### Mean and standard deviation of the distances between letters

The following table shows is computed by calculating the distance between occurrences of letters in Jane Austen's Pride and Prejudice (for example, the distance between e's in the sentence "Hello, my name is Jeremy" is 9 and 2; all punctuation and spaces are ignored).

LetterMeanStandard Deviation
e7.76.3
t11.510.0
a12.911.1
o13.312.0
i14.212.3
n14.212.5
h16.014.2
s16.315.6
r16.514.4
d24.122.2
l25.025.9
u35.634.5
m36.535.1
c39.239.2
y42.342.3
w43.941.9
f44.643.9
g52.850.4
b58.955.6
p63.568.3
v94.492.0
k165.1172.8
j569.2638.9
z582.8834.4
x635.0669.6
q859.4873.9

martijn said…
I take it this is quite useful for cracking simple codes. Did you try other works? More recent ones? Non-fiction ones? Do they differ significantly? How big a sample text would you need for these numbers to approach their 'real' values?

Questions, questions...
Anonymous said…
Presumably there's some kind of mathematical relationship between these distances and the relative frequencies of the letters, possibly distorted by English n-graph frequencies?
Ruben Berenguel said…
And odd post John. Why were you looking at this? Some cryptographic thing, I guess? Or just out of boredom?

Cheers,

Ruben @mostlymaths.net
sesqu said…
Those measurements seem a lot like the actual letters might fit Poisson distributions. I guess that means she has a wide vocabulary?

### Your last name contains invalid characters

My last name is "Graham-Cumming". But here's a typical form response when I enter it:

Does the web site have any idea how rude it is to claim that my last name contains invalid characters? Clearly not. What they actually meant is: our web site will not accept that hyphen in your last name. But do they say that? No, of course not. They decide to shove in my face the claim that there's something wrong with my name.

There's nothing wrong with my name, just as there's nothing wrong with someone whose first name is Jean-Marie, or someone whose last name is O'Reilly.

What is wrong is that way this is being handled. If the system can't cope with non-letters and spaces it needs to say that. How about the following error message:

Our system is unable to process last names that contain non-letters, please replace them with spaces.

Don't blame me for having a last name that your system doesn't like, whose fault is that? Saying "Your last name …

### All the symmetrical watch faces (and code to generate them)

If you ever look at pictures of clocks and watches in advertising they are set to roughly 10:10 which is meant to be the most attractive (smiling!) position for the hands. They are actually set to 10:09.14 if the hands are truly symmetrical. CC BY 2.0image by Shinji
I wanted to know what all the possible symmetrical watch faces are and so I wrote some code using Processing. Here's the output (there's one watch face missing, 00:00 or 12:00, because it's very boring):

The key to writing this is to figure out the relationship between the hour and minute hands when the watch face is symmetrical. In an hour the minute hand moves through 360° and the hour hand moves through 30° (12 hours are shown on the watch face and 360/12 = 30).
The core loop inside the program is this:   for (int h = 0; h <= 12; h++) {
float m = (360-30*float(h))*2/13;
int s = round(60*(m-floor(m)));
int col = h%6;
int row = floor(h/6);
draw_clock((r+f)*(2*col+1), (r+f)*(row*2+1), r, h, floor(m…

### The Elevator Button Problem

User interface design is hard. It's hard because people perceive apparently simple things very differently. For example, take a look at this interface to an elevator:

From flickr

Now imagine the following situation. You are on the third floor of this building and you wish to go to the tenth. The elevator is on the fifth floor and there's an indicator that tells you where it is. Which button do you press?

Most people probably say: "press up" since they want to go up. Not long ago I watched someone do the opposite and questioned them about their behavior. They said: "well the elevator is on the fifth floor and I am on the third, so I want it to come down to me".

Much can be learnt about the design of user interfaces by considering this, apparently, simple interface. If you think about the elevator button problem you'll find that something so simple has hidden depths. How do people learn about elevator calling? What's the right amount of informati…