On a Scale of 1 to 10, Do You Like Bananas?

What kind of question is that, you may wonder.  Either you like bananas or you don't.  If the question is how much you like bananas on a scale of one to ten, that makes some sense, but a yes or no question can't be answered on a scale (unless it is a scale of zero to one).  You either don't or you do.  A scale of one to ten does not measure "yes or no" matters, it measures how much.  So what is the point of this exercise?

The point is that there are two ways at looking at information such as your fondness for bananas.  The first is to simply determine whether you like them or not and the second is to rank them on a scale.  Each method has its own shortcomings and they will, unsurprisingly, both figure in to our discussion of perception and thought.

Let's begin with the scale of one to ten.  We all know it and have used it before.  But what does it really mean?  "How much do you like bananas on a scale of 1 to 10?"  We all accept that 1 means the least amount of love we could feel for bananas and ten the most, but what would it mean to love bananas so much you rank them a 10.  Does it mean you really enjoy bananas?  Does it mean it is among your favorite foods (holding the same rank as all your other "love to the power of ten" foods)?   Could it mean you are obsessed with bananas?    I mean, it stands to reason that no one could like bananas to the power of 11 -- the scale does not go that high.  So if you say you like bananas to the power of 10 and someone else likes bananas more than you, how much does he like bananas?  Would someone who ranked bananas a perfect 10 want to make toys out of them or build their home out of bananas or think of a way to get to work on banana power?  I mean, after all, ten is supposed to be the most you can love bananas, so what does it mean?  Are we talking about just the flavor or are we considering everything that it means to enjoy bananas.  Is the price of the fruit, its availability, its shelf life, its nutritional value, and its cache as a food you could order in a restaurant all figured into the concept of what we mean when we rank how much we "like" bananas?  We'll come back to this.

But let's consider the equally hard question, "Do you like bananas?"  It demands a yes or no answer.  Presumably I either like them or I dislike them.  It is an easy thing to answer if I hate bananas or I love them.  But what if I am kind of indifferent to them?   I mean, let's say I generally like fruit but they are not my favorite fruit.   Let's assume that at a buffet of many options they would not be my first choice but they would not be my last.  What if they fall somewhere in the middle?  Can I say I like them?   And we don't know anything about how hungry I am.  If I am sitting down to Thanksgiving dinner, I may not be craving a banana.  But if I am a castaway on an island with some smart guy, a farm girl, a movie star, a billionaire and his wife, I may be perfectly psyched to have a banana to eat.  Do I like bananas?  That can be a complicated question.

Besides the problematic nature of these banana questions, there is another feature we will want to examine.  That is precisely that the yes or no option is what we can characterize as "digital data" while the other is best characterized as "analog".   Digital data breaks down everything into yes or no questions that can be answered by a single switch (or scale of zero to one).  The switch is either "off" (I don't like bananas) or "on" (I do).  Analog answers everything on a scale.

But to be clear, it is best not to think of analog as a scale of integers from one to ten, but rather a smooth continuum.   Instead of a scale of 1-10 it is more like you have a glass that is nine inches tall and can pour water into it.  (We use 0-9 instead of 1-10 because the glass may in fact contain no water.)  The water we pour in may be 3 inches high, or eight, or it can be just ever so slightly more than 6 and three quarters, something that if we measured to precision might be 6.768349 inches of water.  It can, in the end, be zero or nine or an infinite number of values in between.  In fact the best example of analog would have been to not provide a scale of numbers at all and simply ask someone to "describe how much you like bananas".

The capacity of analog for subtlety is its strength.  It is also its weakness.

Things in nature tend to be analog.  The breeze does not blow in finite increments but along a continuum of movement.  This is fine in that it allows natural forces to combine in an infinite variety of ways, but it is more troublesome if we are trying to measure something.  When we want to get around to assigning numbers to a thing so we can size it up, we end up drawing arbitrary lines that say more about how we number things than it does what we are trying to measure.

Electronic circuits can handle analog values pretty well, because current is intrinsically analog in nature.  We measure current in amperes, but that does not stop real current from flowing in whatever amount it chooses.  Amperes are the "inch marks" we assign, but like water in the glass, the actual current may be flowing in any value between two amps that it chooses.

On the other hand, logic circuits -- like the ones that do the thinking for computers -- require digital precision.  Since they are made up of a series of switches (or relays), these switches are in only one of two states at any time -- on or off.  There is no room for equivocation in a logic circuit.  Either you like bananas or you don't.

I Robot

It is often said that computers are digital and our brains are analog.  But that is really an oversimplification.  To begin with, computers run on electrical current and we have already established that current is analog.  True, this current is used to drive logical circuitry that makes all of its decisions and stores all of its data using 1's and 0's (on and off switches).  But the current that drives the device starts off as analog and must be coerced into behaving digitally.

In the same way, it is true that our brains seem to be able to manage a full spectrum of subtlety between the yes and no of a question.  But our actual neurons fire digitally.  That is, they either fire or they do not.  Yes the electrochemical process in the brain, like the current in computer, is an analog process.  But there can only be two states for a given synapse.  It either fires or it doesn't.

This mixture of digital and analog in computers and our brains will be worth coming back to when we look at how we make decisions and how our mind communicates with our body.

Wheel of Fortune, The Mill Pond, Black Swans and Entropy

That's not just a whacky title.  All those things are related in a pretty simple way that will help us unlock some insights about information and why Black Swans are so transformative.

Let's start with the gameshow Wheel of Fortune.  The puzzle is solved by filling letters into the blanks.  As the puzzle gets more filled in the puzzle gets easier to solve.  Take this puzzle for example:


Historical Figure

_ _ _ _ _ _    _ _ _ _ _ _ _ _ _ _

Do you know who it is?

Maybe this will help.  I'll give you a 't':


_ _ _ _ _ _    _ _ _ _ _ _ _ T _ _

Know it yet?

How about if we buy a vowel.  An 'e':

_ E _ _ _ E    _ _ _ _ _ _ _ T _ _ 

Maybe take an 'r'"

_ E _ R _ E    _ _ _ _ _ _ _ T _ _ 

Still nothing?  The most common selection of consonants on "wheel" can be remembered by the word "Translate" or in other words:  TRNSL, so let's go ahead and add the 'n':

_ E _ R _ E    _ _ _ _ _ N _ T _ N

and the 's':

_ E _ R _ E    _ _ S _ _ N _ T _ N


If you are a good player, you probably got this long ago, since you know what letter combos are suggested when certain letters appear in certain places, but I'll just go ahead and throw a 'g' out there for fun:


G E _ RG E    _ _ _ _ _ N G T _ N

Ready to solve now?  Of course you are.  But wait a minute.  There are still seven blanks in the name. What does it say about these remaining letters if we do not need them in order to decode the name?  It says, according to Claude Shannon, that they do not contain as much information as the other letters do.  The fact that we know the name is "George Washington" without it being spelled out entirely has to do with how much information is carried by the letters we do have.  Once we "see where this is going" we don't need the other letters, except maybe as some sort of fail safe verification of the message.  The first few letters have done all the heavy lifting -- they have done all the work.  That is a very important phrase that we will get back to.  The first few pieces of data have done all the work.

Working at the Mill

Hey, speaking of something that does a lot of work, have you seen that waterwheel?  No seriously, the Mill Pond and Waterwheel have a place in this conversation.  Let's find out how.

We need to start with how the waterwheel at a mill works.  The basic model is that moving water causes the wheel to turn.  The shaft of the moving wheel is connected inside the mill to some machine using gears.  In a very simple example, the moving shaft turns a millstone (or grindstone) in order to crush grain into flour.  Other more complicated variants exist, but each uses the movement of the wheel to accomplish some work.

The classic example of a mill is the "overshot waterwheel" where water from above the wheel spills onto it and causes it to turn before settling in the mill pond.

So what does the actual work here?  The water does the work.  But how? By falling down on the wheel and causing it to turn.  You could make a sensible case that gravity is doing the work.  But that's part of the answer isn't it?  Work is done by the water because it starts off at a place that is higher and ends up at a place that is lower.  All we are really doing is capturing the power of the water flow, and that flow is caused by gravity.  In physics terms, the water is moving from a state of higher potential energy to a state of lower potential energy.  The energy it releases in this process is energy of motion, or kinetic energy.  So the water is all full of potential at the top, releases its energy on the way down, and comes to rest in the mill pond at a lower state of energy.  Now in the real world, unless the mill pond is at sea level, there is still a bunch of potential energy in that water -- it could flow from the mill pond into another brook and continue to move down the mountain to another water wheel and mill pond if it happened to be located there.  But all that's important for our model is to realize what takes place at this one mill.  The water starts high, drives the wheel as it moves to a lower state of energy, and comes to rest having lost some of its energy but having done work in the process.

How much work the water can do is determined by the difference between its potential energy at the start of the process and its potential energy at the end of the process.  And that is determined by how high the water starts and how low it ends up.

Entropy is the Same Thing, Only with Heat instead of Water

The concept of entropy is the same thing we see with the mill pond and water wheel.  Substances which are hot contain a lot of ability to do work, but only if they can transfer their heat to something which is cold.  This is a lot like the water starting out high (hot) and moving into something lower (cold).  The ability of heat energy to do work is measured by the temperature difference between it and the thing it is flowing into -- the same way the ability of the water to do work is measured by how far it falls from start to end.  

For a simple example, let's look at a steam engine.  The water is heated and it is turned to steam.  The expansion of the steam gas (based on how hot it is) drives a piston which turns a shaft and we are right where we were with the mill.  The shaft can be connected to anything.  The turning of the shaft is the work accomplished by the steam.  The rest of the engine is devoted to condensing the steam back to water as it cools and pumping it back to the furnace so it can be re-heated.

There are No Steam Engines in Hell

Here's the funny thing about steam engines, though.  They achieve the greatest efficiency when the steam is as hot as can be (because it expands rapidly) and it is vented to a chamber which is as cold as possible (so the steam can be quickly condensed back to water).  If the condensation chamber is at or near the boiling point of water, the steam will not condense and the engine will not work or will hardly work at all.  This would be like having a water wheel which is driven by water that was only falling an inch or two -- there would not be much chance to release any energy.   In both cases the release of energy is tied to the difference between the two energy states.  Hot water (steam) moving into cold water accomplishes a great deal more work than if the temperature difference is small.

So What Does Entropy Measure?

As you may have guessed, entropy says something about the ability of the heat energy to do work.  The higher the entropy the greater the "spent fuel".   It might be easier for us if higher entropy meant greater ability to do work, but it was not set up that way.  The tendency of a thermodynamic (heat energy) system towards greater entropy simply means that heat tends toward equilibrium, and we already know that if everything is equal not much work can be done.  Low entropy means greater differences between the heat and cold and so greater potential work.  The law of entropy suggests that the universe is gradually mixing together its cold and its hot and will someday be nothing but a big bowl of lukewarm.

Fewer Missing Letters Means Higher Entropy

So let's get back to our Wheel of Fortune game and revisit what Shannon had to say about information and entropy.  In a nutshell what he is saying is that the first piece of data in a blank puzzle has the greatest ability to do work.  In a water wheel we measured the ability to do work by the difference between the high point and the low point.  In a steam engine we measured the ability to do work by the difference between the hottest point and the coldest point.  Well in an information system, we measure potential work by the difference between the blank puzzle and the answer.  The greatest ability to do work is when we have no information at all and we need to arrive at a message.  That first letter accomplishes so much in telling us what the answer is -- far more than the last letter does.  So by the time we have the answer nearly solved:

G E _ RG E    _ _ _ _ _ N G T _ N

Each new letter does hardly any work at all.  The work is measured by the distance we still have to travel to get to the answer and frankly that difference here is not very large.  Sorry, 'o', but you are just not doing much for us right now.  We don't even need you to get the job done.  'G', on the other hand, good job.  Your work was excellent.

One Last Step

Now if we look at the message as being "reality" and information as being that data that reveals reality to us, we need to see the blank puzzle as a state of cluelessness about reality, a literal blank slate.  We only learn about the "Truth" by receiving the information that explains the world to us.  The bigger difference between our blank slate and reality, the more work each piece of information can do.  And that is why Shannon viewed the measure of information as the level of surprise contained in each new piece of data.  If the new data is a 'W' to start the second word, well that is pretty much what we expected.  That information is not doing much work.  If the answer was actually "George Dashington", however, the appearance of a 'D' would rock our world and set our previous assumption about reality on its ear.  That 'D' would be doing a hell of a lot of work.

And as you can see here, George Dashington appears in the 1940 census, so he is in some sense a "historical figure".

So now the question is, was 'D' a Black Swan?  After all who was expecting a 'D' for the beginning of the second name!

Maybe that's pushing it, but there is something interesting we can say about Black Swans in relation to this conversation.

The Black Swan Carries a Lot of Information

If, as we have said before, the "potential energy" of information has to do with the difference between the Answer ("reality") and the Puzzle as we have it filled in so far, then a Black Swan does indeed contain a great deal of potential energy.  Or viewed another way, the Black Swan carries a lot of information because the Black Swan event reveals the disconnect between what we think is possible and the world as it really is.  A Black Swan really is the moment we see the 'D' and not the 'W', only with matters far more important than a silly word game.

To cite one of our earlier examples, Columbus' voyage did not create the Western Hemisphere.  It was there the whole time.  And the difference between the world as it really was versus the world that the Europeans thought existed was huge.  Therefore there was a great deal of work that would one day be done by the information that flowed into this gap.  From an information standpoint, the work done by Columbus' journey was huge.  As Claude Shannon says, the information is the surprise carried by the data.  Well what a surprise it was to discover that there was this huge extra piece of the Earth.  It is no wonder it is treated as such a substantial event in history.  It released a great deal of information energy when it opened the spigot between the two worlds.

Now it is often rightly cited that Columbus did not "discover" the new world.  In the first place there were already people living there, thank you very much.  But even from the European perspective, he did not discover the Americas.  The first Europeans to visit the Western Hemisphere were the Vikings.  But they did not release the potential energy of the reality gap because their discovery was not shared with the rest of the world.  It is not even clear that they knew they had discovered anything at all.  For that matter, neither did Columbus at first, which is why we have the term "West Indies".  He thought he was in the Indian Ocean.  He thought the people watched him from the shore were "Indians".   But eventually they understood where they really were, and the Black Swan event released a great deal of information energy (the difference between what is and what is thought to be).

So where does this leave us?  We now know that the power or potential energy of information is determined by how much surprise it carries, and this sort of informational entropy is measured by the difference between what is expected (smooth sailing to India for example) and what actually is (such as this huge land mass in the way).   Black Swans, by dint of their being so different from what was expected, bring us a huge amount of information.  How we handle that information and put it into context, or form new context to accommodate the new information will be explored later.

Is that a Black Swan or Just a Dark Grey One?

If transformative events that can't be predicted are Black Swans, what do you call the transformative events that some folks could see coming?  The tongue in cheek term "Grey Swan" has been applied to these events, and it is meant to acknowledge that these are not true Black Swan events, but they nevertheless deliver a surprising shock to the system.

The Credit Crunch of 2008 and the Great Recession that followed is sometimes called a Black Swan by folks who misunderstand the phrase.  This may be partially because it was the first earth shattering event that took place after the publication of Nassim Taleb's book.  But Taleb himself suggests the Credit Crunch was no Black Swan.  Many folks (including Taleb) saw the danger building in the financial system and had been warning about it for years.  It may have been a devastating and rare event, but it was not really out of the blue.

Still, when determining what qualifies as a Black Swan, we may run into problems, especially as technology gets increasingly sophisticated and communication gets increasingly powerful.  We already said that just because one nut-job fantasized about some event does not disqualify it from being a Black Swan because it would still be an inconceivable surprise to most people.  But what of the increasing reach of hypotheticals in our lives?  Could our increasing understanding of all the whacky things that can take place in our lives lead to a decrease in events that we would rightly describe as "inconceivable"?

For example if a huge asteroid hit the earth in 1820 and killed millions of people, it would have undoubtedly been a Black Swan.  But what if it happened in 2020?  Can we really say that this would be an inconceivable disaster?  The fact is that scientists have been spending the last couple of decades educating us about Earth's long history of being pummeled from space.  It would seem by our modern understanding that being hit with an asteroid is a when and not an if.  Still, if the asteroid were large enough, it would result in such a devastating chain of events for our planet that it seems disingenuous to deny the event Black Swan status.

If your concern is about the well being of people on a day to day basis, the distinction is not relevant.  If it changed our lives and our assumptions about our own safety on what has till now been a very hospitable planet, the event could be among the most significant in history.  But for strict score keeping about whether it is a Black Swan or merely a dark grey one, the distinction would probably boil down to how seriously the possibility of the event was being considered.  Since we have clever folks tracking extra terrestrial objects this very moment (an international project called "Spaceguard"), mapping out which ones pose risk for potential collision, one could say this event, however devastating when it does finally occur, is not technically a Black Swan.

There is one possibility for Black Swan status associated with such an event, and that is some repercussion from the collision that was not anticipated.  If the collision had some freak side effect that scientists would not have even considered (such as reversing the rotation of the planet) then the event would certainly be a Black Swan.  But a scientifically well behaved natural disaster, however horrible, does not generally qualify as a Black Swan.

The arrival of Europeans in what is now South America would be a good example of a Black Swan, at least to the Myans, Incas, and Aztecs (and all the lesser known native peoples of the time).  It was something that they never spent any time worrying about and it completely shattered their way of life.  The European discovery of the Western Hemisphere some 40 years earlier was also a Black Swan (to the Europeans).  Since Columbus was basically an idiot, he thought he had circled the globe.  The idea that there was a land mass as large as the Americas between Spain and India was, at least to most Europeans of the time, inconceivable.

The proof by circumnavigation that the Earth was round was not, however, a Black Swan.  Even though the popular myth is that Columbus' whacky idea was that the Earth was round, in fact that idea had been well established since the 3rd century BC.  Columbus big idea was that the best trade route to India was to sail West and keep going.

[Aside: The reason I say he was an idiot was that the curvature of the Earth was provable, and most reasonable people knew the approximate size of the Earth.  Columbus contended the Earth was much smaller than people believed and that is why he was convinced that a Western route to India was practical.  Even late in life he denied the science and theorized that the Earth may be shaped like a woman's breast, smaller around the nipple than the other parts.  Seriously, this guy was nuts.]

In any case, over the course of the next few decades, his voyage did prove to be the spark of two major Black Swans, first for the Europeans and later for the indigenous people of the "New World".

And not to belabor the point, but that is how a Black Swan works.  One morning you are waking up to live your normal life and the next morning you are dying of a wound inflicted by a Spanish musket ball and a man you never dreamed existed using a weapon you had never imagined.  Black Swans are not simple surprises, they are game changers.

Grey Swans and Conspiracy Theories

We have established that any "Swan", whether black or grey, is a transformation event.  The assassination of John F Kennedy could not rightly be considered a Black Swan.  The man had Secret Service protecting him precisely because it is dangerous to be President.  Granted the security detail was quaint by today's standards, but the point is that it was not "inconceivable" that a President could be assassinated.  Three sitting Presidents had been assassinated before JFK (Lincoln, Garfield, and McKinley) with McKinley's death being just 62 years earlier.  Sixty two years is not exactly recent, but for comparison it has already been 50 years since JFK's assassination.  In 1963 McKinley was still part of living memory for many people.  So, no, the assassination of a President would not be "inconceivable".

This does not mean that it was not nearly unthinkable however.  The world had changed a great deal in the two decades since WWII and no doubt many people would have assumed that the combination of good will in a prosperous nation and modern police methods had made it highly unlikely that a President would be assassinated.  In any case it was a national shock and certainly a transformational event.  Maybe it didn't change the way each American lived his daily life, but the killing, along with those of Bobby Kennedy and Martin Luther King Jr., certainly changed society.  On the color scale, though, the event would have to be called a Grey Swan. It was simply not inconceivable enough to qualify as truly Black.

The same thing could be said for the 9/11 attacks.  They stunned many Americans.  An early phrase that was used in the first day of reporting was "A New Pearl Harbor".  It was a surprise attack which set everyone on edge and permanently changed the way Americans think.  In terms of lasting daily impact, the hoops we must now jump through to travel on a plane seems the most far reaching, but the impact on the psychology of the nation is not to be underestimated.  It may be hard to quantify beyond bureaucratic and legal responses such as the formation of the Homeland Security Department and the passage of the PATRIOT Act, but the change to America was immediate and far reaching.

Still, even though the notion of hijacked planes being flown into buildings was stunning, it was not really inconceivable.  The 9/11 attacks were quickly accepted as real things that might happen in the modern world.  So 9/11 was not really a Black Swan either. Grey, of course, but not black.

But here is an interesting feature of these and other Grey Swan events:  There are some people who reject that they took place at all, at least in the way that they are commonly described.  To these people, the so called "conspiracy theorists" there was a certain inconceivability to these events.  The events are so tragic and so hard to wrap our minds around that some folks can not accept them.  These people seek answers beyond the common explanation because the truth (or what is commonly accepted as the truth) sounds very wrong to them.  There is no debate that these events are just as transformational to conspiracy theorists as they are to the rest of the world -- in some sense they may be more transformational to them -- but there is some real difference in how willingly they are accepted at face value.

And that is a key connection between Grey Swans and conspiracy theories.  The fact of the matter is that Grey Swans create fertile ground for conspiracy theories.  I have said before that big events with large impacts create instability and a need for order and that this quest for order is what drives the narrative of conspiracy theories.  Well, we now have a framework for understanding what these "big events" are.  They are Grey Swans -- sudden events generally considered to be highly unlikely even if plausible.  The inability to accept the plausibility of such transformational events may be key to unlocking the origin of the explanatory conspiracy theory.

The Dreaded and Misunderstood Black Swan

What is a Black Swan?

Nassim Taleb wrote a NYT bestseller a number of years ago entitled, "The Black Swan, the Impact of the Highly Improbable".  It was successful for what it did -- get the concept of the Black Swan into the mainstream, but it was also unsuccessful for a number of reasons.

To begin with, the book was fairly weak.  It had a compelling central idea, but much of the book seemed to dance around the edges of that idea instead of delving more completely into it.  I spent the first few chapters wondering why he would write a book about something so obvious.  But, perhaps paradoxically, the other reason I consider his book largely unsuccessful is that the term Black Swan is now bandied about in the vernacular with scarce allegiance to it true meaning.  So it seems Taleb successfully produced a buzz-word that may actually obscure the relevance of the concept he was focused on.

Even the book description at Amazon.com is wrong:

A black swan is an event, positive or negative, that is deemed improbable yet causes massive consequences. In this groundbreaking and prophetic book, Taleb shows in a playful way that Black Swan events explain almost everything about our world, and yet we—especially the experts—are blind to them. 

That is, unfortunately how the public thinks of the "Black Swan" but it is not at all what was intended by the concept.

To appreciate what Taleb really meant, we should look at where the phrase comes from.  In Europe, all swans were white.  It was simply considered part of what it meant to be a swan.  So when European explorers discovered black swans in Australia, their minds were blown.  It was not something that was merely "deemed improbable" as the Amazon book description says.  It was not even deemed "impossible".  It was, in fact, inconceivable.  No one had ever bothered to think about the existence of black swans because everyone "knew" swans were white.

So what is the distinction here?  A Black Swan is not an event which is simply "unlikely".  It is a transformational event no one saw coming because no one conceived of it.  Big difference.

Let's work through some examples.  Suppose a guy with a nice paying job as a logistics manager for a trucking company lives just a bit beyond his means.  Then one day he loses his job due to budget cuts in his department.  This is devastating to this man and his family.  But it is not a Black Swan.  He may describe the event as being from out of the blue, and he may have even been doing a good job and have had no reason to think he would be canned.  But no one in this day and age can really say that losing his job is inconceivable.  If this man is now devastated by his lack of savings and planning for rainy days, he can not blame a Black Swan for ruining his life.

But suppose this same man lost his job because the sudden discovery of teleportation made trucking obsolete overnight.  Who could really blame the man for thinking that whatever happened to him or his company, trucking still had a few good decades left in it as an industry?  Did he consider the possibility of teleportation and conclude it was "improbable" (as the Amazon book description implies)?  No of course not.  He didn't think of teleportation at all.  And that is why it is a Black Swan event.

The rippling cascade of changes caused by the Black Swan event is also part of its character.  Let's consider another example.

It would suck to be invisible
and still need glasses

What if one day on Earth we all woke up and discovered that half of the population was completely normal and unchanged from the previous day, but the other half of the population -- for whatever reason -- could become invisible at will.  What would happen?

Well, first of all we can safely say that this is a Black Swan event because until that morning, no one was sitting around discussing invisibility with any sense of purpose.  No think tanks were considering the invisibility problem and re-assuring the public that the event was "improbable".  No, just the opposite, no one was thinking about it because it was (until it happened) simply inconceivable.

But now what happens to society?  The rules of the game have just changed.  Devious people will discover that they now have the ability to spy on others undetected.  Theft is made a whole lot easier if you can walk into the bank or warehouse unseen.  No one knows if he is alone or being watched.  Some folks seek jobs with the military as spies.  Others auction off their services for corporate espionage.  Schools the world over become breeding grounds of mischief and social stigma as no bathroom or locker room is safe from ogling or teasing.  Paparazzi celebrate.  Those who can become invisible find they must do so to combat the lack of privacy they would suffer if they did not.

In response to all the disruption, special body heat detectors made to defeat the invisibility problem will take off.   An entire industry will grow up around the idea of securing privacy and property in the new world populated by invisibles.  The source of the power of invisibility will be widely debated.  Some will ascribe it to God and tie it to the second coming of Christ.  Others will ascribe it to alien experimentation.  Still others a vast global conspiracy -- merely the latest step in the plan of the illuminati to control the world.  Whatever the source of the power, becoming invisible will quickly be made illegal by most governments.  Yet law enforcement will secretly relish the new weapon in the fight against crime -- at least old school (visible) crime.

But what will be missing?  On all the talk radio and 24 hour news devoted to this new dilemma/opportunity, there will be a dearth of those exclaiming, "I warned you this would happen!"  And why is that?  Because, seriously, invisibility?  Who on earth saw this coming?

That, my friends, is a Black Swan -- a transformation event that no one saw coming.

Look Out for Black Swans

You may want to take issue with my example, because I chose something so outrageous that we all know it is not possible.  But that again is part of the point.  The Black Swan event is something so improbable that even if one person does bring up the possibility for conjecture's sake, it is not taken seriously.  This is the source of the confusion about whether Black Swans are "deemed improbable".  But that's the point.  They are not "deemed" anything, because they are not taken seriously.  Even in the unlikely event that someone thinks of them out of sport or a twisted sense of fantasy, they are not studied.  This is not about someone saying, "I don't think it is likely that I will lose my job" but rather someone failing to consider why they may have no job to go to (because of teleportation or whatever).

Why does this distinction matter?  Whether we are talking about highly unlikely things or things out of the blue, what is the difference?  Well the difference is in how we prepare for them.

This has taken on new urgency in popular financial media in light of the supposed Black Swan of the Great Recession.  But the lesson we take away from the existence of Black Swans is wrong if we don't know what a Black Swan is.

Take for example any event we "deem improbable".  How do we plan for it?  Well, we plan for it using the event's likelihood as our guide.  If I want 100 plants but I think that the odds are that 10% won't live to harvest, I need to plant 12 extras (Out of 112 plants, 11 or so won't make it, leaving me with 101.)  If I think the likelihood of failure is 20%, I need to plant 125 (25 plants won't make it, leaving me with 100.)  In each of these cases, my wise course of action is guided by the likelihood I ascribe to the event.

Going back to our logistics manager, if he considered that there was a 5% chance he might lose his job each year, he would think he might have as many as 20 years left at his company.  Viewed another way, in 10 years, he'd have a 50-50 chance of losing his job.  So if he wanted to be prepared for that 50-50 chance, he'd want to put away X amount of money each year so that in 10 years he'd have 10X, which is presumably enough to get him through while he looked for a new job.

If we are managing risk then we are plotting our strategy based on the probabilities we assign to the risky events we are planning for.   A 100 year old building should expect to see ten 10-year floods and one 100 year flood (again, just as an example).  It is all about the odds we assign to the event.

But we have already determined that Black Swans are not something we think of as "rare" but rather something we don't think of at all.  What does that do to our calculus?  It makes it a big mess, that's what.  And that was exactly Taleb's point, especially in regards to financial markets.

Expect the Unexpected

In Taleb's configuration, you can not simply model a market strategy based on risks assigned to each event --whether interest rates will increase or whether this currency will fall versus that one -- because you are leaving yourself exposed to the real risk -- the unseen risk -- that transforms the very nature of the market.

Take for example a World Series baseball game. Let's say you wanted to place a bet on a game.  A friendly bet with a buddy.  You both determine that you will put $100 down and when you get to work the next day, the person who chose the winning team will get to keep the pot.  This seems pretty straight forward.  It is a baseball game that can not end in a tie.  There can only be two outcomes.  Either one team wins or the other one does.

But what if you made that bet with your buddy on October 17th, 1989.  The game scheduled for that night, would in fact be postponed by earthquake.  And again, just to drive the point home, when you and your buddy are making this bet, it's not like one of you says, "But what if the game is postponed by earthquake" and the other one says, "That will never happen."  You are not "deeming the event to be improbable".  You are simply failing to consider it at all.

So what does that do to your risk management?  What does it do to the probabilities you assigned to the outcomes?  You wrongly assumed that there were only two outcomes -- either the Giants would win that night or the A's would.  There could be no "tie".  But of course in retrospect there could be something even worse -- no game.

Now in this case, it is likely that you and your buddy, being gentlemen, would simply agree to extend the bet to whatever date the game was actually played.  But that was not your original agreement.  And if the matter at hand were something more than a casual bet on a baseball game, the disruption could be much more serious.

Why Worry About Something You Can't Predict?

The title of Taleb's book includes the phrase, "The impact of the highly improbable".  We need to consider this a moment.  In the first place, it should be noted that even though these events are not "deemed" to be highly improbable -- that is, no one is considering them and dismissing them because they are unlikely -- they are still, nevertheless, very rare occurrences.  Black Swans come from out of the blue but fortunately for us they don't come very often.

But when they do come, they come with such transformational power that they leave a lasting mark on our lives.  So what Taleb is talking about is how these unexpected events are transformational.

And that brings us to the question of what should we be doing about Black Swans?  Why bother even thinking about them if they are by definition surprising to us?  And the answer is that we need to consider them because they are so transformational.  Black Swans are game changers.  So when you are betting on the game, you may not be able to build in the risk of a particular Black Swan (how could you if they are unpredictable?) but you should still make your moves with the knowledge that the game could change -- even end -- at any time.

For our purposes, one of the most interesting things about Black Swans is that they are context shifting events.  One minute you are worried about who is going to win a baseball game and the next you are dealing with the aftermath of an earthquake.  Or at work you think your chief problem of the day is how you will deal with that bozo in the meeting who likes to take credit for your ideas, and then the report of alien invasion comes over the radio and you are suddenly more concerned with how you will get home and how many cans of food you happen to have in your pantry.

Taleb wrote his book not as a guide in how to plan for and deal with Black Swans, but as a cautionary tale in why we should expect our lives to be turned upside down at any moment.  Living your life like each day is more or less the same as the previous one only works for as long as that is true.  And Taleb shows that throughout history the assumption that nothing will happen to disrupt our daily lives is simply not a valid one.  The timing and nature of any given Black Swan is impossible to predict, but the fact that some disruptive and unpredictable event will happen at least once in any person's life is a near certainty.

Knowledge is What You Know, What You Don't Know, and What You Don't Know That You Don't Know

Black Swans are a natural fit for the Concept Mini Mart, because they are very closely tied to perception and  knowledge.  Donald Rumsfeld famously said before congress that there were "known knowns, known unknowns, and unknown unknowns."  Despite how confusing this was for many people he was exactly correct.

Interestingly, in his book, Taleb explains that military experts were the only class of academic who did not give him grief over his concept of Black Swans.  He explained this as being related to how good military planners do not fall in love with their theories.  If they think that a given strategy should work in theory, they may try it.  But if it does not work, common sense dictates that they should try something else.  Surely there are generals throughout history who fell prey to blind faith in their own strategy, but as a rule, military planning is a very pragmatic exercise.  If the facts on the ground are telling you something different from the theory, then go with the facts on the ground.  But there is also another reason Taleb says that military folks get Black Swans, and that is that they intuitively understand the idea of unknown unknowns.  A good general knows there are things about the enemy he can measure and has data for (known knowns, such as knowing how many troops are stationed in a certain location).  There are also things he can measure that he has no data for (known unknowns, for example how many anti-aircraft missiles they possess or where they intend to attack.)  But beyond these two kinds of knowledge, there is the third kind Rumsfeld was talking about, the unknown unknown.  In a nutshell this is the admission that there may be things which you do not know but which you do not even know you should be looking for or considering.  This is the potential surprise that all good military planners are always cognizant of.  Military strategists know that they do not have the whole picture.  They know that they may not ever get the whole picture.  And they even know that they may not understand how big the picture is to begin with.

Now certainly one could make a case for how all decent scientists should buy into this pretty undeniable fact of reality.  Godel's Incompleteness Theorem even says as much.  What is saying that there are truths which fall outside the realm of any formal system if not that there are always "unknown unknowns"?   Yet many scientists fail to take this to heart.   So when a talented physicist like Stephen Hawking talks about physics, he does it from the point of view of thinking that his science can explain everything.  It may not have yet explained everything.  There may still be "known unknowns" but it is treated as more or less just a matter of time until we get 'round to measuring everything.  Even Heisenberg's Uncertainty Principle, which we will consider in some detail later, suggests that we may not know everything, but it does so by saying what it is we do not know.  In other words, it describes the world through the lens of known knowns and known unknowns.

Can I Ever Know what I do not Know?

Accepting that there are always things which you don't know that you don't know is hard for scientists and thinkers.  Most of them enjoy what they do precisely because they like getting to the bottom of things.  They crave understanding and knowledge.  As such, they generally make poor candidates for accepting that there is a vast swath of reality that is not only unknown, but unknowable.  We will explore how this perception affects our scientific ideals (and our economy) later.

     

Maybe You are Already a Conspiracy Theorist and Don't Know it Yet

What an exciting idea for a movie.  Some guy is just going about his business feeling smug for not being so stupid as to believe that The Boston Marathon Bombing was a false flag terrorist attack, when something happens and he realizes that he has been part of a conspiracy all along.  Or maybe a woman is living a perfectly normal life, regarding the poor lost souls who believe in conspiracies with a mix of pity and contempt when she is suddenly informed that the very principles she uses to guide her own life are nothing but oversimplified conspiracy theories.

Of course, these things could never happen in real life, right?  Because there are those who grasp reality and those who let their imaginations get the best of them.  And we are the smart ones.  We always live in the real world and leave the fantasies to others.  We are so much smarter than everyone else... and proud of it.

On The Rachel Maddow Show the other night, Ms. Maddow interviewed Alice Hoagland, a woman whose son died on Flight 93, the 9/11 plane that went down in Shanksville, PA.

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The interview starts at 14:46.  Alice Hoagland uses words like "loony" to describe conspiracy theorists.  She recounts that she admonished them at one point:

You really need to consider a theory before you take it to your bosom, and, folks, you're being sold a bill of goods here.

She explains that these folks "reduce everything to theory" and

I've come to the conclusion that you really can't talk to these folks, you can't reason with them because they are so invested in the crazy story [they have gotten hold of].

And later she explains she simply thinks of them as "mental patients" because "they are off their rockers".

Well that is a stern appraisal from someone who (we hope) has a firm grasp of reality.  One could assume based on her dismissal of these crazy loons (who are so invested in their own ideas that they can not accept anything else), that Alice Hoagland is a lucid thinker in charge of her own mind.  Certainly she would never ascribe to anything so nutty as a "conspiracy theory."

Well let's think back to a few things we have said about conspiracy theories.  This is what we know:

1) To a conspiracy theorist, everything that happens is intentional.  It is part of a plan.

2) Conspiracy is linked to anxiety.  The more anxious something makes us about our place in the world, the more traction conspiracy theories will have.

3) Conspiracy Theories have an Event, Story, Reveal, Puppet Masters, and a Grand Plan.

And as we have touched upon but have not quite gotten to, the "evidence" that "proves" conspiracy in the minds of those who Ms. Hoagland calls "loonies" is usually not very straight forward.  It usually takes a lot of supposition and stretching to join the logical threads.  The lack of concrete evidence does not deter conspiracy theorists who say you must infer from the cracks in the official story.  The doubt cast in your mind by our imperfect ability to witness reality is where you must draw your assurance that conspiracy theories may be true.  We will explore this more later, but it was a critical component to touch upon now.

Because I want to examine this from a new angle.

What is one of the first things we hear when an inexplicable death occurs, especially of a child or someone in a horrible random event, like a bombing at a public spectacle?  Someone usually says it was part of "God's Plan."  The solace they offer is that we can't understand the mysteries of the world and that horrible and inexplicable and seemingly undeserved tragedies befall us in life, but we shouldn't worry, because God has a plan.


Earlier I wrote:

 It is very unnerving to live in a world where transformative (and usually horrible) events can take place without warning and for no good reason.  So a conspiracy theory seeks to provide peace of mind by showing how the seemingly random event was not random at all but was in fact part of someone’s plan. 

Ms. Hoagland herself claims that the best way she can think of to deal with conspiracy theorists is to use the "serenity prayer".

God, grant me the serenity to accept the things I cannot change,
The courage to change the things I can,
And wisdom to know the difference.

If this is true, we can assume that Ms. Hoagland is not an atheist.  Yet wasn't she just chastising these crazy people for boiling everything down to theory and, basically, not doing the math?

Mr. Universe

I want to spend a great deal of time on this so I will be coming back to it quite often.  Not because I think that if you believe in God you must be insane, but rather just the opposite.  If you can be a sane person and believe in God, then you must be very careful about the names you call others who believe things that they have no evidence to support.

And just as importantly, we need to realize that the quest for answers and order in the universe that leads us to the idea of God is part and parcel the same drive that leads conspiracy theorists to their explanations.


Remember my comment:

The Grand Plan is the explanatory bow that ties up the package into a neat orderly and self contained idea.

I was talking about conspiracy theories at the time, but couldn't I just as easily have been talking about religion?

There are those who will claim that there is a difference here.  But there is no difference, not of any significance.  Whether I believe that the government faked the 9/11 attacks in order to take away our freedoms and start a war in the Middle East or I believe that God hand selected the victims of the Sandy Hook massacre because he has a Divine Plan for how the universe unfolds, I am ascribing speculative motives to powerful forces with not a shred of evidence beyond conjecture.

Now, don't forget, I have gone to some pains in my past comments to stress that part of having an open mind means that you must accept that anything can be true, at least at first blush.   So I am not saying that there is no God and there is no Divine Plan.  But it is undoubtedly the same mental process that makes one seek order from existential chaos which produces the conspiracy theory or makes us quest for God .   Maybe there is a god pulling levers and controlling the universe.  I happen to doubt it. But I wouldn't call someone a loony for thinking so, or at least not any more of a loony than anyone else who believes conspiracy theories.  And I am suspicious of people who begrudge others their quest for order in a chaotic world.  I may find their answers a little too pat.  I may think they don't comport well with reality as I have experienced it.  But that would apply equally well to many religious people I have known as it would conspiracy theorists.  Who am I to be the arbiter of where someone seeks order and meaning?

Is a person who says that the Boston Marathon Bombings were a false flag attack more wrong than a person who claims that a rape resulting in pregnancy is God's will?  What if the person says that neither event was God's will but God had the power to stop it and did nothing (presumably because he has a plan)?  As soon as you bring your faith in God into a discussion of conspiracy theory, you have lost the intellectual high ground.

So one more time, just to summarize.  Ms. Hoagland argues that you just can't REASON with these people, and then cites the serenity prayer as her coping mechanism.  Does that really sound like reason is the guiding principle of her life?  It sounds more like her faith is what gives her strength.  Yet she belittles others for having an unshakable belief in something she disagrees with.  It may be true that they have no rational reason for believing what they do about 9/11.  But does she have a rational reason for believing in God?  Can we really expect others to believe only what is reasonable while we ourselves resort to faith to define our place in the cosmos?  Is there a map that shows us where reason applies and where faith is necessary?   Is faith just something we use when we want to believe something but can't find any evidence for it?  What does it say about your own awareness if you allow yourself to believe in things which are not logical but call others loonies for holding illogical beliefs?

I know, I am probably barking at the moon.  As Ms. Hoagland herself suggested, you just can't reason with some people.

Of Paramecia and Air-horns

Now that we have looked a little bit at how information is (or is not) converted to a signal, it may be useful to revisit the Airhorn Family  and see what they make of all this.

When the air-horn went off, it was simply a loud noise to the baby.  Babies find loud noises scary.  And the rumble of the earth from the blasting was no help either.  But it would be hard to view this information as something encoded in a language the baby could understand.  Or would it?

There must be a reason we find loud noises unsettling.  They make our heart pound and our adrenalin surge.  This can be a great thing when you are at a rock concert but is a very bad thing when you are a sleeping baby. Why would a sudden loud noises cause our heart to pound?  Where is the codebook that says what our brain is to make of this information.  To do anything with it at all, it must be a signal.  And if it is a signal, it must be encoded somehow.  So when did we all sit down and agree that loud noises should be a signal for our heart to beat faster?

To answer this question we must go way back in time and back to the very basic idea of what it means to have senses and to communicate with the outer world.

Suppose we have a single celled organism that lives in slightly salty water.  If the water gets too salty, it  dehydrates and if the water gets too fresh, it basically starves.   Now this little organism lives in salt water lagoons near the outlet of brooks and streams.  The fresh water flowing into the salt water provides the perfect salinity for it to thrive.

The cell uses tiny cilia to "swim" around in the water.  It can basically go forward in a spiral or backward in a spiral.  It would not be a stretch for us to imagine that it could develop the ability to swim back and forth between the saltier water and the fresh, constantly ensuring that the proper salinity is maintained.  Or if you prefer, take 300 of these little guys, with 100 of them always swimming toward the saltier water and 100 always swimming toward the fresh, and 100 of them spending their days swimming back and forth in the sweet spot.  Logic suggests that the 100 back and forth swimmers would find their conditions less hostile than the other two types and so would tend to reproduce more successfully than the others.  Over time, virtually the entire population of single celled swimmers would be the kind that swam away from inhospitable water.

So how would we describe this activity from a signal perspective?  Simply that the salinity of the water signaled to the cell whether it was safe to keep swimming forward or whether it should start swimming backward again.  But how is this signal encoded?  In this case, it is hardwired into the genetics of the cell.  All of the cells that didn't get the genetic memo, so to speak, died.  The ones who survived were all the ones who properly encoded salinity as a signal for how to move.

It doesn't matter whether the cell is conscious of the choices it is making.  All that matters is that, like the resistor that dutifully takes a current and impedes it, the paramecium responds to salinity in a consistent way, swimming forward for as long as the water is safe, backwards as soon as it is not.

This example could be extended quite a bit through many thousands of generations to a level of navigational sophistication that extended beyond our example, but we don't need to go any further to demonstrate the basic point.  On a very crude level, information can be converted into signals at the genetic level.

As Darwin so brilliantly pointed out, the basic method for "teaching" any gene pool how to behave is to simply kill off those who are behaving badly.  Only those who prosper will successfully reproduce (at least in large enough numbers to bother with), so over time genetic selection favors encoding that matches the environment.

Of course we all know this as "survival of the fittest", but this phrase has taken on a bastardization, especially in the social sciences.  To some the phrase means that only the grade A, prime cut members of a group survive -- that the weak ones all die horrible deaths in the big bad jungle.  But Darwin did not mean fit in this sense.  His expression was intended more as "survival of the most apt".  That is, the mechanism of evolution he described was one whereby the creatures who lived would be the ones who had properties and behaviors most suited to their environments.  To take our paramecia as an example, there may have been one really buff paramecium -- the envy of all the others and the starting QB on his high school team -- but if he had only the ability to swim toward fresh water without regard for its salinity, there will be no buff juniors running around any time soon.  His "fitness" does not matter.  His "aptness" (or aptitude) does.

So let's bring this on back to the baby human.  Is there any reason we can think of that sudden loud noises would be genetically encoded to cause a baby to cry?  Of course there is.  A sudden noise in most any natural context for most any creature we can think of would signal danger.  It could be the breaking of a branch to a bird or the sudden pounce of lion to a gazelle, but in most natural contexts, a sudden sound has a high likelihood of needing a quick response.

This means that those creatures who responded to sudden noises with a shot of adrenalin and increased heart rate for a boost of speed and strength would tend to out-live those who had a more laid back approach to sudden danger.  The fight or flight response is simply a genetic certainty.

Now, we could have easily said that the baby was predisposed to not like loud noises and that was why he cried.  But our little thought experiment has taken us beyond that.  Now we can suggest with a straight face that the baby human is genetically encoded to fire up his fight or flight response upon hearing the signal of a loud noise.  So why the crying?  Well that is the baby's response to all the built up energy.  His body just jolted him with energy.  That doesn't mean he is suddenly blessed with adult coordination and problem solving, however.  Those will come later.  For now, the jolt simply cries out for release.  The energy is burned off with a good cry.

I said previously that the baby had no context in which to place the information of the air horn and loud blast.  But that is not technically true.  His conscious brain did not have a context built yet, but on a much more basic level, the context was clear.  Loud noise signals danger.  In this case, the baby was not far off (even though the danger was not to him).  But it also explains why any loud noise, even a happy loud noise like celebratory party favors, may cause a baby to cry.  To know that a given sound is a good loud noise and not a dangerous loud noise takes context beyond the baby's capacity.

Now the cat is very much in the shoes of the baby, context-wise.  In our earlier piece we granted her some perspective she may or may not have had.  My assumption is that animals are generally smarter and more aware than we give them credit for, so I see no reason the cat couldn't learn some predictive elements about the noise -- such as that it never happened at night.  But in any case, the response was very similar to the baby's:  it fired up the cat's fight or flight response.  Again, this is because this signal was interpreted by a very deep part of the brain, encoded with ancient signals stretching back to the dawn of critters.  But the cat had the means to do something with all that adrenalin and she used it to run and hide behind the couch (seeing no obvious opponent to "fight", it was "flight" time).

When we treat information as something that becomes a signal when put into context, we realize more than ever the power and significance of what context is.  For even the baby who was still sizing up the world around him came pre-packaged with a context with which to view the world.  This would, in this case, be the context that is genetically encoded in his mind, his "instinct" for lack of a better phrase.  Only the Mother and Father had the experience and capacity to place the air-horn into a more sophisticated context. And there again, we should remember only the construction worker actually heeded the signal in its intended form.  That is, whatever else the air-horn meant or symbolized to him, when he was on the job site he took it "literally" -- as a warning that a blast was going to occur.   When the air-horn blast served to remind the construction worker's wife that he was at work nearby, it was still a signal.  But it was a signal in a context that she had created herself.  Her context was the result of her relationship to her husband and all of the significance and stress that she assigned to his job and career.  She could "hear him at work", which she found warmly reassuring.  But she was also reminded (not necessarily consciously all the time) that his job was sometimes dangerous.  She knew the air-horn could wake the baby. She knew it scared the cat.  She knew it was sometimes just an annoying distraction from what was on her mind.  The air-horn was all of these things to her.  And each of those meanings was associated with a context.  So for her perhaps more than any of the others, the information of an air-horn blast was a large number of signals.  Her mind quickly parsed each signal every time she heard the blast.  Depending on the facts of her environment (e.g. whether the baby was awake already or had just been put down to nap), her response to this signal would change.  But each time the information was received, her various contexts all played a role in deciphering the signal.

Red Means Stop

Information vs. Signals

I have talked about information a lot without ever defining it.  I have treated it as the implicit data that is present in the outside world.  The coffee is brown, it is 145 degrees, it contains 140 milligrams of caffeine, etc.  Technically the color brown is a perception, not a piece of data, but we can use it as shorthand for “this coffee reflects light in a combination of wavelengths which we call brown”.   But there are a lot of schools of thought about what is actually meant by “information”.  For example, can a message contain information if it has no meaning to the person receiving it?   It depends on who you ask and what you mean by “information”.

Claude Shannon, a pioneer (or THE pioneer) of “information theory” thought of information as nothing more or less than the surprise disorder in a stream of homogenous or predictable data, whether or not this information had any “meaning” at all.  In other words, information related to Entropy (the tendency towards disorder).

Entropy can be briefly described as the tendency of the universe to move toward lower energy states and higher disorder.  For analogy’s sake, consider two tea cups.  One is on a shelf completely intact and the other is on the floor smashed into 100 pieces.   Entropy says that it is much more likely for the tea cup on the shelf to join its shattered companion by falling off the shelf and breaking (achieving both a lower energy state and higher disorder), than it is for the broken tea cup to suddenly assemble itself and jump up on to the shelf (achieving a higher energy state and greater state of order in the process).

If Entropy is the tendency towards disorder, information conveys the breaks in an orderly state – the disorder that we can find within predictable data.  For example, a white piece of paper could be described as having very little information.  It is white.  That is all there is to it.  It is full of order and sameness.  But if it were full of random letters in a variety of colors the paper would contain a lot more information – a lot more disorder – even if the letters and colors had no symbolic significance (no meaning) to us.

This way of thinking about information arose from thinking about how to transmit data about the world (through telegraphs, telephones, television, etc.).  And seen in this way, we can kind of get what is meant in this case by “information”.  It would take very few pieces of data to describe (or transmit) our white piece of paper.  We could for example say “white paper 8.5x11 inches, blank”.   But imagine how many characters it would take for us to describe (or transmit a copy of) the paper if the paper were full of multicolored letters as we have said.  Nothing short of describing each letter and color would suffice.   This inability to compress the description of the object – the need to devote more transmission elements to accurately portraying it – means the multi-colored paper full of characters contains more “information” than the blank page (At least using this definition of information).

There is a halfway point between the blank page and the random letters.  Supposed the alphabet was repeated on the page first in Red, then Orange, then Yellow, then Green then Blue then Indigo and finally Violet.   It would be harder to describe then the blank page but easier to describe than the random letters and colors.  “White Paper, 8.5x11 inches, English Alphabet repeated, each copy in one color of the rainbow starting with Red and going in spectral order.”  There is, in this case more information than the blank page but less than the random letters and colors.  This is because the data is ordered.  The higher the degree of order, the less information it contains and the less data is required to describe or transmit it.  This is why Shannon described information as being the “surprise” in the data.  Very ordered data with few surprises contains very little “information”.  It makes no difference whether the data spell anything or stand for anything or have any significance at all.  All that matters is how they are ordered.  In short, there is no connection between information (in this sense) and meaning.

So what are we to do if we wish to discuss information in terms of meaning?  Well one handy method is to use a different word altogether.  In this case the word I will be using is “signal”.

A "signal" is any piece of information which carries symbolic meaning for its receiver.  Or, more generally so we can include non-thinking signal processors:

A signal is information which has an encoded implication in a defined context.

Consider for a minute that you are walking along in the woods in the evening.  Off in the distance you spot a church steeple.  Two lanterns hang there, burning brightly.  To you this is information, not a signal.  But if you are Paul Revere, and it is April 18^th, 1775, the light is both information AND a signal.  It means the British are sailing up the Charles River.

What takes information and turns it into a signal?  The language or code you choose to unlock its meaning.  This code need not be spoken language or written language or anything nearly so sophisticated.   The information must simply be encoded somehow.  There merely needs to be an agreement or policy that certain information STANDS FOR SOMETHING.  To every American who knows how to drive, or knows anything about traffic at all, a red traffic light is a signal to stop.  Traffic lights are signals which are so well understood by everyone that they are even referred to in some cases as “traffic signals”, or even “stop lights”.   But if you were an alien who had never seen a car and did not know anything about traffic, or even if you were simply Paul Revere pulled forward in time, you would not gather any meaning at all from the pretty colored lights hanging over the roadway.  They would still be “information” but they would not be a “signal”.

So what is the process that absorbs information and turns it into a signal which we can comprehend?  It is quite simply that -- a process for signals.  We’ll call it “signal processing”.

Signal processing takes place any time there is information which is translated into a signal.  This can apply to anything from the simplest electrical component to the most highly ordered brain.  Information is constantly being absorbed and some percentage of that information is translated into signals which carry (at least at the cognitive level) meaning.  At the lowest level of signal processing, we may still use the term “meaning” but there is no cognitive understanding taking place.  (Cognitive understanding and consciousness will, not surprisingly, be set aside for another time.)  Even if there is no understanding though, there is still a discreet action triggered by the signal, so when we say, the motion detector senses motion and that “means” it should turn on the light” we are being philosophically sloppy even while we are being mechanically precise.  The difference between a signal actually carrying meaning and merely triggering a mechanical response is a subtle one full of all kinds of conjecture and puzzles.  It is surely worth coming back to.  But for now we will simply say that a signal X “means” Y.  Two lanterns “mean” the British are coming up the river (if you know the code) and the motion in the yard “means” the light should be turned on (if you are a motion detector which has been programmed properly).

Signal Processing is Transforming Information

Let’s take two cases of signal processing side by side – a very simple one and more “high order” case.  The simple signal processor will be the modest electrical component called a resistor.  The higher order signal processor will be a celebrity’s assistant.  We can see how each of these signal processors function in similar ways and transform the information they receive.

In the case of the resistor, an electrical current comes into the base of the resistor.  The resistor provides drag or “resistance” to the current and some lesser amount of current flows out the other end.  The sole purpose of a resistor is to reduce the amount of current flowing in an electrical circuit. 

One of the duties of the celebrity assistant, on the other hand, is to read the celebrity’s mail (at least in this example).  The assistant reads all the incoming fan mail, business offers and junk mail and filters out most of it so the celebrity does not have to waste her time reading it.  Then when a particularly interesting piece of fan mail or a business offer or personal correspondence comes through the data stream, it is passed on to the celebrity for reading.   In this case, the assistant acts very much like the resistor.  He takes a heavy flow of mail and reduces it, passing on some lesser amount of letters through the other end in a fashion very similar to how a resistor reduces current.  Both components – the assistant and the resistor – are engaged in signal processing.  They take some information and transform it, passing it on in a form that is more useful to the system they are working within.

Now of course, the degree of signal processing that must take place for the assistant to do his job is much more complex than that of the resistor.  The resistor simply provides drag, but the assistant must collect, open and read all the mail. Reading the mail requires a great deal of higher brain function and higher still is the function that allows him to assess the pieces of mail for content and assign some level of priority to them so his employer will only see the important pieces.  This is actually a very long chain of complex signal processing all wrapped up into the task we call “screening the mail”.  But the basic concept is the same.  Some information comes in which is treated as a signal.  Those signals are transformed and pass out the other end as new signals which are new, more useful, filtered, or whatever characterization you want to use.

Let’s revisit the traffic light.  I am driving down the road.  I approach a light in the distance.  I see that it has turned red.  I perceive this information and it is translated into a signal in my mind. The signal says, “stop the car”.  So that signal is then translated into action – I downshift and step on the brake, bringing the car to a timely halt.

See what has happened in the course of this signal processing?  There was Information (the red light) which I put into Context (translated into a signal) and then I took Action (the signal inspired the complex motion of muscles that resulted in the braking and downshifting associated with the skill I had previously learned called “driving a car”.)   What do you suppose would happen if I was hiking through the woods and hanging from a tree was a traffic signal that displayed a red light?   Would I stop and wait for the light to change?  Not likely.  Why not?  Because signals have no meaning when they are out of context.  That is why I have spent so much time considering the role of context in information.   The information is the same as ever – a red traffic light – but the context – walking in the woods – robs the signal of any meaning.  I have no car to stop even in the unlikely event I was convinced that’s what it was telling me to do.

As a fun aside, consider that I would probably retell the story to my friends when I returned.  And I would probably use the word “disorienting” when I recounted how I spotted the traffic light hanging from a tree.  When we are met with information that implies a context but our current circumstances don’t allow us to construct that context, we are “disoriented”.  The word itself spells out how much we expect to be aligned to a certain frame of reference – a context – in our daily lives.  Seeing someone from work when we are at the grocery store can be disorienting, because we want to place that person into the context we call work, but we are not at work.  We will consider much more about the effects and implications of being disoriented another time.

So every signal, to be a signal, must be associated with a context.  It is part of the coding process for the signal itself.  So a traffic light means certain things when I am driving a car down the road.  It does not mean anything to me hanging on a tree in the woods or from the wall of a restaurant or any other place outside of the encoded context.   Suppose Paul Revere had come across two lanterns hanging from a tree in the woods.  Do you think he would have started his famous ride convinced the British were coming?  Of course not.  The lanterns meant something, but the code only applied if they were hanging in the steeple of the Old North Church.

In the real world, contexts overlap.   I know that a ringing sound coming from my phone means I am getting a call.   But the same ringing sound coming from the television does not mean I need to answer my phone.  That assumes of course that I can tell the sound is coming from my television and not my phone.  Anyone who has ever reached for his cell phone upon hearing someone on TV get a call was engaged in very complex signal processing.  The information of the sound was perceived.  The signal was interpreted within the context of the cell phone. The context of watching television was also present but was temporarily dismissed.  Until, of course, the blank screen on the phone makes it clear that no one is calling.  Then the proper context of television is applied to the information and the right action (doing nothing) is applied.

The fact that contexts can overlap and are not always clear greatly impacts the outcome of our daily signal processing.  What’s worse is that some contexts can conflict with one another.  Working at your job and needing to finish a task can compete directly with needing to leave work for a family emergency.  And this is just a very basic conflict of contexts.  Much more subtle conflicts exist constantly.  You may be interested in impressing a young woman at work and engaged in clever banter but you also know that you have a lot of work to do.  You legitimately want to be successful at each task – the work and the socializing – and the overlap of the two contexts is clear to you.  That does not make the signal processing any simpler.  The signals you receive and the things you say and do every day are the result of dozens or even hundreds of overlapping contexts.  Choosing when to get up and use the bathroom should be a basic biological action we are well equipped to perform.  But when the information that your bladder is full conflicts with the expectation of those at the meeting that you will hear what they have to say – or perhaps your own desire to watch and see what happens on screen in the movie theater – simple Information-Context-Action scripts do not unfold predictably.   Just because the process can be described in simplified terms is not meant to imply that the process is itself a simple one.

But let’s look more closely at the process of gathering information and placing it into context.

PERCEPTION

It is sometimes assumed that the act of absorbing information, commonly called “perception”, implies that information acted upon in the brain corresponds with what exists in the “real world”.   In fact, though, the act of perceiving is the first step in context formation.  Just as chewing food is the first step in digestion, perceiving information is the first stage of signal processing.  There is no such thing as solid information hitting the brain for signal processing (context formation) any more than there is whole unchewed food sitting in your stomach awaiting digestion.  In order to swallow the food it needs to be transformed into something more manageable.   So it is with information.  In order to absorb information, it needs to be transformed on the spot by our sensory organs into something our minds can “swallow”.

Sometimes this transformation of information can be problematic.  If you have ever jumped at a shadow you know what I mean.  The eyes did not see a shadow, dutifully report to the mind that it was a shadow and leave the mind to decide “yes, but it is a scary shadow. I should jump.”  On the contrary, your eyes passed along something that was NOT a shadow but something solid and moving and very near you.  You responded not to a shadow but to what you were told the shadow was.  Once you discovered the shadow was a shadow, you knew your response was out of proportion.  Once your eyes corrected their mistake, you could respond more normally.

But hold on here.  Aren’t the light waves just light waves?  Isn’t all the information contained in the lightwaves simply passed on through the optic nerve?  Isn’t it the brain’s fault if something is misinterpreted?

This could easily break down into semantics, but there is no logical reason it should.  If you think of “seeing” as including all the sensory elements involved in collecting visual information, the “seeing” isn’t done until the light waves have been transformed into the image that the brain can work with – just like the food isn’t swallowed until it has been chewed.   So whatever mental processing takes place to interpret the form and its position in external space is rightly categorized as part of the perception process.  When I said that perception is this first step in context formation this is what I meant.   You haven’t perceived an image until your mind has been told what that image is (not what it "represents", but what it is made out to be – a solid branch on a tree bouncing in the wind for example).  The recognition that the branch is a branch is part of the act of seeing and is part of the perception process and, as stated, the first step of context formation.  So if the branch is really a shadow but your mind is told that it is a branch, the information processing performed will be tainted by the mistake your eyes have made.  Your reaction to the branch might be perfectly normal (you may duck).  Only the fact that it is a shadow and not a branch makes your behavior at odds with reality.  But you still reacted appropriately to the information you were given.  You were just given bad intel, that’s all.

Why does this matter?  What is the benefit of breaking out these processes in such a way?  Well simply put, this model will help us understand any number of seemingly unwarranted reactions as actually very normal and appropriate reactions that have been placed in the wrong context.  If we want to look at signal processing, we need to be clear how the basic machine works in order to diagnose its many malfunctions.  So perception should be seen as that initial stage of information absorption.  But it must also be viewed as the very first step in the process of context building.

What is seeing really?  Can we declare that there is a dividing line in the brain that really separates vision from thinking?  As usual, our answer is yes and no.  Consider a coastline on the sea.  We can tell from a distance that there is ocean and there is land.  The distinction is not a controversial one.  Some creatures living in the ocean can not live on land and some creatures living on land can not live in the sea, so there surely must be a difference.  But if we walk along the beach, can we say with any certainty where the ocean ends and the land begins?  With the ocean to our left and dry land to our right we can point in either direction and say, “that is sea” and “that is land”.  But when we look down we see the waves crashing at our feet.  Advancing water swells and retreats, sometimes leaving little pools of water behind.    Where does the sea start and the land end?

This problem is very similar to the types of challenges we face in drawing boundaries in the mind.  There is always a grey area about which function or process falls where.  But just as with the land/sea dilemma this does not mean the two regions do not exist separately.  It only means we can’t always tell where the edges are.  Of course, this is the same problem we had with truth and falseness.  And the same advice applies.  Just because the border is grey does not mean they aren’t real and separate things.

It is not trivial to realize that we face the exact same quandary when trying to draw a line between the “in here” and the “out there”, that is, our “selves” and our “environment”.  We exist in the world, we are part of it, but we are also separate from it.  There is a vast cosmos of internal space that is my mind which I can not share with the outside world.  And there is a vast world of things and people out there which function every day without my knowledge.  (Consider for example the number of people on the planet who are at this very moment waking up from a night’s sleep.   I do not know them, I can’t count them, and I can’t imagine them all as individuals. Yet they are real people living their very real lives, completely separate from my own human experience.)

So the universe, whether mine or yours, contains an out-there and an in-here.  There is no doubt about the distinction.  But that does not mean that drawing the line between the two regions is any easier than determining where the land becomes the sea.   One thing we can say with some confidence, however, is that our perceptual systems occupy the sandy beach separating the inner mind from the outer world.