Sunday, December 9, 2012

Rational Metaphysics: Standard Infinitesimal

EugeneMorrow wrote:How many points are then in one inch and two inches? As many as you want. Everyone knows that. How many points are then in InfA? As many as you want. That's the problem for RM.

That has been a problem for mathematics and Science, but it isn't a problem for RM because RM addresses and fixes that problem.

What does "God" mean? "Whatever you want it to mean."
Why does the universe exist? "Whatever reason you want."
What do you call the things that atoms are made of? "Whatever you want to call them."
What is an elemental wave? "Whatever you want it to be."

That is how you keep a society ignorant and backwards. Establishing a standard is critical for making progress.

How many points are in a 1 inch line? "As many you want."
Well, that part is true. You are free to set the number of points that you "want" to deal with... once. But of course, if you are using logic, you are not free to then change that number as you go. Since a 2 inch line is already defined by being twice as long as a 1 inch line, you are no longer free to just choose as many points as you want. Otherwise logic and math become useless and anything else you say after that point is truly meaningless.

So if you say that there are going to be 1 million points in a 1 inch line, then you are stuck with having 2 million in a 2 inch line, else why bother even talking about it.

But now if you declare that there are an infinite number of points in a 1 inch line, then in keeping with logic and math, there must be 2 times that many in a 2 inch line, "2 * inf". And that is where current mathematics leaves the room, because current mathematics doesn't define what "2 * inf" mean other than to say that it is "still infinite/boundless". Thus in math, 2 * inf = inf, which of course, using math, "(2 *inf) / inf = 1" which violates the rules of math. You can't use current mathematics with an infinite number of points and make any headway.

Thus in RM, you are to set a standard of interest perhaps saying that a 1 inch line has an infinite number of points, thus establishing an "infinitesimal". And that standard is to be named " infA". Now you can know that a 2 inch line has 2 * infA points and "(2 *infA) / infA = 2". Thus both logic and math are still useful... because you set a standard.

How long is one second? "As long as you want"? Well, that doesn't help anyone and forbids reasoning. Thus a standard is set. "How do you know that they got it right? Maybe what they set isn't really how long a second is." It is whatever they set it to be, end of story.


This issue comes into play when dealing with the concern of propagation which is a measure using both time and distance. Both time and distance must have a standard set so as to allow reasoning and progress. And when it comes to the infinitesimal issues of both time and distance, a standard must be set for each, as neither are directly related to the other (yet).

So without a formal standard already being set, one is free to choose a standard and then stick to it, for time and also distance. I am free to say that 1 second has infA points of time in it. And I am still free to pick any standard for the number of points in a 1 inch line. As explained before, no matter what standard I choose for the distance infinitesimal, I will have immediately affixed a ratio between time and distance infinitesimal measurements.

So in RM, I chose that they be the same standard so that the ratio will be simply 1, "infAt / infAd = 1", by definition.

Once that is chosen, it is no longer, "as long as you want". And the relation between time and distance measurements are no longer, "whatever you want". Then by merely choosing a name for each unit to represent that standard we have;

1 tic / 1 toe = 1, by definition.

And as explained before that ratio could have been chosen as anything. But as long as it is chosen and defined, there will always be a fixed ratio between time and distance. That fixed ratio is what allows for propagation to have meaningful, "rational" measure.

Of course you are right in that if you allow anything to just mean "anything you want", then there is no point in discussing anything or attempting to reason. But then that would apply to your TEW and QM as well. QM set many standards so as to make the progress it made, as did all of Science.


Now, since we are dealing with infinitesimal steps in both time and distance, we know the ratio of those infinitesimals.
If the smallest distance is achieved in the shortest time, it occurred at a rate of 1 toe/tic.

EugeneMorrow wrote:RM declares that 1 toe/tic is the maximum rate of change. Why isn't that value the minimum? Why isn't that value the average? Why is there a maximum rate?

The reason that it is the maximum and not the minimum is because it refers to the ratio of the smallest and shortest possible for each unit. If 1 toe distance is achieved, by definition it took infA steps to do it. And in infA steps, by definition 1 tic would have been achieved. If you achieved N toes in distance, by definition it took N*infA steps in both time and distance.

Thus you cannot get a ratio greater than 1. But if you are slowed for some reason, you might not achieve 1 toe in distance during 1 tic, and thus the achieved propagation could be less than 1, but never greater.

Unless you want to use an ontology wherein the laws of physics are arbitrary and change from one point in space to another, the ratio between your units of measure must remain affixed throughout all space. What would be the point in trying to measure something if the next time you measure it, perhaps in a different location, it is going to be arbitrarily different? There would be no point in having an ontology or Science. You are free to set such ratios once, but then throughout all future calculations, that ratio must remain the same.

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