Saturday, 12 June 2010

Day 163, on which John tries to represent fate graphically [12.6.10]

Dag hundrede treogtres. Before we begin, please note that by 'graphically', I mean on a diagram, and not with gore. Anyway, until then we have the compulsory introduction, which I am starting to think distracts from the post itself... ah well. Good day today, really good. And I revised, too. A bit. I have another damn GCSE on Monday, they just don't stop rolling in.

So let's get started. As you know, two days ago I posted about fate, and that got me thinking about whether we can map the choices we make onto some diagram or other. So, I now present what I call the choice-o-gram. I was going to call it a 'fategraph', but I've moved away from the fate topic and maybe once I develop the graph a bit I can add in fate.

So here's a blank choice-o-gram. The idea is that it's meant to represent the possible options you have when you make a choice, and how likely you are to choose each option. I guess if fate were considered, then there would only be one option, which would make this graph redundant.


So, as you can see there are two axis. One axis, the x-axis (horizontal) is fixed. It ranges from a whole probability (1) - when the event will happen, no matter what, to an infinitely small number (1/∞) - when there is the smallest possibility of an event happening. The further to the right (towards 1/∞) the outcome (we'll find out about those later) is, the less probable it is.

The y-axis is not fixed - it can go on for ever, so the graphs are likely to be higher than they are wide, as they can't extend past 1 or 1/∞. There is no fixed scale on the y-axis, which is time. It simply shows what order events go in. The graph should be read from the bottom up.

So let's apply an example. Say there's a kid called Ben. He has a choice of drinks - Coke, water and (for some reason most likely humorous intervention on my part) beer. He could also not choose a drink, and so not have a drink.


So here's the graph for Ben's choice. Note the starting point of Ben's choiceline (red) is a circle. If a choiceline is carrying on from previous events (which they always would be unless it's the start of the Universe or something), then it has an arrowhead in it and the name has a '>', like Ben's circle. So, Ben's choiceline (which we'll just call 'the choiceline' since there's only one) progresses in time (upwards) and meets a decision.

The event is shown by a diamond, which is what queries are shown as in data flow diagrams (so it's not totally out of the blue). The choice/event name, shown with a '!' at the start, is 'choice of drink'. Now you see we have displayed four outcomes - there is an infinite number of outcomes for every event (to keep it simple, we only display the ones we're interested in).

Our four outcomes are grouped into two sections: he chooses a drink, and he doesn't choose a drink. You can see that a line connects coke, water and beer - this outcome group is 'drink', ie. he does in fact choose a drink. The other option, 'none', ie. he doesn't choose a drink is actually a group of its own. It can be argued that all four options are groups of their own, but for now I'm sticking with two groups: one annotated group which contains three displayed outcomes, and one group quantified to one outcome.

If we wanted to continue all the outcomes on to show more events (secondary outcomes), we'd have to expand the 'None' outcome - remember, it's a group of loads of outcomes, and those outcomes will lead to different secondary events and we can't generalise.

So that's why we group the three drinks together, and leave the fourth option on its own. That's all you can see on this graph, so I'm going to leave the rest of the topic until tomorrow. I've got some great ideas on how to develop this...

~John

6 comments:

Matn said...

Okay. Erhm, I'm going to read your three latest posts tomorrow; looks like it's a bit heavy.

Anyway, I'm here to tell you, you have to download Team Fortress 2! :D It's free this weekend (with the Mac launch) and I've been playing it today (instead of learning for exams). I'll probably buy it also for 10 EUR. Nice!

John said...

Yeah, I'm downloading it right now Matn! My friend suggested it to me, and since it was available on Mac, I thought "hey, why not?".

Also, I need something to distract me from exam revision :P

Matn said...

Don't let you distract is too much. I should have been learning all weekend, but instead I've been playing TF2... Oh, well, I still got tomorrow afternoon. ;o

Oh, what's your nickname on Steam? (:

Matn said...

Don't let it distract you too much. That's the correct phrase. :p

John said...

Lucky you Matti, having tomorrow afternoon. My exam's at 9:00 AM on the dot! >:o

My Steam name is Johnallong. Add me please!

Matn said...

I keep clicking on add, but nothing happens! :p

Good luck with your exams! Tomorrow I start at 8.20 AM with English and then natural sciences (blergh). I always have study in the afternoon. :)