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argumate:

You have n problems.
You use an untyped language.
Now you have 0 problems.
Until you step outside, trip over, and explode.

You have n problems.
You store them in a machine integer.
You keep getting into trouble until you have 2^32 problems.
Thanks to modular arithmetic, you have 0 problems.

You have n problems.
You notice n is very large.
You add one more problem.
You still have n problems.
n is a floating point variable.

You have n problems.
Your problems are all orthogonal to each other.
Your problems form an n-dimensional vector space of infinite trouble.
Try to have collinear problems next time.

You have n problems.
n is a function of time that increases monotonically.
You hope that n is logarithmic but fear it is exponential.

You have n problems.
You fix one.
You have n problems.
You fix one.
You have n problems.
You start to suspect the decrement opcode is not working to spec.

You have n problems.
The first n - 1 problems require boolean answers.
The last problem is a constraint across all the others.
Your problems are NP-complete.

notbecauseofvictories:

also that whole tale of aragorn and arwen thing where he saw her in the woods at twenty and fell instantly in love and it’s very beren and luthien? lies.

aragorn decided he was going to marry arwen when he was like, six.

and everyone thought it was just the cutest thing, baby estel with his little crush on the great immortal evenstar, and everyone would tease him about it relentlessly and he would get so mad, and pout, because how dare they doubt his word.

(arwen spent a lot of time biting back smiles and nodding very seriously when aragorn brings this up with her. no, estel, I do not know why they are laughing perhaps they have remembered a particularly funny joke.)

and then aragorn grows into this gangly teen and oh my god can you imagine being a pimply greasy teenager around fucking elves it’s a wonder he has any self-image left. His voice breaks every other word and the laundresses are beginning to wonder if something is wrong with the sheets because estel keeps washing them himself and aragorn wants to die, god, arwen is never going to marry him if he stays all elbows and skinny knees and he can’t even look her in the eye anymore without blushing, eye contact is probably something to look for in a husband–

(arwen, who never had to go through puberty because elves don’t do anything so undignified, tries to comfort him by saying she likes his blemishes. aragorn gives her a look of such utter, miserable despair that she starts laughing.)

(this is a mistake. he spends the next three weeks nursing his wounded ego and refusing to see her.)

estel is twenty when he asks for her hand. he is lean, slender and fair as a new tree, and so arwen does not feel guilt in kissing his cheek and gently refusing. he is still green, he will weather greater storms than this–and he takes it as he should, clasping her hand and swearing to ever be her loyal friend.

they write to each other–when she is in lorien, when he wanders with the rangers of the north, fights alongside gondor, travels to distant lands. it is an inconstant tie–he is rarely afforded time enough to put pen to paper; she is reserved so as not to encourage what may not be. (she signs her letters always, your friend. She likes him too well to be cruel in this.)

the years pass. his weariness and strife creeps onto the page, and she sends him tokens to fend off the darkness–leaves from lothlorien, the ribbon from her hair, snippets of poems. it is not enough it is never enough I am sorry, she writes.

his reply is gentle: you are enough. do not stop writing.

(she carries that letter tucked inside her sleeve for a long while, like a talisman–though against what evil, she does not know.)

she is in the house of her grandmother when a familiar voice calls out to her: my lady luthien!

this is when arwen looks up, sees aragorn–broad of chest and rugged, still wearing his battered mail, with one hand balanced lazily on the pommel of his sword. All the trees of caras galadhon are gold but he is shadow and silver, kingliness resting lightly on his shoulders–

and arwen thinks, oh fuck

nostalgebraist:

@lostpuntinentofalantis

I don’t think the fact that humans are bad at thinking up logical implications is a very strong argument against bayes, in the same way that “But Harold, you said you loved Chocolate earlier!” is an argument against preferences.

So, I will agree that there’s this non-monotonic thing. This is indeed a very good point against using Bayes as a mental tool! I am not disagreeing with that!

What I do disagree with is the idea that it’s ipso facto problematic. I think the correct way to do this is throw out your first estimate as a preliminary one, and then use the other logical implication questions as a way to generate a battery of knowledge in a kinda organic fashion. To use the original “California succession” thing, let’s say I think it’s unlikely, so I throw out 98% as my likelihood, then some else asks me the “USA still together” so I also generically throw out 98% but A HA!!!!!! THIS SEEMS WRONG, because the set of situations involving the US together but California leaving seems I dunno small or whatever, so I end up adjusting the probabilities as,  repeating until I’ve thought of all “relevant” probabilities.

But logically speaking isn’t this troublesome? Isn’t it terrible that in theory an adversary can choose a sequence of questions which allows them to set my probabilities? Well, not really. My claim is that thoughts of these logical implication things provide information because humans are really bad at accessing all the information they have, and that, yeah sure if the adversary controls how a person accesses their information, of course the person is screwed? So you hope that people have good internal “implication generating”  machinery, such that by the time that they have worked through a bunch of subset questions, they have dumped out all relevant information, and the ordering effects are washed out.

Which is a much more elaborate way of saying “guys stop throwing out random probabilities and sticking to them if you don’t have good intuition/facts doing cognitive work aaaaaaaahh”

I guess I can agree that nothing I said above is specifically motivated by Bayes, except for this vague feeling of “well, shit it turns out I’m actually really bad at incorporating all relevant information” and I think it’s really just unavoidable.

I don’t think this is a problem with humans, I think it’s much more fundamental.  The real issue is that these kinds of “obviously nested” statements have a “easy to check, hard to find” property, like with NP-complete problems.

Let’s define “A is obviously nested in B” as “if you describe both A and B to me, it’ll be immediately obvious to me that A is sufficient but not necessary for B.”  And let’s define an “obviously nested pair” as A, B where one is obviously nested in the other.

The “US in 2100″ statements mentioned earlier are all obviously nested pairs with one another.  But the ones mentioned are just a few examples; there are infinitely many statements of the same form, asking about slightly bigger or smaller regions of the US, that also form obviously-nested pairs with all other such statements.

And that whole infinite chain is just one “direction” in hypothesis space.  You can think about any other subject – existence of various markets and sub-markets (will candy be sold?  will lollipops?), demographics and sub-demographics, scientific ideas and special cases thereof, you name it – and produce an infinite obviously-nested chain like this.

In finite time (much less polynomial time), you can only explicitly think about some vanishingly small subset of these statements.  Yet you implicitly know infinitely many facts about them (about each chain, in fact, of which there are infinitely many).  There’s no way to sit down and think enough beforehand that all of the obvious-nesting information has been dumped out into an explicit representation (and that representation would take infinite space anyway).

Now, maybe there is a way to handle this in practice so that it doesn’t hurt you too much, or something.  Such a theory would be very interesting, but as far as I know it doesn’t exist, and it would have to exist for us to begin talking about how a finite being could faithfully represent its implicit knowledge in a prior.

(This is a human problem in the sense that you could make a machine which would lack all this implicit knowledge.  That machine would not have this problem, but it would know less than we do, so we’d be throwing away information if we tried to imitate it.)

Yet you implicitly know infinitely many facts about them (about each chain, in fact, of which there are infinitely many).  There’s no way to sit down and think enough beforehand that all of the obvious-nesting information has been dumped out into an explicit representation (and that representation would take infinite space anyway).

Now, maybe there is a way to handle this in practice so that it doesn’t hurt you too much, or something.

This sounds like a natural continuity/limits problem. It does seem like there could be infinite nesting like this, and that you do know information about each step of the chain. However, I’m not sure this necessarily needs infinitely many facts to describe, perhaps an overarching fact could sum them up, or the facts get ‘smaller’ as the chain does, so that together they form a finite total fact. Thinking about the obvious-nesting information sounds very much like taking a limit.

The geographic example has very literal continuity, with larger and smaller regions of the US. I’m actually quite surprised there isn’t such a theory already! Hypothesis space, even when infinite, is continuous, and that makes a big difference.

On a separate note, I’m not convinced that we couldn’t make do with a model where we only consider a finite universe, with discrete rather than continuous space. That would mean you could not take infinitely many different regions of the US. And it would mean that only finitely many events could possibly occur in a given time period, which intuitively seems like saying there will only be finitely many such different chains of hypotheses to worry about.

While it seems a bit artificial at times, I don’t think it’s too unreasonable to allow a theory like this to only cover finite cases, not when the finite case can approximate the infinite case arbitrarily closely. Then it seems we could reasonably represent our priors. 

ambivalencerelations:

we-kant-even:

• A Socratic relationship, in which you ask a lot of really difficult questions of the other person until they get annoyed and want to poison you. (I have a lot of those.)
  
  
• A Hegelian relationship, in which the two parties disagree about everything but eventually achieve a synthesis. (Come to think of it, I have a lot of those, too.)
  
  
• An Aristotalean relationship, characterized by an extreme interest in what category of relationship this is.
  
  
• A Cartesian relationship, characterized by doubts about whether there’s really a relationship going on.
  A more extreme version of this is the Berkeleyan relationship, characterized by an adamant insistence that there is no relationship going on at all. Both of these can in time evolve into a Wittgensteinian relationship, in which the participants acknowledge that whether there’s a “real relationship” is an ill-defined question that depends more on the structure of their language than on the reality of the relationship.
  
  
• An Aquinian relationship, that acknowledges that an exploration of the nature of the relationship is likely to strengthen rather than weaken it.
  
  
• A Hobbesian relationship – solitary, poor, nasty, brutish, and short. (Sorry, I couldn’t resist.)
  
  
• A Kantian relationship, in which you can morally do anything that it’s OK for everyone else in the relationship to do.
  
  
• A Rousseaian relationship, characterized by the natural behavior of man in the wild, away from civilization.
  
  
• A Nietzchian relationship, where both parties focus primarily on the will to power.
  
  
• A Randian relationship, in which both parties act exclusively in their own self-interest.
  
  
• A Heraclitean relationship, which you may as well not categorize since it’s not only different from all other relationships, it isn’t the same from one moment to the next. (You might think you’ve been in one just like that, but you’re wrong.) 
  
  
• A Stoic relationship, which is also unique, but anyway it’s no better nor
  worse than any other. 
  
  
• An Epicurean relationship, which theoretically isn’t very different from a Stoic one, but sounds like a lot more fun. 

• A Humean relationship, in which what you see is what you get.
  
  
• A Hillelistic relationship, which is platonic (in the vulgar sense) because nobody will do anything to anybody that they don’t want done back to themselves.
  
  
• A Christian relationship, which soon degenerates into a platonic relationship because both parties are doing what they do want done back to themselves, instead of what the other party wants done to them.
  
  
• A Marxist relationship, where each party gives according to – I’ll stop right there, it’s too obvious. Clearly *that* one is doesn’t become platonic. Let’s hear it for Materialism.
  

A Zizekian relationship, where you snort incredible amounts of cocaine and discuss *shniff* eye-dee-ology.

evolution-is-just-a-theorem:

evolution-is-just-a-theorem:

Be a coding consequentialist. Forget the battles over functional vs. imperative, static vs. dynamic, and vim vs. emacs. Exec is not evil, neither is mutable state, and global variables can be fine. A big chunk of the difference between languages and frameworks is familiarity and personal preference, metaprogramming has produced some of the greatest libraries ever, and if anyone tells you there’s a Right way to do something they’re full of shit.

Instead, focus on what you actually want from the code. How long will it take to code? How long will this take to debug if it breaks? How hard will it be for a new coder to understand what this does? How fast will it run? How costly is failure? Does this need to be cross platform? Will I ever need to extend this?

That’s not to say that the purity intuitions are useless. Exec isn’t evil but it is dangerous and it can bite you. Metaprogramming made Boost, but just try debugging it (I haven’t tried this, maybe it’s actually super easy). Functional languages have many useful tricks, tools, and conventions. Just try writing an iterative red black tree (I have done this. Do not do this.) On the other hand for loops are really nice. Dynamic typing is great when you start out, but when you have ten thousand lines and a new coder just came on board and is trying to figure out what the FUCK goes in this dataframe you’ll start wishing you had static types or at least typed documentation.

I’m just going to reblog this every time I want to express the sentiment.

Agreed! Whenever I declare a Right way to do something in this sense, I am fully aware that this is full of shit and am doing it for the sake of humor.

That said, pure functional programming is elegant, and type systems are awesome. 

Are they always the right too for the job… no. But I will have fun saying they’re Right and the absolute best! Mutable state is evil to be avoided. 

I hope Awodey enjoyed writing that sentence. Does it take the record for most uses of various forms of ‘monoid’ per syllable?

preciselywibble:

Your metronome only does it because it loves you and wants to help you improve.

Your compiler only does it because it loves you and wants to help you improve.