, be they artistic or otherwise,

are seen as some throwback to earlier, more primitive forms of humanity?

Based on Lucy Lippard:

•

Is the artist wanted there and by whom? Every artist (and anthropologist) should

be required to answer this question in depth before launching what threatens to

be intrusive or invasive projects (often called ‘interventions’) (Lippard 2010:

32).

p. 463-4

Less concerned with the possibilities of

accurately representing the ‘other’ and his/her culture, the ethnographer nowadays

aims to comparatively relate his/her own cultural frame to that of the ‘other’, in

view of establishing an interactive relation. Ethnographers furthermore look at

cultural practices in which attention is paid to inter-subjectivity, where one relates

engagement with a particular situation (experience) and the assessment of its

meaning and significance to a broader context (interpretation) (Kwon 2000: 75). The

idea that one actually can ‘go native’ and ‘blend in’, so as to completely integrate and

participate in a particular culture, has been criticised as exoticism. Yet the stress on

ethnography as an interactive encounter is of crucial importance, as ‘the informant

and the ethnographer are producing some sort of common construct together, as a

result of painstaking conversation with continuous mutual control’ (Pinxten 1997:

31, see also Rutten and van. Dienderen 2013). p. 465

Ingold (ibid: 10) proposes to shift anthropology and the study

of culture in particular ‘away from the fixation with objects and images, and towards

a better appreciation of the material flows and currents of sensory awareness within

which both ideas and things reciprocally take shape’. p. 465

Relevance and rationality by NICHOLAS ALLOTT

Abstract
Subjects’ poor performance relative to normative standards on reasoning tasks has
been supposed to have ‘bleak implications for rationality’ (Nisbett & Borgida, 1975).
More recent experimental work suggests that considerations of relevance underlie
performance in at least some reasoning paradigms (Sperber et al., 1995; Girotto et al.,
2001; Van der Henst et al., 2002). It is argued here that this finding has positive
implications for human rationality since the relevance theoretic comprehension
procedure is computationally efficient and well-adapted to the ostensive
communicative environment: it is a good example of bounded and adaptive rationality
in Gigerenzer’s terms (Gigerenzer and Todd, 1999), and, uniquely, it is a fast and
frugal satisficing heuristic which seeks optimal solutions.