"Incanter is a Clojure-based, R-like platform for statistical computing and graphics."

"Don’t use scatterplots. Use a density plot such as a hexbin instead."

"The two-player Iterated Prisoner’s Dilemma game is a model for
both sentient and evolutionary behaviors, especially including the
emergence of cooperation. It is generally assumed that there
exists no simple ultimatum strategy whereby one player can enforce
a unilateral claim to an unfair share of rewards. Here, we
show that such strategies unexpectedly do exist. In particular,
a player X who is witting of these strategies can (i) deterministically
set her opponent Y’s score, independently of his strategy or
response, or (ii) enforce an extortionate linear relation between
her and his scores. Against such a player, an evolutionary player’s
best response is to accede to the extortion. Only a player with
a theory of mind about his opponent can do better, in which case
Iterated Prisoner’s Dilemma is an Ultimatum Game."

"Summary taken from G. Polya, "How to Solve It", 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6.
UNDERSTANDING THE PROBLEM
First. You have to understand the problem.
What is the unknown? What are the data? What is the condition?
Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?
Draw a figure. Introduce suitable notation.
Separate the various parts of the condition. Can you write them down?
DEVISING A PLAN
Second. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.
Have you seen it before? Or have you seen the same problem in a slightly different form?
Do you know a related problem? Do you know a theorem that could be useful?
Look at the unknown! And try to think of a familiar problem having the same or a similar unknown.
Here is a problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method? Should you introduce some auxiliary element in order to make its use possible?
Could you restate the problem? Could you restate it still differently? Go back to definitions.
If you cannot solve the proposed problem try to solve first some related problem. Could you imagine a more accessible related problem? A more general problem? A more special problem? An analogous problem? Could you solve a part of the problem? Keep only a part of the condition, drop the other part; how far is the unknown then determined, how can it vary? Could you derive something useful from the data? Could you think of other data appropriate to determine the unknown? Could you change the unknown or data, or both if necessary, so that the new unknown and the new data are nearer to each other?
Did you use all the data? Did you use the whole condition? Have you taken into account all essential notions involved in the problem?
CARRYING OUT THE PLAN
Third. Carry out your plan.
Carrying out your plan of the solution, check each step. Can you see clearly that the step is correct? Can you prove that it is correct?
Looking Back
Fourth. Examine the solution obtained.
Can you check the result? Can you check the argument?
Can you derive the solution differently? Can you see it at a glance?
Can you use the result, or the method, for some other problem?"

"I think one of the main benefits of formal methods is to force you to say what you mean by "right". Proving is secondary."

by using heaps

"In computing, the Two Generals' Problem is a thought experiment meant to illustrate the pitfalls and design challenges of attempting to coordinate an action by communicating over an unreliable link. It is related to the more general Byzantine Generals' Problem (though published long before that later generalization) and appears often in introductory classes about computer networking (particularly with regard to the Transmission Control Protocol), though it can also apply to other types of communication. It is also an important concept in epistemic logic, and the importance of common knowledge. Some authors refer to this as the Two Armies Problem or the Coordinated Attack Problem."

"A computer scientist is a mathematician who doesn't believe in telepathy."

"I think that I shall never envision
An op unlovely as division.

An op whose answer must be guessed
And then, through multiply, assessed;

An op for which we dearly pay,
In cycles wasted every day.

Division code is often hairy;
Long division's downright scary.

The proofs can overtax your brain,
The ceiling and floor may drive you insane.

Good code to divide takes a Knuthian hero,
But even God can't divide by zero!"

"I have a simple question for your “simple” question: What precisely do you mean by “a number”?

Is −0 a number?
How do you feel about √−1?
Is ⅝ or ⅔ a number?
Is 186,282.42±0.02 miles/second one number — or is it two or three of them?
Is 6.02e23 a number?
Is 3.141_592_653_589 a number? How about π, or ℯ? And −2π⁻³ ͥ?
How many numbers in 0.083̄?
How many numbers in 128.0.0.1?
What number does ⚄ hold? How about ⚂⚃?
Does 10,5 mm have one number in it — or does it have two?
Is ∛8³ a number — or is it three of them?
What number does ↀↀⅮⅭⅭⅬⅫ AUC represent, 2762 or 2009?
Are ४५६७ and ৭৮৯৮ numbers?
What about 0377, 0xDEADBEEF, and 0b111101101?
Is Inf a number? Is NaN?
Is ④② a number? What about ⓰?
How do you feel about ㊅?
What do ℵ₀ and ℵ₁ have to do with numbers? Or ℝ, ℚ, and ℂ?"

"A Repa interface to JuicyPixels"

you always end up pixel-tweaking, things just don't scale proportionately

"Use bcrypt or PBKDF2 exclusively to hash anything you need to be secure. These new hashes were specifically designed to be difficult to implement on GPUs. Do not use any other form of hash. Almost every other popular hashing scheme is vulnerable to brute forcing by arrays of commodity GPUs, which only get faster and more parallel and easier to program for every year."

a useful visualization technique used to find a kernel bug (among other things)

"JUNG — the Java Universal Network/Graph Framework--is a software library that provides a common and extendible language for the modeling, analysis, and visualization of data that can be represented as a graph or network. It is written in Java, which allows JUNG-based applications to make use of the extensive built-in capabilities of the Java API, as well as those of other existing third-party Java libraries.
The JUNG architecture is designed to support a variety of representations of entities and their relations, such as directed and undirected graphs, multi-modal graphs, graphs with parallel edges, and hypergraphs. It provides a mechanism for annotating graphs, entities, and relations with metadata. This facilitates the creation of analytic tools for complex data sets that can examine the relations between entities as well as the metadata attached to each entity and relation."

"this paper is that much can be learned both about aspects and the aspect weaver if we think of the functional code as a monadic style program and we couch the different aspects into monads. The weaver then becomes a lifter to transform programs through different monads.
"

pretty good explanation of Goedel's Incompleteness Theorem for a 12 year old

"Today's subject is Fountain Codes, otherwise known as "rateless codes". A fountain code is a way to take some data - a file, for example - and transform it into an effectively unlimited number of encoded chunks, such that you can reassemble the original file given any subset of those chunks, as long as you have a little more than the size of the original file. In other words, it lets you create a 'fountain' of encoded data; a receiver can reassemble the file by catching enough 'droplets', regardless of which ones they get and which ones they miss."

" The Hebrew Calendar is based on very deep and complicated mathematics, involving diophantine approximation, but it is very surprising that the gaps between consecutive Christmas-in-Hanukkah years is always a member of the set {2,3,5,8}. "

"entering the real world after college"

probability is hard

"Every time you shuffle a deck of playing cards, it's likely that you have come up with an ordering of cards that is unique in human history."

children's story that implicitly teaches some computer science concepts without mentioning computers

most claims about fibonacci, phi, and golden spirals are bullshit

determines when various milestone timings pass, such as your 1-millionth second, etc.

representing a rubik's cube in haskell:  type Cube = R3 -> Color

"These pages reflect my visual fantasies on dsp mathematics and applications. Visualisation helped me through complicated topics, like how to write an FFT program."

fun stuff

nice overview reference of good fundamentals

nice intro

"Practical Foundations collects the methods of construction of the objects of twentieth century mathematics, teasing out the logical structure that underpins the informal way in which mathematicians actually argue.
Although it is mainly concerned with a framework essentially equivalent to intuitionistic ZF, the book looks forward to more subtle bases in categorical type theory and the machine representation of mathematics. Each idea is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries between universal algebra, type theory, category theory, set theory, sheaf theory, topology and programming."

not very anonymous at all

because floating point arithmetic is not truly associative

good article on why it's hard to do

a parable about time investment and priorities

he makes them sound pretty awesome

Norvig critiques Chomsky's aversion to statistical learning

the search for concrete examples of seemingly true but provably unprovable statements in applied math

i was pretty proud of myself when i developed a similar visualization on my own

"Abstract: This paper aims to explain why I am still fascinated by the use of functional languages in hardware design. I hope that some readers will be tempted to tackle some of the hard problems that I outline in the final section. In particular, I believe that programming language researchers have much to contribute to the field of hardware design."

using prime numbers to minimize repetition

people have better intuition about logical problems if you frame them in terms of detecting cheating rather than other arbitrary problems

noSQL key/value systems are the categorical dual of relational databases; you can construct a unified query language over them with monads/linq.

many promising titles

Construct a 5×5×5 cube from thirteen 1×2×4 blocks, one 2×2×2 block, one 1×2×2, and three 1×1×3 blocks.

legitimate theorem about bodyswitching

"It is possible to translate any Turing machine into a set of Wang tiles, such that the Wang tiles can tile the plane if and only if the Turing machine will never halt."

an old (1877) mechanical device that calculates bayesian inference with bins of beads

a comment also mentions "Developing an Algorithm for “Enhance” Functionality in Image Processing"

explanation of the matchmaking system

"The model is expressed using a monadic metalanguage built on top of a universal reversible language for finite computations, and hence is directly implementable in a language like Haskell."

it turns out there's a lot of crazy hidden stuff in this dream theater album

lots of good reference links

a problem that's easier to solve if you only know simple math. btw I HATE THE NEW DELICIOUS POST FORM.

seems pretty solid

variety of visualization styles and when to use them

seems pretty sweet

sort of like Khan Academy

describes the Elo and TrueSkill competitive ranking systems

engineering: it's like math, but louder

impressive command line tool

in haskell: "All xkcd‘s fans know the raptor problem: suppose you are standing at the centre of an equilateral triangle with three raptors in the corners, one of them injured (thus going with a slower speed). Knowing the speeds of all entities and the edge of the triangle determine the direction in which you will have to run to maximize your life time."

"Nomic is [...] a game in which changing the rules is a move. Nomic has been used to stimulate artistic creativity, simulate the circulation of money, structure group therapy sessions, train managers, and to teach public speaking, legal reasoning, and legislative drafting. Nomic games have sent ambassadors to other Nomic games, formed federations, and played Meta-Nomic. Nomic games have experienced revolution, oppressive coups, and the restoration of popular sovereignty."

"Given two games, each with a higher probability of losing than winning, it is possible to construct a winning strategy by playing the games alternately."

because otherwise it sounded to mathy to get DoD funding

a modified version of this chess ranking system is used in starcraft 2

Pixar's mathematical tricks for manipulating a complex character mesh with a much simpler control point frame around it

amazingly clear explanations of mechanical computers

"Miegakure is a platform game where you explore the fourth dimension to solve puzzles."

all well-defined computable functions are continuous

"Alas, your own brain secretly thinks that functions are the same thing as procedures that you can implement on your computer. Perhaps you will not admit it, but a careful psychoanalysis of your mind would reveal, among other things, that you never ever concern yourself with non-computable functions."

"This pearl aims to demonstrate the application of Huet’s zipper on stacks of monad transformers for the development of highly modular programs with effects." Type level zipper!