This is based on a discussion I had at work a few days ago. We were talking about people being able to do things out of their own initiative, come up with their own new ideas, inventing their own problems to work on (which would be useful for the firm on the whole) and stuff.

Now if you consider people’s abilities as a multi-dimensional vector (the number of dimensions will be large, since one’s abilities, capabilities, etc. can be along several dimensions), what we realized is that if someone just takes orders from other people and not work on their own ideas and intuition, then their contribution to their role is just the component of their vector along the vector of the person whose orders they are following.

And considering that the probability of their vector and the vector of the person who they’re taking orders from lying in exactly the same direction is close to zero, what this means is that by simply following someone else’s orders they are contributing an amount that is less than what they are capable of contributing (since the component of their ability orthogonal to the vector of the person whose orders they are taking isn’t on display at all).

Hence, it is important to have people in the team who are capable of independent thinking and intuition since that is the only way in which their full possible contribution can be harnessed. On a related note, in order to bring the best out of its employees, and to allow them to contribute to their full capacity, firms should allow the employee to take initiative and come up with their own ideas rather than simply taking orders, since in the latter case only the component of the abilities along the orders is contributed.

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Unnecessarily bringing in ‘logically reasoned and mathematical’ sounding explanations to justify a simple argument is not useful!

I concur, unnecessary display of mathematical terms for a simple argument.

Looking at abilities as vectors may be flawed when ‘comparing’ two vectors (I guess i should say vector components). The abilities are not orthogonal – my ability to solve puzzles will make me a better strategist. For someone who is not very intuitive about these things, the basis directions of ‘puzzles’ and ‘strategy’ will have a different relation.

Another issue with the concept of vectors is that it is hard to gauge a person’s abilities apriori. most firms will only be interested in abilities as they pertain to a certain task, but even then universal orthogonal directions (and an individual’s contribution to each of the directions) will be hard to measure.

If vectors exist for each employee, an attractive option is to manipulate vectors (addition?) to gain teams that are more capable than individuals. Even then, it will be hard to solve a problem because one doesnt know how to employ the abilities, and what sort of problems are worth solving.

As firms grow, it might be counter productive if people get creative. I do not want the lift operator trying to be creative if it affects his performance as the operator.

Creative people (should come across at the interview stage itself) come up with ideas anyway. A little sense of identifying with the firm should help them take ownership of their roles to take initiative. Mentors can help ease new employees into their roles; mentors can also identify junta capable of contributing beneficial ideas to the firm.

There could be a prime set of capability vectors which are orthogonal to each other. My ability in quizzing could be determined by a function of some of these dimensions.

The underlying assumption is that there are a set of primary dimensions which measure your capability.

Your capability in individual facets will be a product of your capability vector with the capability vector for a facet.

Your capability in quizzing is a product of the quizzing ideal capability vector with your personal vector.

There are several HR consultancy firms which are trying to crack this puzzle to map the capability required for a job profile with individual capability. They are not at the realm of primary vectors now but at skill levels etc

I think the overall point is fairly black and white. Would you prefer a person who does just what he is asked to do or a person who does that and more. What would make it interesting is when the extra part is done at the cost of the main work. Then the problem becomes gray. Taking the vectors you drew, assuming I have 7 units of effort. Divided 4 and 3 in the main task and the outside task (orthogonal one) I should get a value of sqrt(4^2 + 3^2) which is 5 and essentially less than 7 and can never be more than 7. However, there is some unknown value in the other task a person does which can come later which can’t be measured (can be disproportionately high as well).

All this assumes that the person delegating work knows exactly what will add value in his area.

Aren’t you assuming that the order itself is always uni-dimensional (i.e. does not give you a chance to take initiatives “around” the order )

except the last line..the use of vector for this seems a deliberate attempt to make this post esoteric..

wimpy! write abt your experience in leh…

Water container with ounces for tracking There is so much information and misinformation out there that’s it hard to know who to listen to.