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."

Continue reading on didacticful

Neuroscientist’s create mathematical model for how the brain keeps a beat

For the musically fortunate, keeping a beat is as natural as breathing. But for those without the talent, the notion of producing and keeping a beat may seem an impossibility.

On Thursday this week, researchers announced a mathematical model that describes a potential mechanism by which the brain may keep a musical beat. The paper, published in PLOS Computational Biology, is a joint effort between Amitabha Bose of New Jersey Institute of Technology; as well as Aine Byrne and John Rinzel of New York University.

Understanding the physics of a pendulum

You've probably seen a pendulum swing, but have you ever thought about why it is that a pendulum swings at all? Further, why is it that a pendulum only swings for some period of time becoming motionless? It turns out, a simple pendulum is a great means through which we can develop intuition about the conservation of energy and the relationship between gravitational potential energy and kinetic energy -- not to mention oscillations.

How high up is outer space?

The Kármán line is the altitude of the boundary between earth’s atmosphere and outer space. This $100$  km or $328, 084$ ft. The value comes from Fédération Aéronautique Internationale, and it’s the same value that NASA uses to define the boundary between our planet’s atmosphere and outer space. 

If you’re like me, the highest you've ever been from sea level is around $30,000$ ft to $40,000$ ft, which is the range of altitudes at which most commercial airliners cruise at. 

Human Beings and the Next Revolution: A Warning About Automation

“Can you believe people actually used to work?”

Some day in the not-too-distance future, people will say words like these.