Symmetric political moment

I don’t usually write about politics but America is at a unique political moment, one of supreme balance between opposing, well, either personalities or civilizations, you pick. On the one hand, we have a politician who speaks words only as a performative utterance, a speech act designed not for its veracity but its effect. This […]

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The physics of a trip

Movement in its simplest form is a trip from A to B. There are two ways one can look at such a movement: (1) as the line segment from A to B, or (2) as the angle between the lines from A to a reference point and A to B. Each of these may be

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From generalizations to universals

John P. McCaskey’s Key to Induction shows what scientific induction is all about: “[Scientists] want to know not only what is generally true but what is universally so, what is true without any possible exception. Below are three cases in which scientists were able to begin with general statements and progress to exceptionless universal ones.

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Measuring movement

The dimensions of an object are measured by movements, whether by moving a measuring device or moving one’s eyes while a measuring device stays in the same position. Movements themselves are measured by comparing them with standard movements, such as a movement with constant velocity. A movement compared with a standard linear movement generates a

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Total time

Since time is three-dimensional, what is the total time given the time in each dimension? The answer is exactly like the total distance. Consider the times t1, t2, and t3. If these are the coordinates of three successive movements, then the total time is their sum: t = t1 + t2 + t3. But if

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Dimensions of movement

The instantaneous movement of a particle may be represented by a velocity vector, which describes an instantaneous motion by its magnitude and direction: the magnitude is the ratio of the differentials of the distance and time in each dimension of the movement (dri/dti); the direction is the direction of the instantaneous tangent in each dimension

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Time on space and space on time

Our culture is oriented toward space, geography, geometry, and spatial relationships. We can easily understand items on a map. Even time can be put on a map, as with an isochrone map such as the contour lines (isochrones) representing equal distances or drive times from an urban center. 3D visualizations extend this to more dimensions.

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Measurement of space and time

To measure means to compare with a standard. A physical movement may be measured in terms of the most direct movement between its beginning and ending. There are two kinds of measures of movement, magnitude and angle, which each have two aspects, spatial and temporal. First, the magnitude of movement: (1) Spatial measurement of the

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