The Learning Curve

A friend of mine brought this up about two months ago and so I want to approach it from a more thorough math perspective.

Occasionally you'll hear that something has an extremely steep learning curve. Naturally we think steep and imagine scaling a sheer wall (or something along those lines) and the sense is that this must be an arduous undertaking.  In reality, that's actually pretty far from the case.

I've set up the "Learning Curve" as a graph, with skill level (y-axis), as a function of time spent learning/practicing (x axis). For non-math people this means we are observing what happens to your skill level as you spend more time practicing.

First of all, I will make the assumption that the relationship is positive - so the more time you practice, the better you get. It doesn't seem very reasonable to think otherwise - at worst your true skill level should remain constant (even if it feels like a particular performance is uniquely horrible).  At the very least, this is likely true for the average person, and so we'll ignore the fact that you're a freak with no real skills while you go cry in the corner.

I'm going to start with two people learning to yodel, with each one's learning curve represented by one of two straight lines labeled 1 and 2.  (See figure below.) Observe that line 1 is steeper than line 2.  Mathologists will note this means 1 has a greater slope than 2, implying that A1/B1 >  A2/B2.  This implies that person 1's skill level increases more for each unit of time spent practicing than 2.  In nerd-light terms 1 is getting better at yodeling faster than 2 is; more accurately if 1 and 2 spend the same amount of time practicing, 1 will reach a higher skill level than 2.

So now we know that a steeper learning curve is a good thing, but how many skills have proportional returns?  I certainly can't think of any, so I thought about what some common learning curve would look like.
Below you'll see learning curves that should hopefully be a bit more realistic.  These two curves should represent the transition from complete beginner to advanced level rider for snowboarding and skiing.

Curve 3 is meant to represent snowboarding.  The first few times you try, it is hard, painful and often progress trickles as freely as chilled molasses (speaking of molasses, I've seen a few people give up the attempt in favor of gingerbread cookies and apple cider... losers).  As the curve describes, this slow start lasts for a little while, until suddenly you find that your board is underneath you, your balance is solid and you are comfortable on the hill.  With each trip to a hill you get better and better, faster and faster until you've earned the right to stop terrorizing skiers and risk serious bodily harm in the terrain park.  Increased risk of injury and paralysis = nirvana.

On the other hand, strap on some skis and you'll be snow-plowing down the hill in no-time.  You're riding chair-lifts and going anywhere you want in a matter of days, and then you hit that rut known as parallel skiing.  It takes seconds to learn the dynamics, and years to master its application - not to mention that it requires constant practice.  Unlike the proverbial bicycle, if you don't use this skill on a fairly regular basis you'll wind up frisky with the snow and intimate with more than a few trees.  Curve 4 tells this story quite well, you start improving quickly, but gradually it gets slower and slower until it may take you a full season to fix a handful of small problems.

While this is far from an exhaustive list, I have demonstrated that a steep learning curve is actually preferable to a flat one, and that was my point (yay me for not getting sidetracked!)

Send in questions so I don't run out of things to brain-vomit about!!!

P.S. Check out my Dad's site http://www.robertswebessentials.com/

Maybe even click some ads on the right side?  Awesome.

Economists ruin all the fun

Captain America unseated Harry Potter and the Deathly Hallows, Part 2 this weekend, raking in 65.8 $mi.

Granted, Harry Potter grossed a whopping 169 $mi, record-breaking first week, so you can't feel too bad for it. Except for the fact that that's a "nominal" record, but not a real one.

"What's the difference?" you may ask. Nominal implies that the numbers are measured in their own right, which is to say that they are not being compared on equal conditions. This is important because lots of factors change from year to year, let alone across a couple of years.

First off, ticket-price creep; box office prices have steadily risen since their "slashing" in the heyday of the economic slump, meaning that it takes less tickets sold at the current price to equal the revenue generated at the previous price.

Second, the massive surge of 3D movies and their subsequent raised ticket prices; ultimately the same effect as before gets taken into account.

Third, there is inflation: the general tendency of prices to rise over time. Essentially, there is no real growth (i.e. there is nothing extra being produced) but prices rise anyway, meaning that a dollar today buys less than a dollar yesterday. This is essentially a furthering of point 1 yet again; inflation means that your hard-earned dollars are now worth less, relative to before so 169 $mi today wouldn't buy as much as 169 $mi a year ago. More importantly 169 $mi today doesn't buy as much as 158 $mi did in 2007. That's right, in inflation-adjusted terms, Spider-Man 3's opening weekend was bigger than HPDHP2.

Interestingly enough, in ticket-inflation-adjusted terms (dealing with issue 1), Star Wars claims 4 of the top 10 total box office values. (I am unsure, but would tend to believe that the numbers for IV, V and VI include the re-releases of the movies.)

It is interesting to think that in relative terms, modern movies aren't cleaning up like the news would have us believe.  That said, this is probably a boring post for most non-economists out there and yet another glimpse at what makes it the "dismal science."

Is it illegal if you don't get caught?

I had the "Is it illegal if you don't get caught" with a friend over a year ago, and our tempers flared enough that the discussion eventually had to come to an end.

I will reprise my argument here and open it up to attack and criticism, though, as always, I shall attempt to hide behind the shield of logic.  First of all, this feels like a rewording of the old adage "if a tree falls in the forest and there is no one around to hear it, does it make a sound?"  In both cases the answer is a resounding yes.

Oxford defines the law as "the system of rules which a particular country or community recognizes as regulating the actions of its members and which it may enforce by the imposition of penalties".

Furthermore, Oxford defines an illegal action as one that is "contrary to or forbidden by law".

By that definition, if an action is against the rules of conduct in the established society, it is illegal.  There is no ambiguity in either definition that could imply the requirement of an observation and charge by an  officer of the law is a necessary condition for an action to be deemed illegal. 

This in no way asserts a link between legality and morality.  The law could tell you that it is illegal to walk on the street instead of the sidewalk, but it seems a rather large stretch to claim that it is immoral.(Morality is a concept I will deal with another time anyway.)  If you perform action X, and the rules of the relevant society state that action X is prohibited, your committing the act has violated this rule and by definition broken the law.  Note again that nowhere are observation, proof, charges or a trial mentioned in the definition of "illegal" or "law", and that "illegal" is logically equivalent to "against the law."

As an extension, just because an individual is found not guilty does not mean that s/he is innocent of a crime.  This type-II bias is inherent in our legal system and the "innocent until proven guilty" structure, but does not imply that the act was not committed, or that the individual is not actually guilty of breaking the law - simply that sufficient evidence is unavailable to convince the court of their actions beyond a reasonable doubt.

Anyway, it seems there's no real philosophic debate to be had here.  If you don't like this, you can take it up with the Oxford dictionary's editors.  They may listen, consider the appalling changes that they've accepted in recent years.

What is a good person, and why fat people intrinsically aren't good.

And now for a taste of something different!

I imagine that this is going to come back to bite me in the butt someday, but here's a thought experiment
that a twitter conversation inspired.

I asked what is a good person?  The other half of the conversation claimed that a good person has a "good heart, [is] well intentioned, generous, caring, kind etc ..."  If we ignore the moderate ambiguity of some of these terms, taking them at face value and ignoring valid philosophic tangents embodied by Socratic and sophist claims as to the nature of good, we can confidently claim to have found a reasonable definition?  I will try to tidy it up by polishing it all down to "an individual who takes others into consideration when making decisions, so as to make everyone as happy as possible. (We could assign economic jargon like uility and welfare to this, but we don't really need them right now, and this way all of the econ-impaired will be able to follow along).  It wouldn't be hard to show how each of the aforementioned characteristics (as well as a few others of equal importance) fall in line with this simplified definition very well, but for sake of brevity, I'm not going to waste my time on that.

We can expect that these characteristics must extend to all people, no?  If so, then they can extend to people who are not yet born as well, as being people, they deserve the same consideration as those who are currently alive.  So then, any action taken should its impact on future generations into account. How does this make fat people bad?  The top ten leading causes of death in America are: 

•Heart disease: 616,067
•Cancer: 562,875
•Stroke (cerebrovascular diseases): 135,952
•Chronic lower respiratory diseases: 127,924
•Accidents (unintentional injuries): 123,706
•Alzheimer's disease: 74,632
•Diabetes: 71,382
•Influenza and Pneumonia: 52,717
•Nephritis, nephrotic syndrome, and nephrosis: 46,448
•Septicemia: 34,828

Of these heart disease, cancer, stroke, chronic lower respiratory diseases, and diabetes are all linked to obesity.  The cost of healthcare in Canada was 172 $bi in 2008 and can only have grown since then.  I wonder how much of this monolithic cost can be attributed to overweight individuals who are prone to more injuries and ilnesses, meaning that we wouldn't have to incur many of these costs but for the fact that these people are overweight. This debt burden isn't being paid now but is being passed onto future generations, as governments continue to kick the can down the road, to use the runaway colloquialism.  (Don't mistake this as an argument for fiscal austerity.)  How about the increase in waiting times because of their presence in the health system?  How many hip or knee replacements they receive because they didn't look after the ones they had?  How many research dollars are being spent to fix problems that are largely related to obesity when they could be directed at other, more universal problems?  This is not to say that we shouldn't be trying to fix these problems; rather it is more a matter of realizing the enormous, far-reaching impact of obesity on our society.

Fat people are placing an excessive burden on society's shoulders, and how many of them can legitimately claim that it is a medical condition completely beyond their control?  At SOME point it was well within the control of many of these people, and yet they ambled on to Krispy Kreme without thinking about how their decision to finish the whole box would affect everyone else.  That society is worse off for their decisions never crosses their minds, and given our above definition, makes fat people intrinsically "not good."

Please bear in mind that this can be extended to smokers, drug users, extreme athletes - anyone who self-selects into a pool of heightened-risk-of-damage.  At the moment though, fat people seem to be the largest drain and the most controversial one to speak of. 

So that's the gist of it - the central pillar of a thought experiment I toyed with earlier today.  We all have our good moments and our bad moments, but it smacks of truth at some fundamental level - if fat people really cared, they'd try harder to get into shape.  Or maybe not - it's just a musing...

Returning!

So I found myself spending too much time trying to make my posts perfect and airtight, which is absolutely the wrong way to approach the webernet. The whole point is dialogue - having everyone work together - even if we come to the same conclusions, we all benefit from the communal thought-experience. I've removed all posts from the past month and a half, as I feel they put the empahsis on the wrong part of the blog experience.

I will try to maintain a semi-regular updating practicing so that nobody gets inundated or bored... Also, if you want to have a discussion raised, feel free to bring and article or a question to my attention. I'll build a post around it, and then leave it open for thoughts, comments and observations.

I bid you adieu for now, but expect a post tonight!!!