Amnesiac’s Dilemma (Aka: Sleeping Beauty Problem)

There’s a probability problem that lacks an obvious solution, despite appearing simple at first glance. It’s usually called the Sleeping Beauty Problem, but I’m uncomfortable with that formulation, as it strikes me as needlessly sexist: it usually revolves around a young woman who is put to sleep by researchers, awoken and questioned about the result of a coin flip, then given a mild memory-erasing procedure, then put back to sleep, etc. Maybe it’s not (always) sexist. In some versions, Sleeping Beauty is said to have consented. But anyone can be made to consent to anything in fiction. At any rate, there’s no harm in changing it, and in some ways doing so makes it easier to think about (in other ways, not so much).

What you see here is my attempt at thinking through this difficult problem, which I reformulate as the Amnesiac’s Dilemma. (Though I’ll refer to it as the Sleeping Beauty Problem as well; I just won’t use that story… much.) The upshot of the dilemma is that 1/2 and 1/3 both seem to be viable solutions (proponents of which have been called halfers and thirders, respectively). Rather than rule the problem indeterminate, we take it that there must be some fact of the matter about which solution is correct given that the problem can be reasonably well-defined by a discrete, finite sample space in which the experiment may be repeated indefinitely.

To make sense of the problem, we need to be clear about its relevant features—for example, about what counts as a desired outcome. It may be that 1/2 is valid for one sort of outcome, while 1/3 is for another. In fact, I ultimately conclude here that, whenever asked “Heads or Tails?”, the Amnesiac (Henry, in this case) should have a credence of 1/2 that the coin landed Heads, even though he may (reasonably) simultaneously assign 1/3 credence to his situation being, say, {(First Question AND Heads)} (Henry’s analogue to Sleeping Beauty’s {(Monday AND Heads)}). Though I don’t take this result lightly (if pushed, I might lean towards 1/2 or agnosticism). This will make more sense (I hope!) by the end.
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Memory and Consciousness (via Audition)

Mnemosyne by Dante Gabriel Rossetti (1881)

Mnemosyne by Dante Gabriel Rossetti (1881)

I’d like to explore the following strong claim: Without memory, consciousness is not possible. Put another way: If you had no memory at all, you would not be conscious. I suspect this claim to be true, even if we take the minimum requirement for consciousness to be experience (of any sort).

I’ll explore this by thinking about the relationship between memory and audition, starting with a thought experiment:

Imagine having an extremely short memory while listening to a melody. So short, that there would be no melody, and instead an unrecognized series of disparate, unrelated pitch experiences. Now shorten the memory even more. Now imagine having no memory at all. Suppose the note A above middle C is sounded on a piano. Strings now vibrate at 440 cycles per second (excluding overtones), and in turn excite the air molecules in the room to vibrate at that same frequency. These in turn are picked up by your auditory faculties, which endeavor to produce in your mind the sensory impression of the pitch A. Without any memory at all, however, you would not experience the pitch. In fact, you wouldn’t be able to experience even one cycle of oscillation (several of which would be needed in order to experience a pitch). For one cycle, your mind must take in and store, over the duration of 1/440th of a second (about 2.27 ms), the entirety of an oscillation, the beginning of which will have been forgotten by the time it reaches its end.

My suggestion here is that, without memory, you cannot connect (i.e., by way of experience) the beginning of a single unit of oscillation, of which there are 440 per second, with its middle or end. Your mind thus becomes an experience sieve. It all just passes through. Continue Reading

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Why We Get the Monty Hall Problem Wrong(?)

I’d rather have the goat.

Part I: The Monty Hall Problem

The Monty Hall Problem (explained below) is one of those math results that strikes most people as not making intuitive sense. The problem is often illuminated by restating it with 100 doors instead of 3 doors. This makes many people go, “Ah, now I get it,” and concede that their intuition must be wrong. Nevertheless, for many of them the 3-door scenario continues to be counterintuitive.

This leads many to ask, “Why don’t I understand the Monty Hall Problem?” Like this person at Quora: Why doesn’t the “Monty Hall problem” make sense to me? The usual response is to try to demonstrate to the person why the correct answer is correct—to try to get it to click. But, even when this works (sometimes it seems to), it doesn’t address why the problem’s solution feels so counterintuitive, nor why the standard wrong answer feels so right. I think I have an idea of what’s going on. We’ll see. (I’ll read this again later to see if I still think so.)

First, a summary of the problem.

Suppose you’re playing a game in which you are faced with three closed doors. The doors are numbered 1, 2, and 3. You are told by the game-master (who does not lie and only speaks the truth) that behind one of the doors there is a car, and that behind each of the other two doors there is a goat. You are not told which door has which item. (The game-master need not know which door has which item, by the way, though the game goes better if she does. See the End Note, however, for how the game-master’s knowing could affect a player’s credence in her guess.) The arrangement of goats and car will not be changed throughout the course of the game. Continue Reading

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Free Will Paradox?

Spike with a chip.

There might be a paradox—or tension?—having to do with how we assess what counts as a negation of free will. Namely, we don’t generally consider that which is physically impossible to count as evidence against free will’s existence; yet to rule out free will is to say that it is physically impossible. Is there a paradox here, or would the matter of free will’s existence be straightforwardly settled once we’ve (correctly) noticed that free will is impossible? Some reflections:1

1. What is required in order to answer the (metaphysical) question: Does S have free will?

2. How is this different from asking: Is S (physically) able to exercise S’s free will?2

3. A standard definition of free will is: The ability to have done otherwise. I’ll refine this as: The ability to have chosen to do otherwise (for reasons I’ll discuss below; though I’m not sure there’s often a need to be a stickler about this wording).3

To elaborate:
(i) Five minutes ago, S chose to do, and then did, activity A. Continue Reading

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Consciousness Explained in Three Billion Pages

An unconscious naked man (1912), Richard Tennant Cooper

An unconscious naked man (1912), Richard Tennant Cooper

Cognitive scientist Donald Hoffman has recently been getting popular attention for a theory that holds consciousness as fundamental—that is, “…not as something derivative or emergent from a prior physical world”1, which he supports with a novel account of the relationship between objects and perception (a relationship that he argues, on evolutionary grounds, is nonveridical, i.e., perception does not faithfully represent or reconstruct objective/external reality); Hoffman’s theory also requires a novel account of the relationship between the brain and consciousness. I’m not going to get into the theory here, though I find it thought-provoking.2 Instead, I’d like to pivot off a nice expression he often employs about our prospects for understanding consciousness (something we seem yet very far from accomplishing):

“Some experts think that we can’t solve this problem because we lack the necessary concepts and intelligence. We don’t expect monkeys to solve problems in quantum mechanics, and, as it happens, we can’t expect our species to solve this problem either.”3

Unlike Hoffman, I agree with the skeptical experts. Before explaining why, some conceptual grounding. Continue Reading

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Four Dimensions of X-ism (and ‘Seminal’ Is Sexist)

A long first draft on a difficult topic. Feedback is welcome!

Watermelons, peaches, pears and other fruit in a landscape (ca 1645–1672), Giovanni Stanchi

I. A Critical Distinction

It’s a common occurrence for someone to be publicly called out for racism, sexism, homophobia, transphobia, or some other mode of X-ism (as I’ll collectively call these and similar -isms/-phobias), only for the accused to earnestly self-defend, “I’m not X-ist! I love X’s! There are X’s among my most cherished friends and family!”

Debates then follow about the person’s status as (an) X-ist. (From here on I’ll use “X-ist” with the understanding that it could be replaced with “an X-ist”; I’ll leave unexplored what I sense to be a significant difference between these phrasings.) These debates often fail to reflect the important distinction between performing an X-ist act and being X-ist. To recognize this distinction is to acknowledge the possibility of there existing an X-ist act without the presence of an X-ist actor. There are further important distinctions to notice; to make sense of these, I propose four dimensions of X-ism: Cognitive, Affective, Behavioral, Dispositional.

My claim is that a person’s activities (or potential activities)1 must span some combination of these dimensions in order for the person to merit the X-ism label—in other words, to be branded as someone who engages so habitually in morally reprehensible activities of the sort we call X-ist, that we are justified in saying that person is X-ist (particularly when these activities defy readily observable evidence; that is, when the agent “should know better”).2 3 Continue Reading

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Sine-Wave Speech

Look familiar? For a visual hint, check out An Introduction to Sine-Wave Speech.

Ever notice that when a familiar song is playing in another room, you can clearly hear the words, but if unfamiliar, you can’t make out the words?

I’ve experienced something similar with self-recording musicians—especially voice-shy ones—who think they’ve set their vocal loud in a mix, but it’s barely audible to anyone else. This has happened to me with solo instruments as well (oboe parts, vocal harmonies, background guitar melodies, etc.).

Familiarity seems to result in experiencing more than is there, more than is actually making it through the walls and the noise—as if your brain, in order to finish constructing the mental content you (unconsciously) expect to experience, is pulling from memory the building materials your environment is failing to provide.

It turns out we can home in on and experiment with this phenomenon with a fascinating technique called sine-wave speech, which I first learned about it on the (excellent) Brain Science Podcast: Andy Clark on Prediction, Action, and the Embodied Mind (BSP 126; January 28, 2016). Listen to the first 2:15 minutes to hear a sine-wave speech demonstration (and I of course recommend the whole episode, especially if you’re interested in embodied cognition, a rising, and I think very promising, interdisciplinary field occupying philosophers, psychologists, linguists, AI-specialists, and others):

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Do Groups Believe?

Exquisite Corpse

Exquisite Corpse, 1928; Man Ray, Joan Miró, Yves Tanguy, Max Morise

1. Introduction

We often refer to the beliefs of groups. We might say we think it’s a lovely day out, or that Americans believe democracy to be the best form of government. To what sorts of phenomena do we refer when speaking this way? In the context of belief, should words such as Americans and we be viewed as shorthand for summing up the individually held beliefs of a group’s members? Or, rather, do such words sometimes correctly refer to a group engaged, as a unified entity, in the collective activity of believing? If the latter is true, then it’s possible for a group to believe that p, while the individuals who constitute that group each believes that not-p. Call this sort of belief, in which a group literally has belief of its own, collective belief (while, for clarity’s sake, I’ll use group belief as a neutral term).

On my view, groups are not capable of collective belief. This distinguishes belief from many other sorts of activities. When Mary sings a C and Larry sings an E, for example, Mary and Larry collectively sing a major third, though neither individually sings a major third. Likewise, they might hug, cook dinner, or make the bed. Belief doesn’t seem to work this way: to correctly say that Mary and Larry believe their house is haunted, both must believe that proposition. Ascriptions to larger groups may afford some leeway in this regard, but still require that most members hold the group belief. Continue Reading

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Rachel Dolezal: Race, Gender, Sex, and Social Group Membership

rachel-dolezalAnd now for the intriguing case of Rachel Dolezal, the Spokane, Washington NAACP leader who was born white but identifies and represents herself as black. This was working well for her — she’s been passing as black for years, apparently — until a few days ago, when her biological parents outed her. [Update: She announced her resignation as NAACP chapter president on 6/15/15.]

This controversial story has sparked important, hopefully long-enduring, discussions about the ramifications of race’s status as a social construct. If it is a social construct, some argue (often as a bluff-calling dig at Caitlyn Jenner supporters; more on that below), then Dolezal’s performance as a black woman should be respected as an authentic expression of the space she occupies in society.

But this is wrong. Even if race is a social construct (which it is; to see this: a white woman can have a black baby, but a black woman cannot have a white baby), this doesn’t mean that Dolezal’s self-identification as black must be honored. Society, through its collective activities, determines the conditions of race identification–i.e., creates the (very real) phenomenon to which we refer when we use the word race. She is not society. Continue Reading

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Pulse: You Are a Series of Non-Repeating Events

gif-black-wallpaperI often find myself wondering with fascination about the role experience plays in shaping our conception of the world. Recently, I was inspired to think about repetition in this context. That is, we have a deep sense that there are repeating events. But such a thing must be true only in experience, given that any event is, in some way, distinct from all others. Put another way, any event is only identical to itself. At the same time, repetition often has great significance for us, a significance that seems to touch on something true about the world independent of human experience.

Here are some brief musings on the relation between ‘event repetition,’ experience, and our world-conception. What there is to be learned here, I’m not sure. Yet I find myself drawn to this line of inquiry, and do get a fuzzy sense that there is something to be gained from reflecting on it.* Perhaps a deeper investigation into event repetition — both perceptually experienced and not — could reveal useful tidbits for when dealing with bigger questions, such as those related to cognitive biases, social interaction (e.g., stereotyping), experience of ‘objects’ over time, cyclical brain-states (e.g., meditation, sleep), evolutionary psychology, personalized medicine, sense of self in the context of personal identity over time (more on this below, in Part II), and induction (experiment repeatability).

There are also moral implications to this that, I think, lend support to a particularist notion of morality: any moral event is only identical to itself. So, to know (or understand) that an event is wrong, is to know something about that particular event. This would be distinct from what I take to be a less useful (though still nice to have), general knowledge about broader categories of moral events, which have particular events as members. I’m saving that discussion for another day, however.

[*I began thinking about this topic after being asked to contribute to a newly founded magazine whose first issue was going to be broadly themed on ‘pulse.’ I drafted notes on two occasions, here presented as Parts I and II (neither of which was finalized, because the magazine folded before publication). Part I is a straightforward survey of the subject. Part II, written one morning while bleary-eyed and half-asleep, is stylized as a kind of letter inviting the reader to think of herself or himself as a series of non-identical, though significantly related, events — as a pulse.] Continue Reading

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