Occam’s Razor

What the heck is Occam’s Razor?

Is it another marvel from Gillette?  Have they managed to pack 7 blades into a razor cartridge now?  (And we all thought they’d stop at 3!)

Is it something like a Ninja star?

Is it a constellation somewhere between Orion’s Belt and Cassiopeia’s Chair?

Is it that 13th Zodiac sign that will line up with the center of the universe and signal the end of a cycle in the Mayan calendar?

 

If you selected none of the above, you are correct.  It is just a more mathematical way of describing the K.I.S.S. principle.

KISS = Keep It Simple, Stupid!

 

Wikipedia has a lengthy entry on Occam.   http://en.wikipedia.org/wiki/Occam’s_razor

This entry states:

Occam’s Razor is attributed to the 14th-century English logician, theologian and Franciscan friar Father William of Ockham who wrote “entities must not be multiplied beyond necessity” (entia non sunt multiplicanda praeter necessitatem). This is also phrased as pluralitas non est ponenda sine necessitate (“plurality should not be posited without necessity”).

 

There are two invaluable uses for Occam’s Razor:

A)     when analyzing something that has already happened; troubleshooting for example.

and

B)  when planning something.

 

The planning scenario and the analyzing scenario make use of the same principle, but in opposite directions.  One looks forward to the future, the other looks back.  When planning, the simplest plan is the one with the greatest chance of success.  When analyzing an outcome, the simplest explanation of the events is almost always the correct one.

 

How does this work?  It’s just a game of probability, really.  Let’s look at the two cases more closely.

 

A)  Analyzing / Looking back:

Applying Occam’s Razor in the reverse direction tells us that the simplest explanation for an event is usually the correct one.  This is why you can quickly throw out most conspiracy theories.  They may be intellectually intriguing and may be entertaining on the silver screen, but the implementation of plans with such great complexity is a totally different story.  Forget about the monumental task of recruiting skilled people who have no day jobs, no families, and no hobbies.  We are only considering the complexity of the plan here!  Such plans are orders of magnitude too complex to work other than in Hollywood films.  The probability of success of the typical conspiracy which plays out in in such theories is not just half that of boring, conventional explanations, it is hundreds or even thousands of times less!

Dispelling conspiracy theories is not the goal of this blog entry, so I won’t delve into any specific example, I’ll just drive the point home with a broad generalization.   No self-respecting conspiracy theory is complete until it involves some kind of COVER UP, right?   Now just step back, zoom out, and pick that one a part for a minute.  Let’s say you’re plotting a conspiracy.  You need 100 other people to carry it out.  All of these people need to stay quiet about it.  You are 99% sure that each of your co-conspirators will not spill the beans.  99% looks like a nice, safe number, but in reality, that plan has a more than a 63% chance of failing.  And if you are only 95% sure about each of the 100 in this fellowship of the thing… you’re totally hosed.  The probability of failure is over 99%.

 

B)  Planning / Looking forward

Let’s say you want to plan an event or create a strategy.  You want to do this because it is your goal to achieve a certain result and you are confident that this result will not simply happen on its own.  That is because Newton’s Law applies to life as well.  Projects at rest remain at rest.  You expect that when you execute the plan, you will get your desired result.  The plan is a sequence of events, all of which must be executed successfully in order for the desired result to occur.  They are links in a chain.  If one link breaks, the chain no longer connects the driving force with the object.

So how can you make a successful plan?

Well, ask yourself how would you make a successful chain?

  1. Use as few links as possible.    A chain with 10 links has 10 things in it which can fail.  A chain with 2 links has only 2 things which can fail.
  2. Use strong links.  A strong link has a low probability of failure.

 

The number of links in the chain is analogous to the number of steps in the plan.  The strength of an individual link is the probability of success of each step in the plan.  Using 2 chains would probability of success by building redundancy into the system.

Here is an example.  Let’s say you live in New Jersey and have an important appointment in the Chrysler Building in Manhattan at 14:00 on the last Saturday before Christmas.  Missing this appointment is not an option.  Being late is even worse.   Normally, you would just drive in early, meet a friend  for breakfast at your favorite diner, and then take care of some shopping.  But, this Saturday is different.  Your child has basketball practice until noon.  Your wife still has her driver’s license, but just barely.  Thanks to her last speeding ticket, she must complete a driver’s safety course.  This course runs on Saturday mornings.  The course lets out in time for her to play taxi driver for the little basketball star, but that makes you the lunch cook and means she cannot play taxi driver to get you to the train station.  Mix all that together and it means you cannot get an early start.  You must make lunch, scarf it down, kiss everybody goodbye and hit the road.  You give yourself a start time of 12:30.  That gives you just 90 minutes to get from your wonderful adventures-in-wreath-making door to the art deco door of the Chrysler Building.

So, you begin evaluating your options:

A)  Drive.


B)  Express Bus –> Taxi

  1. Drive to a bus station
  2. Ride in an express bus in to Manhattan
  3. Take a taxi to the Chrysler Building


C) Train  –> Taxi

  1. Drive to a train station
  2. Ride a train to Secaucus Junction
  3. Transfer to another train and take that in to Penn Station in Manhattan
  4. Take a taxi to the Chrysler Building

 

Which one is the right choice?

Well, if you look at it in terms of simplicity and simplicity alone, then A is the best choice and C is the worst.  There is only 1 link in the chain in PLAN A and 4 links in PLAN C.  But your goal is to get there on time, so it’s not enough to look only at the number of steps.  You have to consider the strength of each link as well.  If the probability of success for each plan were equal, then you’d have to pick PLAN A because it is the simplest.  You do not have to remember  bus numbers or track numbers or departure times.  You do not have the risk of not flagging a taxi in time.  It’s a no brainer.  But, in this case, all the links have different strengths.  Alas… you’ll need your brain this morning.

So now you must evaluate the probability of success of each step.

PLAN A is simple.  There is only 1 step.  Thus the probability of that step is the probability of the plan.  You start to take inventory of all your trips in to Manhattan over the past years.  How many times have you made it in under one hour?   Not many.

How many times have you given yourself 1 hour and it has taken 1 ½ hours?   Many!

How many times has it taken nearly 2 hours?  Not many, but it has happened.

Then you remember that it is the last Saturday before Christmas.  It is going to be a ZOO!  All things considered, you have to give PLAN A only a 50% probability of success.

 

What about PLAN B?

There are 3 links in the chain.  You give each step the following probabilities:

  1. Drive to the bus station:                99%
  2. Express bus in to Manhattan:      60%
  3. Taxi to the Chrysler Building:       90%

 

Usually the express bus is pretty good.  These buses can take the express lanes and can zip right through tolls.  But, slow traffic can still affect them AND they will not be able to avoid the impending zoo.  So, you rate it only slightly higher than the car trip.  Taxis are usually not a problem to find, but you have to account for the possibility of getting a guy on his first day as a taxi driver.  So, that’s not a sure fire thing either.

That looks pretty good, right?  Two steps are over 90% and one is over 50%.  And… one of them is even a 99!  That’s almost 100!

Don’t pop the champagne yet.  Remember that these steps run serially.  All of them have to go right or the plan fails.  That means you have to multiply the probabilities of success to arrive at the probability of the plan.

Altogether, the probability of PLAN B is = 0.99 x 0.6 x 0.9 = 53.5%

Hmmm…  That doesn’t give you that warm, fuzzy feeling so…

…on to PLAN C:

There are 4 links in this chain and you give each link the following probability:

  1. Drive to the train station:           99%
  2. Train to Secaucus Junction:    98%
  3. Another train to Penn Station:  95%
  4. Taxi to the Chrysler Building:   90%

 

Altogether, the probability of PLAN B is = 0.99 x 0..98 x 0.95 x 0.9 = 83%

Now that looks better!

Then you remember some blog you read about shaving or something where the bloke made a pretty good case for keeping things as simple as possible.  So you think of a way to take steps out of the plan.  Perhaps there is a direct train to downtown?  You check NJ Transit online and find out that if you drive to a station on a direct line, you can get a direct train to Penn Station.  Now you have PLAN D which looks like this:

  1. Drive to a different train station:     99%
  2. Direct train to Penn Station:            95%
  3. Taxi to the Chrysler Building           90%

 

Probabilities of each of the steps are the same, but because you have 1 step fewer, the overall probability does up to 85%.  That’s the answer.  Pick the simpler one.

 

What about redundancy?

Having a clone would be handy.  That would certainly increase your chances of success.  The technology is not quite there yet, though.  Luckily, in this case, there are some possibilities for redundancy which do not involve clones.  While in Manhattan, if you can’t find a taxi, you can take the subway or the bus.  You could make a decision tree with some ‘mission rules’.   For example:  “If the wait time for a taxi is more than 2 minutes, proceed to the 34th Street / Penn Station subway and take the 3 to Times Square / 42nd Street, then the 7 to Grand Central.”

Including options which can run in parallel or steps which can be quickly substituted in the case of failure increases the probably of success, but it does not make the plan less complex.  The complexity increases and with it, the effort needed to manage and execute the plan increases.  This is also a source of failure.  Unless you are good at remembering numbers and scenarios, you’ll have to write all this stuff down, or else you’ll be standing there in front of Madison Square Garden (which is actually round) muttering to yourself, “Was it 34th or 43rd?  Was it the 7 to the 3 train?  Or the 3 to the 7?”

 

Exactly this, the visualization of complexity, is the main value of project management software.  Large, complex projects have so many phases and so many steps in each phase that they quickly become abstractions to the mere mortal.  Unless you are John Nash or are born with the latest generation CPU’s like our children are, it is hard to manage risk when it is abstract.  A good project management tool, Primavera for example, allows one to see the steps (aka Work Breakdown Structure (WBS)) of a plan as a flow chart.  This helps tremendously when ‘de-risking’ a plan.  You can visualize which events are running in serial and which are running in parallel.  Or better yet, you can visualize which events COULD run in parallel.

 

And now, I must leave you.  It is time to make my plan to get from my house in Langenthal to a lunch appointment in Bern.  Project management software is not necessary for this mission, though.  The Swiss trains are ALWAYS on time.  (and when they are not, they reset the clocks to put them back on time!)

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