Category Archives: Ideas

Some musings I will probably include in my Treatise…

Lest I forget it in the chaos…

“Does C minor care about the Pathetique, or evolution about Darwin? Will hard work make one equal to the canvas upon which one paints? Of course not; to ask such questions is nonsensical. However, to deny the influence of Beethoven, Darwin, or Picasso on their respective arts would be folly. Thus, the tools and the workers evolve simultaneously, creating a powerful feedback loop that resonates across the ages throughout all of society.

And so we have the meme: an idea that propagates through its users, much as a gene propagates within organisms in which it is present. If the idea as it is practiced is advantageous – that is to say, it is used in a revolutionary way – it will spread as practice imprints itself on theory. Thus the revolutionary becomes commonplace: we associate C minor with heroic struggle, we accept that great complexity may arise from unguided processes over long spans of time, we construct art from simple geometric shapes, and culture advances.

Due to the inherent fluidity of our tools, it would be incorrect to call any of them truly Platonic in nature. Certainly, an Ideal art or science may exist, but what if we were to attain it? Would that system be able to answer all of our questions? What about the Gödelian, undecidable ones? Would everyone agree with the resulting conclusions or aesthetics? And, most importantly, how would our previous work be incorporated into such a system? Would it be a subset of the Ideal? If so, what if we had chosen a different path? If not, why did we come up with it in the first place? Attempting to quantify and describe Ideals in mundane terms leaves us with more questions than we started with. To say that we see shadows is too generous for such a condition; we are stumbling in darkness because we cannot understand the light!”

Results from running time

Some algorithms contain parameters in their running time that actually correspond to their solutions. For example, the vertex cover is fixed-parameter tractable for size k of the cover- the running time is expressed in terms of k rather than n.

If we implement awareness of its own running time into such an algorithm, we can use this to easily determine the solution.

The Significance of a Photograph

The photograph is simply a piece of paper, valueless except for the ideas that it construes. The true worth of the recorded experience is objective, yet we may only experience it through memory… and even that may require visual stimuli from the photograph to trigger.

This is the universalist/relativist duality of which I will soon speak at length.