Tag: puzzle

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Things 108: Mix Shifts, Skrekkogle, 109 Children vs Real Madrid

Previous Puzzle: Guns & Banjos
Previously in Things I asked how a banjo and gun website could see conversion in its individual sections improving, but overall conversion decline. Xuan pointed out that visits to some part of the site not counted in either section could see an increase in non-converting visits and so drive the effect, but this is a loophole – even without such a section, the problem can still arise.

The answer here lies in the part of the data not revealed in the setting: the underlying traffic trends. In particular, if you have one particular section (or segment) that converts at a low rate, and the mix of your traffic shifts towards that group, then that will tend to pull down the overall average conversion, even if conversion within the groups is going up.

To take a simple example, consider the following figures for this theoretical guns and banjos site, with figures in the form [before mix shift | after mix shift]:

Banjo section visits [10,000 | 20,000] – lots more traffic
Banjo section sales [100 | 220]
Banjo section conversion [1.0% | 1.1%] – conversion increases!

Gun section visits [1,000 | 1,000] – same traffic as ever
Gun section sales [100 | 110]
Gun section conversion [10% | 11%] – conversion increases!

Overall conversion before:
(100 + 100) / (10,000 + 1,000) = 1.82%
Overall conversion after:
(220 + 110) / (20,000 + 1,000) = 1.57% – overall conversion has decreased!

In practice you will rarely see an effect this strong. On the other hand, you could well see mix shifts drive a significant part of an overall shift in conversion rate. So watch out for that.

Puzzle: Mix Shift Visualisation
This is a really tough one, but I know the Things recipients are up to the task.

Given that mix shifts as described above can be difficult to spot, how might you visualise your website’s data in such a way that any such effects became obvious?

(I have an answer for this, but I feel sure a better answer must exist).

Quote
Everyone seems to be linking to this surprisingly weakly curated collection of Steve Jobs quotes. One part that I did like expressed something I’ve been thinking for a while:

Steve Jobs: I have a very optimistic view of individuals. As individuals, people are inherently good. I have a somewhat more pessimistic view of people in groups.

Or as I’ve tried to distill it: humans don’t scale.

Link
These guys make cool stuff, even if their website is slightly too clever for its own good.

Video
It’s too easy for imagination to be constrained by what we already know exists. That’s why I like things like this video, which help remind us that many more things are possible. It’s not particularly well edited and there are no particular highlights, so feel free to skip through and enjoy the general sensation of weirdness, which is after all what we generally look for on the internet, and indeed in life. Or maybe that’s just me.

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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).

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Things 55: Cancer, Pentatonics, Handedness and the Police

(Originally sent July 2009)

Films
I saw Moon, which was a very nice bit of old-school sci-fi with a few nice ‘ah-ha!’ moments.

I saw G-Force 3D, and was amazed at how special effects clearly follow some kind of Moore’s law, while good writing remains a nearly insurmountable challenge.

Link
There’s a few sites out there attempting to keep up with what’s referred to as the Daily Mail’s “ongoing effort to classify every inanimate object into those that cause cancer and those that prevent it.” I like the way this one is helpfully laid out.

Of course, what would be nicer would be to use the research papers as a basis for such a project rather than the Daily Mail, at which point you’d probably need better risk-assessment functionality.

For example, I read a proposal to break global warming down to an individual scale – so if collective human actions increase the average temperature by 0.5 degrees over several decades, we could create an approximation for the temperature increase due to the production of any given product or action, and even though it would be tiny it would come to have meaning – e.g. this laptop causes a 23 picokelvin rise, but this one caused 573.

In practice, we’ve seen Carbon labelling, which is I suppose somewhat more accurate and tangible.

Unfortunately risk factors are really too complicated to be distilled to a single number for a single food item.

Video
Bobby McFerrin with a nice demonstration about how intuitive the Pentatonic scale is:

Last week’s puzzle
Why is gravity 37% that of Earth’s on Mars, even though Mars only has 11% of the Earth’s mass? Clearly there are Laws Of Physics at work, and we can’t fairly expect to have an intuitive understanding of how strong gravity ‘ought’ to be on planetary scales.

That said, there are two factors clearly at work:

– Density: Mars is slightly less dense than the earth – 3.9g/cm^3 vs 5.5 g/cm^3, or 71%

– Radius: Mars’ radius is 53% that of Earth’s. If you were somehow standing on a platform one earth radius away from the centre of Mars, the gravity you feel would certainly be weaker than the 37% that you would experience on the surface.

(Side note: if earth (or indeed any planet) were hollow, there would be no gravity on the inside, as the gravitational pull due to the outer shell cancels out no matter where you are in the interior!)


This week’s puzzle
Why are about 10% of people left-handed?


Quote
The Week is a weekly summary of “everything you need to know about everything that matters”, expertly editing together coverage of the main stories of the week into coherent, balanced, and concise summaries.

Here’s a cut down version of their concise version of a story from Germany, which as well as cutting all the fluff from a story that could probably be expanded to a movie adaptation I also liked because it’s a wonderful case of reversing the usual fiction trope that ‘Police are Useless’

“Germany’s wealthiest woman, Susanne Klatten hit the headlines last year when her former lover was arrested for trying to extort €49m from her. He told Klatten that he had made a secret video of them having sex and threatened to make it public unless his demands were met. But Klatten went to the police and he was arrested.

“Last month, three men wrote a letter to Klatten in which they claimed to have a copy of the sex video and demanded €800,000 and a BMW car for its return. Once again Klatten called the police and the three were arrested.”

Okay, it probably wouldn’t make a very good movie.