Tag Archives: answer

Things 121: Kitten Cam, Chain World, Hand-Waving Explanations

Tim Game Thing
If you ever watched Knightmare and wanted to be the kid in the vision-restricting helmet asking “Where Am I?”, or if you wanted to be the team responding “You’re In A Room” and then frantically shouting “Sidestep left”, or perhaps if you wanted to come up with your own ideas for dungeons for those players to explore, then I recommend you come along to Hide & Seek’s free Sandpit event this Friday 25th May (6.30pm-10pm at the Royal Festival Hall near Waterloo), where I’ll be running a game that gives you an opportunity to do exactly those things.

There will also be a lot of other games going on, which sound pretty amazing, so read all about it, and come along.

VideoCat and Kitten webcams
Which is more compelling: a high resolution webcam of some kittens, or low-resolution webcams you can move around and remotely operate cat toys through (if you’re prepared to use Internet Explorer and Silverlight)?

It turns out that even though the latter sounds superficially cooler and more engaging, it’s nowhere near as good as high-resolution kittens.

LinkJason Rohrer’s Chain World
Jason Rohrer has made some very interesting games (I particularly like Sleep Is Death (or at least the idea of it – I haven’t played it yet), Inside a Star-filled Sky, and Passage is apparently pretty amazing (and very short) if you don’t play it stupidly the first time like I did), so it’s not particularly surprising that he came up with the winning concept in a competition to pitch an idea for a game that in some way represented the abstract idea of religion, and which, when actually released into the world, generated some pretty fascinating results.

Heavily Caveated Film Recommendation
The Green Hornet is a Seth Rogen action/comedy vehicle directed by Michel Gondry. If you analyse that sentence you may realise that this was recipe for disaster. With Seth Rogen starring and also writing (with long-time friend and collaborator Evan Goldberg), there was inevitably going to be some creative conflict with a director as idiosyncratic and driven as Michel Gondry (the man behind some of my favourite music videos).

Trailer: (2’06” is the moment that screams “Gondry!”)

Refreshingly, listening to the commentary makes this very clear, as Gondry, Goldberg and Rogen frequently reference the arguments behind almost every good idea in the movie, and occasionally break into new arguments about them (“We had to convince you that this would work!” “No no no! This was my idea! You guys didn’t want to let me do it!”).

This conflict doesn’t particularly damage the movie, but I ended up wishing Gondry had had more things go his way, because all the really weirdly brilliant parts are unmistakeably his. For example, at one point, the bad guy wants to send a message out through his criminal network, and this is how Gondry represents it:

It’s also great to hear his enthusiasm for his own ideas in the commentary, as when this scene starts: “This is awesome, look! Two cameras from one camera! How… did… the hell it happen?!” (Answer: they got the actors to stay in position while shooting one part, then came back to them and picked up shooting from the same position, then forced the shot to match in digital post-production, which is fine, but just count the splits and think about actually pulling that off).

The real problems with this film (to save you the trouble, it’s a 6.0 on IMDb and 44% on Rotten Tomatoes) are I think twofold:

1) Goldberg and Rogen consciously chose to reverse many of the staples (some would say clichés) of a superhero movie, which is admirable, but as is so often said, you need to be very familiar with the “rules” of any art form if you want to break them and still have the thing work, so this sentence ends in just the way you would expect.

2) There’s a fine art to crafting an action movie in which the audience can root for the protagonists, even when they’re harming or even killing bad guys. I don’t know how you pull this off, and apparently neither did anyone making The Green Hornet, because these moments frequently feel wrong.

All of which was fascinating, and I don’t regret watching the movie at all.

Answer 2A and 2B – Temperature/Pressure Pairs
Do there exist a pair of points opposite one another on the earth with exactly the same temperature and pressure? I say yes, and here’s my hand-waving explanation for that.

Stage 1
Let T(x) and P(x) denote the temperature and pressure of point x.

Choose two opposite points, A and B (if T(A) = T(B), do this stage with pressure instead of temperature). Consider a path from A to B (blue arrow in Fig 1a) and the corresponding opposite path from B to A (red arrow in Fig 1a).

In Fig 1b, we chart the temperature of the opposite points as we move around these paths. Just as with the Joss Whedon ascent/descent puzzle, since each line of temperature is continuous, they must cross at least once, and this represents a point at which the temperature is equal on opposite sides of the globe (points C and D in Fig 1b).

Stage 2
We now imagine rotating the circlular path we’ve considered about points A and B (Fig 2a). As we do this, the lines of temperature move continuously (Fig 2b), but since they always start and end at points A and B, the end temperatures remain fixed, and so the point at which the lines cross also moves continuously.

This starts to trace out a line of equal-temperature-opposite-points on the globe (turquoise and purple lines in Fig 2a).

Stage 3
If we continue that rotation all the way around, we trace out a continuous wiggly line of equal-temperature-opposite-points around the globe (Fig 3a, purple and turquoise lines).

We now consider two opposite points on this line, C and D (Fig 3a). We consider the pressure as we trace out a path from C to D (purple line) and the corresponding opposite points on the path from D to C (turquoise line). We can now apply exactly the same argument as in Stage 1 – the two lines of pressure (Fig 3b) are continuous and so must cross at some point, X. At that point, both the temperature and pressure are equal on opposite sides of the globe.

While this is not a proof, it’s reassuring that the Borsuk-Ulam theorem does prove that the result is true, although that’s no garantee that this reasoning is completely sound.

Dom Camus supplied a similarly hand-waving explanation but with a much more audacious line of attack, so if you liked the above, you should definitely check it out.

Phil has a pretty elegant approach, although he didn’t sound that convinced by it. He points out that “On any closed curve (not just great circles), the same sort of argument [as in Fig 1 above] holds […] I claim you can always construct a closed curve containing all its own opposite points and along which the temperature is everywhere equal at opposite points [like the turquoise/purple path in Fig 3]. Otherwise there would be some closed curve containing all its own opposite points, along which the temperature was never equal at opposite points, a contradiction.” You can then repeat Step 3, as above, to reach the same conclusion.

Puzzle Level 3The Crumpled Map
The final level in this series (suggested to me by Tarim) is one I don’t have any kind of hand-waving proof of, but I would love to see one.

Imagine you are on a lovely desert island with a selection of your favourite music, a pencil and paper, and an uncannily perfect map of the island. Actually, only the map is important.

If you lay the map on the ground and align it perfectly with the island itself, it’s quite easy to visualise that there must be a single point on that map which corresponds precisely to the bit of the island directly below it.

Now imagine folding and crumpling the map in any kind of way (but not tearing it) and throwing it anywhere on the ground. Wherever it happens to land, will there still be a point on the map that exactly corresponds to the place on the island directly below it?

Things 120: Olly Moss, Benjamin Franklin Effect, A Difficult Person

Pictures – Olly Moss
Sometimes, as you browse the internets, you get a lovely moment in which you realise the person that made this cool thing you are looking at is the same person that made that other cool thing you remember from a while ago. You check out the rest of their work, and if you haven’t already, probably think about whether it’s worth following their output more closely.

I recently had that, except it turns out that Olly Moss is behind at least six different things (or sets of things) I had admired in the past:

Clearly, they share a certain graphical elegance and pop-culture-ouvre, and in the end the coincidence isn’t that huge, because he’s most likely closely followed by one of the aggregators of content that I browse, although I do recall seeing at least three from reasonably independent sources, so I remain quite amazed.

In short, do go have a browse of his projects. There’s lots more great stuff there.

LinkThe Benjamin Franklin Effect
Summed up nicely at the start:

The Misconception: You do nice things for the people you like and bad things to the people you hate.
The Truth: You grow to like people for whom you do nice things and hate people you harm.

It’s not a totally airtight case, but the article weaves anecdote with data nicely, the results are certainly very suggestive, and I recommend that you read the whole thing.

Quote – A Difficult Person
What I would like to do now is present you with a quote which, out of context, is rather dry and uninteresting, which would be a rather pointless thing to do, so instead I will first attempt to provide you with that context, in the hope that the quote will then seem to you just as striking and memorable as I found it to be. So bear with me here.

In Face of the Crime, or in the original German, Im Angesicht des Verbrechens, arguably better translated as “Face to Face with Crime” or perhaps “All up in the face of crime”, was described by a friend-of-a-friend as a kind of Berlin-based version of The Wire, and unfortunately it isn’t, as the characters are much less engaging, and the realism level far lower, even when one ignores the strange touches of what I guess people would call magical realism. That’s not to say that it’s bad, I actually found it rather interesting in its own strange way, it’s just a matter of setting one’s expectations accordingly.

If you think that sounds promising, and if you are the kind of person that avoids any spoiler for something you might later watch, no matter how small the detail or slim the chances of you watching it, then you may or may not choose to watch the trailer below (which is in German without subtitles and is somewhat NSFW) to further firm up your opinion, and based on that you may prefer to skip straight past this section to the puzzle bit below; but just so you know, as spoilers go, where 1 is inconsequential and 10 is The Sixth Sense, I’d put this at a 3.

So, we have someone I’ll describe as our hero, a straight-laced fellow who rarely betrays emotion, and is just trying to do the right thing, which is tough when you’re a cop in a crime drama with some back-story and Damoclean family tension hanging over you. One gets the impression that you’re supposed to root for him, on account of his moral rectitude, but it’s a little hard to do so, since he mostly does what is expected of him, and just occasionally does something else, but without getting remotely emotional about it.

Meanwhile, there is the heroine, who has a powerful vision of the hero’s face while swimming in a lake (and we know it’s a powerful vision because it gets repeated in the recap at the start of almost every episode), and whom it is strongly implied is destined to meet and presumably fall in love with said hero. She’s got a lot of common sense and a goodly amount of agency, but occasionally must put those things to one side in order to allow the plot to proceed, presumably because she realises that one way or another this will ineluctably lead to her destiny with the hero.

I don’t consider it much of a spoiler to say that they eventually meet, and we know and they know that something magical and destiny-related is happening, even though they’ve barely spoken to one another at this point, and despite the fact that the heroine seems to be all about hope and destiny while the hero is clearly married to his job and gives the impression that truly loving somebody would probably be beyond his emotional register.

I no longer remember the exact details, but there comes a slightly awkward conversational moment, and the heroine’s eyes flicker just slightly, and you can see that while she knows this is her chap-of-destiny, it might actually be that he’s not the best potential partner one could possibly imagine, and she suddenly says, quite bluntly (according to the subtitles):

Could it be that you are a difficult person?

Answer – Climb and Descent
Last week I asked if there was a single time on both the day of ascent and day of descent at which Joss Whedon could be found at the same altitude, given that he began both journeys at midday and ended them at midnight. A nice way to see that the answer is clearly yes is to imagine both journeys happening simultaneously, in which case there must clearly be a time at which the ascending Joss Whedon crosses paths with the descending one.

Perhaps more convincingly, you can draw the answer, as Richard describes:

Trivially proven by drawing two overlaid graphs of altitude vs time.  One line goes top-left to bottom-right, the other bottom-left to top-right.  Short of teleporter accidents, the lines have to cross at some point.  Read off the time and altitude to find where/when.

That was Level 1. Here comes Level 2:

Puzzle 2A – Temperature Pairs
Continuing the series of puzzles Tarim recently introduced me to…

Imagine a straight line that starts anywhere on the surface of the Earth, passes down through the centre of the planet, and comes back out on the opposite side. We take the air temperature at each end of the line. Now imagine rotating that line about the centre, describing a ~circular route of places on the earth’s surface that are all directly opposite one another, and we continuously record the air temperature of those places all the way around (and we do all of this, somehow, in a single moment in time).

(You might also like to imagine that this is all happening in some idealised abstract space where we don’t have to worry about the fact that this entails taking an infinite number of temperatures with infinite precision; I’m just painting the picture in this way because it’s the most convenient way I can think of).

The question (which you might have anticipated if you were trying to see the parallels with Climb and Descent) is this: will there be a position of that line for which the air temperature recorded at each end is exactly the same?

Given the parallels I’m drawing with the last puzzle, you’ll probably be thinking that the answer is yes. But can you prove it?

Puzzle 2B – Temperature/Pressure Pairs
Perhaps that was too easy, so instead consider this: what if we measure both air temperature and pressure at each end of the line, and we consider every possible pair of points on opposite sides of the Earth. Will we be able to find a point that is at exactly the same air temperature and pressure as its opposite on the other side of the Earth?

Trivially proven by drawing two overlaid graphs of
altitude vs time.  One line goes top-left to bottom-right,
the other bottom-left to top-right.  Short of teleporter
accidents, the lines have to cross at some point.  Read off
the time and altitude to find where/when.

Things 119: Journey, Tree Record, Climb and Descent

Game: Journey
If you’re a gamer, you’ve probably heard about Journey. If you’re not a gamer, then you should have heard about it anyway, because it’s quite beautiful and amazing, and only takes 2-3 hours to play through, which means you could visit a friend that has a PS3 and play it in one sitting.

But why would you want to do that?

In this interview, Jenova Chen, the game’s creative director, says:

“Augustine wrote: ‘People will venture out to the height of the mountain to seek for wonder. They will stand and stare at the width of the ocean to be filled with wonder. But they will pass one another in the street and feel nothing. Yet every individual is a miracle. How strange that nobody sees the wonder in one another.’

“There’s this assumption in video games that if you run into a random player over the Internet, it’s going to be a bad experience. You think that they will be an asshole, right? But listen: none of us was born to be an asshole. […] It is the system that made the player cruel, not the player themselves. So if I get the system correct, the players are human and their humanity will be drawn out. I want to bring the human value into a game and change the player’s assumption.”

The reason I say the game is amazing is that it succeeds at this seemingly impossible aim. I’ve played through it a few times now, and each time I’ve had at least one incredibly positive and sustained play experience with a complete stranger.

http://www.youtube.com/watch?v=_mF8KkDiIdk

[Video not working, try this search – metatim, 02/08/15]

Film: The Cabin in the Woods
If you like horror films, you really should watch The Cabin in the Woods. I don’t think it quite succeeds at Joss Whedon’s stated aim (which you shouldn’t look up until after you’ve seen it), but it’s worth it for the wonderfully insane final half hour or so, which, impressively, the trailer largely resists showing any of:

http://www.youtube.com/watch?v=7ENUBUdFswM

[Video not working, try this search – metatim, 02/08/15]

Video: Tree Record / Years
The technology to turn wistful ideas into a reality is in our hands. Look at this device and imagine what you want it to do:

Now check out the video, where it does exactly that:

Read a bit about it here.

Puzzle: Climb and Descent
Tarim recently introduced me to levels 1 and 2 of a puzzle I’d only ever previously heard set at level 3. This week: level 1.

On Day 1, Joss Whedon hikes his way up a mountain, starting at the bottom at midday, and reaching the top (with a few rest stops along the way) 12 hours later, at midnight. He basks in the glory of his achievement for 12 hours, then at midday on Day 2 sets off back down the mountain, reaching the the bottom 12 hours later again, at midnight.

The question: is there a particular time at which he passed through exactly the same altitude on both his Days 1 ascent and Day 2 descent?

Answer: Voice recognition
A long time ago I asked what one could do to improve the chances of having your words understood by one of the many would-be voice-recognition services we find around us today.

After a bunch of googling around, the answers seem to be:

  • Reduce ambient noise where possible
  • Don’t speak too loudly and close to the microphone
  • Leave longer gaps between words than you might in natural speech
  • Speak with the accent the device was tested for

That last point is the one I’m most interested in. The question is, what accent should you use?

It seems the various companies offering this service (Apple/Siri, Google voice search, Xbox Kinect) do have to release different versions for different parts of the English-speaking world (I don’t have a good source for that, but it’s the impression I get from their staged releases, people’s reported experiences, and common sense).

My next plan is to carry out a small personal test in which I try putting on different accents. Results will of course be reported here.

@metatim

Things 112: Eyes, Guessing Cat, Amigara Fault

This week Things has a very slight Hallowe’en theme.

Puzzle
This is one where you should gather some people around the monitor and see who can do best: guess the cartoon (or CG) character from their eyes (mouse over the eyes to see the character outline that should tell you if you’re right).

And yes, it is pretty difficult – I only got 6, and I watch a lot of animation!

Video
Here’s a video that begs the question: is the cat playing the game, or just acting out of blind instinct?

To which the answer is to have a big argument about the definitions being used before concluding that you can’t tell.

Quote
In the wonderfully stylised animation The Secret of Kells, I heard the line “One beetle recognises another” and wondered if it was some kind of proverb. It turns out that it is, and actually – obviously – there are a whole bunch of Irish Proverbs, which in translated form become alternately profound, banal or hilarious, just as I imagine English proverbs must seem if you haven’t grown up with them. Here’s a list of them on Wikiquote, and here are a few of my favourites, for unstated reasons:

“Every beginning is weak.”

“Time is a good story teller.”

“A lamb becomes a sheep with distance…”

“The quiet are guilty”

Comic
The Enigma of Amigara Fault is a horror comic that impressed me with its unconventional approach. It’s 32 pages, and originally in Japanese so you have to read the panels right to left. But if you want a comic that will freak you out for Hallowe’en, it’s worth it. Unless you’re particularly claustrophobic, in which case you should probably steer clear of it entirely.

Answer – Malady X
In Things 111 I asked what the probability of having Malady X is if a randomly administered 99%-accurate test for it comes back positive. As Phil and Thomas noted, you can’t actually answer from this information alone: you also have to know what the probability of a random person actually having Malady X is. A lot of people don’t have an intuition for this fact. I’m going to attempt to explain ways to apprehend that hand-wavingly, mathematically, and visually.

Argument from hand waving and examples:
Imagine the probability of having Malady X is 0% – nobody has it. In this case, it’s certain that getting a positive result means you were simply in the 1% of cases where the test comes back incorrect.
Conversely if the probability of having it is 100% – everybody has it – then you must be in the 99% of cases where it is accurate. In this way, it’s clear the underlying probability influences the chances that the test is correct!

We might worry that these extremes somehow break the puzzle, so let’s imagine less extreme alternatives. Imagine 1,000 people are tested. If 50% (500) really have Malady X, on average we expect the test to come back positive for 99% of them (495) and also for 1% of the 500 that don’t have it (5). In this situation, 495 out of the 500 people for whom the test was positive actually have the disease – 99%.

Alternatively, if 1 person (or 0.1%) out of the 1,000 has the disease, they’re very likely to be correctly diagnosed, and we expect roughly 10 of the other 999 to get a positive result. In this case 1 out of 11 people with a positive result actually have Malady X – fewer than 10%. So clearly the underlying incidence level matters.

Argument from maths:
There are two probabilities at work: the chance the test is correct (99%) and the chance of anyone having Malady X (unknown – let’s call it X%). When you combine probabilities you multiply them, so for example the chance of anyone actually having Malady X AND getting a postive result is 99% times X%.

If someone gets a positive result and that’s all we know, we reason as follows:
A = Probability someone has Malady X and tests positive = X% times 99% times
B = Probability someone does not have Malady X but still tests positive = (100% – X%) times 1%
If you test positive, the chance you actually have it is C = A / (A+B). But if you haven’t studied probability carefully, I’m not sure you could infer this, which is why I like to come up with other ways of getting a feel for the correct answer.

Argument from visualisation:
Since there are two probabilities in question, and we combine probabilities by multiplying, this naturally suggests a visualisation where probability is represented by rectangular area (since area is calculated by multiplying height by breadth).

For example, if we imagine the actual incidence rate of Malady X is 50%, the picture would look like this (click for big):

If the test result is positive, you either have it and the result is correct (big yellow area) or you don’t have it but the test was incorrect (small dark blue area). The chance of you actually having Malady X is equal to the proportion of those combined areas that is yellow. In this case:
Yellow = 99% x 50% = 49.5%
Dark blue = 1% * 50% = 0.5%
Probability you have it = Proportion that is yellow = 49.5% / (49.5% + 0.5%) = 99%.

Alternatively if the incidence rate is, say, 2%, it looks like this:

Here we see the yellow and dark blue areas are very similar, so the chance of you being one or the other is much more even. In fact, it’s:
Yellow = 99% x 2% = 1.98%
Dark blue = 1% x 98% = 0.98%
Probability you have it = Proportion that is yellow = 1.98% / (1.98% + 0.98%) = 67% (ish).

As Peter Donnelly shows in this TED talk, this actually has some severe ramifications, because when the probability of the thing being tested for is extremely low, it becomes overwhelmingly likely that a positive result is false, but people intuitively feel that a 99% accurate test should be correct 99% of the time.

Thomas also noted:

If anyone is interested in playing around with the probabilities (even if you’re not familiar with the maths), I recommend GeNIe:
http://genie.sis.pitt.edu/
It lets you create networks of dependencies, set evidence and work out probabilities in problems just like these.

-Transmission finally ends