Why is this?
You might’ve heard an explanation that goes like this: whenever you drop an egg, or melt an ice cube, or shatter a wine glass, you’ve increased the entropy of the world. You might also have heard the phrase, “entropy always increases”. In other words, things are only allowed to happen in one direction — the direction in which entropy increases.
But this doesn’t answer the question, it just replaces it with a new set of questions.
What is entropy, really? Why does it always keep increasing? Why don’t eggshells uncrack, or wine glasses unshatter? In this piece, my goal is to give you the tools to answer these questions.
Going down this road leads us to some of the biggest unanswered questions about the cosmos: how did our universe begin, how will it end, and why is our past different from our future?
The most common question students have about mathematics is “when will I ever use this?” Many math teachers would probably struggle to give a coherent answer, beyond being very good at following precise directions. They will say “critical thinking” but not much else concrete. Meanwhile, the same teachers must, with a straight face, tell their students that the derivative of arccosine is important. (It goes beyond calculus, in case you were wondering)
Let me start with a question: How do you know if a person is lying? If you’re like most people, your first response will be something like “Liars don’t make eye contact.” In a survey of 2,520 adults in sixty-three countries, 70 percent of respondents gave that answer. People also tend to list other allegedly telltale signs of lying, such as fidgeting, nervousness and rambling. In an interview with the New York Times, psychologist Charles Bond, who studies deception, said the stereotype of what liars do “would be less puzzling if we had more reason to imagine that it was true.” It turns out that there’s no “Pinocchio effect,” no single nonverbal cue that will betray a liar. Judging a person’s honesty is not about identifying one stereotypical reveal, such as fidgeting or averted eyes. Rather, it’s about how well or poorly our multiple channels of communication — facial expressions, posture, movement, vocal qualities, speech — cooperate.
There are four simple steps to the Feynman Technique, which I’ll explain below:
- Choose a Concept
- Teach it to a Toddler
- Identify Gaps and Go Back to The Source Material
- Review and Simplify
You make thousands of rational decisions every day — or so you think.
From what you’ll eat throughout the day to whether you should make a big career move, research suggests that there are a number of cognitive stumbling blocks that affect your behavior, and they can prevent you from acting in your own best interests.
Here, we’ve rounded up the most common biases that screw up our decision-making.
“mpmath is a free (BSD licensed) Python library for real and complex floating-point arithmetic with arbitrary precision. It has been developed by Fredrik Johansson since 2007, with help from many contributors.
The following example computes 50 digits of pi by numerically evaluating the Gaussian integral with mpmath. See 100 mpmath one-liners for pi and the documentation links below for many more examples!
>>> from mpmath import mp >>> mp.dps = 50 >>> print(mp.quad(lambda x: mp.exp(-x**2), [-mp.inf, mp.inf]) ** 2) 3.1415926535897932384626433832795028841971693993751
mpmath runs on Python 2.5 or higher (including Python 3.x), with no other required dependencies. It can be used as a library, interactively via the Python interpreter, or from within the SymPy or Sage computer algebra systems which include mpmath as standard component. SageMathCloud lets you use mpmath directly in the browser…”
“Genetic algorithms are in the class of evolutionary algorithms that build on the principle of “survival of the fittest”. By recombining the best solutions of a population and every now and then mutating them, one can solve remarkably difficult problems that would otherwise be hopelessly difficult to write programs for…”
“Customers ask us for p99 (99th percentile) of metrics pretty frequently.
It’s a request that certainly makes sense, and we plan to add such a functionality to VividCortex (more on that later). But a lot of the time, when customers make this request, they actually have something very specific in mind — something problematic. They’re not asking for the 99th percentile of a metric, they’re asking for a metric of 99th percentile. This is very common in systems like Graphite, and it doesn’t achieve what many people seem to think it does. This blog post explains how you might have the wrong idea™ about percentiles, the degree of the mistake (it depends), and what you can do instead…”