Author: metatim

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Things 57: Webcam-split-screen, Freaks and Potatoes

(Originally sent September 2009)

Forthcoming film
“Surrogates” is due to be released in the UK on the 25th of September. An adaptation of a graphic novel, it looks to be a solid Sci-Fi in what I consider to be the technically correct sense: positing a potential technological development, the story investigates what might happen in a society where such a thing is possible.

In this case the development is ‘surrogates’ – robot avatars that people control remotely, an idea just nicely at the edge of conceivable possibility.

I think the trailer gives too much away, so if you want to see the basic premise just watch the first 60 seconds, and I strongly recommend not watching beyond 1 minute and 30 seconds (seriously!) if you can possibly resist it!

http://www.youtube.com/watch?v=L7NWdxFAHdY

Video
I saw a video pair on YouTubeDoubler (here – pause the left video until the right one tells you to start it) in which two people use two webcams together to create a video for a duet, and I thought “Good, but could do better”. Someone did:

(Starts to get clever at 40”, goes nuts at around 3’10”)

Quote
Webcomic ‘Pictures for Sad Children’ suggests an improvement (site was taken down in 2014 – T.M. 17/5/22) on the ever-unsubstantiated ‘never more than 3 meters from a rat’ saying:

“We’re in earshot of two terrible things at all times”

Link
“Freaks survive because they are strange” – a great headline, a slightly silly experiment involving food-bearing model salamanders, and a plausible-sounding partial answer to the ‘maintenance of variation’ problem with evolution.

Potato Puzzle
You have 100 kilograms of potatoes that are 99% water by weight. You store them in a cupboard, and when you test them again a week later you discover they are now 98% water by weight. How much do the potatoes weigh?

Magical Ground Squirrel Puzzle Answer:
If the magical ground squirrel is able to position the bridges (say) East-West with such accuracy that an imp wanting to go North could not work out which one pointed slightly more Northerly and so had to choose randomly, then the squirrel has good odds of working out the result of the election by doing exactly that and leaving the bridges there the entire time.

If the imps are headed to the good training centres in the East and West, there will be no random choice made by them and when they have all come out 500 will have gone East and 500 West.

However, if the imps want to go to the evil training centres in the North and West, they will be choosing a bridge randomly. In that case, there is (by my calculation) only about a 2.5% chance that exactly 500 will choose each bridge. There’s a 97.5% chance more will go one way than the other, and in this case you could be sure they were evil.

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Things 107: Transmedia Hardware, Rorschmap, Cyborgs vs Robots

Puzzle
Here’s a cute data analysis puzzle, which I’m amazed I didn’t encounter sooner in my line of work.

You run a website that sells guns and banjos, and one day you notice from your web analytics data that the conversion rate of your site (orders divided by visits) is steadily declining over time.

Realising that you essentially cater to two quite different needs, you look at the performance of your two main site sections: the gun section and the banjo section. There is no significant overlap between the people visiting these sections.

Here’s the problem. The conversion rates in both the gun and banjo sections of the site are going up over the same period that overall conversion is going down. How is this possible?


Video
Some serious puppetry:

http://www.youtube.com/watch?v=HFf3ZWNF6EY

Link
Charlie Gower realised he could get old iPod shuffles cheaply on eBay and dedicate each one to a single artist. Generalising, he asks, “How does the (almost) free hardware affect the delivery of the (almost) free media?”

Picture
I’ll let the name of the idea do the talking: Rorschmap.

Puzzle Answer – Cyborgs beat Robots
In the last Things I invited you to guess who would win in a chess match in which humans and computers could team up in any combination.

I recently read of an empirical answer here, which makes the excellent point that there are actually three criteria at work in any team: the chess skill of the computer(s), the chess skill of the human(s), and the friction in the way they work together as a team.

Some may be surprised to learn the most basic observation from the event: that a team of human + computer is much stronger than even an extremely powerful chess-playing computer. As Kasparov puts it: “Human strategic guidance combined with the tactical acuity of a computer was overwhelming.” Humans are useful!

More impressively, the winner of the tournament was a team of two amateur players working with three computers. The lack of friction in their system of working together beat the raw power of chess-playing supercomputers and the strategic brilliance of grandmasters.

This has some serious implications, too. Most simply, since mediocre computers and mediocre humans are more common than highly skilled ones, and since systems can be invented once and then used by all, there is in some general sense much more potential to solve hard problems than we might otherwise have expected in the world.

More extremely, anyone worried about a technological singularity in which we invent AI that is smarter than us (leading to runaway self-improvement of the AI and a very dangerous 4 hours for humanity) can rest assured that human-AI combinations will probably be smarter than pure AI.

Short version: cyborgs are smarter than robots.

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Things 56: Robot Hand, Earth and Moon, Magical Ground Squirrel Puzzle

(Originally sent August 2009)

Quote

“Most problems are side effects of solutions to other problems.” – Eskil Steenberg

Video
Once you have built a machine or robot that can do something, the really cool part is you can then see how fast it can do that thing. In the case of this astoundingly dextrous robot hand, the answer is: alarmingly fast.

Picture
A simple idea – a picture representing the earth, the moon, and the distance between them, in the correct proportion.

(Click for description and links to bigger versions):

Last Week’s puzzle
Why are ~10% of people left-handed?

Implicitly, the question is really why 10% instead of 50% or 100%, either of which would be intuitively more obvious (although you’d still wonder why it was one out of those two).

A frequently given answer is that in combat there is an advantage to having a handedness that most others don’t have, since you will be practiced at fighting opposite-handers whereas most of the competition will be practiced against fighting same-handers. An increased number of left-handed players succeeding in adversarial sports such as tennis is cited as evidence.

What’s fascinating about this argument is that it manages to sound convincing but it cannot possibly be the whole answer. If there was an advantage to being in the minority, and if that trait is genetic, then we would expect that over evolutionary time-scales a 50/50 split would emerge. (If fewer are left-handed and have a survival advantage by this argument, then more of the next generation will be left-handed, and so on until no advantage remains).

For the theory to work, there would need to be an evolutionary pressure that goes the opposite way, making left-handedness disadvantageous in some way, with the net effect of the two pressures to be a 10% incidence rate.

As it turns out, it seems we don’t have a definitive answer, but surveying the various theories and research presented in this wikipedia article below it seems to be connected to asymmetry in brain development (a deeper question in itself), with cultural effects (such as fighting) giving an additional skew in the short term.

This Week’s puzzle
There’s a very nice puzzle in quantum information theory. This is my attempt to set the same puzzle in less specialist terminology, and although it ends up being quite long, it does involve a magical ground squirrel.

There is an island in the centre of a large lake.

On the island is the entrance to a tunnel that goes deep underground to the imp underground city.

To the North and South of the lake are two evil imp warrior training centres.

To the East and West of the lake are two good imp warrior training centres.

There has recently been an imp general election, and they will either have elected a good leader or an evil one. 1,000 imp warriors will now be allocated a training centre, with exactly 500 allocated to each one. So, if an evil leader has been elected, 500 imp warriors will be assigned to the North training centre, and 500 the South training centre. If a good leader has been elected, 500 imp warriors will be assigned to the West training centre, and 500 to the East training centre.

You are a magical ground squirrel that lives on the island.

A pair of bridges connect the island to the lake shore in opposite directions.

Your magical power is exactly this: you can rotate the pair of bridges so they lie in any direction from the island, so long as they remain directly opposite one another. So you could choose to have one bridge head directly North and one directly South, or one directly North-West and the other directly South-East, and so on. However, you must never use your magic when an imp is on the island or a bridge, as they will notice and put you in their magical animal zoo.

The 1,000 imp warriors are about to be sent out, one each hour, to go to their respective training centres. Imps are highly random creatures, and they also have a pretty amazing sense of direction. They will be coming out in a random order, and they will head along the bridge that most closely matches the direction of their training centre. If the bridges seem to be perpendicular to the direction they want to go (for example, if the bridges lie East and West and the imp wants to go North) then the imp will pick a bridge at random.

Using only your magical ground squirrel powers, what is the best way to work out whether the imps have elected a good or evil leader?

(Note: this is not intended as a lateral thinking puzzle! You just have to decide how to rotate the bridges and interpret the resulting imp behaviour. But I suppose you could try solving it laterally as well. P.S. Imps can cross a bridge in under half an hour).

Categories
New

Things 106: Best at Chess, Art of Science, Crowdfunding

Tim Link – Competitive Sandwich Making
Last week Clare and I ran a game based on tessellating pieces of cheese to make the best sandwich for the Hide&Seek Sandpit event. You can read about it and see the photos on my project blog, Tower of the Octopus.

Puzzle
In a chess tournament in which anyone can use any means available to them to come up with their moves, who would win? Some possible answers to give an idea of what kind of thing I’m talking about here:

  • A high-ranking chess Grandmaster
  • A really good chess-playing supercomputer
  • A huge team of moderately skilled players with some method of combining their ideas
  • A moderately skilled player with access to a moderately good computer that can run some basic chess calculations

(I had wondered about this in an abstract way before, but recently found out that has actually been done. I’ll relate what happened in that event next week, but you could of course try to Google as well as guess the answer if you wanted).

Video
(Via Phil): Art out of Science:
(Two views of the same thing. If your browser is up to it, you could try watching both videos simultaneously – start the bottom one 20s after the top):

Links
Kickstarter is one of my favourite things on the internet: people with an idea for something get a platform from which to shout about it, and to collect pre-orders or donations from people that like the idea. If there’s enough interest, the project can go ahead, and everybody wins.

So far I’ve helped fund two comics, the Wormworld Saga app (which saw so much success the creator, Daniel Lieske, decided he could give up his day job), and I’m currently backing The Endangered Alphabets Project, which is the kind of thing I like to imagine in a vague way is going on in the world, but I now have the opportunity to facilitate it directly (also, it’s only just on track to hit target, so do go check it out).

You can follow Kickstarter on Twitter, or go to their home page and scroll to the bottom to sign up for the weekly newsletter which highlights the most interesting projects.

IndieGoGo is similar but for reasons I can’t really pin down doesn’t work as well for me.

Crowdfunder is a UK version which I don’t tend to find as inspiring, but would probably be the best one for someone in the UK to create a project with (since Kickstarter requires a US bank account).

Quote
Overheard in the maths common room when I was studying for my PhD at Royal Holloway:

But nobody knows what probability is! Probability is defined in terms of randomness, and randomness is defined in terms of probability!

Answers to Monty Hall and the Two Envelopes
Last week I asked about the Monty Hall problem, which I should have introduced before the Two Envelopes problem I set two weeks ago.

The Monty Hall problem has a nice Wikipedia page, the most helpful part of which is probably the decision tree showing all possible outcomes.

In brief, the answer is that you should switch after Monty shows you an incorrect door, but certain misguided instincts steer most people away from that choice. The Endowment Effect and Loss Aversion mean that regardless of probability, people fear they would regret “giving up” their first choice more than sticking with it if they end up losing.

The more subtle effect is an instinctive (or partially trained?) feeling that the choices of others have no effect on the probabilities of our own choices in these kind of contexts. This is true when the other person has just as much information as you, but that is not the case here – Monty knows where the car is, and uses that information to ensure that he always opens a door with a goat behind it. So he has more information than you, and when you see his choice you gain some information.

Or to give an answer that might go with the grain of instinct for some people, consider this: there is a 2/3 chance that the car is behind one of the doors you don’t pick. Monty shows you that it definitely isn’t behind one of them. So there’s still a 2/3 chance the car is behind the other one, and a 1/3 chance it’s behind the one you first chose.

As for the Two Envelopes, it turns out this is more difficult than I originally remembered. Again, there’s a great Wikipedia page on the subject, which has quite a lot of detail.

As Thomas noted, a key phrase missing from the subtly specious argument for swapping is “Without Loss of Generality” (WLOG), which one must always be careful to check whenever substituting a variable (in this case, the amount in the envelope) with a specific figure (£10 in the example I gave).

Is it true that the reasoning I gave based on having £10 in the envelope truly retains the generality of the problem – would the reasoning also hold for any other amount? In short, no. For example, there could be 1p in the envelope, or any odd number of pence, in which case we would have to conclude that we had the lesser envelope (although this still means you should swap). More dramatically (here we imagine the envelopes contain cheques, and that these cheques are totally reliable), your envelope could theoretically contain over half of all the money in the world, in which case you can be sure the other envelope contains less. More realistically, it could contain more than 1/3 the amount of money you expect the person filling the envelopes to be willing to give away, in which case you would strongly suspect the other envelope to contain the lesser amount.

If you’re interested, do read the full Wikipedia article, and meanwhile, remember to watch out for unjustifiable WLOGs.