vegetarian lasagne, black coffee

[pigseatingfigs]

OK all you intelligent people, how can I formally represent uncertainty in distances? That is, I want to be able to say, X is a certain distance and angle from Y, but both of these are within +-20%, or something similar. I also need a way of comparing statements so that one with less uncertainty can be given priority. Try to make it in the form

Comments

[pigseatingfigs]

don't know what that error message is all about...

[chickenfeet2003]

It thinks your < and > are the start and end of an HTML tag that it can't recognise

[pigseatingfigs]

stupid machine
no wonder AI is useless. Now, how to generate random numbers? Because of course, any 'random number generator' inside a computer is never going to be truly random.

comment from susanbiscuit

[pigseatingfigs]

(she very nearly missed the plane on the way out)

> i didn't even count that a near miss! we had bags of time. the way back,
> on the other hand, was rather a different story, one which featured us
> sprinting across the tarmac as the plane door was eased shut. i'm not
> even joking.

Re: comment from susanbiscuit

[jen_c_w]

haha ca plus change...

[pigseatingfigs]

erotetica solved the string problem.
well done!

[chickenfeet2003]

I think the string problem requires that the strings be identical and burn faster or slower in some relatively uniform way.

Cut the strings into eight equal lengths maintaining the order and orientation of the strings. Light the same end of each eight string. If the eighths burn for the same time, your 15 minutes will be measured by burning, sequentially, the second 1/8 of one string and the seventh 1/8 of the other. If the eighths take different amounts of time then burn the second 1/8 of each string consecutively.

[pigseatingfigs]

Not quite.... you're on the right track though. The strings are not identical, unfortunately. If you light each end of one of the pieces of string, the whole thing will take exactly half an hour to burn (why?). Can you see the solution now?

[chickenfeet2003]

Light both ends of one string and one end of the second string. When the first string is burnt immediately light the unlit end of the second string. In a further 15 minutes the second string will be completely consumed.

[pigseatingfigs]

yay! well done.
Now.... can you think of a way of measuring 15 mins with just one string? You will never be able to get *exactly* 15 mins, but you can get very close...

[chickenfeet2003]

OK, let's make r+/-e the distance from X to Y and a+/-b the angle.

Now, it seems reasonable to make the metric of uncertainty the area of the the "box" in which Y may lie. This is actally a rhomboid but for reasonably small values of b it approximates to a rectangle, of which the area is 4er.sin(b).

[pigseatingfigs]

bollocks, sorry, I forgot to say that they have to move on a grid, and so all angles must be represented by x=2, y=3 and so on. They can't move diagonally. I do like the box idea though, can I represent that in a grid?

[chickenfeet2003]

So how is percentage error in the angle measured? And can I assume that the metric for distance is the number of grid square sides traversed so the distance from (x1, y1) to (x2, y2) is x2-x1+y2-y1 rather than sqrt[(x2-x1)^2+(y2-y1)^2]?

[pigseatingfigs]

I had to adapt it so that I can say it is 4 squares (+-1 sqaure) left and 5 squares (+-2 squares) up, and so on. So a 20% error on a distance of 4 would be represented by 1 (even though that is actually 25%). In time, I would hope to be able to make the grid squares small enough so that this doesn't matter, but for now they are quite big. Sorry, I should have been clearer - I assume that because it is the main thought occupying my head at the moment other people will be able to see what I mean instantly!