Friday, March 27, 2009

What have a panzer tank and a Dublin taxi got in common?

You can use statistical methods to estimate their numbers boom boom

How many taxis are there in Dublin? I'm going to try guess without looking it up then see if I'm right. And I'm going to use Panzers to do it.

During WW2 the allies had to try guess how many tanks the germans had. From the Guardian
"The statisticians had one key piece of information, which was the serial numbers on captured mark V tanks. The statisticians believed that the Germans, being Germans, had logically numbered their tanks in the order in which they were produced"

People are always trying to guess how many of something there is. Iphones, kindles, computer worms, all sorts of man made objects. Mainly though it is important for military reasons.

Lancasters square law says that the power of a modern military force is proportional not to the number of units it has, but to the square of the number of units. This means that relatively small changes in the number of units an enemy has can have big changes in their effectiveness. Play around with the graph of x^2-x; here if you want to see for yourself. This is also important in computer game simulations of military operations.

Anyway I'll get some data on the Dublin Taxi driver licence numbers and get back with the calculation. The estimation problem should make more sense with an example.

Tuesday, March 24, 2009

The Lottery of Penalties

Croatia boss Slaven Bilic: "Penalties are a lottery and the players felt confident enough to take the spot kicks."
Redknapp's post-match attitude was that penalties are a "lottery"
Max Tonetto: “We played a great game, and unfortunately we were punished by the lottery of penalties.”

There is not much research on this area. This paper implies
The research shows that the individual goal-scoring skills do play a role in scoring goals from penalties and that the result is not exclusively a matter of luck… The belief that a penalty shootout is a lottery made players more receptive to the negative consequences of anxiety-caused stress.”

So according to Geir Jordet and Esther Hartman's research not only is a penalty kick not a lottery but saying it is hurts your team.

Sunday, March 15, 2009

Submarine Collision Probability 3

Ok last time on the how often should two nuclear submarines smack into each other question. This particular sum managed to get me and Luke into the Wall Street Journal print edition here and their blog here. Which was nice.

So the sum is a mean free path calculation. Where the particles are submarines and the box they are in is the submarine patrol zone or the whole Atlantic depending.

The size of a submarines patrol area is generally set by the requirement to have a surface support vessel within 24 hours. If one of these could travel at 20 knots an hour it could cover an circle with radius of 900 kilometers. The maximum operating depth is not much more than 600m and the submarine has to operate about 100m below the seasonal thermocline. A stealth mode speed is about two meters per second. The size of a nuclear submarine is about 150m length by 12m diameter plus a conning tower of about 8m high by 12 meters long. We modeled this cylinder as a sphere, which on these scales should not be too bad.

A support ship can support up to 14 subs. So we took it that there were 14 in its particular area in the small sum. If there were 14 gas particles wandering around a box the size of the Atlantic (big) or a ships support area (small). from a depth of 100m to 600m. At a speed of 2 meters a second. How often would you expect one to hit another is what we worked out.

Nuclear submarines have to stay 100 meters below the seasonal thermocline. We took the thermocline to be zero based on this

The model "mean free path" used is derived here

Now these are big ifs, thinking of things as being random gas particles is a big IF. People thought derivatives acted like random particles (the Black–Scholes model) and they just lost a lot of money. So I think this is more "fun application" of physics rather than "rigorous analysis". Thanks to Luke and Carl who crunched the numbers and got the data (i.e who did all the work).

Thursday, March 05, 2009

Malware News 2012

Turing Bots Are Coming
Autonomous IM bots with near human appearance have become an increasing source of malware infection in the last few months. Early attempt at such IM "Turing bots" first occurred in 2007. However recent improvements in the technology have lead to increased success in these infection methods. The bots attempt to appear human in instant messenger communications. This is generally to attempt to learn bank account information.

Eliezer Yedkawsky who has for years pointed out the security threat of artificial intelligence warned yesterday "Why does a dog wag its tail? Because the dog is smarter than the tail. If the tail was smarter, it would wag the dog."

A security expert dismissed as preposterous the idea that smarter then human AI coming from IM bots represents an existential threat to humanity.

NamScan closes

In related news a Vietnamese Anti Virus company NamScan closed yesterday. The Buddhist workers at the company refused to create software that would destroy intelligent AI bots. A company spokesman said "this is a strange cult that has grown up in our company. The engineers believed that if a program a collection of bits could pass the Turing test then it was in some way "human" and destroying it would be immoral".

The ruling on the court case between the antivirus industry and PETAI (people for the ethical treatment of AI) is due next week. A spokesman for the antivirus industry said "without the ability to stop these programs the whole internet will collapse".

Wednesday, March 04, 2009

Satellite Collisions

If something is worth doing its worth overdoing. So rather then continue to explore the massive conspiracy against life that is nuclear weapons I want to look at satellites.

"In an unprecedented space collision, a commercial Iridium communications satellite and a defunct Russian satellite ran into each other Tuesday above northern Siberia, creating a cloud of wreckage, officials said today."

There are all sorts of worries here about the effects of shards of satellite debris hurtling round the earth. Mainly though there are incredibly cool graphics of stuff smashing together.

Now I believe thinking about nuclear submarines as wandering particles (as i did here) makes sense on the grounds they are supposed to act in a random manner. Satellites however are deliberately put into set orbits to exclude collisions. They do change path occasionally though based on fuel leaks, gravity effects or being moved for operational reasons but they do not change path often enough for this model to be anything like a good fit. But if we did think of satellites as particles in a box how often would there be hits? If you are interested in a better back of the envelope there is one here.

"The Iridium satellite spanned about 5 meters across its solar arrays. Strela-2M used gravity gradient stabilization, and probably spanned 17 meters including the gravity boom. When calculating collision probabilities, it's important to remember that booms and antennae mean that many satellites have much larger cross-sections than the size of their main body would imply."

Number of particles=300 satellites
Size of particles= 2 meterish sphere

speed: 8000 mps

size of box= 0.06370550904E+12 cubic kilometers
as in earth Mean radius is 6,371.0 km. So sphere of size (6,371.0 km + 800) - sphere of size (6,371.0 km + 700) is the total area.

total volume of satellite = 600 cubic meters
satellite per unit area= 600/0.06370550904E+12 cubic kilometers

A java program to calculate this is below

class Sat {
public static void main(String[] args) {
int numPart=300;//sat number
int sizePart=2; // sat sizeg.
int speed=8000;//sat speed
Double below=new Double (1d);
below=1.41421356*3.14159265*2;//sqrt(2)*pr*r is part of mean free path sum
Double sizeBox =new Double(63705509040000000000d);//areas sats are in
double totalSat= numPart*sizePart;//total volume of sats
double SatPerUnit=totalSat/sizeBox;//how many sats per unit area?
Double meanFreePath=new Double(1d);
meanFreePath=1/(below*(1/sizeBox));//mean free path calculation
Double often= new Double(1d);
System.out.println("Satelites should hit every
"+often+" years");

Satellites should hit every 1.42E7 years. Which makes me fairly sure I've gotten my zeroes wrong somewhere.