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The Amen Break

Geoff — Thu, 26 Aug 2010 18:22:53 +0000

Imagine you’ve just phoned into a radio station as part of a contest. You’re the ninth caller, and you can win a fabulous vacation simply if you identify the song about to be played. The radio DJ will play a 15 second snippet, and you have 30 seconds to identify this song. He asks if you’re ready, and then he presses play…

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Audio MP3

Alright, 30 seconds to think, don’t panic… the first few second sound like some random trumpets, but that drum beat in the middle – you know that beat! You’ve heard it everywhere, hundreds of times. That “dum-dum-tish” break has driven itself into your brain, but you’ll be damned if you can remember where it’s originally from.

	Is it “Straight Outta Compton” by NWA?
	You can definitely hear part of it in the Powerpuff Girls theme song.
	It sounds like it’s in the beat of Slipknot’s “Eyeless“.

But it’s originally from none of those. Not David Bowie’s “Little Wonder“, not Oasis’ “D’You Know What I Mean“, not Maestro Fresh Wes’ “Bring it On“, not Orbital’s “Satan“, nor Nas’ “Hip Hop is Dead” – but instead the song “Amen Brother” from funk and soul outfit The Winstons recorded in 1969.

Hip Hop and Sampling

The song “Amen Brother” was initially recorded in 1969, but it took until the late 1980s and early 1990s for it to be begin to be revived as an integral part of pop culture. This was the time when samplers, machines which allowed short bits of music to be recorded and played back at will, finally became affordable to the hip hop artists of the streets. Short bit of drum beats that could be stored in a sampler were called “break beats”, or simply “breaks”. No one is certain who was the first to sample the Amen Break, but its use became ubiquitous in early nineties hip hop. Eventually the beat became overplayed, and the Amen Break seemed to be a flash in the plan, something brought up for nostalgic value if anything on new tracks.

Jumping the Pond

But as “Straight out of Compton” was selling millions in the US, the rave scene was exploding in the UK. This was a scene with little money, little social support, and was a subculture by any definition. But it was growing rapidly, and it demanded new music. The Amen Break was adopted as a foreign son, and the very basis for an entire genre and hundreds of songs. The break was sliced up into tiny pieces, each high hat, each snare, each bass drum hit cut into a tiny piece of audio. These pieces could be saved in a sampler, and played back in any permutation or combination. At first the variations were homages, but quickly the variation and volume spread. A sampler was cheap, the breaks were freely passed along, and flimsy acetate records of your new track could be written in the morning and played at the rave in the evening. This organic creativity caught the attention of the art scene, and effectively undanceable constructions were born, a fusion of the fundamentalism of the Amen Break homage and the polymeter and highbrow musical structure of the new creators who now went to art school. A prime example of this new wave was Tom Jenkinson, known as Squarepusher, who created multiple albums worth of songs all based on chopping and mixing the Amen Break.

The Rewards of Sampling

But what of the Winstons, the creators of the oft-sampled beat now so widespead that Fortune 500 companies use it in their ads? Did they blow the royalties on the fleeting rewards of fame, or have they hidden themselves and their fortune away? The staggering fact is that despite a recent Supreme Court ruling that even three notes can be considered a sample and subject to royalties, the Winstons haven’t received a single cent. Instead of property, the Amen Break now appears to be a part of the popular collective unconscious, ever-present and unownable.

For more detail, check out this great video by Nate Harrison from 2004.

Rumors of God

Geoff — Fri, 16 Jul 2010 16:15:11 +0000

The Higgs boson is one of the most important, most abstract, and most interesting ideas in current physics. Dubbed the “god” particle after an editor disallowed one of the co-discoverers from calling it “that goddamn particle”, it is the only remaining particle in the Standard Model that has not been directly observed by humans.

The fact that we’ve never seen any evidence of its presence is a big deal. The Standard Model is a shining jewel of modern physics, a mathematical model describing the most basic facets of the world using a symmetry group. The predictions of this model have been confirmed so many times and in so many different ways that it’s almost become more exciting to think of what it would mean if the theory were broken by some strange event than to rejoice at yet another correct prediction.

So this is why the missing Higgs boson fascinates so many. But why is it missing at all? The answer comes from the Standard model itself and its mathematical foundations. Like the sides of a many-faceted jewel, a symmetry group has many parts, all reflecting some basic property of an underlying structure. Every single observation so far indicates a jewel of a certain shape, and we’ve seen every face except for one. There seems to be no other possible structure that would fit the observations and create a complete crystal to speak, so we’re left inevitably with the conclusion that one face remains in the dark.

Broken Silence

But now something very interesting has happened. Evidence of the Higgs boson may have been found! Not at the new and fancy Large Hadron Collider, but the good old Tevatron, home of Fermilab. Apparently a rather prominent physicist passed some rumours going around the physics world to a blogger.

On a completely different issue, I’ve heard that there’s a rumor going around Aspen that the Tevatron will be announcing discovery of gluon + b → b + Higgs, which would then require large tan(beta), which would fit the MSSM. I guess we’ll find out in a couple of weeks.

This is big news – the observations indicate a “light” Higgs boson, which is why the older Tevatron was able to find it when everyone thought the higher power Large Hadron Collider would be required. What does a light Higgs boson mean? Something very inspiring – that particle physics isn’t quite done figuring out the world quite yet.

…a light Higgs boson pretty much proves that there has to be new physics beyond the Standard Model well below the Planck scale. The new particles should be bosons and the only natural reasons why the Higgs, or the new bosons, should stay light is supersymmetry.

The best fits based on this assumption imply that the squarks and slepton masses – and more generally, other superpartner masses – should be close to 500 GeV or so and they should be observable by the LHC, possibly by the end of 2011.

But what does Fermilab, the apparent source of this grand discovery have to say about it?

I find it interesting that there is not an explicit denial, but a statement that these rumblings in the physics community are “just rumours”. Rumours can’t be published in scientific journals – so I suppose we’ll have to wait and see just what this all means.

Our Modular Minds

Geoff — Sat, 10 Jul 2010 20:57:24 +0000

I believe that ultimately human consciousness can be described by a program. Now this doesn’t mean we’re all in the Matrix, simply that our mind is a giant seething logical machine with values that are manipulated by rules. There is no strange new science in the sense of new specialties that must be discovered in order for the mind to be understood, but a progression in a new kind of science as Wolfram dubbed it – the study of how complexity arises.

A List of Rules

When I first heard that you could program a computer as a child I was amazed. A strange wonder that I could only spend a few shared minutes with at school, something that could draw, add, and write far faster than I could ever dream of – and I could tell it what to do? I wasn’t quite sure how to inform it to bend to my every wish, so I started with Turtle (actually called LOGO I later found) upon my teacher’s recommendation. I fed Turtle long lists of instructions – move forward, draw a line, turn left, repeated in all and any ways I could think of. He would draw glowing green shapes across my screen, and never tired.

The Need for Modularity

The only problem was that while the Turtle seemed infallible, I certainly could not say the same. I was making the classic beginner’s mistake – I would write one giant chunk of code that was supposed to cause my turtle to dance in precisely the way I wanted. Any little mistake would send it widely off course and I would end up with a mess that barely looked like the original design at the best of times. I later learned that using a programming concept called “modules” could help me isolate these errors and make code more efficient and reusable. Just like a company could have a manufacturing and engineering division which could communicate with standardized blueprints, a program could have different modules that would exchange data in a standardized manner. A modular program is more stable since mistakes are typically limited in influence to the module they’re contained in, and each module can be modified by separate influences with only the understanding that they are supposed to behave and communicate in a certain manner.

Damage as Evidence

So is our mind modular? Well, if it wasn’t, we could assume that a brain injury affecting a certain part of the brain would have a consistent and general impact across all of our consciousness. The only problem is that we generally only see a nonspecific mental decline like this from a nonspecific trauma, say impact blows to the head over a long period of time. Injuries in specific areas seem to be correlated with deficits in certain mental abilities – while leaving others totally intact.

A stroke can basically be thought of as an incident where blood flow is drastically affected in a certain specific area of the brain. This subregion of the brain is unable to function due to lack of blood flow, and very strange things can occur.

Howard Engel is a Canadian novelist who had a stroke. Upon waking one morning, he found that the morning paper seemed to be written in some strange script, an alphabet he could not understand. Everything else appeared normal, except his visual cortex had been damaged in a specific area which prevented him from visually parsing letters and words. As a writer, he despaired – it seems that his livelihood had been lost. Soon he realized a critical distinction which gave him hope – he may be unable to read visually, but could he write? Howard sat down and traced these strange looking symbols, his pen gliding over the bizarre shapes over and over. And eventually, the concepts came back to him. In a strange sense, he could now read again. Years and years of writing had associated certain movements of his hand with letters and concepts. Instead of words in his head put to paper by hand movements and a pen, he had to move concepts in the opposite direction – moving his hand over shapes written previously by others, the concepts echoed back up his motor cortex.

And it worked. There was irreparable damage to his visual cortex, a critical module malfunctioning. So he hacked his brain, redistributing resources from his motor cortex which had been trained to recognized these same symbols and concepts necessary for reading by his constant writing. Howard now traces the shapes he sees on the inside of his front teeth with his tongue. His speed has steadily increased, and he says he can now read about half of the subtitles in a foreign film before they flash off the screen.

It doesn’t seem too strange to suggest that there are different localized modules in the brain for motor control, visual interpretation, and other concepts easily identifiable with different aspects of the physical world. But are there modules with finer distinctions, working on different parts of our mental experience rather than different parts of the physical world?

The Wason Selection Task

The Wason selection task is a very interesting experiment in the field of psychological reasoning. Before I spoil it for you by talking too much, let’s just do it right now. Look at the following cards.

Assume the cards have a number on one side, and a color on the other. What cards need to be flipped over to make sure that all even numbers have red backs? Make sure you’ve picked a card or cards.

Got it? Now a bit of unsettling but ego-salvaging news. When this experiment is done with undergraduates, only 10 to 20 percent get it right. The correct answer is to flip over two cards: the number 4 to make sure it has a red back, and the blue card to make sure that it doesn’t have an even number on the other side. Most people suggest flipping over the 4 and the red card – this is wrong, as it doesn’t matter if the red card has an odd number on the other side.

Now let’s mix it up a bit. Instead of numbers and colors, let’s try people and social activities. Assume the cards have a drink on one side, and a person of a certain age on the other. What cards need to be flipped over to make sure everyone drinking beer is old enough to do so?

Now the answer flows quickly and easily, and almost everyone gets it correct. We need to flip over the beer card to make sure that the person on the other side is old enough, and we need to flip over the card showing the underage drinker to make sure they’re playing by the rules.

The weird thing is that both examples are logically equivalent. Instead of numbers and colors, we’ve just used people and drinks. But something very important has occurred, and it happens time and time again as these tests are administered. It seems that people are fast and accurate at solving this task only if it is described as a test of social obligations. They both can be described identically with logic – but that doesn’t appear to matter to our mind. We appear to have a module dedicated to social reasoning and conflict, and can only solve these problems quickly if it involves determining if someone is cheating or breaking social conventions. This ancient module would hold significant survival value – a general logic verification module not quite so much.

Modules Upon Modules

There appears to be significant evidence for a modular mind, not just in terms of divisions between senses such as sight or hearing and other actions like movement but also more abstract modules that deal with concepts such as social rules. Stroke victims can literally rewire their brains, passing concepts upward into their consciousness through paths never intended to be used in such a strange manner, duplicating the work of other modules lost to injury. These modules live in a strange world of physical interaction and abstract mental space, a huge interconnected mass with no clear outline behind it. The big question now becomes: is a sufficiently complex system able to understand itself, and are we that system?

Quaternion Travels

Geoff — Mon, 10 May 2010 17:27:47 +0000

Relax to a slow flythrough of an interesting neighborhood of the quaternion Julia sets.

Monday Miscellany

Geoff — Mon, 19 Apr 2010 22:33:09 +0000

Solar flares, Chinese hobos, and undersea noises on deck for this Monday.

Live in STEREO

One of the largest solar flares in recent history was captured last week by STEREO, a pair of satellites staggered along Earth’s orbit to obtain a constant clear view. The flare was about half the width of the sun, or 800,000 km at its largest. Here’s another view from the Solar Dynamics Observatory.

Brother Sharp

A homeless man with piercing looks and an oddly consistent sense of fashion was dubbed “The Ultimate Gorgeous #1 Passerby Handsome Guy” by Chinese bloggers, or “Brother Sharp” when photos taken of him by a passerby appeared online. This led to a “人肉搜索 (Rénròu Sōusuǒ)”, or “human flesh search” as hundreds of people combed the streets to find him and his story. Unfortunately, it seems that Brother Sharp has some big issues and won’t be designing couture anytime soon. A local blogger spoke:

“Long ago in 2008 I encountered him. Most people who see him will avoid him, treating him as a beggar and the link, but actually this is not accurate. 乞丐 [qǐgài "beggar"] in our country’s ancient words first appeared as a monosyllabic word. The meaning of 乞 [qǐ] in the golden texts was “to beg”. But he does not beg, nor does he know how to beg, because he has psychological problems (in Ningbo they call it “great fog sickness”). They do not have an identity, they do not have family, they’ve even forgotten who they are. They are a group of people abandoned by society, and their final outcome is to die without anyone inquiring about them. They wander in the space between humans and animals. Help them a bit and they become humans, ignore them and they are animals.

He once said this to me: “Find a girl to love me.”

Bloops and Bleeps

The VENTS group has a collection of six unknown noises captured by undersea microphone arrays, including the infamous “Bloop” signal.

The “Bloop” signal was detected repeatedly by the Equatorial Pacific Ocean autonomous hydrophone array, which uses U.S. Navy equipment originally designed to detect Soviet submarines. The signal was traced to somewhere around 50° S 100° W, a remote point in the south Pacific Ocean west of the southern tip of South America.

The noise rises rapidly in frequency over about one minute and was of sufficient amplitude to be heard on multiple sensors, at a range of over 5,000 km. The system ruled out any known man-made origin such as a submarine or bomb, or familiar geological sounds such as volcanoes or earthquakes. While the audio profile of the bloop does resemble that of a living creature, the system identified it as unknown because it was far too loud for that to have been the case: it was several times louder than the loudest known biological sound. If it was biological, it would have to be produced by an animal far larger than any currently known to science.

More of Wain’s Kaleideoscope Cats

Geoff — Sun, 18 Apr 2010 17:47:22 +0000

One of my most popular posts continues to be Wain’s Kaleidoscope Cats, illustrating the strange transition of Louis Wain. A popular artist in England in the late 1800s and early 1900s, he drew thousands of pictures of cats engaged in everyday activities which were widely published. He was eventually committed to a mental hospital after displaying schizophrenic symptoms. From Wikipedia:

“He had always been considered quite charming but odd, and often had difficulty in distinguishing between fact and fantasy. His behavior and personality changed, and he began to suffer from delusions with the onset of schizophrenia. Whereas he had been a mild-mannered and trusting man, he became hostile and suspicious, particularly towards his sisters. He claimed that the flickering of the cinema screen had robbed the electricity from their brains.

When his sisters could no longer cope with his erratic and occasionally violent behavior, he was finally committed in 1924 to a pauper ward of Springfield Mental Hospital in Tooting. A year later, he was discovered there and his circumstances were widely publicized, leading to appeals from such figures as H. G. Wells and the personal intervention of the Prime Minister. Wain was eventually transferred to Napsbury Hospital north of London. This hospital was relatively pleasant, with a garden and colony of cats, and he spent his final 15 years there in peace. While he became increasingly deluded, his erratic mood swings subsided, and he continued drawing for pleasure.

Some speculate that the onset of Wain’s schizophrenia was precipitated by toxoplasmosis, a parasitic infection that can be contracted from cats.”

Large rotated block lettering: “Oh!!! I have no feelings for others, it is all inside.”
Smaller block lettering: “I am a bit gone on myself and have to make it up with my feelings.”
Corner mirrored cursive script: “Who I met someone I have just met. I am his card now, but I want to part with it.”

Monday Miscellany

Geoff — Mon, 29 Mar 2010 20:05:31 +0000

A few little things for Monday. I made a new video using the same engine as the fish school simulation described in the post In This Virtual Fish Tank, You Make the Rules.

This video shows 5000 fish swimming while the weightings of the three behavioural rules vary using sinusoidal functions. I love the “borders” created as large fish schools collide, and fish attempt to escape along the plane of intersection.

Triumph of the Golden Rule was also linked to as recommended reading for MIT course 6.033 Computer Systems Engineering – one of the best compliments I’ve received. Thanks Evan!

In This Virtual Fish Tank, You Make the Rules

Geoff — Tue, 23 Mar 2010 17:12:27 +0000

In my last post, I discussed how individuals following simple rules cause cause coordinated group behavior to arise. The boid model created by Craig Reynolds used three rules – alignment, separation, and coherence. But how much attention does each individual pay to each rule? In situations like migration, alignment might be the most important rule. If you’re being attacked by predators, sticking together and paying attention to the coherence rule might keep you from being eaten.

Clearly different situations might have different approaches. I was very interested in how different weightings of these rules might behave, so I decided to create a program that would allow you to change the relative importance of each rule at will. You can see a video of it in action below (the three sliders on the bottom left control the influence of the various rules).

Smaller screen, older computer, or just want something more simple? Load the standard definition fish school simulation.	Big screen, fast computer, and want to give the fish some more room to swim? Load the high definition fish school simulation.

	Alignment: This slider adjusts how much each fish wants to head in the same direction as other fish around it.
	Cohesion: This slider adjusts how close each fish wants to be to its neighbors.
	Separation: This slider adjust how much each fish wants to space itself out from the others.
	Click anywhere in the water to add a new fish.
	Press this button to reset the simulation.

I hope you enjoy it – please leave me a comment if you have any questions, comments, or find any bugs.

Herds of Android Birds Mimic Ad Hoc Flocks

Geoff — Thu, 18 Mar 2010 09:00:33 +0000

In winter during the late afternoon before settling down to roost, flocks of thousands of starlings will twist and turn, turning the sky black with strange curves that seem to move with a mind of their own. The flocks of up to a million strong form for warmth, for security, and for social contact. The video below shows a small group of 80,000 starlings. If you’re the impatient type, skip ahead to 1:15 to see some of the most impressive forms and transitions.

These seething clouds of birds have no leader, no planning, and yet produce a dance that seems choreographed in its precision and beauty. So how do they do it? Some strange ability given to them, a unique skill among the animal kingdom? Well, perhaps not quite. Consider that humans seem to be able to move in crowds with the same ease, although some might say with a bit less beauty.

People seem to move in clumps, in the same direction, and manage to not trample each other or collide. There seem to be parallels in crowds of organisms, that this order emerges consistently and that somehow each animal “knows” what to do on a small scale, resulting in cohesive and sensible group movement. The question then becomes – what exactly are we doing unconsciously to organize like this?

The Boid Model

In 1986 Craig Reynolds produced a computer model describing how large groups of animals such as schools, herds, and flocks could be able to move in unison with no central coordination. He called his creations “boids”, and imagined that each would follow some simple, sensible rules to navigate around. He also knew a single animal would never be able to keep track of every other animal in the group, and assumed that they would only pay attention to their immediate neighbors in the flock.

So if you were a boid, what rules would you follow?

Alignment: Look around you. Where is everyone else going? Probably a good idea to go there too. Alignment is a rule that finds the average direction your neighbours are going, and tells you to go there too.
Cohesion:Predators look to pick off stragglers on the edge of the pack. Cohesion is a rule that finds the average position of your neighbors and tells you to go there, pulling you into the relative safety of the center of the pack.
Separation: When crowds get big, they can get dangerous. Animals can trample each other, and birds can collide. Separation is a rule that tells you to make sure to give your neighbors some space.

How do we know how to do this? Well, the tautological answer is that it simply works. The beauty of these rules is that each of them is amazingly simple, and seem to make sense to us on an intuitive level. We tend to go with the crowd, stick together, and still try to give everyone a bit of personal space. But are these rules enough to produce the complex dance of the starlings, or are we missing some detail?

A Boid Dance

It turns out these simple rules produce patterns of movement that are anything but.

We can see that it looks flowing and wonderfully organic – but it’s not quite the same as the starling flocks. We can play with the boid model, tuning its various parameters to see how the resulting crowds might react.

A school of fish trying to avoid predators might be modeled best by weighting the cohesiveness rule very heavily, attempting to keep together at all costs while not worrying too much about personal space or where precisely they’re heading as long as it’s away from what’s trying to eat you.
A flock of geese flying south for the winter will focus on heading in a certain direction (alignment), then space themselves out to ensure they can see in front of themselves (seperation) while staying close enough and on the same plane to experience the aerodynamic benefits of flying in a group (cohesion) producing the “flying V” we see so often in fall.
Migrating animals are primarily concerned with making sure they’re going in the same direction as everyone else (alignment) while ensuring that no one is trampled (seperation) and that young and weak animals are protected in the center of the herd (cohesion). For instance, the wildebeest stampede that killed Simba’s father in the Lion King was generated using the same theory as the boid model.

This simple model has a wide range of possible applications, and a huge amount of flexibility allowing it to produce a wide range of behavioural simulations. This gorgeous installation of light graffiti uses the rules we’ve just discussed to create hypnotizing patterns of artificial creatures.

The boid model has been used to animate realistic looking behavior over a huge range of media. If you’ve seen a computer generated crowd moving in a vaguely sensible manner anywhere, it likely uses the same basic theory. The power of the model comes from its construction, assuming simple behaviors competing for influence that result in a complex outcome not unlike our own consciousness or political systems. Not too shabby for a research project from over 20 years ago.

The Golden Rule in the Wild

Geoff — Fri, 05 Mar 2010 10:00:14 +0000

In the previous post, we discussed the Prisoner’s Dilemma and saw how a simple strategy called Tit-for-Tat enforced the Golden Rule and won a very interesting contest. But does Tit-for-Tat always come out on top? The most confounding thing about the strategy is that it can never win – at best, it can only tie other strategies. Its success came from avoiding the bloody battles that other more deceptive strategies suffered.

The major criticism of Axelrod’s contest is its artificiality. In real life, some may say, you don’t get to encounter everyone, interact with them, and then have a tally run at the end to determine just how you did. Perhaps more deceptive strategies would do better in a more “natural” environment where losing doesn’t mean you get another chance at another opponent, but that your failures cause you to simply die off.

Artificial Nature

So now let’s look at the same game, with the same scoring system, only this time there’s a twist. Assume that this contest takes place in some sort of ecosystem that can only support a certain number of organisms, and they must fight among each other for the right to reproduce. There will be many different organisms, and they will all be members of a certain species, or specific strategy. We can then construct an artificial world where these strategies can battle it out in a manner that seems to reflect the real world a bit better.

In order to determine supremacy, we’ll play a certain number of rounds of the game, called a generation. At the end of the generation, the scores are tallied for each strategy, and a new generation of strategies is produced – with a twist. Higher scoring strategies will produce more organisms representing them in the next generation, while lower scoring strategies will produce less. Repeat this for many generations, observe the trends, and we can see how these strategies do as part of a population that can grow and shrink, rather than a single strategy that lives forever.

So let’s look at an example. Suppose we have a population that consists of the following simple strategies:

Initial Population	Strategy	Description
60%	ALL-C	Honest to a fault, this strategy always cooperates.
20%	RAND	The lucky dunce, this strategy defects or cooperates at random.
10%	Tit-for-Tat	This strategy mimics the previous move of the other player, every time.
10%	ALL-D	The bad boy of the bunch, this strategy always defects.

So what will happen? Was Tit-for-Tat’s dominance a result of the structure of the contest, or is it hardier than some might think? A graph of the changing populations over 50 generations may be seen below.

It’s a hard world to start. ALL-C immediately starts being decimated by the deception of ALL-D and RAND who start surging ahead, while Tit-for-Tat barely hangs on. ALL-D’s relentless deception allows it to quickly take the lead, and it starts knocking off its former partner in crime, RAND. Tit-for-Tat remains on the ropes, barely keeping its population around 10% as ALL-C and RAND are quickly eliminated around it.

And then something very interesting happens. ALL-D runs out of easy targets, and turns to the only opponents left – Tit-for-Tat and itself. Tit-for-Tat begins a slow climb as ALL-D begins to eat itself fighting over scraps. Slowly, steadily, Tit-for-Tat maintains its numbers by simply getting along with itself while allowing ALL-D to destroy each other. By 25 generations it’s all over – the easy resources exhausted, ALL-D was unable to adapt to the new environment and Tit-for-Tat takes over.

This illustrates a very important concept – that of an evolutionarily stable strategy. ALL-D was well on its way to winning, but left itself open to invasion by constant infighting. ALL-C initially had the highest population but was quickly eaten away by more deceptive strategies. Tit-for-Tat on the other hand was able to get along with itself, and defended itself against outside invaders that did not cooperate in turn. An evolutionarily stable strategy is something that can persist in this manner – once a critical mass of players start following it, it cannot be easily invaded or exploited by other strategies, including itself.

I Can’t Hear You

But there’s one critical weakness to Tit-for-Tat. We’re all aware of feuds that have gone on for ages, both sides viciously attacking the other in retaliation for the last affront, neither one precisely able to tell outsiders when it all started. And if we look at the strategies each use in a simplistic sense, it seems that they’re using Tit-for-Tat precisely. So how did it go so horribly wrong?

It went wrong because Tit-for-Tat has a horrible weakness – its memory is only one move long. If two Tit-for-Tat strategies somehow get stuck in a death spiral of defecting against each other, there’s no allowance in the strategy to realize this foolishness, and be the first to forgive. But how could this happen? Tit-for-Tat is never the first to defect after all, so why are both Tit-for-Tat strategies continually defecting?

The answer is that great force of nature, noise. A message read the wrong way, a shout misheard over the wind, an error in interpretation – all can be the impetus for this first initial defection. No matter that it was pointless and incorrect, the strategy has changed. While Tit-for-Tat’s greatest strength is that it never defects first, its greatest weakness is that it never forgives first either.

All of these simulations we’ve seen so far do not include noise, and it can have a catastrophic effect on the effectiveness of Tit-for-Tat. Its success was built on the strategy of never fighting among itself and allowing other deceptive strategies to destroy themselves by doing the same – but with noise, this advantage becomes a fatal weakness as Tit-for-Tat’s inability to be taken advantage of is turned against itself.

So what does a simulation including noise look like? You can see one below, and it contains an additional mystery strategy, Pavlov. Pavlov is very similar to Tit-for-Tat but slightly different – it forgives far more easily.

We see a similar pattern to our previous simulation. ALL-D has an initial population spike as it knocks off the easy targets, but Tit-for-Tat and Pavlov slowly climb to supremacy with ALL-D eventually eating scraps. But the influence of noise causes Tit-for-Tat to fight among itself, and Pavlov begins what previously seemed impossible – to begin to win against Tit-for-Tat.

Puppy Love

So what is Pavlov and why does it work better in a noisy environment like the real world? Well, Ivan Pavlov was the man who discovered classical conditioning. You probably remember him as the guy who fed dogs while ringing a bell, and who then just rang the bell – and discovered that the dogs salivated expecting food.

The strategy is simple – if you win, keep doing it. If you lose, change your approach. Pavlov will always cooperate with ALL-C and Tit-for-Tat. If it plays ALL-D however, it will hopefully cooperate, lose, get angry about it and defect, lose again, switch back to cooperation, and so on. Like a tiny puppy or the suitor of a crazy girlfriend, it can’t really decide what it wants to do, but it’s going to do it’s damndest to try to succeed anyways. It manages to prevent the death spiral of two Tit-for-Tat strategies continually misunderstanding each other by obeying a very simple rule – if it hurts, stop doing it. While it may be slightly more vulnerable to deceptive strategies, it never gets stuck in these self-destructive loops of behavior.

So there’s a lesson here – life is noisy, and people will never get everything correct all the time. Tit-for-Tat works very well for a wide variety of situations, but has a critical weakness where neither player in a conflict is willing or able to forgive. So the next time you’re in a situation like that, step back, use your head, and switch strategies – it’s what this little puppy would want you to do, anyways.