Wednesday, March 08, 2006


"The first step to knowledge is to know that we are ignorant" - Socrates

"The beginning of knowledge is fear of God" - David

A few weeks back, I came across the first of those three quotes, and decided that it was an interesting thought that would serve me well to keep in mind, so used it as the first entry in what I thought would become a quote wall inside my cubicle (as you can see, I tend to start things and then forget about them). While working today on a transport phenomena problem set, I looked up at that quote, and began to think about it (anything to avoid working on my homework, after all). The second quote, from the last verse of Tehillim 110 (111?), sprang into my head.

To provide a little bit of background information about what I spend my days doing, transport phenomena is, in the general sense, the study of gradients, that is, the study of differences in a system's properties over space that serve as a driving force for changes in the system's properties over time, to the point of reaching some steady state where the system's properties do not change over time (which may or may not be an equilibrium, which refers to the case when not only do the properties not change with time, they are also constant for all spatial locations within the system). The field deals with the transfer of heat (conduction, convection, and radiation), the transfer of mass (diffusion and convection), and the transfer of momentum (fluid flow).

The equations that are used in this field are differential equations, that correlate changes in spatial and temporal dimensions to one another. When one integrates a differential, one always ends up with some unknown constant. This is logical; if one travels east at 60 mph for 3 hours, one knows that one is 180 miles east of one's starting point, but still has no idea where one is. In mathematical terms, one's location would be expressed as C + 180 - but C could be anywhere in the world. The only way that one can determine one's spatial location based on a differential equation is if one knows one's starting point. In engineering patois, this is called a boundary condition. If one has enough boundary conditions based on knowledge of a system's temperature at given points in space and time or based on knowledge of a solution's concentration, one can obtain real, useful results. If not, one's final answer will be nothing more than an academic exercise.

The statements of King David and Socrates appear to be expressing this dichotomy. Socrates points out that before one acquires knowledge, one has to realize that one must start from a blank slate, with no preconceptions and no loyalties that will cause one to pervert the knowledge that one will obtain in order to fit into a pre-existing system. David, on the other hand, notes that the beginning of knowledge is fear of God. Rather than fear of God being a hindrance to knowledge, in that it forces one to subjugate one's intellect to a system whose reasons one may not intellectually understand, fear of God is actually a prerequisite to knowledge. No one has a monopoly on logic; the world is full of intelligent people of all stripes and of all ideologies. How, then, is the world filled with such differences of opinion? The key factor, I believe, is boundary conditions. To use a previous metaphor, if two people each drive 60 mph east for 3 hours, but one starts from Los Angeles and one starts from Paris, they may have traveled down identical strips of asphalt in identical vehicles, listening to identical CDs, but they will end up in very different locations.

According to the relativist, this is a natural situation in the world. Since there is no right and wrong, no absolute morality, it can not be any other way but that people will come to different conclusions; this one will be a liberal and that one a conservative and this one a capitalist and that one a socialist. And the world is better this way, reasons he, as it allows for full intellectual expression. David, though, notes that this is not the case. We do have boundary conditions and initial states - and, rather than stifling the power of the intellect, they channel it, allowing for us to come to absolute definitive answers, rather than relative solutions that use unknown constants. The Torah is the source of our boundary conditions. If the Torah says that something is good, we know that it is good, and we can use our intellects to apply this knowledge to situations that are not stated explicitly.

The source of our knowledge that these are our boundary conditions is another discussion whose place is not here. The analogy is not exact, of course, as even starting from the same boundary conditions, there are still differences in opinion in the interpretation of the Torah for our everyday lives. However, it must be noted that the differences are nearly negligible relative to the full scale of the system. This being understood, it comes out that the analogy is not so inexact after all, as what we call temperature is never based on absolutely uniform physical conditions, but rather is based on the average motion of the molecules of a system. When dealing with the motion of a fluid, this concept is known as Brownian motion. In light of this, perhaps we can also arrive at a better understanding of the concept of "Eilu v'eilu divrei Elokim chayim" - These are the words of God and those are the words of God, and despite their mutual contradiction, both are entirely true.

To know what we know and to know what we do not know: This is knowledge. - Confucius

The opposite of a truth is a lie. But the opposite of a profound truth may well be another profound truth. - Niels Bohr


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