Albert finds the light…

This commentary is based on ideas expressed by Michael Guillen in his book “Five equations that changed the world.” I must admit that the conclusions reached in the book are beyond my capacity to comprehend to the fullest. However, I challenge the curious to contemplate these esoteric pontifications.

The story of Albert Einstein’s journey to intellectual knighthood is intriguing. As the story goes, after many years of ruminating, he had an epiphany. He decided that the speed of light is constant from any point of reference. From this idea sprung many answers to centuries old questions. For one, as an object’s speed increases, its mass and energy expands by the reciprocal of the shrinking factor. This factor refers to any process where the whole of something is shrunk by some small amount. He expressed his conclusions on this subject most eloquently in words, but, more importantly, he also expressed the ideas in the more exact terminology and symbology of mathematics.

For example, when thinking of the change of mass in reference to the speed of light, he considered the following variables:

sf=shrinking factor
esf=Einstein’s shrinking factor
ml=mass lost
n=number of times shrunk
s=amount of shrinkage
k=kinetic energy
m=mass
c=speed of light
e=energy

Albert knew that the equation for the shrinking factor is:
Equation 1: sf = 1 – (n * s) = (1 – s)**n

Using that knowledge, he theorized that as the speed of an object decreased, mass decreased by the following equation:
Equation 2: esf = 1 – (½ * v**2/c**2) = (1 – v**2/c**2)**½, where n = ½, s = v**2/c**2.

Which meant that the mass decreased as follows:
Equation 3: ml = m * ½ * v**2/c**2.

Einstein also knew that the formula for kinetic energy was:
Equation 4: k = m * ½ * v**2,

He noted that if he divided both sides of the kinetic energy equation by c**2, the result was:
Equation 5: k/c**2 = m * ½ * v**2/c**2,

So, if he combined equations 3 and 5, the result was:
Equation 6: k/c**2 = ml

Then, by multiplying both sides by c**2,
Equation 7: k = ml * c**2

If e is substituted for k (since both are energy) and m is substituted for ml (since both are mass), the result was:
Equation 8: e = m * c**2

What an elegant and simple expression of one of the most complex thoughts ever conceived. An important point to note is that while the ideas are complex and the words one uses to express them are subtle and vague, the mathematics behind these ideas could not be simpler.

The application of mathematical logic is a beautiful thing to behold. Unfortunately, even though the formal logic of mathematics is excellent for defining and resolving scientific issues, it is woefully inept at deciphering the nuances of everyday verbal and written communication.

It is easy to fall into the trap of attempting to use logic to analyze human thought and communication. Mostly, humans speak in a nuanced manner, without regard for logic. Just as a foreign language is difficult to decipher without extensive study, verbal communication between two humans using the same language is often illogical and difficult to decipher. In this verbal world, subtlety must be diligently studied and applied if one desires to communicate effectively and to comprehend the arguments of other humans.

However, there is a good side to this vagueness and ambiguity. Humans have the opportunity and ability to create great poetry and literature by amplifying the enigmatical and often comical conclusions they draw from their own inept interactions with one another.

In a perfect world, human communication can be both nuanced and logical. But, for now, we must plug along with the tools we have.