Data Anxiety

Fun With Very Large Numbers

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.

Good times.

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

The importance of being discrete: Life always wins

Imagine an area inhabited by a population of eternal agents A, which are spread out uniformly with average density n_A and move around randomly, with diffusion coefficient D_A.

Imagine now a race of mortals, B, which also are spread over this area, with initial uniform density n_B(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 D_B.

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.

Unusual features

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.

A Visual, Intuitive Guide to Imaginary Numbers

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…

clearscience:

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

via chxor:

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.

via leftoversignals:

omg this is seriously my life. wow.

(via leftoversigils)

via Math math math - Imgur

The “distressed” effect i.e. yellowed, old and dried out, makes this even more charming.

I was surprised how much I liked this, even beyond the aesthetic appeal. Usually, I am most comfortable with the literal and tangible. Or matters validated by personal experience. Such preferences are NOT consistent with a data visualization of complex numbers! Anything that is described as “transcendental”, regardless of context, is subtle. Enigmatic.

But this isn’t confusing (or irritating!). That’s because there is a single “leap of faith”, requiring only one axiom* I must accept as truth. Once overcome, all other relationships are either transitive or can be derived as a closed-form solution. That’s math-speak for paper and pencil.

Closed-form solutions are empowering

Why? Because external help is unnecessary. No numerical analysis. No Monte Carlo simulation. Nothing relying on computational methods. No statistical analysis programming application. No PC. (No mainframe running TSO/MVS, SPF and JCL either!)

Closed-form solutions require something to write with, something to write on, and ME! I love to feel so capable and self-reliant.

roomthily:

The Map of Complex Numbers

via visualizing

*Actually, acceptance of three or half a dozen axioms might be required

I’m uncertain because I can’t clearly see everything in the image. I guess the “leap of faith” is better described as “bouncing”.

Kinetic energy

When a vehicle stops suddenly, the energy has to go somewhere

via The Republic of Mathematics blog