Earlier today I was talking to Baada and to Aadisht (independently) about jobs, and fit, and utilization of various skills and option value of skills not utilized etc. So it is like this – you possess a variety of skills, and the job that you are going to do will not involve a large number of these. For the skills that you have that match the job’s requirements, you get paid in full. For the rest of the skills you possess, you only get paid the “option value” – i.e. your employer has the option to utilize these skills of yours and need not actually utilize them.
Hence in order to maximize your productivity and your pay, you need to maximize the cos theta.
Assume your skill set to be a vector in a N-dimensioanl hyperspace where N is the universe of orthogonal skills that people might possess. Now there are jobs which require a certain combination of skill sets, and can thus be seen as a vector. So it’s about maximizing the cos theta between your vector and your job’s vector.
So it’s something like this – you take your skills vector and project it on to the job requirement vector – your total skills will get multiplied now by the value of cos theta, where theta is the angle in the hyperspace between your skills vector and the job vector. For the projection of your skills on the requirement, you get paid in full. For the skills that you have that are orthogonal to the requirement, you get paid only in option value.
One option is to of course build skill set, and keep learning new tricks, and maybe even invent new skills. However, that is not a short-term plan. In the short to medium term, however, you need to maximize the cos theta in order to maximize the returns that your job provides. But as Baada put it, “But there is slisha too much information asymmetry to ensure that cos theta is maximised.”
There are two difficult steps, actually. First, you need to know your vector properly – most people don’t. Even if you assume that you can do a lot of “Ramnath” stuff and get to know yourself, there still lies the challenge of knowing the job’s vector. And the job’s requirement vector is typically more fluid than your skills vector. Hence you actually need to estimate the expected value of the job’s requirement vector before you take up the job.
The same applies when you are hiring. It is actually easier here since the variation in the hiree’s vector will not be as high as the variation in the job profile requirement vector, and you have a pretty good idea of the latter so it is easy to estimate the “projection”.
This perhaps explains why specialists have it easy. Typically, they have a major component of their skills vector along the axis of a fairly well-defined job profile (which is their specialization). And thus, since theta tends to 0, cos theta tends to 1, and they pretty much get full value for their skills.
At the other extreme, polymaths will find it tough to maximize their returns to skills out of a single job, since it is unlikely that there is any job that comes close to their skills vector. So whichever job they do, the small value of the resulting cos theta will cancel out the large magnitude of the skills vector. So for a polymath to maximize his/her skills, it is necessary to do more than one “job”. Unless he/she can define a job for himsel/herself which lies reasonably close to his/her skills vector.
(there is a small inaccuracy in this post. i’ve talked about the angle between two vectors, and taking the cosine of that. however, i’m not sure how it plays out in hyperspaces with a large number of dimensions. let us assume that it’s vaguely similar. people with more math fundaes on this please to be cantributing)
7 thoughts on “It’s about getting the Cos Theta right”
In more precise terms: you seek to maximize the dot product of the skills and requirements vector. Its a fairly standard scoring function for optimization, although I doubt if I’ve ever heard it in the context of life and work !!!
The concept of “comparative advantage” addresses this problem more directly.
not really. there you are comparing two employees against each other. here it’s one employee and the job
This brings to mind a corollary on another pertinent subject. Skill set exploitation to gain competitive advantage in the arranged scissors market. Of course, ‘skill set’ encompasses a lot of interesting concepts in this market. Its like the inverse theory to CMP.
We will talk this when I’m stuck in Ghatkopar traffic soon.
absolutely. i think that’s just a special case of this general theory i’ve put here
However, I wouldn’t agree to it completely. Additional skills are built with each job and the larger the “theta”, the more skills you build. (In mathematical language, the skills vector is the cross product of itself and the job requirements). The more skills you build, the better you can match them with future job requirements. It’s like a tradeoff.
The objective is not to maximize the “theta” for every job. The objective is to maximize the “theta” between your “dream job” and your “acquired skill sets” !! 😀
Dont mind me “barging in”. Just couldn’t resist it! 😛