Natural Science: Hegemony of the Right Angle Paradigm?

Philosophy Forums Science, Technology, and Math
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Natural Science: Hegemony of the Right Angle Paradigm?

If we watch carefully a group of carpenters building a house we can see that their building paradigm is the right angle and this constraint is standardized by the plumb-bob and the level. The building integrity is assured by the support of right angle structures and these supports are interconnected with linear members. [b]The building paradigm is right angle support interconnected with liner members.

The natural sciences have a similar type of universal paradigm.[/b] The natural sciences’ greatest instrument for success is linear mathematics. Anything that is non linear is generally discarded or is solved by brute strength over design. These sciences have been successful by eliminating the negative and accentuating the positive; that which is linear is positive and that which is non linear is negative. Recent studies in fractals have helped us to better comprehend the nature of the natural sciences.

Philosophy has been determined to emulate this sort of paradigm in the hope of achieving similar success in the domains of knowledge focused upon human to human interrelationships. Recent efforts by cognitive science and associated neurological sciences have, in the last few decades, shown us the errors inherent in these attempts.

Objectivism is a philosophy that understands the world as made up of determinate, mind-independent objects with inherent characteristics or “essences”. This philosophical view of reason is that reason is capable of “mirroring” objects with their qualities and relationships in a linear and undistorted fashion. Objectivism holds that principles are high order generalizations that can function as fundamental laws that characterize categories, which are the necessary and sufficient definition of objects of reality.

Rationality is framed and contained by the systematic nature of human conceptual processes. “Human rationality is motivated…imaginative rationality is indeterminate in more-or-less predictable ways.”

“The concept of motivation…has nothing to do with subjective intent, but rather refers to what makes sense of—that is, what structures, constitutes, and enables—particular thought.”

Traditional philosophical objectivism assumes (i.e. takes for granted) “that reason is available to control and direct the movement from authoritative sources to the logical decision of a concrete case”.

In legal matters “reasoning consists in abstracting from a judicial opinion or other authoritative legal text the principles that express the necessary and sufficient conditions, properties, or criteria that characterize it.” In normal everyday considerations reasoning consists in ascertaining the categories that characterizes the situation.

Quotes from A Clearing in the Forest: Law, Life, and Mind Steven L. Winter, Law Professor

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I like this analogy a lot, and I think it can be extended and deepened considerably.

Linearity is a central tool and candidate modeling assumption in the sciences. But there are many scientific/mathematical theories and models which are very important and nonlinear, including (off the top of my head) air drag, the boltzmann equation, soliton theory, and the theory of sparse/compressible signal recovery. Linearity is so important in science because a linear model is highly likely to be easily solvable, produce testable predictions, and be simple and robust enough to be used as a component in more complex theory.

Right angles and linear structures in buildings are similarly a central tool and candidate building-design assumption. There are many important building design elements that are either not right-angled or not linear, like the top of a roof, a tunnel, or a pipeline. But a right angle is easy to construct, behaves predictably, and is simple and robust enough to be used as a component in more complex structures.

There is a movement in architecture to do more challenging things (spirally skyscrapers, wild abstract designs) and break the right-angle paradigm as our engineering tools become more powerful. Similarly in math and science we are freeing ourselves from linear paradigm as our computational tools become more powerful. New central paradigms are emerging as we discover the powers and limits of our tools.

In both architecture and science, man’s imagination has always reached for far greater heights than his hands and tools could achieve at the time.

I’m reminded of a question I’ve grappled with from time to time: what do we mean when we say that there is an external, mind-independent world? I think we all agree this is true; yet there is no direct evidence that such a world exists, since all our perceptions of this world come through our minds, so that it is impossible to tell whether they came from an external world, a matrix-like environment, our own mental activity, or no cause at all.

I think “there is an external, mind-independent world” is shorthand for “my perceptions of the world are similar to what I’d expect them to be if they conformed to the rules of a certain mental simulation I am running in my mind, a simulation I call ‘living in an external, mind-independent world.’ Further I expect that future perceptions will continue to conform to this model.”

The strength of this formulation is that it neither affirms nor denies the “reality” of an external world, hence it avoids getting tangled up in the unfounded speculation of “brain-in-a-vat” type scenarios. It says nothing at all about that world, hence avoids the vicious circularity of assuming an external world while justifying your belief in it. But neither is it solipsistic – our perceptions are similar to the model, but I do not say that the model encompasses completely the perceptions. In fact, we sense that our model of the external world is always growing and changing, which strongly indicates that it never has and probably never will entirely encapsulate the universe we live in.

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I would say that linear equations are the metaphors of natural science.

I would also say that the natural sciences are like archetecture while the human sciences are like sculpting.

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There’s nothing special about linear equations philosophically. It’s just that they’re usually easier to solve than nonlinear equations. Many nonlinear equations are just as solvable and just as important as linear equations. Heck, the equations describing planetary motion are nonlinear! but of course NASA uses them all the time.

Likewise there is nothing special about right angles philosophically in building, they’re just easier to use than other angles in most cases.