How many times I "googled it", June 2012 to present
Apr 3, 2015
Today at 4:13 pm I got the urge to google “google search history”.
I figured that google was keeping all kinds of tabs on me, but at google.com/searchhistory you can find a nice browsable catalog of everything you’ve ever searched for while logged into your google account. Many people disabled this feature when they noticed that they were getting targeted ads and personalized search results, but all my ads are blocked and I’ve never been bothered enough to disable it.
Thoughts from one American mind upon closing "Closing of the American Mind"
Jan 27, 2015
I have just finished reading a very strange book, and I want to try to make some personal sense out of it because it was a little unsettling. I’m really not sure what I just read, and I don’t think I agree with much of it. But I know that there were some extremely provocative ideas presented here and intellectual honesty compels me to confront them, hence the present post.
"The Greatest Equation of All Time"
Dec 19, 2014
Sorry to have been so long away from the blog! The purpose of this post is to give some intuition for Euler’s identity (“the most beautiful theorem in mathematics”) to those who haven’t seen it before or to those for whom it is meaningless because they lack the math background.
This was never introduced to me in any class, and unless you majored in math or physics the same is probably true for you.
"Important Peculiarities" of Memory
Dec 18, 2014
In my high school psychology class I was told that human memory capacity was unlimited …and it has bothered me ever since. How, I mean? Aside from the physical limitations on information storage, how could a system that remembers everything forever be evolutionarily advantageous?
This is a question I hope to explore in a deeper way sometime soon; for now, I want to talk to you about a few “peculiarities of human memory” that begin to shed some light on the situation (Bjork & Bjork, 1992).
2 x 2 Statistics
Oct 31, 2014
Modern data analysis has gotten very complicated! Let’s forget all that for a moment. I wanted to take this opportunity to examine several useful statistical techniques and measures of association that involve nothing more than a 2x2 contingency table. A 2x2 contingency table (also called a cross tabulation or cross tab) is a simple grid that displays the frequency distribution given two variables–one variable for the columnsand one variable for the rows.
The Math of Secrecy: RSA Cryptography (and Shapes You Can Draw!)
Jul 13, 2014
When Gauss was 19, he discovered that of the infinite number of polygons that have a prime number of sides, a mere five of them can be constructed with a ruler and compass (i.e., using only straight lines and circles). These prime-sided polygons can have 3, 5, 17, 257, or 65537 sides, but only these five are possible (probably).
Indeed, the only shapes you can draw with an odd number of equal-length sides are the multiples of these 5 primes: 3, 5, 15, 17, 51, 85,…, 4294967295
Circling the Square & Squaring the Circle!
Jun 26, 2014
In A Mathematician’s Lament, Paul Lockhart roundly decries the way our school system sucks the soul out of mathematics; what was forced down most of our throats was an insipid husk of repetitive calculation, plug-in formulae, and rigid formality, all of which we were called upon biweekly to regurgitate. Most painful for him to see is the way geometry is taught:
"All metaphor aside, geometry class is by far the most mentally and emotionally destructive component of the entire K-12 mathematics curriculum.
Smart Drugs: Special Topics in The Neurobiology of Learning/Memory I
Jun 21, 2014
Smart Drugs & LTP: Enhancement of Long-term Potentiation Through Actions on AMPA-Receptor Initiation and CREB Consolidation Unlike the previous installment, this post presumes a great deal of background knowledge on the part of its readers. My intended audience has taken a class in general biology, neuroscience, or physiology at the college level and are familiar with terms like synapse, action potential (depolarization, ion channel, electrochemical gradient), neurotransmission (axons, dendrites, receptors, ligands, inhibition (IPSP), excitation (EPSP)), neurotransmitters (especially glutamate, GABA, acetylcholine, dopamine, serotonin, epinephrine), and gene transcription/translation.
Base-10 Blocks to a Billion!
Jun 18, 2014
Everybody who went to public elementary school in the USA after the mass production of plastics (1940s and 1950s) and before, say, the advent of the iPad, knows what these things are:
In case any of my readers do not meet the above criterion, these blue (sometime orange) plastic blocks are manipulatives used in classrooms to help teach kids all sorts of mathematical concepts, from addition and subtraction to place value and volume.
Miles and Miles!
Jun 17, 2014
This post considers the humble mile. You know, the unit of distance. 5,280 feet… 1,760 yards… 8 furlongs of 660 feet a piece… Have you ever thought about how nicely divisible our mile is? I have two principal goals in writing this post; they are, in order of ascending importance, (1) to talk about the history of the mile, and (2) to demonstrate an effective algorithm for finding all the factors of a number.