Things 122: Linda, Sledding Crow, Brand Promises as Modern Myths

Puzzle The Linda Problem
I see this come up every few years, and get annoyed by it every time. Here’s a typical wording:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

  1. Linda is a bank teller.
  2. Linda is a bank teller and is active in the feminist movement.

Most people get this wrong. Why?

Usually I follow up on a puzzle in the next edition, but this one is so annoying I’ll address it below, after these other things.

VideoCrow Sledding
The Atlantic has the perfect headline for this video: “Science Can Neither Explain Nor Deny the Awesomeness of this Sledding Crow.”

At the time of writing, their version of the video is down, but this one isn’t:

(Extended version with same amount of sledding but more corvid activity here)

LinkColour perception and language
Ever since reading 1984 I’ve been doubtful but curious about the extent to which language can influence the way we think or even perceive. In a brilliant couplet of articles about colour on Empirical Zeal, I found out about some really nice experiments that demonstrate a real (albeit small) effect, so I highly recommend reading both part 1 and part 2.

ComicMartin Zutis – Being
In a comic shop in Vienna I came upon a small self-published comic, ‘Being’ by Martins Zutis. Packed with surreal imagery and insights that float around the border between madness and brilliance, I particularly liked this observation:

The news reports we don’t question are myths.

Here’s a tiny snippet, or you can read a slightly longer extract here.

Martin Zutis - Being

Answer – The Linda Problem / Conjunction fallacy (see above)
Most people (85%, apparently) will answer that option 2 is more likely, “Linda is a bank teller and is active in the feminist movement.”

At this point the person who set this problem usually laughs like a supervillain and points out that the probability of two things both being true must always be less than or equal to the probability of just one of those things being true. They will say this is a demonstration of the Conjunction Fallacy.

However, these people are wrong. What it actually shows is that if you choose to go against the cooperative priniciple in communication, people will misunderstand you so much that any attempt to isolate the Conjunction Fallacy is lost.

Consider a slightly different scenario:

Boris: I have two sisters. Alice is a bank teller. Eve is a bank teller and a feminist.
James: Oh, that’s interesting. Why do you think Alice doesn’t consider herself a feminist?
Boris: I didn’t say she wasn’t.

When I ask people where the mistake arose in this conversation, the surprisingly consistent judgement is that Boris was “being a dick”.

More formally, as noted in that article on the cooperative principle, we tend to implicitly assume that when someone is telling us something, they will narrow their focus to only that which is relevant. When Boris states that Eve is a feminist, this suggests this information is (for whatever reason) relevant, so the fact is was not noted for Alice strongly suggests she isn’t a feminist.

Some researchers then restate the problem by making it clear that option 1 is “Linda is a bank teller and may or may not be active in the feminist movement”, and still 57% of people think option 2 is more likely. But the assumption of relevance is still a confounding factor: the lead-in to the question is assumed to be relevant (when in fact it’s explicitly designed to be misleading), so I suspect people will be drawn to option 2 more because of this assumption (perhaps assuming they’ve misunderstood some part of the question) than because they misunderstand probability.

The Wikipedia article on the Conjunction Fallacy is much better than when I first reviewed it, covering these concerns and giving a much better demonstration of the fallacy in question.

(As an aside, I will note that I’ve often indulged in similar deviations from the cooperative principle for the sake of setting some kind of puzzle, although hopefully this is usually clear by context – for example, as I asked in Things 4, how far can a dog run into the woods?)


Things 48: Bike Parkour, Limits of Men, Wolfram Alpha

(Originally sent May 2009)

I’m considering switching to a blog format for Things in time for Things 50. Let me know if you have any strong feelings on the subject. [You’re now looking at it! – T.M. 28/5/11]

Danny MacAskill does parkour/free-running but on a bike. Having seen these kind of videos before, I know a lot of them are clearly a collection of flukes edited together – but in this case the man has a staggering raw skill and most of the things he does (with the exception of the first) you get the feeling he could pull off 10 times in a row.

A slow build up, but worth it:

Two quotes capturing a similar idea – decide for yourself just how gender-neutral ‘man/men’ is in each case:

“Every man takes the limits of his own field of vision for the limits of the world.”
– Arthur Schopenhauer

“Men perceive the world from their own point of view, which they confuse with absolute truth.”
– Simone de Beauvoir

With no regard to downplaying expectations, Wolfram|Alpha is going to attempt to launch within the next 24 hours. In some sense a web front-end for Mathematica, it will essentially curate public knowledge (population demographics, poker probabilities, mathematical algorithms, and who knows what else) and make it queryable with natural(ish?) language.

The hype:
“Wolfram|Alpha is in a sense the “killer app” for Mathematica. It is a chance for Mathematica to show off the astonishing range of things it is capable of doing when it is deployed, not against a specific problem, but against all problems.”

A lovely little .pdf summarising the ‘quest for computable knowledge’ in 2 sides of A4, where Wolfram|Alpha is naturally the next great step.

A bit of geekish chest-thumping as they assert how mighty their works are.

Showing off the maths bit.

The Reality:
From Douglas Lenat:

“[it] covers a large portion of the space of queries that the average person might genuinely want to ask. […] It handles a much wider range of queries than Cyc, but much narrower than Google; it understands some of what it is displaying as an answer, but only some of it […] The bottom line is that there is a large range of queries it can’t parse, and a large range of parsable queries it can’t answer.”

Assuming they can withstand demand, you will be able to try it for yourself very shortly – they will commence launch preparations at 1am tonight / tomorrow morning.

[Of course, it’s now live, and Lenat’s observation remains accurate – T.M. 28/5/11]

Dresden Codak
‘s Aaron Diaz, sporadically brilliant webcomicer, illustrates 7 types of plot twist and how they manifest across six genres, from the Reverse Macguffin in a Thriller to Double Shyamalan Mystery.

Puzzle answer: The Space Stick
Can information travel faster than light if you poke an incredibly rigid stick one light-year long? The answer is no. As many of you observed, ‘pushing’ a solid object does not magically transfer force instantaneously through it, but rather creates a compression wave as atoms or molecules push up against one another, and this is bounded by the speed of light. (There’s also the issues of the necessary rigidity being impossible, the huge amount of inertia you would be working against, needing something to push against, and gravitational complications if you’re anywhere near a planet or other large celestial body).

Many of you chose to focus instead on the general problem of faster-than-light communication. In summary, quantum entanglement does involve ‘spooky action at a distance’, but fascinatingly stops just short of being spooky enough to transfer information. Wormholes, on the other hand, are seemingly permitted by General Relativity, which would seem to lead to paradoxes, and remains a mystery.

This week’s puzzle: Wired’s “Color Scheme”
The US issue of Wired this month is guest-edited by J. J. Abrams and features a lot of interesting puzzles as well as a meta-puzzle (I think). I highly recommend ‘Color Scheme’, which you can try here [link broke, try here – metatim 03/08/15], although you’ll have to resist just clicking for the answer on the link bizarrely placed immediately below the puzzle.


Things 32: Busaba Toilets, Colour Test, Slow Motion Squirrel

I saw Mirrors last night. It started off as rubbish and ridiculous as it looked from the trailer, but then got a lot better, with a suitably ridiculous climax.

This week, Quantum of Solace, no more need be said.

Owing to extreme hecticness in the next few months, I have cancelled my Cineworld Unlimited card. The Films section may well disappear for a bit.

Puzzle Part 1
I ate at a Busaba Eathai last week. When I went to the toilets I was confronted with the two signs you see in the image below. I paused, then figured I had cracked the code. Where did I go? Make a guess now, then try part 2 at the end of this email.

A link
…which is also a puzzle. Test your ‘colour IQ’

A quote or anecdote
When paying for my ticket to see ‘Mirrors’, the guy at the till dropped a one pound coin into the vat of popcorn. Pretty soon three employees were scooping the popcorn around trying to find it while a manager was shouting ‘just complete the transaction!’ at them.

A video
Link courtesy of my mum – squirrel leaping in super slow mo from Autumn Watch:

Pictures of the sun taken using science:

Puzzle Part 2
Looking at the Signs for the Busaba toilets (above) I concluded that they represented the two modes of toileting: standing and sitting. I further inferred that this implied gender. I entered the door marked by the kinked line. It was a simple square wood-panelled room, and all I could see was urinals and sinks. Urinals were not sufficient for my needs at that time.

What would you do?