Category Archives: Math

Q: How do you define the derivatives of the Heaviside, Sign, Absolute Value, and Delta functions? How do they relate to one another?

Posted on April 12, 2014 by The Physicist

Physicist: These are four standard reference functions.  In the same way that there are named mathematical constants, like π or e, there are named mathematical functions.  These are among the more famous (after the spotlight hogging trig functions). The absolute value … Continue reading →

Posted in -- By the Physicist, Equations, Math | 10 Comments

Q: What does “E=mc2” mean?

Posted on April 7, 2014 by The Physicist

Physicist: This famous equation is a little more subtle than it appears.  It does provide a relationship between energy and matter, but importantly it does not say that they’re equivalent. First, it’s worth considering what energy actually is.  Rather than … Continue reading →

Posted in -- By the Physicist, Equations, Philosophical, Physics, Relativity | 25 Comments

Q: If you flip a coin forever, are you guaranteed to eventually flip an equal number of heads and tails?

Posted on January 10, 2014 by The Physicist

The original question was: Lets say we have a fair coin that is flipped a hundred times and at the end of the trial there have been 40 tails and 60 heads. At this time there have been 20 more heads than … Continue reading →

Posted in -- By the Physicist, Math, Probability | 39 Comments

Q: How do we know that π never repeats? If we find enough digits, isn’t it possible that it will eventually start repeating?

Posted on December 20, 2013 by The Physicist

Physicist: In physical sciences we catalog information gained through observation (“what’s that?”), then a model is created (“I bet it works like this!”), and then we try to disprove that model by using experiments (“if we’re right, then we should … Continue reading →

Posted in -- By the Physicist, Geometry, Logic, Math | 40 Comments

Q: Are some number patterns more or less likely? Are some betting schemes better than others?

Posted on November 29, 2013 by The Physicist

Physicist: First, don’t gamble unless you can be sure you won’t get caught cheating or you enjoy losing money. Games of chance come in two flavors: “completely random” and “not quite completely random”.  It’s not always obvious which is which, … Continue reading →

Posted in -- By the Physicist, Combinatorics, Entropy/Information, Math, Probability | 10 Comments

Q: How do we know that atomic clocks are accurate?

Posted on November 7, 2013 by The Physicist

Physicist: It turns out that there is no way, whatsoever, to look at a single clock and tell whether or not it’s accurate.  A good clock isn’t so much accurate as it consistent.  It takes two clocks to demonstrate consistency, … Continue reading →

Posted in -- By the Physicist, Experiments, Logic, Philosophical, Physics | 12 Comments