Absolute, relative, and perceived knowledge

Every now and than I happily realize that my absolute level of knowledge K_abs in my field of work steadily increases.

One can define the relative knowledge K_rel as the ratio of one’s absolute knowledge to the total available knowledge K_tot in the respective field:

K_rel=K_abs/K_tot

If the temporal development of K_tot is neglected in a zero-order approximation, one’s own relative knowledge will rise with the increase of one’s own absolute knowledge. This increase usually comes naturally with working on some topic, as exemplified by my introductory remark.
However, the objective quantity K_rel is of little relevance to any one individual, as one usually is not aware of the total knowledge K_tot. Rather, one is only aware of the perceived total knowledge K_tot^*, a quantity that will also increase during one’s occupation with the respective subject. Therefore, the decisive quantity will be the perceived relative knowledge

K_rel^*=K_abs/K_tot^*

The temporal progression of K_rel^* during one’s occupation in a field of work would certainly be interesting to study. The question arises if the perceived amount of total knowledge available rises in the same manner as the the level of absolute personal knowledge in the field. Partly based on my own experience I would conjecture the following three regimes in the progression of K_rel^*

1. A strong increase in the beginning of one’s occupation with the topic, when the basics are learned fast.
2. A pronounced decline, when the personal absolute knowledge still increases but is by far outweighted by the realization of the huge amounts of knowledge available “out there”.
3. A rather moderate increase, with an asymptotic approach to unity, i.e. the personal absolute knowledge slowly becomes close to equal to the perceived total knowledge. This will happen when one starts to really master his field of work, and in this case K_tot^* might even reach K_tot, also implying that the perceived relative knowledge K_rel^* will coincide with the objective relative knowledge K_rel.

Of course everything becomes even more complicated when the temporal evolution of the total knowledge is taken into account. In this case the question will be if the personal level of knowledge can keep up with the ongoing increase in total knowledge.

This entry was posted on Monday, April 2nd, 2007 at 22:58 and is filed under English, Uni. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.