scintillating scotoma

a few minutes ago (~22:35), reading, and i notice that letters are hard to see. that sensation of having a bright afterimage at fixation; it's moving rightward, usually it's been leftward (I haven't taken notes on the past 2 occurrences, sadly..); this it is at least the first of the last 4 to go through the right field, if not longer.

it begins with just a weird sense of scotoma-ness, very near fixation, but the blind areas are hard to pin down - they seem to change very rapidly, or else it's more a sensation of blindness rather than actual blindness. it's strange how it sticks at fixation even as it arcs out into the periphery; it seems it always arcs into the lower field, after arcing just a bit above fixation. i've not noticed yet one passing across the field, maybe it is restricted to hemisphere?

it's almost gone at this point (almost 30 minutes after the first signs), and all that's left is a flickering at the very top of my visual field, as if there's a light flashing on my eyebrows; interestingly, if i look up, it disappears, which is strange because it should be attached to the field location. i can look up, it disappears, look down again and it reappears. maybe was an interaction with the reflection of room/computer lights off my eyeglass frames? can't test, it's all gone now..

and i have a headache (actually it started a few minutes in; the light show was so slow to start, i thought we were skipping straight to the headache for a few minutes, a bit of disappointment, but it worked out!)

also, some hints: today and yesterday, i several times wondered if i wasn't going to get a headache soon, without understanding why. not sure what sets off those feelings.. this afternoon, i thought i saw some flashes at some point when i was walking down the hallway, and that really made me suspicious; and, all day, really tight, painful muscle spasm throughout my upper back, both sides trapezius.

23:05

map below: i have a few of these now, should get to processing them this summer..

Edit: look at what this guy has done: http://www.pvanvalkenburgh.com/MigraineAura/MigraineAuraMaps.html. pretty amazing.

also, i did wind up writing a script to analyze these plots; once I get some stuff settled, i'll post those in a new entry.

lazy friday dark adapt

Spent afternoon of Friday, 4-20-12, with a ~3 log unit (~.2%) ND filter over my right eye. Made the following observations:

(Took the filter off after about 4 hours. It wasn’t bothering me much anymore, but I think the plastic and rubber stuff in the goggles was irritating my eyes, which were starting to feel kind of dry and red. Light adaptation is really fast, it’s just been a minute and the (formerly dark adapted) right eye’s image only seems slightly brighter than the left’s.)

1. Noise: the dark adapted eye’s view is noisy, and the noise intrudes into the dominant view. It’s irritating. The dark adapted view isn’t being suppressed, though, it’s there like a ghost. Double images, from depth, are strikingly noticeable, not sure why.
2. Pulfrich effect: first time I’ve really seen this work. I put my index fingers tip-to-tip and move one from side to side, fixating on the still one, and the moving finger looks like it’s rotating. My hand even feels like it’s rotating.
3. Pulfrich effect 2: Fusion isn’t always working, but I seem to be ortho a lot of the time. I just noticed, though, that if I make quick motions, e.g. a flick of a finger, there’s a delay in the motion between the two eyes; the dark adapted image is delayed by several hundred milliseconds! Especially obvious if I focus at distance so I have a double image of the finger. Explains the strong Pulfrich effect.
4. Noise 2: Just looked at some high frequency gratings. With the dark-adapted eye, the noise was very interesting, looked like waves moving along the grating orientation, i.e. along the bright and dark bars there’s a sort of undulating, grainy fluctuation.
5. I still have foveal vision and color vision, but both are very weak. Dim foveal details are invisible. High contrast details (text, the high frequency gratings) are low contrast, smudgy..
6. Motion is kind of irritating, I think because it brings about lots of uncomfortable Pulfrich-type effects. Even eye movements over a page of text can be bothersome, because there is always an accompanying, delayed motion. I’m guessing that the saccade cancellation is being dominated by the light-adapted eye, and so I’m seeing the dark-adapted saccades. I don’t notice a depth effect, but walking around in the hallways I do feel kind of unsteady, maybe because of motion interfering with stereopsis. If objects are still, stereopsis seems to be okay.
7. If I take vertical and horizontal gratings (64c/512px), add them together, then look at them at 25% contrast from about 30cm (here at my desk), I don’t see a compound grating – I see patches of vertical and patches of horizontal. I’ve never noticed this before; I wonder what differences there are with scotopic vision and cross-orientation suppression..
8. I tried to watch my light-adapted eye move in a mirror, but the dark-adapted eye just couldn't see well enough. I think a weaker filter would make it possible.

Memes and Pharmacies

That rivalry proposal went in last Monday with no problems, along with a long-festering manuscript, so it seems I took a week off from writing. Now I have progress reports to do, presentations to prepare, other manuscripts to complete, on and on.. I need to make sure I keep up with this journal, which seems to be helping in keeping my writing pace up.

Vacation is over!

About 12 years ago, I read the Meme Machine by Susan Blackmore. It was around the time that I decided to major in psychology, and I was reading all this Dan Dennett Douglas Hofstadter stuff, but it was her popular science book that really had a big effect on me - I would say that it changed my worldview completely, to the extent that I would identify myself as a memeticist when discussions of religion or that sort of thing came up (it was still college, see) - I really felt like it was a great idea, that human culture and human psychology could be explained as essentially a type of evolutionary biology. I still believe it, and so I suppose this book still really sits near the base of my philosophical side, even though I don't think about these things so much anymore.

I bring this up because the other night Jingping and I were talking about being tricked, since this was the topic of a Chinese textbook lesson I had just read, and I recounted the story of being completely conned by a thief once when I was a clerk working at CVS. I wound up going on more generally about working there, and I remembered that I had worked out a memetics-inspired 'model' of that store, which I hadn't thought about in a long time. One of the things about the memetics idea that had really gotten to me was that you could see social organizations as living creatures with their own biological processes - not that this is an idea original to Blackmore, and I'm sure that's not the first place I had heard it (like I said, I was also reading Dennett and Hofstadter at the time), but she did work it into a larger sort of scientistic system which seemed to simplify and unify a lot of questions.

Now I realize that the criticisms of memetics that I heard from professors in college (when I questioned them about it) were mostly right, in that it mostly consists of making analogies between systems; only in the last few years, with the whole online social networking advent, has a real science of something like memetics actually gotten off the ground (this is a neat example from a few weeks ago), and it's very different from what had been imagined when the idea was first getting around.

Anyways, I thought I'd detail here my biology-inspired model of a CVS store, ca. 2001. I have a notebook somewhere where I had detailed a whole system, with functional syntax and everything, for describing social organizations in terms of cellular, metabolic systems. This might have been the first time that I had tried to put together a comprehensive model of a system, now that I think of it. The store, I thought, was itself a cell in a larger CVS system dispersed across the city, which itself was a system dispersed across the country. I was mainly interested in the store level, where you could see different components acting as reagents. It was a strongly analogical system, but not completely analogical, to plant metabolism: a plants needs carbon, so it uses sunlight to break down carbon dioxide, releasing the unneeded oxygen back into the world. A store needs money, so it uses salable products to break down a money-human bond, releasing the human back into the world.

Of course, with plants the sunlight comes free from heaven - all the plant can do is spread out and try to catch it - while salable products must be delivered from another part of the CVS system: the distribution center. The distribution center emits reagents to the stores, where the money-human bond is broken down. The CVS system also emits catalytic agents into the world - advertisements - to facilitate the crucial reaction. The money absorbed by the system is energy which is used to drive the system through a reaction not unlike oxidation - the money-human bond is reformed systematically, with employees as the human component. This reformation is what really drives the system. Those new human-money bonds then go out into the world and fulfill the same function, breaking apart, as they interact with other businesses.

Looking at a business in this way totally changed the way I understood the world. Businesses, churches, governments, political parties, armies - all of them can be thought of as living creatures, or as organs of larger creatures, rather than as some sort of human means-to-an-end. By changing perspective between levels, we can see ourselves as means to the ends of these larger systems, just as our cells and organs are means to ours. Now I'm finally getting around to reading straight through Hofstadter's GEB, and so I can see that this general idea of shifting perspective across levels is an old one that has been astonishing people for a long time. But for me, coming to see human culture as as being alive was a fundamental shift in my intellectual development, one that hasn't really been superseded since. I haven't become a real memeticist yet, but it's all still there, underneath... these tiny tendrils of memetics live yet...

dream post!

recurring dream:

jingping and i are trying to get to the train station. the city is like a cross between boston and chicago - it's boston but with lots of overhead walkways and more of that chicagoesque feeling of sharp-edged criss-crossedness.

lots of things happen as we're on our way, it's like we're being chased, but the recurring part is where we get into the station and have to start climbing a stairwell, up and up. i know what's going to happen as the dream progresses. there's a fear of falling down the stairwell, but what happens is that it gets narrower and narrower, less and less place to put your feet, and you're crawling finally up a spiral tunnel, until you can't go further because there's just not enough space - around this point i know it's a dream, because i'm thinking that it can't really be this way, and i'm trying to change it because it's so damn uncomfortable. even in the dream, i'm thinking, why does this happen, why can't i fix it?

once it got to that point, i realized that my eyes were closed, but i couldn't open them, and yet i could still kind of see the twisting stairwell tunnel ahead - and there was a confusing sensation of being able to see but not being able to see, at the same time (interesting relevance to the visual consciousness stuff i was wondering about earlier, which is really why i'm writing it down). i was feeling around for the gap ahead, to see if i would fit, and i knew jingping was behind me and i couldn't back up, but i also felt like i could see it all...

i think i woke up soon after. i figure that noticing my eyes were closed and not being able to open them, and yet still having a sense of vision, must have been REM atonia - sleep paralysis, the sort of thing that gives you the feeling of being trapped and immobile in a bad dream.

anyways, i'm pretty sure i've had this dream a few times, the "shrinking stairwell dream".

dream post, yeah!

model update

I'm working on other things lately, but I did finally get that multi-channel rivalry model working - main problem was that I had written the convolution equations out wrong. I had to do the convolution there in the code because the filter array is irregular - there's no function to call for 2d irregular-array convolution, much less for switching the convolution between different layers.

Here's what I had done:

Z´(x) = Z´(x) + F(x)·Z(x), where x is a vector of spatial indices, Z is the differential equation describing the change in excitation or adaptation over time, F is basically just a 2-d Gaussian representing spatial spread of activation for the inhibitory or excitatory unit, and Z´ is (supposed to be) the differential convolved with the spread function.

Now that doesn't make any sense at all. I don't know what that is. In the actual code that equation was actually 3 lines long, with lots and lots of indices going on because the system has something like five dimensions to it; so, I couldn't see what nonsense it was.

This is how it is now:

Z´(x) = Z´(x) + sum(F(x)·Z(x))*F(x)

THAT is convolution. I discovered what was going on by looking at the filter values as images rather than as time plots; Z and Z´ didn't look different at all! Z´ should look like a blurred version of Z. Such a waste of time...

Anyways, it kind of works now. Different problems. Not working on it until later in April. The 'simple' single resolution model was used to generate some images for my NRSA application. Here's a sample simulation of strabismus (with eye movements):

standing at fenway station, thinking, as usual, "what's my problem", and i came up with a nice little self-referential, iterative statement of it: it's pablum, but i'm not usually this verbally clever, so let's write it down:

don't do what you don't believe
can't believe what you can't understand
won't understand what you won't do

so that's the problem; it's not exactly as i would normally say these things. if you asked me before i formulated this, i would probably say, "i don't like to do what i don't understand", and that's what i started out thinking. but then i asked, "why is that?", and decided that if i don't understand it, i can't really attach to it - then i saw the loop.

interestingly enough, the solution is the negation of the problem, literally:

do what you believe
believe what you understand
understand what you do

both of these statements have a sort of inertia; once you have one of the predicates, it starts rolling and keeps going. since they aren't specific, both statements are generative or productive - the referents don't need to be the same on each loop, but of course they should be logically linked.

(really, the middle statement isn't necessary in either one, with 'believe' replaced with 'understand' in the first line. i feel like the middle line adds some depth, though, so there it is.)

vision includes the world

I need to procrastinate slightly more productively, so here is a short essay relating some of my thoughts on visual consciousness.

For years now, I've understood visual experience or consciousness (experience is easier to say and write, and has less near-meaning baggage, so let's continue with that term) as having two components:

1. The image. A part of vision is direct, which means that when you see an object, it is true to say that what you see is the thing itself, or at least the light reflected/emitted by that object (this similar to the idea of the 'optic array'). This is a difficult position to hold, but I think it is a necessary default. The alternative, which is definitely more popular these days, is to say that what you see is entirely a representation of the thing itself, instantiated in the brain. This sort of idealism is attractive because the brain is obviously a self-contained system, and because experience also seems to be self-contained, and because every aspect of experience seems to have a neural correlate. If I say that vision involves processes or structure outside the brain, I have to explain why we don't see what we don't see; why don't I see what you see, for example?

It seems to me that in placing the contents of consciousness somewhere in the physical world, there are two possible null hypotheses: either everything is absolutely centralized, completely contained within the brain, or everything is absolutely external, completely outside the brain. The second account is rare these days (see Gibson), as the only job it leaves for the brain is sorting out of responses to visual experiences. It seems clear that much of vision actually does occur within the brain, and I'll get to that in part 2, below. Now, these null hypotheses: that everything is internal is an objective hypothesis, based on e.g. a scientist's observations that the brain is correlated with experience; that everything is external is a subjective hypothesis, based on e.g. my observations that what seems to be in the world is actually there, i.e. that my sensations are always accurate.

Since visual experience is a subjective process which cannot be observed, I like to stick to the subjective null hypothesis: everything is external unless shown otherwise. Immediately on stating this hypothesis, we can start to make a list of the components of visual experience which are surely neural.

2. The brain. Let's start with the subjective null hypothesis: everything you see is there, in the world. Just a little thought proves that this can't be true: faces are a great example. Look at two faces, one of a person you know well - your sister or brother, maybe - and one of a strange that you've never seen before. There, in the faces, you see a difference that you can't deny, because one seems to have an identity and the other does not. This difference isn't purely cognitive or emotional, either, because one will easily make the admission that the face of his sister is his sister. Seeing her face, he will say, "That is her!" Clearly, however, the identity is not in the face - it is in the observer.

If this isn't a satisfying example, color perception must be. Color is not a property of images, it is a construct of the brain - this is not difficult to show, either with the proof that identical wavelength distributions can yield different color percepts in different conditions ('color constancy'), or with the inverse proof that different wavelength distributions can yield identical color percepts ('metamers'). We understand color as a brain's capacity to discriminate consistently between different (simultaneous or asynchronous) distributions of visible radiation. It is something that exists only in the observer.

These are easy, but it does get harder. Consider depth perception. In a scene, some things are nearer or further from you, but there is nothing in the images you sense that labels a given point in the scene as being at a particular depth. There is information in the scene that can be used by the observer to infer depth. So, depth is another part of the brain's capacity to interpret the image, but it is not a part of the scene. This is a more more difficult step than with faces or colors, and here's why: whereas a face's identity, or a light's color, is plainly not a property of the world itself, we know that the world is three dimensional, and that objects have spatial relationships; and, we know that what we see as depth in a scene informs us as to these spatial relationships. However, we then make the mistake of believing that visual depth is the same as space; on reflection, however, we can begin to understand that they are not the same. Depth is an neural estimate of space based on image information.

Let's keep going. Spatial orientation is another good one: 'up' and 'down' and 'left' and 'right' are, in fact, not part of space. I've already made my complaint about this one: spatial orientation is created by the brain.

If we keep going like this, what do we have left? What is there about visual experience that is not in some way created by the brain? How can I state that there is an 'external' component to vision?

The only feature of vision, it seems, that is not generated by the brain is the internal spatial organization of the image, the positional relationships between points in the image - what in visual neuroscience is recognized as retinotopy. Spatial relationships between points in the visual field do not need to be recovered, only preserved. A person's ability to use this information can be lost, certainly, through damage to the dorsal stream (simultanagnosia, optic ataxia, neglect, etc). This does not mean that the visual experience of these relationships is lost, only that it is unable to contribute to behavioral outputs. I think it is a mistake - commonly made - to assume that a patient with one of these disorders is unable to see the spatial relationships that they are unable to respond to. Assigning to the brain the generation of positional relationships needs evidence, and I know of none. A digital, raster image based system would be different, of course: a video camera detects images by reading them into a long, one-dimensional string of symbols. Positional relationships are lost, and can only be recovered by using internal information about how the image was encoded to recreate those positions. The visual system never needs to do this: it's all there, in the very structure of the system, starting at the pupil of the eye.

So, here is my understanding of vision: it is a stack of transformations, simultaneously experienced. The bottom of the stack is, at the very least, the retinal image (and if the image, why not the logically prior optic array?). Successive levels of the stack analyze the structure of the lower levels, discriminating colors, brightnesses, depths, and identities; this entire stack is experienced simultaneously, and is identical with visual consciousness. But, the entire thing is anchored in the reality of that bottom layer; take it away, and everything above disappears. Activity in the upper levels can be experienced independently - we can use visual imagination, or have visual dreams, but these are never substantial, and I mean this not in a figurative sense - the substance of vision is the retinal image.

This view has consequences. It means that it is impossible to completely reproduce visual experience by any brain-only simulation, i.e. a 'brain in a vat' could never have complete visual experience. Hallucinations must be mistakes in the upper levels of the stack, and cannot involve substantial features of visual experience - a hallucination is a mistaking of the spatial organization in the lowest levels for something that it is not. Having had very few hallucinations in my life, this does not conflict with my experiences. I can imagine that a hallucination of a pink elephant could actually involve seeing a pink elephant in exactly the same experiential terms as if one was there, in physical space, to be seen, but i don't believe it, and I don't think there's any evidence for vision working that way. Similarly, dreams are insubstantial, I claim, because there is nothing in that bottom layer to pin the stack to a particular state; memory, or even immediate experience, of a dream may seem like visual experience, but this is a mistake of association: we are so accustomed to experiencing activity in the upper stacks as immediately consequent to the image, that when there is activity with no image, we fail to notice that it isn't there! I think, though, that on careful inspection (which is difficult in dreams!), we find that dream vision has indeterminate spatial organization.

Anyways, that's my thinking. This has gone on long enough, I need to work on this proposal...

oscillate, explode, or stabilize

must learn about runge-kutta methods,
must learn about runge-kutta methods,
must learn about runge-kutta methods.

clearly this too-complicated model is suffering because of the temporal resolution. i've spent nights now trying to figure out why the thing wasn't working right - and did find a few errors along the way, which i don't think would have made or brake the thing anyways - and finally i conclude that the response time constant was too small. this is strange, because the same model works great with a 2d network, and perfect with a single unit; apparently there's something about this network, which is essentially 3d, which effectively makes the time constants faster... it must be that compounding the differential during the convolution, over multiple filter layers, effectively speeds everything up.

it's not like i wasn't aware of this problem at first. i thought i had solved that by doing the global normalization, where the convolution stage would basically be treated as a single layer. last night, i decided that collapsing that stage to one layer was a mistake, because it resulted in the pools everywhere being overwhelmed by the finer-grain channels, since those filters are more numerous. that may actually be correct, with some sort of leveling factor, but at any rate i took out the collapse. it didn't change performance much, but that's when i was using a too-complex test case (two faces), instead of the current test case of two gratings. now i realize that the pooling was accelerating the responses, resulting in useless behavior by the network - turning up the interocular inhibition to any level that did anything tended to result in ms-to-ms oscillations.

so, the compounding of responses was doing it, i guess, and would be doing it even if i had the pooling collapse still worked in. but now i can't understand why i didn't get the same problem, apparently ever, with the fft-based version of the model. now i'm suspicious that maybe i *did* get it, and just never perceived it because i wasn't doing the same sorts of tests with that thing.

not quite back to the drawing board. i wish i could get away from the drawing board, for just a few nights, so i could work on this goddam proposal like i should have been doing for the past 2 months.

An Instantiation of a General Problem

(I wrote this, but never finished it, in China back around Christmastime. Randomly remembered it today, and thought this would be as good a place as any for it.)

The key was to be found across the city, in the old commercial district. We had tried simulations, implanted demos, viewed stereoscopic images through a haploscope we found in storage in the medical school. After all of these, we had tried hallucinogens to modulate the imagined presence of the key, but it was all to no avail. At least, we said to ourselves, when we finally approach the key we will be familiar with it. The front end of the process will not be a surprise.

The approach, however, to that front end, would be horrendous. First, our camp was protected from the feed. This kept the peace from finding us, but it also meant that our emergence into the feed would stand out like a tree in the desert. We had monitored the security cycles for days. Most would say that such monitoring was futile, since the cycle paths were random, generated with new seeds every minute give or take another random cycle. Any attempt, most would say, to predict gaps in the cycle would result in no better chance of unnoticed entry than no attempt at all, with the added hazard of false confidence to mask the creeping signs of detection.

It was possible, though, to closely estimate the number of cycles. We could detect the passes themselves, which gave us data for the estimation. The different cycles were unique, originating from different security servers, each assigned its own identification during its current generation. Given all these data, we had a method for estimating, at any given moment, the likelihood of a pass. The optimal estimate could be made using the previous twenty seconds of data. You could have pointed out that a likelihood is the opposite of a certainty, at least along a certain conceptual dimension. You could also have pointed out that the optimal estimate was lousy if those twenty seconds contained a generation update. We would have ignored you.

Once inside, we would have to obtain city ids from an admin, which was not trivial, but not a problem as long as we could quickly make contact with Tsai, our woman on the inside. We knew she was still online and that her admin was current, so as long as she wasn't in some unshakable stupor, she would tie us on and we'd be set for the rest of the trip. Anyways, persisting for a few minutes with unregistered cids wasn't as dangerous as suddenly emerging out of the void. An impulse is like that tree in the desert and the primary means of detecting aliens, while trouble finding a cid registration is a basic function of the feed servers, which would be checked in serial, assuming corruption or damage first and alien somewhere further down the line. Tsai could just tie us onto the oldest and most remote server, plot a false geographic history of intermittent reception and an outstanding service request, and there would be nothing in the feed to mark us out. The tree would dissolve into a puff of dust.

The next problem would be the actual emergence into the city. Feed presence can be smoothed over, anyone can appear to be anyone, fit into any group, assume any identity. The body, however, is much less convenient to modify. Their hair is long, but ours is short. Their skin is yellow, but ours is brown. We stand head and shoulders above them on the street, and we have no choice but to travel on the street for the most part, by foot, in the open, making stark and clear the comparison between foreigner and local. But, there are other foreigners in Haisheng. They are few and far between, but there are others, and though we draw attention it is natural, because who can ignore a brown spot among yellow? The noticing is in itself not a threat. But when others are looking for you, being easily noticed is a step away from being easily found. We did not want to be found, but there was no choice but to be noticed.

The final hazard was beyond any interaction with the first two. At the time I could not imagine how, but I was still cognizant that there was a possibility that the locked id had already been accessed by my competitors before I had retrieved it. If so, they may even have already decrypted it, outformed the important information inside, and restored the encryption. This was beyond any vital worry on my part, since the main danger was that knowing the key, and that I was looking to open the id, they might be waiting for me at the site. This meant I would have to move slowly through the streets, below them when possible, work quickly when it was time to get the key, and maintain vigilance on all channels at all times. There was nothing else we could do but be vigilant.

I can tell you more about the key without compromising the truth of the mission. Someday down the line, you may be able to put two and two together, but by that time whether or not you know such an obscure truth won't matter much, and you'll be occupied with obscuring your own. Anyways, it is an interesting detail, and may spark one or another interest in you.

The id I had retrieved was that of a neural engineer from a century or so earlier. We needed to query it regarding some interactions it had had at one time with our main objective, whose id at the time was missing and presumed destroyed. As it turns out this engineer had dabbled in id encryption, which was a new field in those days, specifically in encryption through perceptual experience. Though the field was active at the time, it was - and remains - completely unknown to the science that this particular engineer had worked on the problem. It was a private pastime, perhaps a paranoid fear that a great advance might be stolen, or maybe it was just a fear of inadequacy in an outsider bringing to the field such an idiosyncratic development. At any rate, this engineer had come up with something exquisite, which was probably unmatched by anything else produced by her generation. She may have meant it entirely for herself. Today, it's a work of art, but the tech is fundamentally outdated.

This is a digression, I'm sorry. Outdated or not, it was a good lock, and on site we still needed the key to open it. The encryption was applied to the id by taking the online state of some suite of perceptual systems, definitely including visual, possibly other - and by the way, don't take my ambiguity as indicating anything other than an intention to be ambiguous - and using this neural state as the key for the encrypted id. The entire state couldn't  be recorded, of course, since the subject would have to be standing out in the open at the location, i.e. a true state scan would be impractical, especially in those days. Instead, something was probably worn, perhaps obvious or perhaps hidden, instantaneously recording a blocked brain state amounting to just a few terabytes. It was a functional state, meaning that it could be reproduced in other human brains, but our initial estimate that a good visual simulation would suffice proved wrong. We needed to be there, unless someone could explain exactly what composed the key, and the only person who could tell us that, it appeared, was the one locked in that id.

Back to the problem. Being noticed, maybe being scooped, these were mostly outside our control. But skipping as an alien into a secure feed using random-cycle maintenance, that's something we can deal with. Look at the figure field. We used standard methods to monitor the cycles and establish their regeneration characteristics, how many there were, durations of the cycles, amplitude of the duration modulation - everything here is something you've seen before. You all have four minutes to generate the optimal estimate from these data, starting - now.

multi-channel M-scaled discrete filter convolution

Okay, so, I built this really neat discrete filter-based visual field model, planning to use it to measure binocular image statistics and to generate more realistic rivalry simulations. I hoped that doing the simulations would actually be quicker using the filters, since there would be far fewer filters than pixel images (I was using image-filter convolution to do the simulations I showed 2 posts ago), and the filters only needed to be represented by their scalar responses. Hoped but did not believe..

So now, I just spent the weekend (wrote that first paragraph a week ago) staring at the code, trying to figure out how to do, essentially, convolution of a function with an irregular array. It is complicated! I wrote a function to get local neighborhood vectors for each filter within its own channel, and then stared at that for a couple of days, and then realized that I should have written it to get the neighborhood without regard to channel. It's a pretty gangly operation, but it does have a good structural resemblance to stuff I've been thinking about for years. Ed and Bruce's relatively abstract idea about the broadband gain control pools, well, I've built it. Not for the intended purposes, since there's not going to be any gain control here - the only suppression that will be involved is like an 'exit gate', the permission for information in the channel array to be moved out to the later stages ("consciousness", we'll call it).

And, I say again, it's complicated. It's definitely not going to be faster than the rectangular filter convolution; in fact, it's likely to be 3 or 4 times slower, and it's going to produce rougher looking images on top of that. All this just to incorporate stupid M-scaling into these stupid rivalry waves. I swear, I can't think of a better way to do it. And the thing still isn't going to know anything about surfaces or faces or houses or any of that stuff, and it's going to take forever to debug and proof since it's going to be so slow...

But it's going to be cool.

retrograde inversion

Several times in your life you may hear it noted that the retinal image is reversed and upside-down. Fewer times than that, hopefully, you may then hear it noted with curiosity that the brain somehow undoes this retrograde inversion. When you do hear this, please interject with the following:

"The brain does not reverse the coordinates of the retinal image. The brain does not know or care about about the retinal image's orientation relative to the world; as far as the brain is concerned, the image is not upside-down, or upside-up, or flipped or double-flipped. It is not delivered to the brain with reversed coordinates, but with no coordinates at all. The brain assigns spatial coordinates to the visual information it obtains from the eyes. It does this by integrating information about body position, gravity, and other consistent sensory cues about the state of the world. There is no reversal or correction of coordinates, there is only assignment of coordinates."

You will promptly be thanked for clearing up the misunderstanding, and hopefully your interjection will serve to end one strain of a particularly irritating bit of pernicious nonsense.

Thank you.

Rivalry and Diplopia

A simulation of binocular rivalry and fusion with eye movements:

First, the input:

If you can cross-fuse, you want to fuse that white rectangle (and the matched noise background). It's hard to do, especially since there will be a strong urge to fuse the face, not the background. If you succeed, the girl's face will be diplopic (seen double). The video below is a simulation of what is happening in the parts of the visual field where the face is seen.

The photo of the girl is represented at two different ('disparate') locations for the two 'eyes' (just different filter streams in the simulation), while both eyes see the same background (noise with a little white block below the photos). At locations where the two eyes get different inputs (i.e. wherever the photo is seen), the two streams suppress one another and 'binocular rivalry' is induced. This rivalry is unstable, and results in periodic fluctuations where either one or the other eye's image is seen, but not both.

On the other hand, when both eyes get the same input, there is no suppression between streams (this isn't physiologically accurate, just convenient in this simulation). This results in 'fusion' of the two eyes images.

Every second, the filter streams - the eyes - shift to new, random coordinates (they are yoked together of course). You can see that by the shifts in position of the little black dot, which starts out near the white block.

(Both of these videos look a lot better if magnified, i.e. hit that little box in the lower-right corner and look at them full-screen.)

 

To make a little clearer what's happening, here's a color-coded version:

 

Here, locations where one eye's image gets through to be 'seen' are colored red or green (depending on which eye - geometrically it only makes sense that green-is-left and red-is-right, which would mean that the photo is between the viewer and the gray background), while regions where there is fusion are colored yellow or brown. The stream marker is now a blue dot (not really; the googlevideo encoder seems to favor dumping small blue dots against red/green backgrounds, go figure)!

Look at that mess of imbalanced fusion that builds up all over the scene. What a mess!

Process

Draft 1: Write 5000 words in 2 days.
Draft 2: Delete 1000 words, change 500 words, write 250 words in 2 days.
Draft 4: Delete 250 words, change 100 words, write 50 words in 2 days.
Draft 8: Delete 50 words, change 20 words, write 10 words in 2 days.
Draft 16: Delete 10 words, change 5 words, write 2 words in 2 days.
Draft 32: Delete 2 words, change 2 words, write 1 word in 2 days.
Draft 33: Delete 500 words, change 250 words, write 1000 words in 2 days.

Two Dilemmas

The Train Dilemma:
If you run to catch a train which from a distance you saw pull into the station, it will depart just as you arrive. Next time, you will believe you can't catch it, and you will walk. If you walk to the station believing you can't catch the train, it will still depart just as you arrive. You will believe that if you had run you would have caught it, so next time, you will run. Ad infinitum.

Assume that all other things being equal, walking is preferable to running.

e.g.
run_speed >> walk_speed
distance / run_speed = "t_to_departure" + epsilon (very small interval), therefore just walk
distance / walk_speed = "t_to_departure" + epsilon, therefore run

The illusion here, or the problem in reasoning, is that the departure time of the train is somehow correlated with your decision to run or walk. If this is so, then the correct solution is to retain your dignity and walk coolly to the station every time. But it is unlikely that this is so.

Clearly the solution to this problem is to run every time, but it might take you a few failures to convince yourself of that. I've been in this situation many times on the way home from TKD, walking down the alley off Brookline that leads to Fenway Station; that's exactly where the D-Train comes out of the underground, and if when I get to the end of the alley I hear a distant screeching of metal wheels on metal rails, I know the train is coming, and I know I should start running.

The Bus Dilemma:
Let's say you have multiple paths to a destination, one of which includes a bus ride, but you don't know the schedule, only that the bus comes at a certain interval.

The dilemma here is whether or not to take your other option. Often, you might feel that you have committed enough time to waiting for the bus that you should abandon other options and just wait until the next one comes - otherwise, you've wasted all that time.

If the following propositions are true, then the dilemma occurs:
1. time_by_bus < time_by_other
2. time_by_bus + bus_period > time_by_other
3. bus_phase is unknown or undependable

If these are true, then it can be hard to decide just what to do. Keep waiting, or take the other route?

Again, the answer is probabilistic. If the bus phase is unknown, we can represent 'wait time' as a uniformly distributed random variable in the interval [0 bus_period]. We can then combine the after-weight travel times for the bus and the other route in the following way:

t_wasted = rand[0 bus_period] + t_bus - t_other

If t_wasted is positive, then the wait was too long and time would have been saved by taking the other route. If it's negative, then the wait was worth it, and time was saved by taking the bus. How do you use this to decide what to do? First off, look at what happens if t_bus and t_other are equal - in that case, t_wasted will always be positive, i.e. it makes no sense to wait at all, and you should take the other route every time.

At the very least, you want to break even on average. To do this, (t_bus - t_other) has to be equal to negative half the bus period, i.e. taking the other route should take as long as taking the bus plus half of the maximum wait time. Otherwise it's just not worth it, unless you get lucky. That's why those three propositions are necessary; otherwise you'll always know what to do.

After writing this out, I googled "bus dilemma", and what do you know: there's an arxiv paper on a similar problem. Here, he's considering whether to wait or walk along the same route (in which case you can also try to account for the chances you might have to catch the bus as you're walking), which wasn't how I was thinking of it, even though it's similar to the main example I had in mind. I was thinking about two situations: the bus stop in front of my old building in Louisville, where the bus came every 20 minutes or so, took 5 minutes to take you to campus, and was set against a 20 minute walk to campus. On average in this case, you would come out ahead, but I eventually decided waiting was boring, and the few minutes gained on average were better spent walking down 3rd Street.

The other example is of coming home from Davis Square in Cambridge, and deciding whether or not to catch the 86 bus home from Harvard Square or to take the D train home from Park Street. That one is more complicated since there are multiple waits involved, but since several times I've gotten lost looking for the 86 bus stop, the problem has run through my mind several times there...

Psychophysics and Consciousness

I reread this paper by David Chalmers yesterday morning for the first time in several years. I had been reminded of it because of this commentary by Kaspar Meyer in Science last week. The commentary was mildly interesting, and pointed out some of the current neuroscience perspectives as to just what consciousness is: e.g. is it the sensory experience with a background of knowledge and cognitive processes ("bottom up"), or is it a sort of best-estimate of what reality is given current and recent circumstances, using sensory input as a sort of reality check ("top down")? He finishes off in what seemed to me to be pretty fuzzy territory, but it was at least evocative of interesting ideas.

I'm vaguely familiar with some of this stuff, but I've never gotten too deep into because it doesn't satisfy me the way the philosophers do. The neuroscientists are looking for the "neural correlates of consciousness", which I guess is all that one really can look for. What this science reveals is the structure of consciousness, i.e. what is and is not included, what are the boundaries and how are they determined by the nature of the brain, and as indicated above, what exactly is the seeming 'core', or experiential reference point, of conscious experience, in neurobiological terms.

It is good stuff, but it always seems to me that the proposed theories far outstrip the basic science that is supposed to underpin them (e.g., in the commentary, Meyer cites experiments that demonstrate internally generated excitation of sensory cortex, and more generally recurrent activation, as evidence for the interesting idea that perceptual experience "would result from signals that descend through the sensory systems, just as behavior results from signals that descend along the motor pathways"). I don't know, that seems a bit of cart before horse, but like I said, I've only ever really skimmed the surface of this research. Meyer, Damasio, Dehaene, these guys are all basically frontal cortex cognitive neuroscientists, not perception scientists, and I've never really had cause to sink into that part of the science.

Now, the Chalmers paper. That's what I was going to go on about, not the Meyer commentary...

Anyways, in that paper Chalmers isn't really describing new ideas or new ways of thinking about consciousness (there is a subsection on some sort of "Kripkean" analysis of some philosophical point which I think actually subtracted from my comprehension of other parts of the paper, but it doesn't seem crucial). What he does is lay out a taxonomy of theories of consciousness - and the consciousness he's talking about isn't the "easy" kind, as he calls it, i.e. the NCC business that Dehaene is always going on about, but the "hard" kind, i.e. the fact-of-phenomenal-experience. I was thinking about that taxonomy yesterday evening, and wondering how psychophysics as a science fits into it, whether or not it biases one towards one or another way of thinking about phenomenal consciousness and just what it could be, or where it might come from.

As far as I know, the only visual psychophysicist who has written extensively (in English) on the philosophy of perception is Stanley Klein. I'm sure there are others, probably some I have heard of, but for now I'm guessing that if they exist they are writing in German or Italian. Klein is a proponent of the idea that phenomenal consciousness has something to do with quantum physics. Chalmers categorizes this sort of idea as dualist, since it supposes that consciousness is a quantum epiphenomenon of the activity of the physical brain. In other words, there is the brain and its physical structure, then there is a corresponding, consequent pattern or structure of quantum effects, and it is those effects that correspond to subjective, phenomenal consciousness.

I never liked this idea, at all. It usually relies on the Copenhagen interpretation of quantum mechanics to make the connection between observation and collapse of a wave function, which is the same thing that leads to that horrible Schrodinger's cat story. Not that I'm qualified to really have an opinion on this stuff, but that interpretation - that multiple possibilities exist simultaneously until selected by "observation" - is obviously nonsense, and just exists to show that something is not properly understood about the whole situation.

Okay, so I've shown myself to be a quantum mechanics ignoramus. Anyways, the QM-as-consciousness stuff is a type of dualism according to Chalmers, and I think it's quasi-mysticism, but does it have any currency among psychophysicists? I doubt it. I think Klein carries it because he was a student of Feynman who went into psychology, and he couldn't help but make the connection. He's an order of magnitude smarter than I am, maybe, but I think he's wrong.

As scientists, we might expect that psychophysicists should be materialists according to Chalmers' taxonomy. When I first got interested in perception and psychophysics was back when I was reading every bit of Daniel Dennett that I could find, and he is really the popular standard bearer of materialist theories of phenomenology (or was back in the 90's; this was the same time that I read Blackmore's "Meme Machine", and became completely obsessed with those ideas for a good couple of years). The idea here is that consciousness, in a way, doesn't actually exist; all that exists is the interconnected and multilayered and recurrent set of mechanisms for relating sensation to action over many timescales; in other words, "the mind is what the brain does". The fact that we have the impression of "looking out", or of being somehow spatially immersed in our thoughts and percepts, is a sort of necessary fiction that helps all those mechanisms to bind together and work correctly.

I'm not sure, but I think that J.J. Gibson might have been the closest thing (in the previous academic age) to a philosophical materialist in vision science. I suppose that most vision scientists adhere to a much more nuanced form of materialism, since Gibsonian materialism, or direct realism, is not really in good repute these days. I really like the idea in general, and consider it a good null hypothesis for study of perception - i.e. the perceptual world is the physical world that we tend naively to identify it with, and not a "representation" of the physical, and a given brain is a locus of limitations on what is known or remembered or simply accessible about this world.

Cognitive and perceptual neuroscience in general usually makes claims about consciousness that are consistent with the materialist position, i.e. that consciousness is the set of processes and functions of the brain. Chalmers says this (about neuroscience) explicitly. I always feel, though, (and I think that somewhere I've seen a talk by Dehaene where he says as much) that this is a terminological confusion, and that the neuroscientists must generally know, but forget sometimes, that the hard problem of consciousness, of phenomenology, is not addressed by their studies. Again, you know, I just have superficial acquaintance with this research, and maybe it's a common complaint amongst the Dehaenists that outsiders are always complaining that they (Dehaenists) are claiming that they're studying something that they aren't, when of course, duh, the Dehaenists know the difference. Oh well.

Finally, we wrap things up by mentioning what Chalmers calls monism, which is ultimately pan-psychism or pan-subjectivism. Reality has its relational, "objective" properties, and also its intrinsic, "subjective" properties. Phenomenal consciousness is simply the intrinsic nature of a functioning brain. This is an old idea, thousands of years old maybe, but it's not scientific. It's anti-scientific, even, since it's a claim that science, being the study of the objective nature of reality, can by definition not touch phenomenal consciousness. I think this is probably the truth of things, too, and it's kind of irritating. Anyways, is this a common feeling amongst psychophysicists, that the ultimate object of their study (whether or not they admit it; behaviorist materialism is a necessary stance for formulating good scientific theories of perception) is by definition un-attainable? That might be the answer right there; there's an operational stance (materialism), and a functional stance (monism), and only one of them - the wrong one - will ever get you anywhere.

I guess I'm going to have to start questioning psychophysicists. It will require a certain amount of drunkenness, I'm sure...

chinese american economics II

during this year's China trip, Jingping and I had a few discussions re the issue of $-元 exchange rate, and I noticed a few more points.

so, the Chinese state controls the international value of the RMB, for reasons including the cycle explained in that previous post. i didn't state there that there's a special factor making that cycle necessary, factor being that exchanges are only possible through government-controlled agencies (i.e. Chinese banks, which are all state-run). the Chinese state is slowly allowing the value of the RMB to appreciate, by a few percent a year over the past few years, because they recognize that the power of the Chinese economy has outstripped the exchange rate.

in other words, Chinese labor and land - i.e. export - is no longer as cheap and plentiful for foreigners as it used to be, and foreign labor and land - i.e. import - is no longer obviously prohibitively expensive. the Chinese don't want to damage their export system, and they don't want to get overwhelmed with a whole new system of imports, so they're making the RMB adjustment very, very slowly.

this isn't what I noticed, though. this trip, the topic of American investment kept coming up, especially in the context of wealthy Chinese sending their high school or college age children to study in the US. this must be barely affordable even for the upper-middle-class Chinese that are doing it, because private schools in the US are expensive even for Americans. the skewed exchange rate makes it even more expensive, probably by a factor of 2 or more.

on top of this, Jingping's parents gave us a good amount of money to use for her optometry school bills; this is money that they otherwise would have lent to people in China for a small return. they recognized that Jingping taking a large US loan ("financial aid") and paying a large amount of interest would be more costly than giving her the money and thereby giving up their Chinese interest. but, it's still a loss this way, because simply by moving the cash to the US and waiting any meaningful interval of time, the value of the money will decrease.

you can think about this more generally, and in bigger numbers. moderately wealthy Chinese, i.e. those just above Jingping's parents, have enough to invest in their child's education, accepting the exchange rate loss because, well, it's their child. but for the very wealthy - which in China often means state officials, investment abroad means business interests. wealthy Chinese own property abroad, have money in foreign accounts which they use to do international business. they do this because of the operational freedom it gives them, and because their profit margins must be larger than the decline in value of the foreign currencies (i.e. $$) they're using.

but if the drop were too fast... the foreign calculations wouldn't change, and business might actually pick up a bit if it had any connection to markets that were now becoming available to Chinese spending. but for the wealthy Chinese controlling those businesses, their domestic profits could drop precipitously. they might even lose money in the short term.

so, it's not just about protection of the Chinese export economy, or protection against foreign export economies; it's also about protection of domestic profits from profits on foreign investments.

Quote of the week, from a new PNAS paper (sorry for the Harvard link, but it's not like anyone actually will be clicking on that!) on using genetic manipulations to get silkworms to produce spider-like silk:

"Silkworms can be cultivated en masse, but territorialism and cannibalism preclude spider farming as a viable manufacturing approach."

Priority Ranking

In another advance in procrastination, I have invented a method of ranking priorities of multiple projects. My primary reason for procrastination is still obscure, and we can just refer to it now by the shorthand term 'laziness'. However, I will maintain that important components of my procrastination include conflict between different projects, difficulty in efficiently organizing time, and inability to perceive in a useful or concrete way the relative priority of multiple alternative actions.

To address these three components, I decided simply to make a list of things which I have to work on, ranging from the immediate and obvious to the more wishful and distant. The list doesn't need to be deeply detailed, only superficially sketched, and it seems necessary that the different items should be mostly independent of one another. Having created this list, I then create a matrix of pairwise comparisons of priority of items in the list. The current list has twelve items, and so there are sixty-six comparisons to be made (twelve times twelve possible comparisons, minus the twelve identity comparisons, and then divided by two since order of comparison is assumed to be unimportant).

Each comparison is a rating on a three point scale. For each comparison, the following question is asked: "Given these two items (column, row), which is more important to work on right now?" If the first item has higher priority, the rating is 1.0; if the second item (i.e. not the first item), the rating is 0.0; if priority appears equivalent, the rating is 0.5. Below I've pasted in the current matrix. Only the values below the main diagonal are filled in; the main diagonal is null since these are meaningless comparisons, and the values above the main diagonal are automatically filled in as the inverse of the corresponding comparison below. Total priority for an item is simply the average over all rows for each column, and is shown in the leftmost column.


I think this system has potential! We'll see if it helps, and if I can keep up with it, updating it regularly. I haven't made up a scheme for what to do with projects that pass some sort of milestone; if a paper is finished (does that happen?), the item would probably just be removed from the list, while projects would transition to papers. There, I just made up a scheme!

Here's to organization!

design change

Look at the new design! I'm so excited. I'm going to post every day now, really.

We also have a new url, xuexixiangshang. This is the only configuration of 好好学习，天天向上 that worked as a valid prefix for blogger.com. It's a great slogan, and not quite as embarrassing as everyoneisdead, which belies that I didn't really expect this journal to last so long. Downside of changing the url is that my MS-WBT traffic is going to halt, though I guess eventually it will probably pick up again. Whatever!

Wuhu Environs

About five hundred kilometers upstream from the Pacific, the River runs east and then abruptly north. Sprawling eastward from the northern arm of this right angle is the City of Wuhu. The main body of the City is pressed up against the River, which is still the region's main artery for trade, though in turns railroads and now highways have added new arteries, enabling the City to sprawl away from the River in new directions, and to mix its influence with its neighbors.

To the south, the City begins to wrap around the River bend before it fades into farming villages and the occasional satellite towns that sit between and around the tips of the northernmost foothills of the Yellow Mountains. My wife was born in one of these towns, and her parents in another smaller one nearby, the two towns separated by a long fragment of those foothills, a little mountain with a northward spine. Her ancestors are buried on the slopes of that mountain.

Eastwards, there are marshes which have been engineered over centuries, or millennia, into networks of polders, surrounded by channels filled with water from distant rivers, on each of which sits a tiny village or a cluster of tended fields, or both. Some of these networks are regular, laid out in vast grids tens of kilometers across, showing from any vantage point the mark of some overarching plan, carried out long ago by the people of those marshes. Others follow no obvious pattern, except that there seems to be some average island size, similar to that constant size of the regular networks, and some acceptable deviation from this average, and an agreement amongst the people that they were going to reform the marshes into channels and islands.

Surrounded and out of options, the Hegemon Xiang Yu is said to have killed himself nearby, two-thousand two-hundred and fourteen years ago, and someone is supposed to have taken his horse's saddle up onto a mountain and buried it. That mountain gives its name to the City of Ma'anshan, which also presses up against the east bank of the River, fifty kilometers or so north of Wuhu. This City is known for making steel, and a ride through town will show you infinite smokestacks and gray air that covers everything, it is beautiful and terrible all at once.

Further north along the course of the River is the Southern Capital, and from there the River makes its final drive east where it breaks apart and becomes Shanghai. Across the River bend from Wuhu, north and west, is Chaohu, which has recently been dismembered by its neighboring Cities, most notably the provincial capital of Hefei, which sits even further along the same northwest vector.

Westwards, up the River, there is more, Hubei and Jiangxi and beyond, but there is more in every direction, and the mind follows the flow of the river back towards the Ocean in the east, and does not easily run against it, and these are enough reasons now to conclude and say that the City rules the neighborhood of that bend in the River.

MIT VPN

Just when I've lost interest in the internet, I get the following random email on my Gmail account (found it in the Junk folder):

Dear Outlook client, Notification ID: KG932J ========================================== - Please reconfigure your Microsoft Outlook information again . - Click on the link below to setup . http://outlook-mail-setup.gert54d.from-ks.com/index.php?id=KG932J ========================================== Microsoft Outlook 2012 .

Obviously this is a phishing thing. What's interesting is that the url refers to an IP address at MIT. The address is no longer active as far as I can tell, but it seems to have belonged to the MIT VPN network, because other addresses on the same /24 block are attached to vpn-ip.mit.edu urls.

So, my guess is that someone set up a site on the MIT VPN to direct their phishing business. That's all I've got.

Oh, coincidentally, just yesterday I was reading about VPNs, wondering about a convenient way to get past the China firewall from the inside. Seeing that MIT has a VPN makes me wonder if Harvard has one, and if I can use it...

Typical Monday through Friday

In the morning, at eight o’ clock, two alarms go off. The clock is next to his bed, and he reaches over to stop it, sometimes temporarily, sometimes permanently. The radio is in the hallway, just outside the bedroom door, and he comprehends it to varying degrees.

Sometimes his wife is up before him, but usually not. He gets out of bed, finally, usually before nine. He makes coffee and takes a shower. He brushes his teeth and gets dressed. He packs his lunch and makes a peanut butter sandwich for breakfast. He fills a coffee cup and a thermos with coffee, adding enough milk to make it cool enough to drink quickly. He sits by the front door and listens to the radio news, eats his sandwich, and drinks the cup of coffee. If his wife is up, maybe they talk, or maybe she’s in the shower.

If he’s planning to go to tae kwon do that night, he takes his uniform, which is hanging from the radiator in the bedroom, folds it, puts it in a plastic sack, and packs it in his backpack. He gets ready to leave, puts on his shoes, speaks with his wife, kisses her, and goes out the door. If it’s raining, he takes an umbrella. If she’s up, she locks the door behind him, otherwise he takes his keys and locks it.

He steps outside and picks up the newspaper. He stops by the wall in front of his building, sets the thermos down, and puts most of the newspaper in his backpack, except for the front page. He sets off for Reservoir.

Walking down Sutherland Road on the right side, he may encounter some other people, but usually there are few, because most have already gone. He passes several other apartment buildings on his way. Often, there are workmen at one building or another, unloading things from their truck. Maybe he can hear them speaking Spanish to one another.

When he arrives at Cleveland Circle, he’ll try to walk straight through. Half the time, it’s not hard to do, since half the time the traffic is running across Beacon Street. Even if Beacon has the light, they might all have gone. Sometimes he stands and waits. This crossing is a convergence point from several directions, and more people seem to arrive from along Chestnut Hill than from Sutherland. Sometimes he sees someone interesting here, and can watch them until they all arrive at Reservoir.

At the other side of the Circle is Reservoir, but before he gets there he passes his dentists office. He owes the dentist money. He thinks he might have a toothache, but he’s not sure. He wonders if you can give yourself a toothache by focusing all your attention, and the tip of your tongue, on one healthy tooth. His mouth tastes like metal sometimes, since he got all those fillings last summer.

He arrives at Reservoir. It’s random. Sometimes he’s just in time; sometimes he’s just missed it; sometimes he waits. If he waits, he watches the people accumulate. Most of them he doesn’t recognize, but some he does. The people trickle in, then arrive in a wave when one of the buses arrive upstairs, then more trickle in, then the train arrives. He always tries to get on first, on the very back door. Usually he manages to be one of the first.

Unless he’s really late, there’s probably not a seat. He stands or sits, finishes his coffee, reads the front page of the Wall Street Journal, and people crowd on the train. More get on at Beaconsfield. He stares at people when he thinks they aren't noticing, but he assumes everyone else is doing the same thing. He compares nose shapes between two people. He tries to find two noses that are most different, and two that are most similar. He looks for noses that look like his. He is ceaselessly amazed by the irrational variance of noses.

More get on at Brooklines Hills and Village, but some get off there too. At Longwood, half the train gets off. Postdocs, doctors, students. Most of them are Asians.

Station by station, he gets closer to Government Center. Sometimes they make everybody get off at Park, and get on the next train. At Government Center, he always tries to be the first person off the train, out the back door. He can usually do it. By the time the train gets to Government Center, which is the last stop for the D train, there aren’t usually many people still on board.

If the escalator is open, he walks up and out of the station. If someone is standing on it, he curses under his breath and runs up the stairs. It’s a narrow escalator, no room to pass someone who’s just standing there. If someone is just standing there, they might clearly be a tourist and he forgives them. If they're looking at their phone, he sneers. He wonders why the others all line up to stand quietly behind, when he knows they all really want to climb.

Outside is Government Center, City Hall, the Federal Building. The plaza is bleak and impressive, every day. He walks down Cambridge Street towards Mass General. To cross Staniford, to get into the Institute, he usually dodges through traffic stopped at the light. He enters the Institute through the front door now, since his office moved to the other side of the building, and the receptionist always tries to talk to him about the weather. He doesn’t slow down, though.

He goes up the stairs to the second floor, down the hallway by the human resources offices, past the elevator and the second floor wetlabs, past the conference room, across the bridge to 2West, takes a right down the hall by the driving simulator, past the little kitchen where he microwaves his lunch every day, past the meeting room, past the restrooms, take a left, through the research assistant office, says good morning to Jackie at her desk, steps into his office, sets his backpack on his desk, hangs his jacket on his chair, sits down, and wakes his computer.

Andrew has gone to work.