The Maths and Physics of Discworld

nesf

My IMSA speech/lecture as promised. It's nothing special, but you Pratchet fans out there might like it...

It's got alot of gaps and gibberish due to formatting and pictures in the finished piece, but it should be fairly readable. But the maths may take a few looks to get.

Enjoy



The Maths and Physics of Discworld.

Books = Knowledge = Power = Energy = Mass

ð Libraries = Many Books = Large Quantities of Mass

ð Libraries Distort Space-Time


From “The Science of Discworld”:


“This is why all second-hand book shops seem so much bigger on the inside – and why all libraries everywhere are connected.

Only the innermost circle of librarians knows this, and takes care to guard the secret. Civilisation would not last long if it was generally known, that a wrong turn in the stacks would lead into the Library of Alexandria, just as the invaders were looking for matches, or that a tiny patch of floor in the reference section, is shared with the library in Braseneck College, where Dr Whitbury proved that gods cannot possibly exist, just before that rather unfortunate thunderstorm…..”

















Probability on Discworld

From “Guards, Guards!”:

“No we won’t do it, the chance is only a few thousand to one. It must be precisely a million to one for us to do it.”

“Why?”

“ Everyone knows that one in a million chances crop up 9 times out of 10. It’s the kind of odds the gods like.”

P(xe) = (1 x 106)-1

P(xd) = 9(10-1) = c(1 x 106)-1

ð c = 1 x 105(9-1)

c is the deitiological factor of probability, i.e. the gods do play dice, or at least they cheat (but aren’t very subtle).

From “The Colour of Magic”:

“The Lady nodded slightly. She picked up the dice-cup and held it steady as a rock, yet all the Gods could hear the three cubes rattling about inside. And then she sent them bouncing across the table.

A six. A three. A five.

Something was happening to the five however. Battered be the chance collision of several billion molecules, the die flipped onto a point, spun gently and came down on a seven.

Blind Io picked up the cube and counted the sides.
“Come on”, he said wearily. “Play fair.”

So from this we have a new factor allowing chance to be altered by the gods, for instance lets look at the odds at getting a perfect hand in a game of bridge.

We of course assume that c is constant for all odds greater than a million to one.

Therefore we will take P(xd) = cP(xe)

P(xe) = (52-1)13

ð P(xe) = (2.03 x 1022 )-1

P(xd) = cP(xe)

ð P(xd) = (4.07 x 1016)-1



This is an increase in your chance to get a perfect hand of bridge by over 49,877,149 % » 50 million percent! So we can see that life as a casino owner on Discworld, isn’t very nice…


As for poker, a royal flush has a probability of..

P(xe) = (3.8 x 108)-1
Or 380,000,000 to 1

P(xd) = (3.5 x 104)-1
Or 35000 to 1





The Speed of Light on Discworld…

ce @ 3 x 108 km s-1

but from “The Science of Discworld”:

cd @ 600 km s-1

This variation can be explained by this passage from
“The Light Fantastic”:

“The sun rose. However the sunlight didn’t. What did happen was that the famous Discworld sunlight travels very slowly through the disc’s magical field, sloshed gently over the lands around the Rim and began it’s soft silent battle against the retreating armies of the night. It poured like molten gold* across the sleeping landscape – bright clean and above all slow.


*Not precisely, of course. Trees didn’t burst into flame, people didn’t suddenly become very, very rich and extremely dead, and the seas didn’t flash into steam. A better simile, in fact, would be ‘not like molten gold’ “


We can “explain” this slower lazier light by two means.


Firstly by creating a new constant, i.e. the thaumatalogical constant Ψ.

Now b the thaumatalogical factor is defined by..

b = WY

where W is the magical field strength measured in Thaums

A thaum is defined as the quantity of magic needed to create 2 doves or 3 average sized billiard balls.


We will take for convenience that the magical field strength of the disc is approx. 20 Thaums.



Now to find b we can do the following…

ce = (e0m0)-1/2 = 3 x 108 m s-1

cd = ce / b = 600 m s-1

ð b = c / cd

ð b = 5 x 105


Now since b = WY

ð Y = b / W

ð Y = 2.5 x 104

The other way we can explain Disc light is by taking a new value of e and m in magically charged “free” space.

ð cd = (mded)-1/2

but b2e m = ed md

Next we will assume that e and m are proportional to each other.

ð m = ke

ð k = m / e

ð k = 1.41 x 105

ð b2 k e2 = md ed

ð md ed = 2.76 x 10-6

But since m = k e

ð k e2 = 2.76 x 10-6

ð ed = 4.4 x 10-6

ð md = 6.24 x 10-1


This is quite a difference considering that m = 1.25 x 10-6 and that e = 8.8 x 10-12.









From this we can see that Capacitance on Earth versus Discworld is related by:

Cd = b Ce


ð A 10m Farad (i.e. 10 x 10-6 F) capacitor will have a capacitance of 1 Farad on Discworld.

This could be taken as a reason for why electricity is not common on Discworld, the conducting wires alone would build up very large capacitances even at relatively low voltages.

Let us now look at the energy difference stored in each.

Assuming that the voltage across each resistor is 12V, and that a d.c. current flows through each.

ð E = ½ CV2

ð Ee = 7.2 x 10-4 J = 0.72 mJ

ð Ed = 72 J

ð There is an increase of 10,000 % in the energy required to charge the capacitor. This could result in make it very, very difficult to create the small capicitances needed for modern electronics.

ð





Gravity on Discworld



Gravity has a kind of sentience on Discworld. It’s a vengeful and has a bad temper, probably due to the strength of the magical field. Now hopefully we can model such effects.


First we must postulate a few principles.

1. The force of gravity is inversely proportional to the square of the vertical component of the magical field.

2. The human mind when anxious absorbs magical energy from the area surrounding the body.

3. There’s no such thing as Santa Claus.

Obviously 1. and 2. give a whole new meaning to the phrase, “Whatever you do don’t look down!”. This phrase originated from the tendency of people to become anxious when looking down from a height, and becoming anxious, which increases the strength and pull of gravity, which causes their anxiousness to be very well founded…











Thus we can add a b to our gravitational formulae.

ð F = G(m1 m2/ r2 b2)

ð Fe = b2 Fd

Now since b = W Y we can state that,

F µ 1/W2


Thus the levitation techniques used by a tribe in “The Colour of Magic” can be explained using the above relationship.


This tribe had developed a form of skimmer for travelling over the sea or lakes, it worked on the basis of 4 guys, one placed at each corner, who had a very strong hate of water. They started concentrating on their hatred and the skimmer then rose off the water and floated on.

We can explain this by assuming that anxiety and hatred are very closely linked in their ability to absorb magic from the surroundings to “fuel” the emotions involved.

This we can represent using the anti-thaum model. It is similar to that of the state of knurdness. Knurdness is state of being knurd, this is a state opposite being drunk, but far past the point of being sober. For example Captain Vimes in “Guards, Guards!”



“He was the kind of man who needed a few drinks just to get sober.”



Hatred and anger are two of the few emotions in Discworld that causes the emitting of anti-thaum particles. These cause a state of anti-magic field around the person if they have been specially trained to focus their hatred and find a physical expression for such a deep anger.


Kind of like bouncers on earth. On Discworld bouncers would merely float off into space when they got into such a state. This is why trolls (who are made from rock) are most frequently used as bouncers, not because rock is very heavy and resistant to the pull of gravity, it’s just that it takes along time for rock to get that angry…

So if the there are sufficient quantities of anti-thaum particles created then the skimmer can float off the water and allow such travel.

Therefore we have found a way to get anti-gravity! All we have to do is to crowd a lot of people into the same plane and make them very angry by feeding them very poor food and making them sit in very cramped positions deprived of nicotine……



Well perhaps looking at the number of experiments of this type carried out “in the field” by airlines across the world, maybe this wouldn’t work on earth. Maybe…

nesf

Actually, it's bloody unreadeable! Anyone interested in seeing how its going to look can PM me and I'll send you the word version which looks alot nicer and is far more readeable, esp concerning the maths!

nesf

Well to all who are interested, i.e. very few The lecture went quite well, even though I was suffering the most terrible of hangovers after the celebratory few wines at the dinner the night before, i.e. few = roughly 4 bottles


Still not feeling too good after it...