How does one set about proving that between the numbers two and four exists a three and how does one set about proving that beyond the aforementioned numbers the logical continuation is a six? Mathematics, while not exactly one of my strong points, can be appreciated for the promise that it embodies. Mathematics is a structured system that exists upon the metaphysical level and is perceived to manifest in all things in life. It is a system that humans readily apply to all things artificial and natural, attempting to lay a finger upon every phenomenon in search for a discernible etch, a perceivable hint of structure beyond the silky flat of chaos and all in the name of furthering our understanding.
Aside from its importance in our everyday lives, the use of mathematics for interpolating and extrapolating upon existing series or patterns of values to which we have given meaning has provided ourselves with a lot of what we know today. It gave us a means of trying out new things on the basis of intelligent guesswork rather than mere random chance. It is the logical expression of the concept of building within and beyond that which exists.
Present-day music is largely based upon previous music and other producible sounds. New technologies are mostly based upon previous technologies. New philosophers tend to draw upon old philosophers and experiences in life. Drivers in developing countries use prior knowledge of the road to prevent accidents while blinded by the headlights of oncoming vehicles. Any knowledge that is gained without direct blind trial and error or direct experience is the result of the mind extrapolating or interpolating upon existing knowledge. The ancient Greeks figured out that the World was round thanks to observations of the stars and observation of the world around them. Various aviation pioneers took inspiration from birds that used less energetic sweeping wing movements such as seagulls. The deductive processes involved in crime investigation done right is also an exercise in extrapolating upon the available evidence. If we were to take bridge repair as a means of illustrating working beyond the existing then extrapolation would be a matter of extending the structure across the divide while interpolation would be similar to bridging the gaps between the support struts or columns.
Both techniques also have a place in determining truth from fallacy. After all, not all sources of information are honest and likewise the information that one is fed by sources may also be similarly skewed. The interests of the provider of information can taint objectivity. Truths do not need to be altered into fallacies so as to mislead. Truths can be selectively chosen and provided, or omitted altogether. Information can be provided with baggage attached, conveying positive or negative influence as intended by the interests concerned.
Even sources that we should be able to trust are not necessarily without taint. The television stations. The papers. This web log too has the interests of myself riding within it and should therefore be taken with a pinch of salt. The only way to sort through the mess of conflicting information is to attempt to extrapolate and interpolate upon the knowledge available in search of the most consistent net or web of integrated information upon which to base your opinions and thoughts. Without a reliable grasp of the information available I am afraid that it is likely that the decisions that you make will be the most sound that they could otherwise have been. Of course it is our right not to be deceived to begin with, but the bad shepherd could care less.
Tags: extrapolation, interpolation, knowledge, mathematics
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[...] – Of interpolation and extrapolation saved by piangers2009-03-27 – Adaptive interpolation in Fourier domain saved by [...]
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