You want to shoot a target, but as soon as you pull the trigger the target is dropped and starts to fall. Should you aim above or below the target to hit it? Actually, neither. The bullet and the target will proceed to fall at exactly the same rate downwards due to gravity. If you fall with the ball and the bullet, then you will see the bullet travel in a straight line no matter which way you shot it (right hand picture). So if you point the gun straight at the bullet, it will certainly hit it. [more (video)] [code]
Matthen has returned from vacation!
I have a few unresolved questions about this particular Newton-style thought experiment. They may be addressed once I look at the video and code, which I haven’t done yet. I suspect that it is merely a matter of assumptions and frame of reference that I need to reconcile. I couldn’t wait to do that, as I am just too eager to share!
 Any complaints should be directed at me, not Matthen, as I usually vet anything that I re-post, if it is of a “vet-able” nature. As analogy, consider the shamed, and now financially bankrupt DigiNotar B.V. certificate authority. Though the analogy is imprecise, and this entire paragraph is starting to sound sanctimonious, I don’t want to be a weak link in the chain. (How’s that for over-thinking all the fun out of something?)
 Video is on YouTube, and code is on Pastebin. For those who fear malicious links, unintentional as they may be. Yes, I recently read an entire study by NSS Lasbs about socially-engineered malware a.k.a. “SEM”. They’ve been doing these studies on a quarterly basis for 5+ years.
 Idle conjecture: SEM is the ultimate form of Black Hat SEO.
Look! This is Google’s doodle for today! :D
No one has solved this one yet. Except for Fermat. Maybe.
I do wish this were a larger-sized image. My fault for not taking a screen shot when I had the chance (yesterday).
“With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”
-Attributed to von Neumann by Enrico Fermi, as quoted by Freeman Dyson
Reminds me of when I used to sit in engineering class idly finding formulas, like 69! that came as close as possible to exceeding the mantissa limits of my old IT calculator.
Try Robert Baillie: Fun with Large Numbers for four research papers on Arvix.
All are written by the same author, with a similar theme e.g. “Fun with Fourier Series” preceded by “Fun with Large Numbers”, as initially noted by P. Kedrosky. Submission of the latter was May 2011, so these are not all research relics.
* Some with full text, others are abstract only, alas
Imagine an area inhabited by a population of eternal agents A, which are spread out uniformly with average density nA and move around randomly, with diffusion coefficient DA.
Imagine now a race of mortals, B, which also are spread over this area, with initial uniform density nB(0). The agents die at a constant rate, μ, (B→μ) and proliferate (divide) when they meet the “catalyst,” A, with rate λ (B + A→λB + B + A). The Bs are diffusive, hopping at the rate DB.
What will happen?
The study of diffusion limited reactions (3) already has shown in the past deviations from the continuum theory because of the quantized nature of the reactants. In the present case the effect is even more dramatic. It constitutes the difference between life and death. The continuum approach predicts extinction whereas the direct simulation uncovers the emergence of a thriving, adaptive, developing system….
We find that in conditions in which the continuum approach would predict the extinction of all of the population (respectively the vanishing of the invested capital or the concentration of a chemical substance, etc.), the microscopic granularity insures the emergence of macroscopic localized subpopulations with collective adaptive properties that allow their survival and development.
In particular it is found that in two dimensions “life” (the localized proliferating phase) always prevails.
Via End-to-End Analysis of the Spam Value Chain
An excellent study! It was short, easy to understand and full of original content.
Links to supporting research (with no pay walls in the way!), news, fun stuff too! E.g. “Anatomy of a Spam Viagra Purchase”.
End-to-end Analysis of the Spam Value Chain is a recent study researched and sponsored by The International Computer Science Institute in Berkeley, California.
The International Computer Science Institute
The ICSI is one of the only non-profit independent research organizations in the U.S.A. It is also a leading center for computer science research, worldwide.
Imaginary numbers always confused me. Like understanding e, most explanations fell into one of two categories:
It’s a mathematical abstraction, and the equations work out. Deal with it.
It’s used in advanced physics, trust us. Just wait until…
The reason small changes in a logarithm (like MMS scale) mean big changes in what the logarithm is applied to (like actual earthquake magnitude), is because logarithms count what are called orders of magnitude. A plain-English way to say this is that logarithms tell you how many zeros a number has.
Things in the hundreds have 2 zeros. Things in the millions have 6 zeros. You see how it goes. For this reason, a logarithmic scale can be used to talk about huge ranges, such as the size of the solar system compared to the size of an atom (which is about 23 orders of magnitude in difference).
Logarithms also have properties that we humans often perceive as beauty.
Avoiding stopwords in random strings
If you use base 28 for URL shortening or for encoding randomly generated strings you can avoid many of the worst English-language swear words.
Base 28 has no S, T, or U.
Think about it.
As originally tweeted by @64.
I guess there’s no longer a reason to feel shame. I loved math.
omg this is seriously my life. wow.