Friday, February 14, 2014

Life is not fair.

Unless you look at the average...

Sometimes, life spits in your face.
We are all told that work leads to success. That's the American dream - right? No matter how bad your initial conditions are, you can make it. If you just work hard enough, be smart enough, creative enough - you will surely "win". And just as you buy into this idea, reality hits you like a brick wall.

You studied so much for that exam - why did you fail? You are better qualified for that job - why did they take someone else? You worked so hard this year - why didn't you get that bonus? You planned your trip perfectly - why did you miss your plane? You spent weeks getting ready to approach that girl - why wouldn't she even talk to you?

Usually the answer is, as Facebook put it, "it's complicated". There is a multitude of elements affecting each outcome, and most of the time only a small part of this underlying complexity is revealed to us. For example, perhaps the boss that denied you the raise knows he wants to offer you a promotion in a couple of months so the motivational benefits of the bonus would be "wasted" on you. Maybe the other guy actually worked weekends and just didn't talk about it. Maybe the decision was forced from above because the big boss once saw you reading a blog instead of working and now thinks you're a slacker. Maybe that report you worked so hard on was presented to the management only after the bonuses were already fixed.
Who knows?

Some of these possible reasons are easier for you to control/be aware of, some are harder, but every outcome is affected by a multitude of unrelated, independent events and decisions. In the case of the missed plane things are even more complicated (as an example - the creation of traffic jams is a subject of scientific research), not to mention the romantic tragedy (how could you know that you remind her of her father - so she is secretly attracted to you but would never admit it to herself :) ).

Now that we are sufficiently convinced that all is lost and we have zero control over our life - Gauss comes to (partially) save us. The Normal (Gaussian) probability distribution (also known as "bell curve") is perhaps the most widely known and used distribution, the reason being its universality (explained here using bunnies and dragons). Roughly speaking, if you are interested in some attribute and it depends on a lot of underlying independent variables - it will be distributed according to a Gaussian. A popular example is human height - which depends on a variety of mechanisms: from the health of the mother during pregnancy, to the quality of food in the area, not to mention an assortment of different genetic configurations.

Another important property (of any probability distribution) is that the more samples you collect - the better the resemblance of the measured data to the theoretical curve. For example, if we roll two 6's on a pair of fair dice we wouldn't be really shocked - even though it's a relatively rare event (1/36). But if we would sit all day, roll dice and get 6's every single time - we would think a miracle just happened (or, much more likely, the dice are loaded...). The same is true for any other random process: we shouldn't be surprised if an unlikely event happens here and there - it's not impossible just unlikely - but if we repeat the experiment many times we should mostly observe the most probable outcomes (obvious - right?).

Armed with this probabilistic knowledge, we may get back to reality. Lets say you are looking for a job (an example from my own life these past 6 weeks). The decision whether you are accepted or not (or whether you advance to the next interview) is affected by a multitude of factors: does your resume reflect the skills they look for? did you serve in the same army unit as the interviewer? did she laugh at the joke you made? did you shave that day? do you have managerial aspirations? Are you the last candidate that day and she has a headache? do you have managerial aspirations and the current team manager is scared for his position since you are better :) ?

Some of these effects can be anticipated and prepared for (just shave in the morning...) - some are harder to foresee, but anything I don't know and/or don't control is random for all I care. Lets define a "perceived adequacy" measure of how good of an impression I left on the interviewer. Since it is constructed of many attributes, and my masters degree has nothing to do with how much she likes my sense of humor (so the attributes are mostly independent) - a reasonable statistical model of this variable is a Gaussian distribution. There is some level of perceived adequacy above which you get hired (which in reality depends on the other candidates - but you can't affect them so for you it's constant), and below which you fail:

The yellow line represents the hiring threshold. Blue is the perceived adequacy distribution (probability density). Play around with the sliders and see how your chance to fail changes. Note how "difficult" it is to bring the chance of failure to 0. In reality you have no control over the uncertainty (width of the Gaussian), only over the expected adequacy - the average.

You control the average when you study in high school. You control the average when you go to a university. You control the average when you practice your people skills. When you dress appropriately for the interview. When you show up on time. When you choose to read a book instead of watching TV. When you pick up a new skill. Every step of the way - you can better yourself.

But sometimes, even if you worked hard and your expected value is high, you fail. That's when you feel that life isn't fair, that everything sucks, and what's the point of trying in the first place? You must remember - rare events do happen from time to time. You must move on, try again and again, conduct enough "experiments" so the results represent the probability distribution - including your hard earned high average.

Life will catch up eventually.
And who knows? Maybe next time you'll be luckier than you "deserve" to be.

Until next time, may your choices shift the Gaussian in the right direction. 

Michael Shalyt.

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