"As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality." -Albert Einstein
BE FOREWARNED! The subject of debating paradoxes can be offensive by nature. Either side you are on, you have the onus of trying to tell someone else that they believe something that is illogical. Many people will take offense to that alone instead of realizing that it is not their fault if they were misled. Additionally, because the subjects are so subtle, the presenter of the argument must put a lot of emphasis on points of illogic. This also seems very inflammatory, but it is a necessary tool. With this in mind, please take some of my side commentary as an attempt at humor. If you take offense to someone being a smart-ass, then this area will just piss you off ,and that's really not my intent. Do not believe that I am completely unwavering in my beliefs and ask you to do differently. Please do bring up points of contention in the discussion area. I enjoy the challenge and the opportunity to solidify the truth in my own mind; whatever it is!
Unfortunately, paradoxes are a little too subjective to be discussed in a purely factual manner because it would not be a paradox worth discussion if there were hard evidence to prove one way or the other. In this section I'm taking a break from being entirely serious while we explore some pretty "funny" aspects of relativity. After all, relatively speaking, the faster you go the slower you move! In fact, I’m the fastest human being on earth; Every move I make is very close to the speed of light. It just so happens that the percentage of the speed of light I’m moving at is just enough to slow me down to the point at which I look like I’m moving at a normal speed from your frame of reference…
Why are paradoxes important? Aren’t they just a case of laypeople, commoners and other riff-raff not understanding the math??
When a grade school student encounters a word problem, they are supposed to use their logic, rationale, and deductive reasoning to determine what math is required, and how it is to be structured, to properly solve the problem. If that student produces a perfect, beautiful and complex equation and it produces reliable results as well as being mathematically flawless, is it the correct answer? What if he uses a well known and useful equation and solves it perfectly? Is it correct?
No, not necessarily. By examining paradoxes, we are critiquing the logic and understanding of the problem that the originator of a theory used to determine the math instead of the accuracy of the math itself. Unfortunately there is a large community of people who do not separate the logic required to formulate math from the math itself. There is a prevailing (and irrational) belief that a correct equation is a correct answer.
Laypeople can actually be qualified to examine pure logic but when a layperson recognizes a fundamentally flawed concept, they are given a very generic answer, a brush off, or the typical meandering unintelligible response so rife with vagueness, condescension and artificial complexity, that the hearer is supposed to just back down. This is a typical stratagem found in corporate offices across the USA. As my scientific reference I’ll use the comic Dilbert. Feel free to study it in depth if you are unfamiliar with BS’onics.
In response to those generic answers I will pose the following:
- It's all in the Math? I can build a mathematical model of absolutely anything and everything in it will work perfectly as described in that model. Here’s the important part though: Just because the model works and will produce the same outputs for the same inputs does not mean that it is reflective of reality. One such mathematical model of this type is called “Toy Story”. (This piece of reference material can be found at the media library known as blockbuster) I argue that the math used is, more often than not, very tenuously connected to reality. It is similar to saying that we both came to the answer of 7 and it does not matter if I used 6+1 and you used 4+2+1. You could, from one perspective, say that 4+2 is equal to 6 and therefore unnecessary, but seen from an accounting(GAAP) perspective the folly is revealed. If this thought process was followed in an accounting system then you'd find that when you need to make calculations in the future they could very well be wrong though sometimes they would be right.
- Experimental Data? The very nature of experimental data has become a slippery slope since the inception of relativity. The interpretation of that data should not be given the same validity as the data itself. Unfortunately, as I provide elsewhere in these pages, there are many cases of experiments that are performed horribly wrong or the instrumentation is terribly inaccurate: Hafele-Keating is one of my favorites… The interpretations of experiments ever since the advent of relativity have become completely one-sided in nature. The Sagnac Effect which proves Aether (disproves relativity) is purportedly interpreted using general relativity or they arbitrarily add a universal reference frame ("proper time") which is exactly what Aether is!