A Gambler In Heaven

A gambler has just lost all but one $1 in Vegas and decides to go for a walk.  Unfortunately he gets hit by a bus but, having lived mostly a good life aside from the gambling, is shown God’s mercy and lands in heaven.  They only have one type of gambling in heaven, it is a simple choice-free game with the following rules:

A coin is tossed.  If it comes up tails, you lose $1.  If it comes up heads, your entire bankroll is tripled.

The gambler only has the $1 he had on him when he died (turns out you keep your money when you go to heaven).  Here is a possible outcome of his playing this game:

  • $1 – H -> $3
  • $3 – T -> $2
  • $2 – H -> $6
  • $6 – T -> $5
  • $5 – T -> $4
  • $4 – T -> $3
  • $3 – T -> $2
  • $2 – T -> $1
  • $1 – T -> $0

And thus he is broke.

The question is this: starting with his $1, what is the probability he will live the rest of eternity broke in heaven? The alternative, presumably, is that he spends eternity doing what he loves most: gambling.  Do all paths eventually lead to bankruptcy a la Gambler’s ruin, or is there a nonzero probability of playing forever?

You may leave your ideas in the comments, and I will post a solution in a few days.

What do you say when you have nothing to say? What do you do when your song is a nice accompaniment to a vocal line, and there are no words to accompany?

I could talk about my life. I could mention my new teaching job, the cosmic interference with my busking, the flood… those all seem so incidental.

Maybe silence is okay. Maybe I am saying something — I am writing a lot of music, after all. I’m feeling pressure from Amanda (my girlfriend and closest friend) — not in any way that she is instigating, just a side-effect of who she is — to say something meaningful, something important. I can’t. I don’t feel like my ideas are important in that way, in the way that they are ready to jump from my mind into another’s and have any benefit. I think only vague half-truths: a strong conclusion, a value to hold on to, feels miles away. I know personal truths, I am feeling confident in them, and it is a great feeling, but words always miss the mark. They always make me seem either more certain or more uncertain than I am, with them I don’t know how to walk the fine line where I really communicate. And if I could . . . would I put it in a song; would I write it here?

I don’t think I would be bothered if my music felt complete without words. But I have a couple of songs in the oven that are just begging for words, that’s musically obvious to me. The missing instrument is words. I see a symbol, a metaphor: my life for the song, the words for… what? But it does feel that way — my life has a great groove but is also missing something. Missing lyrics.

I would normally argue that my lyricless music is saying something — it does have a message — but, like my thoughts and my truths, words cannot communicate it. But I’m incredulous. That argument doesn’t have the ring it used to.

I –

Why dream of being awake?

To every action, give your whole self; I am wholly procrastinating, fully indecisive, completely half-listening. Mr. mindful, awake, clear-headed, be careful, pictures can be projected on the fog. We are all blind, stumbling pigeons, wholeheartedly. The most committed are those who believe they have conquered life — how would you say that a delusional maniac “doesn’t have his heart in it”? Then there are those of us who envy such commitment — to be stuck only wanting a delusion — is that a lesser or greater commitment?

There is a transcendence here (, man). I want to experience my whole self, so I can’t just give up being lost and absent. My self includes my guilt, my self-judgments, my unacceptance of those judgments — no spiritual or psychological change I can make will do justice to my self. Nor will stagnation realize my true potential (a concept that makes the very same error).

But we get trapped again. We can’t stop intending to change because it would not do justice to self; nor can we stop intending to stop intending to change. To lay a path to spiritual betterhood is to believe that you have, in some small way, failed to be a blind, stumbling pigeon. This is false but, as we have already covered, admirable.

There’s nothing new to accept. This line of questioning is wrong. Self-acceptance is a vacuous goal. When that sinks in — when you really believe that — something changes inside of you. It plants the seed of the real self-acceptance, not that fuzzy-wuzzy kind you wanted. You’ll know when you have Achieved real self-acceptance because nothing happens, except maybe you will think and/or feel differently than you would have in some situations (it is unclear what that mechanism is).

Then what? Well of course, self-acceptance is only one step along the path — after which there can be no more — the steps no longer look like steps, but flat step-like objects. But I have to ask again, now what? What do I do now? What is the next .. the next ..

These are the chirpings of an analytical mind with nothing to analyze.

Shhhhhhh…

Life as a Musician?

So, it turns out I’m not dead. How about that?

I have dropped out of school, and am busking for a living. It is tiring (especially when I forget to drink enough water), sometimes discouraging (when I play things to no response whatsoever or make $5 in an hour), but mostly great. My job is making music! And more importantly, my job is making my music, or music I am in love with — although certain pieces tend to attract more tippers than others, so it’s not truly free (what is?).

My grandmother contacted me telling me about a startup mixer so I could find a job. I don’t think she really understands my decision. I can understand that — she wants me to get a stable, well-paying job, have kids and a family, and go to church. The usual narrative. The other day I was idly contemplating being a father. Not now, of course. But I can see the draw; I can see that being a pretty special thing. The question is whether it is worth it to me. Sacrifice is part of love. But do I sacrifice for my child, or do I sacrifice a child (umm! — sacrifice having a child) for my other loves? That is not a question I am remotely prepared to answer.

I used to think — perhaps I still do — that big questions like those aren’t really worth answering, at least not rationally. I suppose this “used to” is fairly recent, as I had spent a long time on them prior, and they led me nowhere but in circles of unfulfilled dustkicking. My self-image can be so limited at times, and the rational mind is a slave to its images. What I can really do, what I’m really made of, I perhaps thought, won’t be small enough to be so easily decided — it must be eased into, made part of myself through exploration and long, gradual growth. But the liberation I feel from this new occupation of mine has shown me that perhaps at points along this process such a life decision is valuable, that it can be a beacon that reminds me that I chose this because it was important to me — more important than anything else at one time — and so gives me something to hold onto in times of uncertainty or suffering. It sounds very compelling, doesn’t it? But I am still in the honeymoon phase of my relationship with my life as a musician, so the only thing I can be sure of is that my thoughts about it are distorted.

And am I really good enough to make this a living? Maybe Boulder is the only place people appreciate public performances of amateur classical music. Maybe when I migrate for the winter I will be met with indifference or contempt, and I will be stuck in a new city with no job. Maybe when I improvise or play my originals people only tip me because I have brought the piano out, not because the music speaks to them in any deep way — I know that is not true, my second piano sonata is almost always met by applause, but it has been 10 years since I wrote that; do I still have it? A teenager passes by and plays most of the pieces I do — not as well, but not badly — and he will surpass me by my age. Will I ever have the guts to sing out there?

A thousand fears and doubts dance their rite around my dream — all I can do is to go out there every day and hope it goes well. I think it’s proof that I’m alive. I pose this question to myself: would I rather be wildly successful in a software company, or wildly successful as a musician? The latter, by any metric. “Wildly” need not even appear. Standing on a plank and singing to the jury, my heart beating a thousand times a minute, with the conviction of a soldier — this outshines any vision of a successful software idea.

I’m not leaving software. But my most exciting software ideas aren’t the kinds of things one can easily make a living on. I’m working on a browser-based programming environment which explores a new way of designing and organizing code. I don’t want to say too much about it because as I code the idea continues to develop in my mind, and I don’t want to nail it down yet (maybe ever). But anyway, to make money with that would sacrifice its beauty; this tool is not for productivity, at least not at first: it is exploring a way of thinking. It is easier to make a living making the music I love than the software I love. If my life is to overflow with love and happiness, music is the breadwinner.

Again — only a month in. But I think this is the way to do it, for me. I’m not setting myself up for a comfortable life, but comfort is a trap anyway. It is the contrast that feels so good, and without that contrast comfort is just normal. Without discomfort to prepare the contrast, comfort is dull and boring. Anyway, that’s how I see it. Funny coming from a hedonist like me. I guess I’m having a stint of long-term hedonism at the expense of short-term.

Maybe someday I won’t even feel the need to justify my choice anymore. That’s when I’ll really be in it.

Heart

It is part of growing up, I keep telling myself — doing what I know — for some definition of know — is right, despite the advice of my family and almost everyone (but my best friend who is my only beacon in this whole mess). I have a good family — supportive, have my best interest in mind, certainly not the image of the disapproving father so pervasive — and partially I haven’t been completely honest with them, because it’s scary. Nonetheless, I feel a lot of pressure from their attempting-to-be-neutral positions, and I know what I want — what I need to do, but when the time comes to say it I can’t, condemning myself to this purgatory.

I’m not going to finish college. I am very close, only a few credits away, but it is not going to happen at the end of this semester, and everyone is like “but it’s just one more and it’s important for the future” — not so different from my reasoning for returning to college in the first place — I have been at this decision point before, and did convince myself with the assistance of my family that it was the right thing to do. Maybe it was once, and although I did not achieve the goals I set for it, it isn’t right anymore.

Here’s the really hard part, and I have to speak this with less certainty than the other, because different parts of my mind and body are fighting over it. I don’t think I’m going to finish this semester. Try as I might (whatever that means) I cannot commit myself to something that I don’t truly believe is serving me, and right now that is school. I don’t have that kind of control over myself. My grades are really slipping; each moment here feels like trying to run in a dream, suspended in the air. I know, what’s another month? It really doesn’t matter either way. It would matter if I wanted to go to grad school, but years of getting to know myself and being friends with grad students, I don’t think it is the place for me. I am too disorganized, my intellectual exploration is founded in too much curiosity and not enough desire to contribute. Suddenly a pursuit will become uninteresting and another will take me by surprise, but you can’t just switch like that in school.

But you can just switch like that in life. Why would I arbitrarily obligate myself to someone else when I am exploring what I love? Out there in the cruel, forgiving, free world, I can pursue whatever I like whenever and however I like to. Yes, I need to make money, but that’s not such a huge deal. I don’t really get why people make their way of earning money the centerpiece of their lives. Insert canonical white-picket-fence rant.

I don’t have a good phrase to describe who I want to be or what I’m going for. I think of such phrases as potentially guiding, locally, but ultimately limiting. To define myself with words is to forget every moment the words do not account for — when would someone include the Pepsi they had for breakfast in their self-definition? — but that bottle of salt and sugar is part of me, negative or however you want to judge it. Of course, not having such a phrase makes it difficult to assess the value of a difficult easy decision like this, and without a mechanism for assessing value I have no choice but to be human and follow my hearts — there’s nothing else that I can say with my vocabulary that doesn’t sound like a waste of my life.

I have long valued every moment of my time. A year of my life spent unhappy in order to support the remainder of my life never seemed worthwhile to me — I know that sounds irrational — but that seems to be the way I relate to time. A month spent in school, a month not making my living by sharing my musical heart, a month depressed and careless, a month of missed opportunity.

And yet, it is only a month. But why would I stay? I can’t articulate any convincing reason. It will make it less work should I ever decide to come back and finish — but that is actually false. One class is just as many as four, if not more.

I have had my struggles, but at important times I have always listened to the guidance of my family, I think I have always made what they saw as the best choice. This time, I think, their poor choice is the right one — if only symbolically, if only to remind myself whose life I am living.

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List of Awesome Things

from the Lang.NEXT conference this week. I heard most of this stuff not from the talks, but from the awesome people who were attending the conference.

  • Alloy – A language for relational models. You enter a specification of your problem in a first-order relational language (quite powerful) and then it tries to find counterexamples within some small space. If no counterexamples are found, you can have a fairly high degree of confidence in your model (as they say, “most assertions are wrong; most flaws have small counterexamples”).
  • Combinatorial Sketching. “Here’s what I want my algorithm to do, and I know that it probably involves a for loop and addition and multiplication. Figure it out for me, kthxbye.” (Thanks to Peter Alvaro for the last two links; check out his research on Bloom, too: a very nice way to simplify and analyze distributed systems)
  • Cyc, a queryable database of “common sense”.
  • Labanotation – a standardized system for recording human motion. Traditionally used to write down choreography.
  • Structure and Interpretation of Classical Mechanics, in which Sussman (creator of Scheme) writes about classical mechanics in a functional style. I have read the first chapter, and I have to say, functional calculus notation makes a lot more sense to me than the traditional notation. Go figure.
  • Algorithmic information theory
  • Smooth interpretation — a way of smoothing out digital programs so that their parameter spaces can be searched by gradient descent.
  • Lytro, the coolest piece of hardware I have seen in years: it’s a camera which records the directions of incoming rays, so that you can focus the picture after the fact. For example.

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Music

I define a model to be a simulation of external reality within a mind. It is an approximation, a system by which we can make some predictions that are somewhat accurate most of the time. Some confuse their models with reality itself — since I use God to inform my morality, there must truly be a God; since quantum mechanics makes probabilistic predictions, the universe must be fundamentally non-deterministic. These kinds of judgments fail to realize that True external reality is not accessible to us.

I am speaking from the perspective of a model in which there exists a True reality for models to approximate. As I have defined, the reality being approximated is not accessible, so what could I be referring to by “True external reality?” I don’t refer to the True external reality, but an approximation within my model. And the same goes for my model itself — I cannot refer directly to my model, which is a pattern of True reality that occurs in my mind, but only to an approximation of my model from within itself.

This is the problem I have with metacognitition. I have spent a great deal of time introspecting, trying to figure out what I think, what I believe, why I do the things I do. But I cannot access the True answers to those questions (are questions a part of True reality?), I can only answer them from the perspective of my model of myself. A little less than a year ago, a Bodhisattva Sirened me in to catalyze an understanding that my self-model is unsound, that I had ideas about myself that were incorrect, that I had memories which may not have actually occurred, that I had a fabrication mechanism which was creating reasons for my actions after I had already done them, or already committed myself to doing them. I lost my trust in my metacognition, and from there,

What is True? We can be like Descartes and try to deduce a sound foundation from almost nothing, but that is just model-play, desperately trying to construct a model which is reality. This is in vain, there is no perfect representation. Every word in this post echoes falsity and lack; I can’t say “there is no perfect representation” with any certainty. Logical argument is a model, relying on the framework of propositional knowledge — humanity invented propositions — biology invented truth.

Of what I know or think I know or think I cannot know, I exist regardless. This proposition is provable and refutable, and the proof and refutation are both devoid of any True meaning. Can I think myself into oblivion? or is it just that my mental structures complicate themselves until my mental structures are really complicated? Experience, not thought, is the foundation. Thought is model, language is model, thought about experience is model — but experience: that is True.

I cannot say, recall, or think with certainty (certainty itself is a property of propositions). But I experience with certainty, if you will allow the metaphor. I am not trying to communicate a truth or a Truth — this is very important — but a feeling. Can you feel this intermittent feeling of mine, this freeing, relaxing, empty feeling which the conscious mind resists fervorously? It occurs discretely, not as a lasting experience, but like the sound of a clap the instant it reaches my ear; there is no meaning yet, that comes later. The only way I know I have this feeling is through my memory, and like every truth it is not to be trusted. I now have a feeling that if I could make a continuous clap, it would accompany a continuous darkness in my mind. You could hardly tell the difference in me, and I would be too occupied with noticing it that I would not be able to report or even remember doing so. Perhaps I achieve it for great lengths of time already –

Can you believe I strive for this?! I seek my own inability to remember — should I achieve my goal, I will be on my deathbed before it is tomorrow. Life could be lying in her bed preoccupied by the necessity to one day leave it — or it could be a dream and orgasm. One is a long life in which future disappointment is love; the other is a whole river, reaching the sea the same moment it melts from the snow.

Love do not care. The mind will tire of obsessing on the contents of the black hole, but the heart will still beat to a rhythm. This final sentence arouses its beating, because I know, in every model, that I have a True love –

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Constructive Reality

I would like to address a statement by Paul Snively during a Twitter conversation.

The notion that math has meaning apart from being computable is perverse.

I admit that all involved in the discussion are computer scientists, and so we would be predisposed toward constructivism and, in particular, this kind of value system. Indeed, I consider myself “a constructivist” — in the right setting, I will fiercely argue with a classicist that “there exists” does not mean what they think it means — but I will not go this far.

The underlying idea of constructivism is that the form of the theorem describes some evidence that must be used to support it. Evidence for (P or Q) needs either evidence for P or evidence for Q; evidence for (exists x such that P(x)) needs a concrete value (e.g. a number) x and evidence for P(x) for that x; evidence for (P implies Q) is a function that maps evidence for P into evidence for Q; and so on. The two theorems (1) “given any integer, there is a prime number larger than it” and (2) “there are not finitely many prime numbers” are in fact different statements. The evidence for (1) must be a computable function which maps integers to prime numbers which are larger; the evidence for (2) is a function which takes evidence that there are finitely many prime numbers (essentially an exhaustive list) and produces a contradiction. (2) is the form of Euclid’s famous proof, but it is not as strong as (1), which gives a computable process that generates primes. Idiomatically we would call (1) constructive and (2) non-constructive, but the finer distinction is that constructive mathematics distinguishes these two statements while classical mathematics considers them equivalent.

In practice, this means that you cannot use proof by contradiction, the identity that “¬∀x. P(x)” implies “∃x. ¬P(x)”, or the axiom of choice (which claims the existence of a function without giving a way to compute it). The necessary evidence can be extracted from proofs constructed using the remaining axioms.

If you alter the laws of evidence, you can recover the law of excluded middle (proof by contradiction), which says that for any proposition P, (P or not P) is true. Classical mathematicians consider it true that “there are either infinitely many or finitely many twin primes”. Constructively, however, this says if you have a proof of this statement, then you either have a proof of P or a proof of (not P). At the time of writing, this is not true of whether there are infinitely many twin primes; we do not yet have a proof either way. But if you allow into your language of evidence the ability to invoke continuations, then we do have such evidence: the one we have is a proof of (not P), which is a function that takes evidence for P and produces a contradiction. So you pass this function evidence for P because you need the contradiction, but instead of giving you the contradiction you wanted it goes back in time to change its mind, now saying that the evidence for (P or not P) is the evidence for P (which it was just given). Yes, it’s ridiculous, but could be considered constructive if you have a different slant on the meaning of evidence.

But don’t be so hasty in using this ridiculous interpretation against the law of excluded middle. The Ackermann function — a function which grows extremely fast — is constructively definable. However, A(4,4) is far, far greater than the number of elementary particles in the known universe. Using the numeral for A(4,4) as evidence is physically impossible, and yet it is considered valid constructive evidence. This puts constructivism on less sound scientific footing: a constructive theorem need not have actual evidence, it need only have evidence in principle. But what principle? How can one justify that A(4,4) is more real than a well-ordering of the real numbers? — we can give concrete evidence for neither. The proof that A(4,4) is a well-defined number relies on abstract reasoning founded in the same logical ideas that gave rise to the law of excluded middle.

This style of argument is associated with ultrafinitism — the idea that even very large finite numbers may not exist (pay attention to the word may — the idea that a finite number does not exist is intentionally outside the realm of ultrafinitism’s ability to answer). Classical mathematics says there exist arbitrary choice functions, constructive mathematics says those may not exist but A(4,4) does, ultrafinitism says that A(4,4) (and sometimes even numbers as small as 2100) may not exist. These distinctions seem all to be rooted in a sort of fight over which Platonic abstract concepts exist. Perhaps some, such as my friend Paul, would say “are meaningful” instead, but it’s the same idea. It is not as if only one of these philosophies has information to extract. Ultrafinite arguments construct observable evidence, constructive arguments construct idealized evidence, classical arguments discuss idealized existence. If you were to rephrase a classical existence argument “there exists a non-recursive set of integers” to “not every set of integers is recursive” then it becomes constructively valid (it is a diagonal argument). In fact, every sentence provable in classical logic has a corresponding sentence provable in constructive logic, by a simple syntactic transformation. I find it, then, irrational to consider that the former be meaningless and the latter meaningful. So we are merely arguing over the semantics of the word “exists” (and in general, “or”, “implies”, etc. as well). We are arguing about what the sentences mean, not whether they are meaningful. Classical existence is different than constructive existence, and neither corresponds to physical existence.

Paul says, “you can’t actually cut a sphere up and reassemble it into two spheres identical in volume to the first.” I respond by saying that you can’t actually separate an arbitrarily small piece of a box either (first of all, a box made of what?), which constructively is allowed. Mathematics is about mentally idealized objects — if we can “in principle” separate an arbitrary piece of a box, then we can also “in principle” cut a sphere up and reassemble it into two spheres of identical volume, they are merely operating by different principles. Fortunately, we can examine the proofs of these theorems to find out by which principles they are operating. But if you are going to bless one “in principle” as meaningful and banish the others — which I beg you not to — I can see no other way than to resort to the physical reality we are given, to ultrafinitism.

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Beliefs and Truth

I have now met the fourth person who has said that they don’t have beliefs.

Perhaps I am still stuck in a naive conception of truth that they have transcended. I still unconsciously assign beliefs to be axioms, as assumed truths upon which to base my inferences, and as such not having beliefs would seem impossible. Perhaps they have already achieved what I merely strive for: just living, just being the little perceptrons they are, already embodying the consequences of truth as a linguistic construction and not a fact of the world. They know that whether an idea is true is irrelevant — that there is nothing more than successful ideas being successful — and as such to “believe in” any truth is only to be enslaved by a clever, self-reinforcing idea: that ideas can be true.

This transcendence must have been achieved after many years of thought and meditation — we are perhaps even born clinging to truth as though it were unitary and absolute. Wars have been fought over is and is not, as if ignoring the evidence shining in their swords, both could not coexist. We have a deep genetic drive, because the uncertainty introduced in realizing the paradox of accessible truths is enough to delay a life-saving decision by a few milliseconds, and thus has been bred out of us. The option that there is a representational barrier between your perceptions and the world is not an option for the animal at the edge of survival. But perhaps there is a latent genetic drive toward the non-believer’s enlightened state after all — once you stop worrying about what is true, you can react faster, having closed the analytical gap between cause and effect. You are a wild animal, your thoughts having proregressed into instincts. Indeed, when time is of the essence, this idea could be more successful than the idea of truth — perhaps their meditation was to put themselves in life-threatening situations in which they needed to be lightningfast to survive.

They see the intimate connection between the words “belief” and “truth”. An idea must be able to be true in order to be believed. But they do not reject these words, for an idea must be able to be false to be rejected. The collusion of “belief” and “truth” makes them very hard to break out of: each reinforces the other. When it comes time to communicate, the non-believers see that language is built around truth, and one cannot communicate without presupposing it. So for them to communicate that they are not where you think they are, they must use a sentence which by its very utterance contradicts itself: “I do not have beliefs.”

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The Creative Urge

I have an uncomfortable yearning, a yearning to create something, but I have no ideas about what specifically I want to create. My mind falls back on those things which I have enjoyed creating in the past: a programming language, a piece of writing or music. They are taunting me with old half-ideas that never became anything, and they remain half-ideas that are not sufficiently developed to become something. I have no constraints; I am blinded by the endless possibilities the world offers me and cannot even see into the next hour. I have no goals; my former underlying goal of progress has shown itself to be illusory, at least for now, so all I have to guide me is my own creative pleasure. It is picky and has the attention span of a gnat, except for when I manage to summon that elusive, intense weeklong focus which I am not sure I’ve had for years.