Friday, May 20, 2011

Heidegger explained with differential equations

A differential equation is one that captures the relations among relations.  The rate of change of this is determined by the quantity of that. The amount of heat lost depends on temperature difference, and as heat is lost, the temperature difference reduces. Differential equations are essential tools for engineers.  But, they don't specify actual behaviour - the actual behaviour is a solution to a differential equation.  So the temperature D.E. might look something like dT/dt = -kT where k is a constant representing something about how big the exposed surface is and how well it emits etc etc.  (It might not look anything like that actually, I struggled with DEs).

That differential equation doesn't tell you what the temperature is, though.  You need to know the starting time and starting temperature, but it still isn't an equation that you can just read an answer off.  To find that, you need to make a leap - what kind of equation might satisfy this DE?  We remember that d/dx e^x = e^x, and it gives us an idea that d/dt e^(kTt) might look something like e^kTt and thus enable us to make a derivative function that can be equal to the function its a derivative of.  And so on.  (I really need to brush up on this stuff, gosh, I'm flubbing this explanation of DEs terribly.)

Anyway, Heidegger reminds me of differential equations.  He's interested in the way everything is always already in relationship, and he tries to see through the visible behaviour to the deeper, 'more primordial' structure.  The 'ontic' is the e^x. A good description of it will make your fortune and give you a law.  But the ontological is the DE.  The 'ontic' exhibits a complexity and richness that draws you in: but the DE shows you something more general.

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