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Context in Science

Eshu was walking down a road one day, wearing a hat that was red on one side and black on the other. Sometime after he entered a village which the road went through, the villagers who had seen him began arguing about whether the stranger's hat was black or red. The villagers on one side of the road had only been capable of seeing the black side, and the villagers on the other side had only been capable of seeing the red one. They soon came to blows over the disagreement which caused him to turn back and rebuke them, revealing to them how one's perspective can be as correct as another person's even when they appear to be diametrically opposed to each other. He then left them with a stern warning about how closed-mindedness can cause one to be made a fool.

Lets look into the interesting phenomenon of Gestalt shifts. The ability to suspend one’s context and wholesale take upon new ones at will can be very useful, especially to science.

From a strictly interpretative level we can easily apply this method of Gestalt shifting to any work. Some works are designed towards this end however. Figure i shows us a cube. First, we have the illusion hidden in our Observational Language showing us a three dimensional image portrayed through our knowledge of its intended subject in spite of its two dimensional representation. On the other hand, it is just as valid to see it instead as a set of lines on a flat surface, portraying a completely different message conceptually and mathematically. One could easily imagine it as a map of a few streets, for example.


Figures i, ii, iii

A popular, and perhaps more visually striking, application of this switching of context is found in Figure ii and Figure iii. Depending on which context set you view Figure iii from you may either see an Old Lady or a Young Woman; likewise for Figure ii you may see a rabbit, or perhaps a bird. One may even be able to hold these two different concepts in your mind at the same time, once having had the relationship revealed sufficiently. We do not cease thinking of Newton’s laws when we have been introduce to relativity.

Until such relationship is sufficiently disillusioned it remains hidden - forcing us into choosing one context or the other. One can imagine from the reference of either context the opposing contextual choice seems nonsensical or even blatantly incorrect and silly. At the very least we can expect some signs of discordance and discontinuity between sets, and likely some additional continuities as well.


Figure iv

Another parallel situation can be found in the Rorschach Test. The Rorschach Test is a psychological test in which the participant interprets inkblots (Figure iv). Their analysis of these blots are then analyzed by a professional. Through these interpretations these otherwise contextless works are thought to be a reflection of the individual’s context. The subject gives them his context through faith that his context is realized

This is an interesting case in its minimal intent to represent. The original artist or contextual set is essentially void of purposeful order. Given a somewhat random set of data, it shows a subject tends to read into it a context that seems as continuitous as possible. Given no outside clues, this continuity is to the subject’s context.

This is not merely relevant to images, psychology and art interpretation. This shift is prevalent in a wide range of fields, if not arguably all fields. Steven Pinker talks in depth on the importance of frame flipping to him in the advance of linguistics in The Stuff Of Thought. It is a common theme in mythologies and faerie tales across the world - take the tale of Eso at the head of this section.

Why would it be so curiously absent in scientific and mathematical thought?

We can answer this question simply: It is not. Many when they think of science prefer to think of it as a drudge of accumulation of facts. A simple matter of bookkeeping and ultimately a small dent one makes in a very specialized area. While this view and path is perfectly acceptable, valid, and useful to us we are simply discussing the cases which do not conform to this pattern.

To examine shift as it happens in scientific methodology or mathematical models, let us first look at a simple incarnations of this, and then examine a few instances of this same illusive behavior briefly across mathematical and scientific disciplines.

Most should be at least familiar with is the illusion between Polar and Cartesian coordinates depicted in Figure v. Sin is not by nature different in these two graphings, we are simply viewing them from a different context.


Figure v

Historically, this shifting has been a tremendous help, and again has shown us that ideas that are apparently false are the most valuable to scientific endeavor. This is not only due to their tendency to show us new contexts and tools for examining the available data, and their inherent promise in superseding existing theory, but also due to the relationships they betray between the incumbent worldview and that of the new imposer.

It forces us to ask: Why does this new view “work”? What does it say? What does that, in turn, say about the previous world-view? Where did it come from - or what need caused it to arise? What is the reaction? Further, and perhaps more importantly, what does it say about the relationship of all such possible worldviews to each other, and ultimately, to some objective truth (or even truths ability to be objective at all)?

Consider a few notable advances in science and neo-zeteticism and examine how they, at least at the time, were faith based choices due to the equivalence of the theories involved.

Galileo’s Tower of Pisa

First we turn our attention to one of the most notable and important scientific shifts in thinking and the scientist behind this shift. Galileo whose work to support Copernican views were instrumental.

It is true that it can be shown that Galileo’s work is faulty at its start: in example it’s mathematical model that predicts one tide per day an everyday observation that one cannot possibly imagine he would be ignorant to. We must like Einstein conclude that “his endeavors are not so much directed at factual knowledge as at comprehension.” Let us then examine what some have called his most fruitful attempt at lending comprehension and discuss the famous Leaning Tower of Pisa experiment.

The Tower Experiment was a central obstacle to Galileo’s argument. Galileo uses an imaginary conversation between three people. On the second day of conversation attention is brought to the tower argument: if one were to drop a ball from a tower, if the earth was moving it should appear some distance away from the tower greater than its distance from the tower when dropped. Since the tower is fixed to the ground, it is assumed in the Aristotelian view that the tower would move with the ground while the ball, not fixed to any moving element, would then be seen to move relative to the tower horizontally, which is to say the tower, due to the rotation of the earth, would rotate away from the ball which would fall in a straight line towards the earth.

The illusion Galileo illuminates for us here hides an equivalence between a rotating earth and a terra firma. Obviously the ball will experimentally fall down either way. This is shown to us by dissolving the idea that the ball doesn’t leave the tower with the momentum of the tower. Both explanations explain just as well, and given current knowledge of the time are just as correct.

Similarly, noting wind doesn’t rush at us at high speeds can lead us to the conclusion the earth is not rotating. Likewise, if we switch our context, we have no implication that the atmosphere rotates as well.

Gaussian Gravity

Another case of this in both physics and mathematics is that of Gaussian gravity vs a more purely Newtonian approach. The case of using a Gaussian surface to examine gravitational phenomenae is indeed . Yet we can still show it is mathematically equivilent to a Newtonian view of gravitational interactions.

Eratosthenes vs Huai Nan tzu

Often times Eratosthenes is cited as having shown us the Earth was round and as having given us calculations of its circumference using only comparisons of the lengths of shadows at various points on the earth. It can be seen upon inspection that this is indeed no proof at all. Consider the cosmology in Huai Nan tzu which takes the same practice, identical validity of reasoning, and similar measurements with instead the intent to measure the distance to the heavenly bodies, in contradistinction to the purpose of Eratosthenes - to measure the circumference of the pre-assumed round planet.

In the the case of Eratosthenes he must begin with the first assumption in his contextual language of a round earth. Without this framework and modelling his data is meaningless. On the other hand, when we look at the Huai Nan Tzu when confronted with a similar issue we are left with the realization of close planets and stars of a smaller size and a flat earth, the same view developed in the 1900s by the (mostly) Christian Flat Earth theorists.

Einstein’s Equivalence Principle

We shall therefore assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system. Albert Einstein

Einstein was fond of a form of inquiry known as thought experiments. In a thought experiment, a premise is assumed to deduct from it the possible consequences. One of these thoughts experiments in particular involved a solitary passenger on an elevator that is alone in the universe.

When the elevator starts accelerating upwards, a pull downwards is felt by the passenger. This is due to the passengers momentum. Recall that in accordance with Newton’s Laws, a body at rest tends to stay at rest. Einstein hypothesised that since this pull, caused by the momentum of the passenger fighting against his acceleration, is indistinguishable from gravitational influences, it is only logical to assume that they are one and the same phenomenon. Comparatively, another pseudo-force like this arises from a rotating reference frame, say if one is on a spinning carnival ride one would presumably feel a pull away from the center.

Consider the scenario of this elevator accelerating upwards at 9.81m/s/s. If the passenger were to jump in the elevator while it was accelerating upwards at 9.81m/s/s (the rate at which we are pulled to the earth by gravitational forces) he would observe the same effect as if he was jumping on the earth. An initial resistance would be felt; the ground, or elevator floor, would recede away from him at 9.81m/s/s until he has traveled enough distance to expend the force given by jumping. Then the elevator floor would rise up to meet him at 9.81m/s/s. This can be seen as an observational illusion: much like that of Galileos’, the elevator floor can be seen to either be accelerating upwards at 9.81m/s/s or the passenger could be seen as falling towards the floor. To the passenger - its indistinguishable! Einstein’s inductive leap here was the realization that perhaps the forces are indistinguishable because they are. They both are accelerating frames of reference. This is known as the equivalence principle.

The equivalence principle also comes into play in an outdated yet still modern flat earth belief. It was, and still is in some circles, believed that the earth is accelerating upwards at 9.81m/s/s like our passengers elevator. This is what accounts for gravitational influences towards the earth in this model. It should be clear why this model is foolish - it completely discounts gravitational phenomena on smaller scales and the role of matter in gravitational interaction. The view presented next is far more cohesive.

The Ferrari Effect

No doubt you’re familiar with Einstein’s theory of the curvature of space. If space is curved - and modern physics is based on that assumption - the Earth, from space, would appear circular. It’s a simple optical illusion. Leo Ferrari

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