Simondon's Theory of Allagmatics

Allagmatics is a fancy term that originates with an old greek word: άλλαγμα, which originally entailed an exchange. A subjugated form of this word is extant in Homer:

Iliad VII: 299-300

After a long bout of brawling, Ajax and Hector are stopped by characters with cooler heads, and admonished, and so they give each other gifts as a symbol that they'll quit fighting with each other. This exchange of gifts is the original meaning in classical antiquity. The exchange of gifts being an outward symbol of an internal transformation in each of the combatants.

This internal transformation is what Simondon takes as the foundation of his study of ontogenesis, or the study of how things come to be. On pp. 21-29, of Individuation in Light of Notions of Form and Information (University of Minnesota Press, 2020), Simondon would like us to consider the construction of a common brick. 

Recall that Aristotle holds that ὕλη (matter) contains both the physical "stuff" of which things are constructed, as well as the potential to create them. It is μορφή (form) which is both the outer manifestation of the thing-at-hand as well as the immaterial expression of its being and place in the world. This hylomorphism is what Simondon would like us to question with the illustration of brickmaking. Aristotle would tell us that the brick's potential is bound up in the clay with which the brick is molded. Simondon argues that the formation of any object (such as a brick) is the consequence of a process, rather than the unbundling of some inherent potential encoded in matter.

Simondon encourages us to see both the clay and the mold as an energetic field or a system. Putting the clay in the mold and pressing it into shape is a detemporalized, reciprocal transformation or exchange (άλλαγμα) which individuates the brick as an object-of-use. This seems abstract, but it's actually a very homespun, accessible thing to contemplate. It only seems foreign because we all grew up in schools which taught us western traditional concepts like hylomorphism.

The electrical fields of the atoms in the clay interact with each other and with the electromagnetic field of the atoms in the mold. With the application of specific pressure and temperature and humidity factors, inherent contradictions are resolved, and the field becomes metastable: a brick is individuated and therefore becomes ready for technical use.

Simondon's concept of allagmatics is not merely applicable to inanimate objects. Human beings are individuated. Collective bodies of people and discourses (social, religious, political, etc.) are transindividuated in this same system. Allagmatics is the framework through which we might understand systems and individuals as existing in a dynamic, fluctuating, ever-changing and interconnected world.

On Whitehead's Relational Learning

Alfred North Whitehead's concept of relational learning has been a profound influence on my own development as an educator. I recently re-read The Aims of Education (link) and thought I ought to break down my impressions of some of his pedagogical ideas.

Whitehead's primary advice for educators is to defend his lectures from what he terms 'inert ideas.'

"In training a child to activity of thought, above all things we must beware of what I will call "inert ideas" -- that is to say, ideas that are merely received in the mind without being utilised, or tested, or thrown into fresh combinations... Education with inert ideas is not only useless: it is, above all things, harmful: corrupto optimi, pessima" (13).

A teacher ought to appreciate his position as the guarantor of a sort of trans-cultural teleology, encouraging in the listener a receptiveness to aesthetic beauty and sensibility. One only achieves success in this context if the information he provides his students is readily accessible and applicable. What Whitehead terms 'irrelevant scraps of information' allow a pupil the simulacrum of education, depriving him of the ability to contextualize information to his own life. Every interaction with a student ought to encourage a dynamic connection of ideas with his own experience and with his pre-existing body of knowledge. Inert ideas resist practical testing or integration into the student's understanding of the world and his own place within it.

Effective teaching, for Whitehead, also includes an interdisciplinary openness which is often neglected in the contemporary classroom.

"Technical education is doomed if we conceive it as a system for catching children young and for giving them one highly specialised mental aptitude... training should be broader than the ultimate specialisation, and the resulting power of adaptation to varying demands is advantageous to the workers, the employers, and to the nation. ...it is impossible to narrow down scientific study to a single thin line of thought" (65).

This seems intuitively obvious. An effective lecture on the declining population of Madagascar's lemur population, one necessarily needs to speak with some authority on history, ecology, statistics, and likely also the sociological factors that drive habitat loss, which may lead to a minimal discussion on economics and urban planning.

A competent educator, in Whitehead's opinion, will encourage what he calls an 'imaginative grasp' of new material which is dynamically integrated into his pre-existing body of knowledge through practical testing or by making mental connections. To some extent, Whitehead repeats himself over-and-over, but he clearly wanted to set imagination as the keystone of effective teaching praxis.

"In a simpler world, business relations were simpler, being based upon immediate contact of man with man and on immediate confrontation with all relevant material circumstances. Today, business organization requires an imaginative grasp of the psychologies of populations engaged in differing modes of occupation; of populations scattered through cities, through mountains, through plains; of populations on the ocean, and of populations in mines, and of populations in forests. It requires an imaginative grasp of conditions in the tropics, and of conditions in temperate zones... It requires an imaginative understanding of laws of political economy... It requires an imaginative vision of the binding forces of human organisation... It requires that discipline of character which can say 'yes' and 'no' to other men, not by reason of blind obstinacy, but with firmness derived from a conscious evaluation of relevant alternatives" (98-99).

So relational learning encourages active imagination and personal engagement with course material, and Whitehead's position is that this is the primary avenue toward the acquisition of useful knowledge. "Unless the pupil is continually sustained by the evocation of interest, the acquirement of technique, and the excitement of success," he warns, "he can never make progress, and will certainly lose heart" (49). Imagination plays the primary role in this conative process that propels students to mastery of new forms of knowledge.

Interspersed in all of his essays, but never explicitly defined, is the presupposition that relational learning is a communal process, which organically develops in the context of the collective.

"The combination of imagination and learning normally requires some leisure, freedom from restraint, freedom from harassing worry, some variety of experiences, and the stimulation of other minds diverse in opinion and diverse in equipment" (102).

New ideas are readily tested in collaboration and argument. This requires interaction with a social group composed of fellow learners.

Whitehead isn't typically considered a pioneer in critical pedagogy, and I think that's a shame, because all of this coheres very well with ideas promoted by contemporary thinkers like Paulo Freire, bell hooks, and Henry Giroux. By fostering connections between lived experience and new material, by using imagination, and by fostering an interdisciplinary approach to integrating information, students are inherently empowered to propose new solutions to complex social problems, and to act as thoughtful agents of positive change within complex hierarchal structures. Earlier educational theorists hoped that students would better navigate the world. Whitehead expects them to transform it.

 

Numbers and Necessity

I have taken to opening my classes by assigning my students a puzzle, which originated in Howard Pospesel's Propositional Logic textbook (Saddle River: Prentice-Hall, 2000), p. 8.

I don't do this to make my students hate me, though I am satisfied with the possibility, as I've found that the more they hate me, the more they end up learning. It's a seductive problem, which illustrates the value of deductive reasoning. It is quite simple, though a great number of students (some of them much brighter than I) tear their hair out over it. I first encountered it thanks to a logician named James Garson (at the University of Houston) and I solved it in about ten minutes. That has more to do with the fact that I got over the math anxiety which is common among even the brightest people.

If you're here, it's likely because you're one of my victims; and (given that you're a university student) the laws of probability suggest that you're at least as bright as I am. The only advantage I've got on most of you is the fact that I'm an old man who has a head start on reading boring books. That aside, this is the question, and below is the answer I gave to Dr. Garson, back in the summer of 2015.

As someone once told me: going fast slows you down... A careful reading of the problem will save time later.

We should read the problem in good faith and take the text at face value. The first thing we notice is that there are three clues, and no clue is extraneous, vacuous, or trivial. All three clues are necessary for the solution.

Clue No. 1: There are three numbers, x_1, x_2, x_3, such that (x_1)(x_2)(x_3) = 36
Clue No. 2: There is some positive integer, x_4, such that x_1 + x_2 + x_3 = x_4
Clue No. 3: The eldest son has red hair.

We know x_4 is a positive integer because the post office doesn't number addresses with irrational or negative values.

The last clue is interesting, and clearly designed to provide us with the means of solving the problem, while simultaneously providing us irrelevant information in an attempt to confuse us. We don't care what color hair the boy has. His father said that "the oldest one" was unique. That means there will be one, and only one, eldest child. There are no triplets, and there are no elder twins.
For various number theoretic reasons, we can safely assume that the ages of all the boys will be positive integers also.

The first thing we can do is to define our system of equations.

The next thing to do is to find all the prime factors of 36.

If we were trying to find the ages of four children, then the first clue would alone be sufficient for a solution. In fact, there are three children, and so now we have to work backwards, and attempt to find possible solutions for the second equation in our system.

I switched to pencil, because I found the smudges annoying. In any case, we can see all the possible solutions to our system of equations, listed in descending order.

There is one, and only one, repeating possible solution, suggesting that the building's number is thirteen.

If we take the text at face value, as logicians should, we can now intuit our answer, based upon the necessity of the final clue. Note that one of our solutions admits two elder twins, followed by a younger brother. This contradicts Rule No. 3. Thus we know that the eldest boy is nine, and he is followed by younger twin brothers, each aged two.

Checking our solution against the defined system, we find everything in order.

James-Russell Theory of Time

My grandmother at center: Munich, 1927

The James-Russell Theory

A Reconstruction

Bertrand Russell began constructing his first philosophy of time, at around the same period he was writing his Essay on The Foundations of Geometry (1). In this formulation, time was one of two externalities (the other was physical space). This first Russelian theory of time was abandoned along with his neo-Hegelian interpretation of mathematics, as he transitioned from idealism into realism.

Russell never wrote a coherent philosophy of time thereafter, but time was essential to the theory which came to be known as logical atomism. In passages pertinent to other arguments, Russell first deprecates a prevailing theory, namely that a human subject possesses the ability to apprehend or intuit the passage of time. "If we only knew present occurrences which are in fact related to past occurrences, we should never know this relationship" (2). The first thing that is interesting about this claim is its challenge to his erstwhile collaborator, Alfred North Whitehead, who described time as "drops of experience" (3). Russell's claim subsequently entails something surprising, namely that the human subject has direct access to some of his past experiences. If we follow his argument to its conclusion, we see Russell implying that evental objects, which existed, still exist, concretized in the present, for some subjective measure.

The first assumption that tempts the reader is to position Russell within a specific camp of time-theorists, who adhere to a metaphysical notion commonly called "the growing block theory." What the growing block theory posits is a measure of existence for everything that ever existed, up until the present. Future potentialities become concrete as they are instantiated in the present. Once instantiated, these concrete objects persist, in some sense, forever into the future. Peter Forrest (4, 5) is a fair example of a contemporary growing block theorist. For a number of reasons, Bertrand Russell is difficult to posit in this camp. I will try to illustrate the differences between the propositions implied in Russell's theory, and those held out by fans of the growing block theory.

We must first adopt a bit of jargon from engineering and computer science, in order to make our subsequent work a bit more accessible. An "evental object" is something that erupts into the lifeworld of the subject, in such a way as to remap the ontology of the subject's phenomenal environment. An evental object is a word that is heard and intuited. An evental object is a word that is read and understood. An evental object might be a bolt of lightning, noticed in the distance, or it could be a taxi, which suddenly appears around the corner. We spend much of our lives being shaped by evental objects, without ever really noticing their true phenomenological import.

Russell's late theory of time is specifically relevant, not only to logical atomism, but to his work in the philosophy of language. Analytic languages (like English) tend to encode meaning with word-order. In our language, "Brutus killed Caesar." carries a converse semantic sense than "Caesar killed Brutus." (The smart folks call English SVO - for "subject verb object"). Because we apprehend the words as they are heard (or read) in order, we understand and have direct access to the metalinguistic proposition. It is when we attempt a meta-analysis of this process that Russell asserts (correctly) that we risk falling into an infinite recursive loop, which provides us no new information. To speak the words "...the word 'Brutus' preceded 'killed,' and 'killed' preceded 'Caesar'..." not only imply a temporal sense of the first-order sentence we are analyzing, but they also have a temporal sense themselves, and thus we are faced with an additional demand to explain the phenomenon (6).

Russell solves this linguistic problem through an expansion of the definition of the present, to include what is actually the recent past. When one hears the phrases "Brutus killed Caesar," and "Caesar killed Brutus," we are dealing not with the phenomenon of three words in two different permutations, but of "two wholes comprised of somewhat dissimilar parts, which are simultaneous," each of which is "characterized by its constituents, and does not need the further mention of arrangement" (7). Basically, Russell's view is that we have direct access to sense data in the recent past, for at least the time it takes to discern word order in a sentence. This makes intuitive sense, and we can apply it to the fading tones of notes in a piano concerto, or the tolling melodies of the angelus bells.

A careful reading of Russell suggests a model for the rejection of akoluthic sensations. What the heck are these? The word 'akoluthic' is a fancy term, which implies a linear descent, from present to absent, on the timeline. In contrast, Russell contends that temporal passage and its awareness in the human subject might be modeled by something like a piecewise rational function. For example:

If we wanted a geometric model of the probability of direct access in the first few moments of experience, we'd see something like this.

With (0,1) being the immediate present, where we have direct access to all available sense data. The graph above is symptotic, and thus a bit misleading. Direct access tends to drop, as sense data transitions into memory rather quickly. and at some point (I'm calling it μ) we've got an absolute end to the point in which we have access to past sense data. 

So the function is discontinuous and piecewise, and at t = μ , f(t) = 0, with predictable end behavior. Russell's description implies that as every rung bell eventually settles into a ground state, where it quits reverberating entirely. 

Growing block theorists posit a simple linear function: f(t) = 1

One problem with Russell's theory is precisely the theoretical strength of the growing block theory, namely the need to account for the subjectivity of this supremum. Where it occurs is partly a function of the subject's attention span, and partly of his overall cognitive ability, and partly just due to his psychological state at the time. It's fair to say that a guy like Gauss could have kept far more things in his mind at once than the average person. And it's also fair to say that when Gauss got drunk, he was less adept at working with the mathematical models he was famous for. 

The ideological origins of Russell's system are probably the most surprising. We have already seen that they differ, fundamentally, from his erstwhile collaborator on the Principia. His positions immediately appear to conflict with his otherwise strong sympathies toward (and place within) neopositivism. The lack of distinction between time-as-container and time-as-thing-which-contains recalls a Husserlian analysis (8). An even earlier source alludes to an equally surprising origin. "Spatial and temporal relations," Russell declares, "must sometimes be included, in the case of a swift motion falling wholly within the specious present" (9).

The term "specious present" is a reference not to any logical positivist, but to one of the fathers of pragmatism. William James defined it as "the prototype of all conceived times... the short duration of which we are immediately and instantly sensible" (10). In order to make sense of this instant sensibility (sorry), we ought to study a previous passage, where James explains in detail.

"The practically cognized present is no knife edge, but it is a saddle-back, with a certain breadth of its own, upon which we sit perched, and from which we look into two directions into time. The unit of composition of our perception of time is a duration, with a bow and a stern, as it were -- a rearward and a forward-looking end" (11).

Never explicitly stated, but safe to assume, is the rough equivalence of the specious present, as James describes it, with that of Russell's individual sensory datum, persisting in the "specious present" as something to which the recipient has direct access, even as time passes, for a definite but finite interval.

James' ideas, old as they are, do not appear to have originated completely with his thought. They seem to have been built on an earlier model, published pseudonymously, under the name "Mr. E.R. Clay" (12). With whomever it originated, the thinker manages to resolve the paradox of being able to explain seeing something in motion, despite the fact that motion occurs over a spatio-temporal interval, and despite the fact that human beings generally like to slice up time, with "the present" being something like a single instantaneous frame in an old celluloid filmstrip, all without treating instantaneity as though it were entirely cut off from history. We can construct a plausible proof.

P1: What we conceive of in our minds via sense data, we conceive of as the present
P2: We conceive of objects moving.
P3: Objects move through time, as well as space.
...: What we conceive of as the present is actually composed of an interval, containing elements of the past.

Despite the inherent difficulties, James makes an attempt to well-define the specious present in physical terms, understandable to a general population.

"The specious present has... a vaguely vanishing backward and forward fringe; but its nucleus is probably the dozen seconds, or less, that have just elapsed... The smallest figure experimentally ascertained was by Exner, who distinctly heard the doubleness of two successive clicks of a Savart's wheel, and two successive snaps of an electric spark, where their interval was made as small as about (1/500) of a second" (13).

Here he does something particularly notable: he differentiates between the limitations of sensing duration via sight as opposed to sound. "With the eye, perception is less delicate," he declares. "Two sparks made to fall beside each other in rapid succession on the center of the retina ceased to be recognized as successive... when their interval fell below 0.044" (14).

We have drawn an important distinction between what we will now call the James-Russell theory of time, and the growing block theory, which is reconciled here. If Russell makes any modification to James' theory of temporal awareness, it is in placing the observer slightly closer to the front of the interval. James may have been riding a saddle, but Russell was riding the nose of a surfboard, watching evental objects instantiate in real time. The interval to which Russell claimed access to newly concretized objects was almost entirely in the very recent past, where they were soon to drop off, making way for an endless procession of new ones. Like growing block theorists, the past contains concrete objects, but unlike them, the objects do not remain accessible forever. The subject does not have direct access, in the James-Russell theory, to objects in the past or the future; but, the subject does have direct access to objects in the James-Russell specious present.

Ambiguity and Errata

At least two immediate problems arise in the attempt to rigorously define Russell's theory of temporal awareness. In the first place, there is a difference between what any human subject perceives as instantaneity, and the duration of his memory as he parses English sentences. This fact is evident in the subtext of Russell’s argument itself (he wouldn’t have to point out the akoluthic sensation of ‘Brutus’ as extant into the end of the sentence otherwise.) If we hear the angelus bells at church, we capture and experience the instantaneous at the playing of a single note. Human beings do not tend to think of past notes as existing in the specious present, except as a convoluted mental exercise in an attempt to explain questions like the ones posed to James and Russell.

An identical visual illustration can be used to illustrate a problem Russell was surely aware of. When schoolchildren learn about “an instantaneous rate of change” in their freshman math courses, they know and understand one application instantly: the problem of perceiving the motion of a physical object. Children learn to find the first derivative of a continuous function, and their associated daydreams often involve finding the precise acceleration of a rocket ship as it moves toward its destination. The calculus of the real numbers is useful because human beings have the experience of seeing accelerating bodies moving through physical space constantly, with no way to accurately judge the rate of change of acceleration visually -- which they would have if the James-Russell theory was an accurate phenomenological model.

When the (sober) human subject views a rocket ship accelerating from the launch pad, his visual sensations do not include seeing, along with the present picture of the rocket, earlier “tracers” of the rocket ship, that fade away gradually, as they pass from the specious present into the past. The rocket does not have a trail of earlier images in the mind of the viewer, fading into obscurity gradually. Without hallucinogens, the James-Russell theory fails to provide an accurate picture of the standard phenomenon of perceiving motion.

In the second place, there is the subjectivity of the experience itself. Double-blind studies suggest that the phenomenology of temporal awareness is mutable, based upon drug use and withdrawal (15). The perception of duration appears to be an unfalsifiable neurological process that resists any attempts to test its accuracy from one person to the next. Attempts to do so, at best, reveal a degeneration or alteration in the faculty, with evidence that while one’s perception of time can not accurately be measured as reliable, it can be tampered with through pharmacology. Every human being would agree that he can perceive the passage of time, but no one has an objective baseline with which to compare his own unique experience.

Not only is the experience of the passage of time subjective and unfalsifiable, we have already seen that it seems also to change when tracking different types of events (16). The aforementioned math student who decides to watch a rocket launch in person will find that the entire show, from liftoff to disappearance, will be about 45 seconds. Despite that interval, after the event, he will generally be able to recall the point of liftoff, and describe what the rocket looked like before ignition. The same person will have a hard time recalling a sequence of names in a sentence after 45 seconds.

Conclusion

We have seen that despite his reticence to devote an entire paper to the topic, Russell did have a coherent theory of the phenomenology of the passage of time. We have also seen that it originates in a surprising place. The sympathies that Bertrand Russell appears to show for the James’ philosophy of time runs counter both to his place in the neopositivist movement and to his antipathy for pragmatism, which he felt brought philosophy “back into the marketplace” (17). Russell never, unfortunately, gives a holistic analysis of how the human subject has direct access to newly concretized objects, as they pass slowly out of the specious present, nor does he build any epistemological theories as to how or why we are able to access them here. While these are problems that are beyond the scope of this paper, the overall effectiveness of the theory and its applications throughout Russell’s related works speaks to his open-mindedness and his pragmatic (sorry) approach to accepting the worthwhile facets of other thinkers, even in those cases where he is generally opposed to the totality of their thought.

Bibliography

1. Russell, Bertrand. An Essay on The Foundations of Geometry.
(Cambridge: C.J. Clay & Sons, 1897): 156-157.
2. Russell, Bertrand. An Inquiry into Meaning and Truth.
(London: George Allen & Unwin, 1940): 40.
3. Whitehead, A.N.. Process and Reality.
(New York: MacMillan, 1929): 25.
4. Forrest, Peter. The Necessary Structure of The All-Pervading Aether
(Frankfurt: Ontos/Verlag, 2012): 167-172.
5. Forrest, Peter. "The Real But Dead Past."
Analysis No 64, 4 (2004): 358-362.
6. Russell, Bertrand. An Inquiry into Meaning and Truth.
(London: George Allen & Unwin, 1940): 39.
7. Russell, Bertrand. An Inquiry into Meaning and Truth.
(London: George Allen & Unwin, 1940): 40.
8. Husserl, Edmund. Phenomenology of Internal Time-Consciousness.
(Bloomington: IU Press, 1964): 98-99.
9. Russell, Bertrand. Our Knowledge of The External World.
(London: George Allen & Unwin, 1926): 83.
10. James, William. The Principles of Psychology.
(New York: Henry Holt & Co., 1890): 631.
11. James, William. The Principles of Psychology.
(New York: Henry Holt & Co., 1890): 609.
12. James, William. The Principles of Psychology.
(New York: Henry Holt & Co., 1890): 608.
13. James, William. The Principles of Psychology.
(New York: Henry Holt & Co., 1890): 613-614.
14. James, William. The Principles of Psychology.
(New York: Henry Holt & Co., 1890): 614.
15. Klein, L.C., et. al.. "Smoking Abstinence Impairs Time Estimation Accuracy"
Pharmacological Bulletin 37, No. 1 (2003):45
16. James, William. The Principles of Psychology.
(New York: Henry Holt & Co., 1890): 614.
17. Ryan, Alan. "Dewey and Russell"
 The Wilson Quarterly 14 no. 1 (1990): 141.

Cheating With Combinatorics

Combinatorics, which is just a fancy word for the study of counting, is a neglected part of the average undergraduate education. That's a shame, because graduate school is replete with practical examples supporting the benefits of a passing familiarity.

This is a typical preparation worksheet for a graduate school comprehensive examination. Ten possible questions are listed, and the candidate is informed that four of the ten questions will appear on the exam. Out of the four questions, the candidate has his choice of two questions to answer.

What the typical student confronts is a question as to how to maximize his efficiency in studying for the examination. How deeply to study each potential question is a function of his time, which is limited. This is ultimately a probability question, which is underpinned by counting.

There are only a couple of important questions, when approaching this combinatorics problem. The first is order. Does the order of the selection matter? In this case it does not matter if the proctor decides to select question no. 4 before question no. 2. The second question is one of repetition. Is it reasonable to expect the proctor to select any one question more than one time? The implication here is that it is not. If the proctor selects question no. 4, he will consider that question unavailable for his next selection.

The first thing we need to do is to count up the total number of all the ways in which a proctor might select four questions out of the ten. In his first choice, he has ten choices, in his second, he has nine, in his third, he has eight, and in his fourth, he has seven. We multiply those numbers to get 5040 - but we have overcounted, as order does not matter! So, we divide out our duplicates, which number 24.

5040/24=210

Which is the number of possible arrangements when choosing 4 questions from a pool of 10.

Now our student wants to maximize his time and study as many problems as deeply and efficiently as he can. Let's suppose that he decides to study five questions, and discard the other five. At this point, we're working in the abstract, so it doesn't matter which five he ultimately chooses. What he's really doing is dividing the total pool of problems into two sets.

Set D={discarded questions} and Set S={studied questions}

In his first example, he's going to let the cardinalities of D and S be equal to 5. What is the probability that of the 4 chosen questions, all will be in the set D of discarded questions? In other words, if a student studies 5 out of the ten problems, how likely is it that he will fail his comprehensive examination, and be thrown out of graduate school? 

This is, again, a combinatorics problem. We have our number of possible selections, and now we need to know what statisticians call the event space, or the number of ways our event might happen. The first thing we need to know is how many ways can our proctor select questions that we won't be studying?

Guys who are pros with arithmetic call this "5 choose 4" or 5C4. The number of ways in which our proctor can choose only questions our student has not studied is 5. We divide this by the total we came up with earlier, and get an estimate as to our student's chances of failing the exam.

5/210 or 1/42

Of course, our student will also fail the test if three of the four questions include those he hasn't studied. We can add this probability 5C3/210 in our heads if we remember our stats courses, and come up with about a 1/14 sum.

To summarize, we have a student who has been presented with ten questions, of the ten, four will show up on an examination. Of the four, he has his choice to answer two questions. He wants the maximum amount of time to study the smallest number of questions possible, while minimizing his chances of failing the exam. What he doesn't want is sit down and be presented with three or four unstudied questions. 

If he chooses to study five of the ten questions, he will have a 1-(1/14) or 13/14 (about 93%) chance of passing his comprehensive exams. 

Ideally, of course, our student would study all ten questions deeply, but we don't live in an ideal world. If I were such a student, I would want better odds than 93%, and would choose six of the questions (preferably those with which I had the least familiarity) to study. That would put me at about (41/42) or 98%

Good luck!

Elise

 
Do what you want
You woman
You high-heeled observer
You night whisperer 

All fire and shale
You crimson volcano
Born in the shade of Denali
You lap up my soul like the tide

You maker of speeches
You tow-headed devil
Whose brown eyes
Are nothing like the sun

Shout on your summit
You, voice of the world
Whose demands issue forth
To the infinite heights

You lover of sunsets
You tropical diver
You destroyer of worlds
You painter of paradise

You crystal vase
You china doll
You wolverine
Do what you want
With me

Liberation

They teach you the poem
With nods and grins and pats on the back.
They tell you it's a machine
A living organism
A game

I'll teach you
To save the poem from the teachers
A poem is not a game
A poem is the kind of work
That doesn't feel like working

A poem is not machine
I am not an operator
I am any other hand
On the oil lease, just west of Odessa
I go to work and feel
The bolt creak beneath my wrench
The iron groans
I lever this rig into
Dreadful deconstructive disassembly.

A poem is not a tree
I am not a tourist in a sticky arboretum
I am any other hand
On the logging crew, just east of Vancouver
I feel the ring
Echo up through the bones in my forearms
The song of the hammer, meeting the stake
I hear the pulp crack
The verse splits its trunk.

The poem is, or ought to be
The voice of any other hand
The poem ought never be
That which keeps the worker from reading
That which obscures ain't poetry.

The poem is the call of our fathers
Who toiled in the inky mines
Who tilled the fields past sundown
With batty cries and echoes
Keeping track of who was where.

It is the song our mothers sang
Who washed our socks,
The sound of their tiptoes, candle lit
In the early mornings of our history
Preparing the way for sunrise.

Our mothers and our fathers
Didn't speak in esoterica
We never required translators
We passed the bounties
Of the hunt and of the harvest
Both ways around the table.

Poetry is not a prison house of language
Not a bedlam of meaning
A poet is not a saffron swathed swami

Poetry is the collective property
Of the people who produce
And those who produce are poets
Even, or especially if
Their produce isn't poetry.

You, reader
Can you hear me?
I'm speaking to you
Shouting through the page
Calling up through the lines.

In the name of the people
I commission you poet
And order you out
To liberate poetry
Get up off your knees
Take up your pen and fight
It's as easy as you make it.

We need no tricks
No fanciful fonts
No artsy enjambment
We poets
Of the popular front
For the liberation of the poetic
We need but to shout
Our love in the dark.