Born to do Math 169 - Squares, Cubes, Rectangular Prism, Hypercubes: Circles, Spheres, Hyperrectangular Prisms, Hyperspheres
Scott Douglas Jacobsen & Rick Rosner
May 15, 2020
[Beginning of recorded material]
Scott Douglas Jacobsen: So, when you have a 2-dimensional surface, you're dealing with an x and a y-axis as the dimensionality, so squares and circles, etc. You can calculate the area in the 2-dimensional surface. If you expand this with z-axis, you have volumes with spheres, cubes, etc. So, when someone wants to block off something in some abstract 3-dimensional space, they will calculate the volume of the 3-dimensional space. If they want to block off a 2-dimensional space, they will block off an area. It can be part of the overall geometry if in 4-dimensional geometry. What is the proper terminology when blocking off a spatiotemporal volume?
Rick Rosner: It doesn't come up much. It would be a worldline. A worldline is the history of an object's position in space over time. So, I assume something like a world-volume. You trace the history of a region of space over time. In geometric terms, that is a hypercube or a tesseract or a hyperrectangular prism depending on the dimensionality. Not exactly, because the time dimension, the units or the extent of the 3 spatial dimensions, or the scale of the spatial dimensions, has to be the same. An inch in each direction is still an inch or the same. If you have the time axis with whatever scale preferred, you take a cube. You extend the cube along a unit line in a 4th dimension. It gives you a hypercube. But the time dimension doesn't have to be; it can be whatever scale you want, so you may not end up with a hypercube, but a hyperrectangular prism. A prism being a bunch of hypercubes stacked up if you've stretched the time scale sufficiently. It is a stack of hypercubes or some hypercube times some x, which is a product of what scale you've chosen for the time dimension. There's nothing profound about that.
Jacobsen: From my view, human beings are natural objects. We're just part of the natural world, which we describe with math. Can human beings, in some future time advancement of science, be described by a worldline in more precise terms?
Rosner: There's Marcel Duchamp's "Nude Descending a Staircase," which is a cubistic rendering of a woman every step that she is coming down. So, you've traced her worldline during the time that she was coming down the stairs. You see all these effects in videos with people tripping. They leave a trace or in sports, sometimes. There are effects. People trip to the basket, as seen in a series of stills. So, you can trace somebody's worldline. There is a physicist whose autobiography was called "My World Line."
Jacobsen: What does this mean in terms of the math? Or is this preliminary in the research?
Rosner: It is just a framework. There is a profound idea of Hawking's. That the dimensions of time and space interchange at T=0. So, the 4 dimensions form the base, not that a hypersphere has a base (every point is a base); they form the bottom of a bowl. I forget exactly how it works. But there is no time before that. Your time comes from no matter where you go; you're moving forward in time from the bottom of the bowl. It is like the South Pole. The only direction that you can move is North. People do mess with how the dimensions relate to each other. There's Special Relativity, which has an equation of possible simultaneity, which involves a Pythagorean formula for all the square roots of the spatial dimensions. Each squared versus the time dimension squared to decide whether two events are within each other's light cone or something.
Jacobsen: For those who don't know when reading this series, if we assume a range of physics knowledge, what is possible simultaneity?
Rosner: Under Special Relativity, there is no simultaneity because what you see happening of two events separated by space; the spacing in time of when they happen depends on where you're observing those events from. Although, there's not much give or leeway if the two events are only separated by like half of an inch. If two events are synchronized, so that somebody standing a quarter of an inch away from each point sees them happening at the same time, then the greatest amount of time difference in the signals arriving at you as a an observer and someplace else is half of an inch divided by the speed of light, which is like a billionth of a second. It is the greatest separation in time between the two events, the two flashes. But there's a fairly easy geometry of that.
Jacobsen: Now, there was another term used following on the same point of clarification. For those who don't know, what would be a light cone in this context?
Rosner: Imagine a 2-dimensional sheet of paper, which is your universe with a third dimension perpendicular to the axis, which shows the progress through time of your universe; so, the light cone is having a flash of light emitted at T=0. That becomes a circular wave front on the piece of paper, which gets bigger and bigger the more time passes. If you are ten miles away from the flash, you will certainly know of the flash within a second because the speed of light is 300,000 km/s. So, the radius of places that can know about the flash that will see the flash is anything not blocked within 300,000 km. within the first second. So, if you are ten miles away from where the flash happened, the light cone - this expanding circle that is getting wider and wider, thus making a cone - advances along the vertical axis will intersect you within 1/18,600th of a second because you are ten miles away. The speed of light of 186,000m/s. That's what a light cone is. You can do interesting things with a light cone in a gravitational field moving close to the speed of light and tilt the thing over. In the case of Special Relativity, it is semi-basic trigonometry. In General Relativity, it is more complicated, but still geometry.
Jacobsen: What extends an information framework into this? Why? What justifies consideration of an information-based cosmology into this framework? These types of geometry considerations.
Rosner: If you go back to Quantum Mechanics being about the ways the universe can define itself through the interactions of its particles and its space, then shared information is the basis for the existence of the universe and its appearance. Essentially, the universe is always being constituted by the interactions among its constituent parts and the history of those interactions.
Jacobsen: We're dealing with the large-scale too. How are you justifying the large-scale geometric concerns that are going to be around worldlines, light cones, and different scales of objects still macro like human beings and orbiting bodies into the framework?
Rosner: These are the tools you need to use, or the tools the universe paints itself with. If you are looking for deeper stuff, then you have to look at why the universe is locally, spatially 3-dimensional. I believe that has to do with degrees of freedom of information. That each part of the universe is defined versus other parts of the universe by its informational history versus the informational history of other parts of the universe. So, parts of the universe, the less information or the less history, the fewer interactions, over time that two parts of the universe have had with each other. The more that they are going to be farther apart, the farther apart they are going to be. The universe is arranged spatially with regard to commonality of information. Stuff that has a lot in common with you is close to you. Parts of the universe that don't have much in common with you are far away. The amount of variation, every part of the universe that only has 90% of the information in common with you. It should, on average, be a certain distance from you. Ditto for parts of the universe that only have 80% of interaction in common with you. That missing information allows for variation. Let's say, you have a set of 10 marbles. There's only one set of ten marbles. It is the set of all of them. However, if there were ten sets of nine marbles, one for each marble that can be left out. There are 45 possible sets of 8 marbles, of 2 marbles being left out, because there are 45. 10*9/2 combinations of two marbles that can be left out.
So, if you're sitting at the point in the universe that is all ten marbles, and the points of the universe that are each a set of nine marbles, it is going to be some distance from you, and then double the distance for double the amount of missing information. Then your universe at radius 1 has ten points. At radius 2, it has 45 points. At radius 3, it has 120 points. 10*9*8/6, which is 120 points. Because there are 120 possible sets of 7 marbles because there are 120 possible sets of 3 marbles that have been left out. At radius 0, you are right there. At radius 1, your universe has 10 points. At radius 2, it has 45 points. At radius 3, it has 120 points. So, it is growing weirdly. I believe that at small distances; the missing information that allows for the variation in the size of the universe that's missing a tidbit of information versus you, which means that it is all close to you. The way that that expands is by the square of the distance. So, you've got a set of spheres defining each distance from you, which necessitates a 3-dimensional or a locally 3-dimensional universe.
Jacobsen: I want to make a customary set of caveat questions because I know in the United States and in Canada a little bit less. There is a wide range of what is termed woo. How is this disconnected from any kind of magical, mystical, supernatural claims?
Rosner: The aim of science is to explain things without resorting to supernatural handwaving. So, basically, the aim of physics, at least, is to get everything down to things are the way they are because that's the way they have to be, according to some inarguable principles. There's always going to be room for handwaving questions, "Yes, but why?" Why does something have to exist or not exist? Isn't that the Law of the Excluded Middle? Something either is or isn't. There is no half is, except under quantum physics; there are indeterminate states.
Jacobsen: It is the most tested and confirmed theory to date. In other words, those three laws of thought of Aristotle are fundamentally wrong in some sense.
Rosner: The deal is, you want a universe that exists in the way it does because, according to the principles of existence, it has no choice but to follow these principles. You want to start with some stuff being easy to see as being justified in itself. Although, it is not really justified in itself because for something to exist; it has to exist for a non-zero length of time. Because something that exists for zero time doesn't exist. That seems true within itself. Although, if you poke at it for a while, there are all sorts of questions. Why does existence require duration in time? Is there something else besides time that some thing could exist in or because of? Somebody could argue about mathematical objects. They don't exist in time. They exist in the rules of math and our minds as we imagine them. They don't have a duration in time. When we think of a triangle, our thinking of a triangle may have duration, but the triangle exists in the pantheon of mathematical shit, which is timeless. So, you can pick apart the idea that to exist; something has to have duration because we just thought of a whole class of objects, which have some kind of existence that isn't necessarily temporal. It is like a mental existence. We can think of it. It leads to a whole new set of questions to tamp down or get back on something that resembles firm ground. You are never on firm ground because you can always come up with important quibbles. The idea is to push the quibbles and the handwaving and the mystical "it is because it is, because God is so powerful; that he doesn't have to a creator, because he is that powerful." You try to push away the magic as far away as possible.
Jacobsen: The end.
Rosner: Okay.
[End of recorded material]
American Television Writer
(Updated July 25, 2019)
*High range testing (HRT) should be taken with honest skepticism grounded in the limited empirical development of the field at present, even in spite of honest and sincere efforts. If a higher general intelligence score, then the greater the variability in, and margin of error in, the general intelligence scores because of the greater rarity in the population.*
He has written for Remote Control, Crank Yankers, The Man Show, The Emmys, The Grammys, and Jimmy Kimmel Live!. He worked as a bouncer, a nude art model, a roller-skating waiter, and a stripper. In a television commercial, Domino’s Pizza named him the "World’s Smartest Man." The commercial was taken off the air after Subway sandwiches issued a cease-and-desist. He was named "Best Bouncer" in the Denver Area, Colorado, by Westwood Magazine.
Rosner spent much of the late Disco Era as an undercover high school student. In addition, he spent 25 years as a bar bouncer and American fake ID-catcher, and 25+ years as a stripper, and nearly 30 years as a writer for more than 2,500 hours of network television. Errol Morris featured Rosner in the interview series entitled First Person, where some of this history was covered by Morris. He came in second, or lost, on Jeopardy!, sued Who Wants to Be a Millionaire? over a flawed question and lost the lawsuit. He won one game and lost one game on Are You Smarter Than a Drunk Person? (He was drunk). Finally, he spent 37+ years working on a time-invariant variation of the Big Bang Theory.
Editor-in-Chief, In-Sight Publishing
Scott.D.Jacobsen@Gmail.Com
(Updated January 1, 2020)
[1] Four format points for the session article:
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