## Things to read about

### Review - “The Last Days of Socrates”

The story of Socrates is both comforting and distressing to me. In “The Last Days of Socrates,” Plato tells of a figure that is absorbed in and committed to a life of reflection and thinking. He is a person in pursuit of the most everlasting gift: wisdom. He sometimes waivers between being humble and pompous; and he certainly doesn’t get everything right. But perhaps what I respect most about Socrates is this facet of his personality and thought — that he would and does admit his ignorance and unashamedly. He is genuinely concerned with the most profound and rewarding of activities: the exploration of thought itself as a means to finding truth. Anyone interested in such ways of life, I believe, as did Socrates, must maintain a disposition of not fearing one’s ignorance or errors in thinking but understanding the relationship between such frustrations with respect to pursuing wisdom and truth. I find it comforting that others, such as Socrates, have walked this Earth. The distressing aspect of Socrates’s story is his death. I suppose I am like many of his followers in that this distress is my own but not his, despite his willingness to discuss his reasons for greeting his death sentence with joy not sorrow. Perhaps there is a wisdom in his reasoning, but it has yet to bring me an assured sense of relief from the troubling pattern of man’s willingness and need to murder the heretical thinker whose goal of thinking is most surely for the benefit of the human soul. I find this truth — that man seeks to silence those who seek truth about existence — when he fails to understand what is sought and found, one of the most troubling and terrifying aspects of the nature of the human condition.

### Review - “Anthem”

Say what you will of Ayn Rand’s philosophical ideas, especially those she worked on later in her life; but as a story, how can one not be horrified by the potential of “Anthem” and thus find relief in the awareness brought about by this short tale? As a scientist, perhaps I feel a constant need to remind every generation of the value of individuality, the pursuit of curiosity, and the freedom to think and speak differently than others. But surely if these things are of value, they necessitate protection. By examining the ways in which such things may be lost and the subsequent realties of such loss, “Anthem” serves the purpose of having tried to safeguard these precious qualities of life.

### Excerpt from "The Man Who Loved Only Numbers" - The difference between physicists and mathematicians

"The Man Who Loved Only Numbers" by Paul Hoffman is a biography about the memorable personality that is Paul Erdős, the prolific mathematician, who published with over 500 collaborators. Erdős, who is well-known for his contributions to number theory, set theory, probability theory, graph theory, and more, as well as the invention of the Erdős Number, a measure of one's proximity to having collaborated with him, is of course a subject himself. That said, in Hoffman's biography of him, there is a bit about the behavior of mathematicians and a lone physicist that does well to embody the spiritual and cognitive differences between the two groups, both of which share a passion for mathematical thinking but nevertheless are separable beasts.

The excerpt of interest tells of a mathematics conference in which a group of mathematicians return to the coffee table after a talk only to find a puzzle.

### Review - "The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom"

I am not sure if others would find it dry -- or rather as exciting as I did. Dirac is a strange character, absolutely. The ultra logical but emotionally flat physicist is obviously a mathematical genius. If you have never studied the derivation of the Dirac equation, you should, and if you do not find yourself in awe of his intuition, then perhaps you are the better physicist than I. This book, though, does not go into any of that but perhaps it will provoke your interest; rather it is a telling of a physicist who has no doubt suffered emotional pains that led him to retreat from the world of feelings towards that of theoretical physics. A somewhat sad tale at times, Dirac's life is one of its very own, unique meaning, captured and told well by Graham Farmelo in “The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom.”

### Review - “Sapiens: A Brief History of Humankind”

There are few books that can be recommended seriously and broadly to many, and Sapiens is on this short list. Admittedly, it, like any historical narrative, is one that features its author's bias, but this is a certainty of a field that is not and cannot be objective. That said, rather than penalize Sapiens for such a trait, I suggest we celebrate it for telling an insightful, coherent, detailed, and fascinating tale of our origins, filled with a wisdom sorely missing of this age, that dares to consider the realities and obviousness of the direction our species treads. Highly recommended.

### Introducing didacticful: a live textbook about physics

I have recently launched a new venture: didacticful, a live blog-style textbook that is devoted to topics in physics. Currently, I am writing a textbook on particle physics, which you'll find on the blog. Along the way, you'll also find posts related to interesting topics in physics.

Continue reading to find topics on mechanics and special relativity

### Lorentz invariance of the relativistic dot product

Perhaps you are familiar with the idea of the dot product and its invariance. That is, for the dot product, $a \cdot b$, it is true that $a \cdot b = a' \cdot b'$, where $a'$ and $b'$ are the vectors $a$ and $b$ after some translation or rotation operation has been applied. In other words, the dot product between two vectors doesn't change if you rotate or translate $a$ and $b$ together -- the dot product is invariant under such transformations. The reason for this invariance is because these two transformations do not alter the length of $a$ and $b$ nor the angle between the vectors $\theta$, so the value of the dot product is unaffected by such transformations. To see this, write: $a \cdot b = ab \cos\theta = a' b' \cos\theta' = a' \cdot b'$

It turns out that there is an analog to the dot product with regards to four-vectors. That is, there is a quantity that we can calculate that is unaffected by a certain kind of transformation. We call this quantity the "relativistic dot product" and this transformation the  "Lorentz transformation." This form of invariance is often referred to as "Lorentz invariance."

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