klog

I was lying in bed last night, wondering how the Monty Hall trick works, and finally figured it out by twisting around my perception of the problem.

What is the Monty Hall problem? Consider three doors. Behind one is a car, and behind two others are goats. You are asked to choose one door - if it’s the one with the car, you win. otherwise, you lose.

you choose one car. Then Monty (the gameshow host) opens one of the other doors to show a goat behind it. You are given the chance to change your choice of door to the other closed one - should you?

The answer is Yes. the /intuitive/ answer is that there is a 50% chance either way, but mathematically, there is actually a 66% chance.

Took me a good few minutes to figure out how to verify it. I kept thinking of it as “there is a 33% chance of me picking the right one. door opens. I now have… 50%?”. Couldn’t seem to make the leap for some reason.

That was a result of wrong perception - you need to think of it from the point of view of what is /not/ the right door.

1. choose one door. the chance of the car being behind one of the other doors is 66%.
2. one of the other doors opens. the chance is still 66%!.
3. You now have two closed doors. the door you /did not originally choose/ has a higher chance than the one you did choose, so you should switch.

Sorry if this post is totally bonkers - I’m a layman but like to think about this stuff.

Got an email newsletter from Galaxy Zoo today. In it was a link to a recent Telegraph article pointing out the apparent lopsidedness of the universe. In short, most galaxies that we see in the universe appear to be rotating in the same direction, where the direction should be random.

I had a thought about this, and it occurred to me that this could be explained if there was some sort of “coriolis force” acting on space itself.

How can this be? Surely space is just space? Well, not according to quantum loop gravity, which describes space as a load of interlinked nodes. Where you think there is nothing, there is actually a load of interlinked points.

The “coriolis force” is hard to explain. A short explanation might be this: on a planet that is spinning, if you have a solid object which is sitting still (relative to the planet surface) on any latitude of the planet other than 0 or at the axis, then one side of the object is actually moving through space faster than the other because of the slight difference in radius of the sides’ paths through space as the planet rotates. Yeah - headrush.

Anyway - what it means is that objects sitting on the “north” hemisphere tend to turn clockwise instinctively, and vice versa.

So, what does this have to do with galaxies?

Well, if most galaxies are rotating in a specific direction, then that could indicate a coriolis effect happening on space itself. This could happen if the universe itself was rotating.

A further implication is that if you map the rotation of all galaxies and analyse them carefully, you may find that you can actually pinpoint the centre of that rotating universe. This is something that traditionally has been thought of as impossible, because the universe might not have a “centre” at all.

Anyway, please comment if you think this is stupid, but give a reason why it is.

I’ve been doing well over the last two weeks - I started with an ANN which can balance a pole, and upped that by then creating a net which could recognise letters.

The plan for today is a bit more ambitious. I’m writing it down here in case it takes longer than a day to write it. In general, I want to write a PHP application which will allow you to upload images, which the ANN will then try to recognise. If it gets it right, all well and good. If it gets it wrong, you can correct it.

Some milestones for the project:

• readers can upload images and have them tested and/or added to the training sequence
• extraction of image pixels using <canvas>
• automatic creation of new neurons as they are required
• best net is stored on server, so new readers always start with a working net

I think this may grow into a damned cool thing - I’m already thinking of other cool features like distributed nets, or background nets which can be placed in other pages of a site so the thing can continue training even though the user is not actively viewing the thing (that might be a bit cheeky though).

Anyway - now that I’ve written what I intend to do, I suppose I’d better actually do it.