Tag Archives: philosophy

We Should All Argue More Selfishly!

We would all love an argument to end with “wow, you’re right, you have convinced me!” Why then do they so seldom end that way?—if you’re like me, most arguments (especially online) seem to end by giving up in frustration, together with a reinforced idea that the person you were arguing with (and usually, their whole kind of person) is an asshole. So the ultimate effect of arguing is that we all despise each other a little bit more.

Somehow the resolution to stop engaging in arguments is not satisfying. I’ve tried this one. My experience of the internet devolves into a bland echo chamber of likes and positive affirmations. I do not feel intellectually stimulated; interacting with the internet begins to feel like vegging to daytime TV. My ideas are not refined, my critical intellect is not challenged.  Restricting the sphere of my interactions, I become so accustomed to the culture of affirmation, eventually the fact that anyone could disagree becomes upsetting and confusing, and when arguments do occur, they are more horrible than ever since I have not been exercising my ability to critically engage.

I have a solution.  My solution is superior to many other solutions you will see about discourse, because it is local — it only requires that I change my own behavior; everybody else can carry on as they were. No grand cultural transformation needs to take place; if you read this and engage in arguments this way, even if nobody else reads this article, you will be more intellectually stimulated and have more fun arguing.

I claim that we are all arguing backwards.  Let’s ask, what does it mean to win an argument?  Conventionally, it means that the position you held going into it ended up being the one that both parties hold at the end.  Vindicated!  However, if you win an argument in this sense, you have not learned anything new, besides the boring affirmation that you were right.  It would have been just as useful to spend your time sitting in your room alone, repeating to yourself the mantra “I’m right, I’m right, I’m right.” The idea has won, but you have lost.  Whereas the conventional “loser” of the argument has got a whole new perspective on this issue; their lens has been upgraded, their mundane life has come alive with new patterns, their world has been enriched. Beyond the ten seconds immediately after the argument concludes, feeling the sting of my deflating pride, I would much rather be the loser. The winner has provided a service to the loser at the cost of her own time.

The results we experience in arguments thus make perfect sense.  We are all trying to “win”; we are all trying hard to be the one who is not enriched. And we all succeed; nobody is enriched. If we were all a little more selfish, maybe we would start to get something out of arguing. Try to lose! Focus your energy into guiding the argument toward your own utterance of the words “wow, you’re right, you have convinced me!”  Win in life by losing the argument.

I’m not claiming you should just lay down and let people walk all over you.  To reap the benefits of the loser above, you must authentically lose, you must be earnestly convinced. Never surrender your honesty.  Engage in the argument by finding your own objections, discovering those things that are preventing you from being convinced, and asking for the data and logic that will sway them.  Assume that your adversary possesses an argument that would convince you, and try to find it. Sometimes this strategy may fail and your adversary will discover they are unable to provide the necessary information; oh well, not every interaction goes your way.  Better luck next time!

In conclusion: Don’t go around life helping others by convincing them.  Be selfish and make them convince you!

Blogging as Service

As I mentioned in the last post, I have been feeling a lack of meaning in my life, as though where I am putting my energy doesn’t matter.  However, when I try to find a project to invest my energy in, I am overcome with a feeling of confusion.  We all want to change the world, but I don’t know what I want to change the world into, nor do I feel I can even see clearly the world I ostensibly want to change.  I am growing ever more tired of the political rhetoric I’m exposed to, which seems more and more a tribalistic war; people are not interested in finding real solutions and compromises to the problems we face as a people, rather they care only about whether I am expressing that I am one of the good guys or one of the bad guys.  Not only do I find this pattern unhelpful for the advancement of humanity, I find it boring, and so my instinct is to disengage with politics and cultural criticism altogether.

Lately I have been reading and writing a lot in an attempt to see more clearly.  However I have an aversion to publishing my thoughts, because I feel they are naïve or incomplete. In this post I wish to criticize this aversion and defend the social value of publishing these intermediate writings.   My claim is that publishing my incomplete and imperfect thoughts is a meaningful and positive use of my time.

The Absurdity of Genius

I seem to have a belief something along the lines that you have to be a “genius” in order to have valuable thoughts: the only philosophical perspectives worth reading are those of the approved Great Thinkers, and that mere mortals cannot have any true insight. I think this comes from my schooling, in which the people we study have large names and are exalted and praised.  Of course it is ridiculous.  How else could someone become a great thinker than by working with and refining what they have?  Furthermore, the concept of “great thinker” itself is subject to the same laws of popularity that put Maroon 5 on the Top 40.  Furtherurthermore, all theories are amalgams (at least in as much as words themselves are socially constructed, and clearly much more), so it not out of the question that a world-changing theory could be influenced by my ideas.

I am reading Michel Foucault’s “The Order of Things” (which is awesome, by the way).  In the introduction he says that the book was inspired by a passage by Jorge Luis Borges, which in turn was written as a critical response to a proposal for a “universal language” by John Wilkins.  Here we can see the flow of ideas.  Wilkins writes something which Borges thinks is stupid; Borges’s response makes Foucault laugh and then write an insightful book essentially about what is funny about the response; Luke reads the book and decides to start publishing his writing.  Perhaps a future Borges will read my naïve theories and make a joke about them which will be the seed of another insightful work.

Refinement by the Risk of Criticism

The lens of publishing helps me refine and add nuance to my thoughts.  Insofar as my journal is a log of my thought process, I might write some absurd nonsense that would not hold up to criticism in my journal, and never give it a second thought.  That thought-structure is allowed to continue existing in my mind, unexamined.  If I publish, even to my meager blog following, I am forced to consider my opinions more deeply, so that I don’t embarrass myself.  There is added incentive for me to re-read what I have written, thus to organize it, considering more distant combinations and interactions between my ideas and my knowledge.  As a result, a more refined and well-examined knowledge base will, in principle, help provide a stronger theoretical foundation to my future actions, so I don’t get lost in the well of meaninglessness so easily.

Encouraging Nuanced Reflection

One of the problems I identified in the introduction is that I feel that thought is losing nuance and converging toward a few tribalistic echo chambers.  I feel that the world would benefit if people would philosophize a bit more.  It is certainly possible to navel-gaze too much, but I feel like we are in a period of over-activism and under-reflection.  We are in a time of huge protests with tiny results––this indicates that we do not have a clear foundation for our activism.  We’ve got the pathos but not the logos.  This is not helped by the popular social media platforms, which seem as though they are designed to promote simplistic, echo-chamber discourse.  Ideas are communicated in tag-line form, and sealed with a blue checkmark––an idea is good if a popular person said it and we like how it sounds.  I believe people are monkeys who imitate each other, so by raising my own standard of discourse, even if my ideas are silly, I am helping to promote a culture of reflection and nuance.  I am demonstrating that I value trying to figure it out, rather than having it all figured out, which is doubtless a message I can get behind.


It could be argued that I should keep my ideas to myself until I feel like I have something important to say, otherwise I’m just adding noise.  Indeed, it’s something I’ve struggled with in my artistic pursuits, of publishing things that I don’t feel proud of.  When I have had a corpus of material available online that I am not proud of, it makes me shy about promoting myself, for fear that I will be discovered as incompetent.  But I am not afraid of that here––I don’t care about being a popular writer, I care about refining my own ideas, I care about building a strong theoretical foundation for positive action.  So the argument breaks down, it doesn’t matter whether I am proud of my work in this case.

It could be argued that I should be more informed before writing, that I should not claim things which I don’t know for sure.  Since I do not have a large reader base I don’t think this is a problem; if I did, I might take this more seriously.  I think it is important to plan for your own success––it’s a good question to ask whether, if you did somehow become successful, it would even be a good thing.  But just I don’t think it’s important at this stage; the other benefits of publishing outweigh this risk.

Seal Of Permission

In light of the aforementioned arguments, I hereby grant you, Luke Palmer, permission to publish silly sounding ideas in your blog, even if you believe in them.

Death and The Singularity

When a particular mutation causes some cells to start dividing faster than the others — a self-replicating explosion that is characteristic of life — we call them cancer and they kill their host. With their host they also die. The latent bacteria and fungi kept in delicate balance by the sophisticated systems of the body take over, each exploding in its own way, recycling and reintegrating the materials that composed this human machine into the larger world.  What was the human’s individual consciousness reintegrates into the Earth in whatever way that happens.

At some point a mutation in the memetic code altered humanity.  We began wearing clothes, building houses, and with this developed a concept that we are separate from each other and the rest of nature — Self, Ego. We have expanded much faster than our surroundings, and the amount of the Earth’s resources we consume to continue doing so outweighs the value we give back into our host.

The Singularity is based on the observation that the rate of technological innovation has been accelerating for a long, long time. This mystical belief system projects what might happen as this acceleration continues.  What happens as the structure of self-replication and transformation of nature continues to its limit?  By analogy, what happens when the small mutation that causes cells to divide faster continues to mutate for its own propagation? In some accounts, a structure of energy will be created that expands outward at the speed of light, integrating the consciousness of our local nature into the universe — Stepping into the Light.

The Singularity is a concept of death.  Environmentalists see our unhealthy habits and want to get our act together so we can continue living a healthy life; technologists see the unstoppable advancing tumor and are trying to accept our fate and embrace death — not the end of all things but indeed a major transformation in being resulting in the loss of all our attachments. It is a peculiar contradiction, in a divine-truth sort of way, that many technologists believe that we will invent a way never to die. Each of us transforming ourselves through the advance of technology is participating in the larger process of death that the Earth faces. Environmentalists hope that our cancerous expanse can reconstruct a functioning body on top of ourselves, keeping the host just alive enough to preserve our Selves — restoring the Earth to the past in which humans are few and in parity with other animals is not what we have in mind.  With hope and desperation we awe in Mother Nature’s embrace.

We belong to the Earth, and she is dying.

Motivating Dualities

The act of striving to become more, to learn more about living is a prominent part of many people’s lives; it certainly is for mine. However, I’ve observed a form of suffering which is associated with growth and striving, which I suspect is pervasive in progressive society. I will talk about the underlying beliefs that cause this suffering and the complex of dynamics that occur as they come forward for transcendence. I analyze these beliefs for the purpose of undermining them. However, I seek to undermine them not to cease striving, but to elicit understanding the cause and mechanism of striving-suffering, bringing it into clearer focus and illuminating the path to transcendence.

The core of the belief system I’m speaking about is the pair I’m not good enough : I need to be good enough. I name beliefs of this form motivating dualities. They begin when we set a standard for ourselves, here denoted “good enough”, and acknowledge that we do not meet that standard. This pair creates a vector — a drive to become more in the direction of our standard. Without both sides of the pair, these beliefs would not be motivating.

When the standard is concrete, this pair can integrate peacefully into a growing human being — it is equivalent to setting a goal and acknowledging where we are in relation to it, motivating us to close the gap. This pair will cause striving-suffering as we begin to identify ourselves with the abstract act of striving and/or achieving, separated from the goal to achieve. I’ve seen this both in cases where the person believes herself to be achieving highly and where he does not. When this identification occurs, the underlying belief system that created the vector is cemented into place — to transcend the motivating duality means letting go of striver as part of our identity; simultaneously, our identity as a striver is formed by these underlying beliefs, so we cannot let go of that in isolation either. We become trapped in a Nash equilibrium of beliefs and identity.

As we develop, we will eventually meet our previous standard, but because our identity and beliefs are trapped in this equilibrium, they mutate to adapt to their environment. The concrete standard that formed the initial vector is abstracted, and we begin to feel that we aren’t “up to standard” as a general principle. Goals that once had concrete action steps for growth become fuzzy, and we begin to grasp for Good Enough in the abstract. This grasping is the core of striving-suffering. We strive but never near our goal, because it is now too abstract to be measured.

I should be clear about the way I am bringing in some Buddhist philosophy, specifically that attachment is the cause of suffering. To interpret me well, it’s important not to read suffering as “bad” or “thing to be avoided”. It may be that all striving is attachment and thus suffering, but when we are nearing a goal, when we see the gap of a motivating duality closing, we feel pleasure and fun. Living while oscillating between suffering and pleasure/fun is an often pleasurable and fun life which includes suffering.

Striving-suffering is calling me for analysis because it undermines its own end. The striver-sufferer seeks to expand herself and her consciousness, however she is blocked from transcending this aspect of her beliefs and identity. Someone trapped in striving-suffering will often not be able to access universal consciousness — the deeply peaceful identification of self as the universe — because they are unable to take off the lens of “good enough” because it would mean the collapse of their identity. Striving-suffering is a common condition in progressive culture, and we see its effects: many highly talented and accomplished people, dedicated and hard-working, with narrow, inflexible consciousness.

So, while the motivating duality I’m not good enough : I need to be good enough drives us to grow, to continue growth of our consciousness we must eventually transcend it. One path to transcendence is to undermine both beliefs at once by breaking down the core concepts upon which these beliefs are built. Breaking core concepts to the point of existential crisis is a practice I engage in more often than most; it is often deeply overwhelming and confusing, and many don’t feel they have the freedom of lifestyle that would allow such frequent crises. A smoother path is to unlink the self-reinforcing complex so that each aspect is free to go without being pulled back into place by its companion. A striver-sufferer can do this by, for example, observing and reinforcing himself as someone who naturally seeks to grow, so that the motivating duality is no longer the sole support for that aspect of his identity. This frees the motivating duality to be transcended without invoking a crisis of identity.

A striver identity supported by natural seeking is more flexible than that supported by the motivating duality — it requires a less hefty lens, and the lens can be removed without threatening our identity. It moves our motivation from extrinsic — motivated as a means to an (impossible) end — to intrinsic, which can be trusted while beliefs and ways of perceiving shift, freeing the consciousness to expand in new domains.

Great people often seriously experienced their mortality or frailty in some way.  John Coltrane had four family members die in three months; Stephen Hawking contracted that motor thing he has; countless great musicians have lost a sense.  I can see how experiencing something unexpected and tragic would kick you in the pants to go all in on what you love, and do it now! These people understand their power and their freedom through their commitment.  Isn’t it ironic or profound that we can’t or absolutely would not choose to have such an experience, even in exchange for greatness?  In order to do what you love with the passion of greatness, would you choose to have most of your family die?  Could you give up sight, hearing, or movement?  Even if you did, would you not be filled with guilt or regret rather than experiencing the preciousness of life?  In this sense, nature blesses and curses at the same time, seemingly at random; we cannot invoke it or avoid it.  

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.


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.


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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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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