# mathematics

### Simple and heuristic optimization

June 29, 2012 |

This week, at the Rmetrics conference, there has been an interesting discussion about heuristic optimization. The starting point was simple: in complex optimization problems (here we mean with a lot of local maxima, for instance), we do not ne... [Read more...]

### multiplicitiesoffreedom demonstrates Chaos Theory in Excel. If…

June 29, 2012 |

multiplicitiesoffreedom demonstrates Chaos Theory in Excel. If he filled in more initial values, you would see a thick bar—like a picture of white-noise. Butterflies flapping their wings in Vermont to change the wind in Hangzhou? A drop of water on ... [Read more...]

### How do I Create the Identity Matrix in R?

June 27, 2012 |

I googled for this once upon a time and nothing came up. Hopefully this saves someone ten minutes of digging about in the documentation. You make identity matrices with the keyword diag, and the number of dimensions in parentheses. __ diag(3) [,...

### How to outrun a crashing alien spaceship

June 11, 2012 |

Hollywood movies are obsessed with outrunning explosions and outrunning crashing alien spaceships. For explosions the movies give the optimal (but unusable) solution: run straight away. For crashing alien spaceships they give the same advice, but in this case it is wrong. We demonstrate the correct angle to flee. Running from ... [Read more...]

### Nonconvexity, and playing indoor paintball

April 6, 2012 |

Following the two previous posts (here and there), on the number of people that don't get wet while playing with water pistols, consider now an indoor version, in a non-convex room (i.e. player behind wall are now, somehow, protected). In the previ... [Read more...]

### Playing with fire (or water)

April 2, 2012 |

A few days ago, http://www.futilitycloset.com/ published a short post based on the fourth problem of the 1987 Canadian Mathematical Olympiad (from on a problem from the 6th All Soviet Union Mathematical Competition in Voronezh, 1966). The problem i... [Read more...]

### How Not To Draw a Probability Distribution

March 7, 2012 |

If I google for “probability distribution” I find the following extremely bad picture: It’s bad because it conflates ideas and oversimplifies how variable probability distributions can generally be. Most distributions are not unimodal. Most dist... [Read more...]

### Penny pinching yields pennies

January 26, 2012 |

A Greek Professor of Economics has written up a thought-provoking series of articles on complexity fetishism. As part of his …Continue reading » [Read more...]

### Random matrix theory and APT’s daily global model

January 25, 2012 |

Someone emailed me recently and asked about how APT uses random matrix theory in their factor model. Another question I …Continue reading » [Read more...]

### Even odds

January 22, 2012 |

This evening, I found a nice probabilistic puzzle on http://www.futilitycloset.com/ "A bag contains 16 billiard balls, some white and some black. You draw two balls at the same time. It is equally likely that the two will be the same color as diff... [Read more...]

### Error Handling in Lyx & Sweave: using Quantmod (and R, of course)

November 8, 2011 |

I do reports for clients with LyX and Sweave. It took me an extremely long time to get them working, but now that they’re working I can do more in an hour and thus charge more per hour. If you’re not familiar, here’s a rundown: LaTeX is ... [Read more...]

### Hey! I made you some Wiener processes!

September 7, 2011 |

Check them out. Here are thirty homoskedastic ones: __ homo.wiener for (j in 1:30) {  for (i in 2:length(homo.wiener)) {          homo.wiener[i,j] for (j in 1:30) {        plot( homo.wiener[,j],           type = "l", col = rgb(.1,.... [Read more...]

### Seriously … why don’t math classes use computers?…

August 31, 2011 |

Seriously … why don’t math classes use computers? Excel, simple Python scripts, Mathematica / Sage, everything beyond the TI-83. Kids could be creating totally sweet visuals instead of cribbing formulae. And thinking instead of copying. I can sa... [Read more...]

### the batman equation

August 13, 2011 |

HardOCP has an image with an equation which apparently draws the Batman logo. Read More: 1295 Words Totally [Read more...]

### LaTeX Typesetting –Basic Mathematics

August 1, 2011 |

LaTeX is very strong for typesetting mathematical equations. Fast Tube by Casper Other useful resources are provided on the Supplementary Material page. [Read more...]

### The foundations of Statistics [reply]

July 18, 2011 |

Shravan Vasishth has written a response to my review both published on the Statistics Forum. His response is quite straightforward and honest. In particular, he acknowledges not being a statistician and that he “should spend more time studying statistics”. I also understand the authors’ frustration at trying “to recruit several ... [Read more...]

### The foundations of Statistics: a simulation-based approach

July 11, 2011 |

“We have seen that a perfect correlation is perfectly linear, so an imperfect correlation will be `imperfectly linear’.” page 128 This book has been written by two linguists, Shravan Vasishth and Michael Broe, in order to teach statistics “in  areas that are traditionally not mathematically demanding” at a deeper level than ... [Read more...]

### Twitter Math Puzzle and Solution

July 7, 2011 |

Yesterday I posted a very simple math puzzle to Twitter that I found in Jonathan Baron’s book, Thinking and Deciding. The puzzle is the following: Show that every number of the form ABC,ABC is divisible by 13. The puzzle comes up in Baron’s book as an example of ... [Read more...]

### B*tchin’ six dimensional 6-cube. The rainbow colours and…

July 1, 2011 |

B*tchin’ six dimensional 6-cube. The rainbow colours and glass panes really help this visualisation.  Examples of 6-dimensional things If it’s hard to envision 6 dimensions, consider this: the possible tunings of a guitar constitute a 6-dimensio... [Read more...]

### Easiest way to start imagining four-dimensional things is by…

January 15, 2011 |

Easiest way to start imagining four-dimensional things is by numbering the corners of a 4-cube. First realize that the eight corners of a cube can be numbered “in binary” 000—001–010–100—110–101–011—111. Just like the four corners of ... [Read more...]
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