Point on a Line, a Line on a Plane, and a Plane in Space

Logic, Mathematics
Each point has a specific location. Two points determine a line. Three points determine a plane. Let us consider some simple math derivations to arrive at a format for each. For simplicity’s sake, we will use the familiar x, y, z Cartesian coordinate system. We begin with a point on a line. First, Point on a Line In space, a single point has an x value, a y value, and a z value. If the coordinate system chosen for the point is a simple 1-D line, then only one variable – say x – is needed to describe it. Then, since there is no y or z to consider, the mathematical description of the point is x = c But let us, for reasons that will be understood later, write…
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Not Infinitesimal Point Coordinates

[caption id="attachment_7388" align="alignright" width="480"] A coordinate system.[/caption] Infinitesimal point coordinates or not? Do you occasionally enjoy speculating? Even if one has technical training, if he speculates outside his field of expertise, he is opening himself up for possible difficulty. What he speculates, if he voices it, could result in his being labeled someone who doesn’t know what he is talking about. But I never was bright enough to avoid speculation, though I always acknowledge it for what it is. So humor me here… So if you know something of all this and what I'm writing either doesn't jive, or you can 'supercharge' it, please let me know. Mathematicians’ Points – Reality? Generally, a point in space is seen as a dot in space, having infinitesimal point coordinates, that is, no…
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Edge Effects for the Universe?

[caption id="attachment_7377" align="alignright" width="480"] Introducing the universe.[/caption] A strange thought crossed my mind. I was in that twilight state between awareness and sleep. What about the edges of the universe? Does the universe experience edge effects? Materials all have their own properties. Metals, for instance, have a melting point. They have conductivity, density, malleability, and ductility. Liquids, gases, and plasmas have properties as well. A material or an object can act differently at its interior, than at its edge. Consider some objects interacting with electromagnetic radiation. Magnets and Capacitors Capacitors exhibit so called Casimir edge effects. The electrical field between capacitor plates behaves differently at the edges, than between the centers. The same is true of the edges of magnets. Frequency Skin Effect Electrical engineers understand the high frequency skin…
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Some Reasons I Disbelieve in Time Travel

[caption id="attachment_7363" align="alignright" width="440"] I disbelieve in time travel.[/caption] I love a good science fiction precept. One of the classic precepts is time travel. Books have been written. TV shows aired. Movies released. I can’t get enough of it, especially if some fresh nuance concerning time travel is postulated. Despite that, I totally disbelieve time can be traversed, or indeed that it is anything other than one-dimensional and forward moving. I have a few reasons for feeling so. The last one I present represents for me the final sword thrust, the coup de grâce, for time travel. Time Travel – My First Difficulty The first concept of travelling in time is doubtless to return to the age of dinosaurs. The notion of travel to the past is abundant in classic…
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Where Does Light Go? Why is the Universe Dark?

[caption id="attachment_3236" align="alignright" width="480"] The Andromeda Galaxy (M31)[/caption] Where does light emitted from a flashlight go? On a universal scale, what happens to all the light? If Space is not infinite, goes the line of incorrect reasoning, then all the light that has ever been radiated by stars and galaxies should make the Universe a blindingly bright place. Hence, the universe, based on this reasoning, must be infinite. But, if the Universe is not infinite, the light should bounce back and forth, building up. Most scientists consider the universe to be expanding, yet not infinite. So where does all the light go? First, let's discuss what light actually is. What Is It? Light is a form of energy that radiates outward — radiant energy. Radiant energy can be readily absorbed,…
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