TENTH BRIEF: The Velocity of Light as a Nonterminating Decimal

The Euler Number (designated e) is the most interesting mathematical phenomenon there is. Like π, e is a nonterminating decimal. It seems to crop up all over the place, partly because there are numerous ways to derive it. It’s considered the fundamental constant of mathematics and is most commonly derived with integral calculus by integrating the equation y = 1/x (the fundamental asymptote, see 8th Brief). This integral is equal to ln x, which is equal to the area under the curve subscribed by y = 1/x, with integral limits of 1 to x. The base number of the logarithm is equal to e.

It turns out that if x = e, then the integral (the area under the curve of y = 1/x) is equal to one (unity). To further complicate things; by writing the logarithm as a linear equation we find the “fundamental exponential equation.” Namely: y = ex which is the most bizarre equation there is.

It’s bizarre because this equation is equal to its slope equation. That is, the differential (slope derivation) of ex is equal to itself.

Thus, if y = f(x) = ex: then f ’(x) = ex, f ‘’(x) = ex, f ‘’’(x) = ex and so on.

This equation is “non-differentiable.” No matter how often we differentiate it (or integrate it) the answer is always equal to itself, ex.

And also, when x = 1 then y = e, and e is a nonterminating decimal and as such, is a constant. Thus its differential (slope) is equal to zero. And if the slope is equal to zero, the curve is linear, except for one problem. Since e is nonterminating, its decimals go on endlessly, and therefore a nonterminating decimal cannot actually reach linearity. That is, the slope can never really equal zero. As it is with the asymptote, we just keep getting closer and closer to linearity, but can never actually get there.

Now, here it seems there is a similarity to the velocity of light and the Euler Number. Velocity is a ratio and is differentiable. But in accordance with the Lorentz Transformation, the velocity of light is an absolute “constant” and therefore the differential of the velocity of light is equal to zero. Theoretically, this indicates that the velocity of light is actually a nonterminating decimal (like e) and is thus asymptotic to a linear state within the confines of unity (essentially if we set the Universe equal to “one” rather than infinity). That’s why we cannot exceed the velocity of light in an approached linear system; the velocity of light is a nonterminating decimal. It has no absolute definition, because here again, the decimals go on endlessly.

In other words, since the velocity of light is a constant in a linear coordinate system, it appears that velocity is asymptotic to a linear state, and the velocity of light is thus a nonterminating decimal relative to the Universe as a whole (unity).

Could it be that the two fundamental constants, one in mathematics (Euler number, e) and the other in physics (velocity of light, c), are in fact the same thing? Or perhaps related in some way that is unknown at this time?

To be continued.