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Things 78: Nuclear, BODMAS, Curvy tube map

Video
While not perhaps the best way to view the data (using time to represent time always feels strangely inefficient, although it’s difficult when you also want to present geographical data), this video might nonetheless be a good way to actually take in the data:

Quote
John Hodgman “A stopped clock is correct twice a day, but a sundial can be used to stab someone, even at nighttime.”

Puzzle
I’m sometimes called upon to help people with their children’s maths homework, and I found this problem particularly hard.

The solving method is explained as follows:

When you are working out a sum with more than one operation (eg 8 + 2 x 3), follow the BODMAS rule. Without these rules you could have more than one right answer, so getting the order of operation correct is important. You should calculate in this order;
Brackets
Order (powers/square numbers)
Division
Multiplication
Addition
Subtraction

The first problem in the ‘level 1’ set of problems is simply this:

2 + 4 — 3 + 5

What answer would earn you a tick from the teacher?

You can see the original problem sheet here, and the level 2 and level 3 problems here.

Picture
This curvy tube map is rather nice (although the full-size version doesn’t seem to be available any more):

Some of you may recall the scale tube map from Things 18.

Last Week’s Puzzle
Last week I asked about Trigger’s Broom (also known as the Ship of Theseus problem): the broom has had both head and handle replaced many times, so we might ask “Is Trigger’s broom still the same broom? If so why, if not why not?” This question has stimulated debate and discussion for centuries and Things recipients were no exception. I’m going to paraphrase people’s responses here to prevent this issue of Things becoming even longer.

Both John and Laurence point out that the Sugababes present a similar problem (as does the Wikipedia article, which is an excellent starting point for anyone that has not delved into this subject before)(naturally “as does” could refer to both “point out” and “present a similar problem”).

Thomas makes the distinction “There are two questions: “Is it the same?” and “Is it the same broom?”,” pointing out that the former question is trivial, but for the latter “we don’t insist on new labels, new identities for every subtle change in an object … so things like the functions it performs and who possess it as better ways to identify them”.

Laurence counters “what if these heads/handles were replaced when they started to show wear, but were still functioning. If I rescue Head_1 and Handle_1 from the bin at different times and join them, what do I have?”

As Angela noted in her original setting of the question: “based on the fact that none of the cells in your body now are the same as they were when you were born, are you actually you??”

This was touched on in the puzzle from Things 41 (yet to appear in blog form), which went:

A famous bit of trivia that has been passed around for years holds that over the course of 7 years, every cell in your body will have been replaced with a new one. Are there any simple ways to disprove this?

To which there are some interesting answers.

Without diving down that rabbit hole too deeply, I first note my original answer to Angela on the personal identity issues raised by Trigger’s Broom:

Identity is a convenient fiction that we are hard-wired to believe in.

Second, I highly recommend making time for this cartoon which sheds some light on the subject, which I saw many years ago and Laurence managed to find on YouTube:

http://www.youtube.com/watch?v=pdxucpPq6Lc

A famous bit of trivia that has been passed around for years holds that over the course of 7 years, every cell in your body will have been replaced with a new one. Are there any simple ways to disprove this?

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Things 77, Time Slices, Innovative Pricing, Trigger’s Broom

Video
Imagine frames of a video printed on the side of a sequence of decks of cards. Then imagine all of those decks combined with a perfect n-riffle shuffle. What would the result look like if played back as a video? Something like this:

Surfing the 4th Dimension from Don Whitaker on Vimeo.

A bunch more, by phyrworks, can be viewed here.

Link
I love the idea that seemingly obvious things that work pretty well are actually only local maxima, and if you move far away enough from the norm you can actually find something far more effective.

The nicest example of this I’ve come across so far can be found here; some great data to show that under some circumstances combining the two pricing strategies of pay-what-you want with half-goes-to-charity produces a significantly better outcome than either option alone, or standard pricing. (This was anecdotally demonstrated by the Humble Indie Bundle back in May, but that clearly lacked a fair “control” for comparison).

Puzzle
As suggested by Angela last week, the problem of Trigger’s Broom, more conventionally known as the Ship of Theseus Paradox:

Trigger: And that’s what I’ve done. Maintained it for 20 years. This old broom’s had 17 new heads and 14 new handles in its time.
Sid: How the hell can it be the same bloody broom then?

Is Trigger’s broom still the same broom? If so why, if not why not?

Picture
Jeremey’s Place fake food emporium finds a clever way of shifting their otherwise fleetingly-entertaining spilled-food novelty items:

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Things 76: Bikes, Polaroids, Kanye Tweets

Video
For some reason it’s the most pointless things that make me feel most encouraged about the human race:
httpv://www.youtube.com/watch?v=kTYGmjgSMv8

Picture
I am naturally drawn to extremely long term, incremental projects. This probably explains why I have chosen to serialise 50+ issues of old Things on this blog at a rate of one a week; why I have spreadsheets tracking my sleep data going back nearly 10 years; and perhaps why it took me 6 years to complete a PhD. But as the title suggests, “He Took a Polaroid a Day” takes that kind of thing to a whole new level.

Quote
Leonard Bernstein: To achieve great things, two things are needed: a plan, and not quite enough time.

Last Week’s Puzzle
Last week I asked why buses come in clusters. I think the main problem is the feedback loops – any traffic fluctuation that causes a bus to become slightly delayed means a longer wait at the next bus stop, which means more people are likely to turn up. More people take longer to get on board, and as Xuan points out make it more likely the bus will need to stop more often. Meanwhile, when the next bus turns up there has been less of a wait since the last bus left, so fewer people board, and by the same token the bus can make faster progress, so the gap between buses is closed by feedback loops at both ends.

One answer is to hold buses to “even out gaps in the service” as does indeed sometimes happen. Xuan also suggests better data on how crowded imminent buses are would encourage people to wait for the next, more empty bus, easing the feedback loop. I also think the surfacing of real time public transport data – as could be viewed a few weeks ago – will help us collectively improve efficiency in a similar way.

Pictures
Kanye West begins tweeting in a rather ostentatious way. In a stroke of inspiration, someone thought to use his tweets to re-caption New Yorker cartoons. Examples below; full story here.

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Things 75: Fast robots, Inception links, Buses

Video
It’s strangely easy to forget that sufficiently well-made robots can move and react ridiculously fast. Here’s some nice reminders:

httpv://www.youtube.com/watch?v=MvRTALJp8DM

httpv://www.youtube.com/watch?v=v9oeOYMRvuQ

Links
Spoiler warning: if you haven’t seen Inception, these links are not for you. Move along to the quote.

I saw Inception and particularly liked the way you can enjoy it at face value or try to make out a deeper underlying truth. Whichever camp you fall into, I recommend checking out this YouTube video (more accurately audio), and if you’re trying to piece things together you might be aided by this simple diagram, or this more ambitious one.

If you want to dive deeper into working things out, I recommend you start with the IMDb FAQ which has some pretty good answers, then move on to the InceptionTheories forum.

Quote
Piet Mondrian: Creativity is allowing yourself to make mistakes. Art is knowing which ones to keep.

Puzzle
Here’s a classic: why do buses come clusters?

Last Week’s Puzzle
Last week I asked why walk-in freezers have doors that cannot be opened from inside. As Richard pointed out, the answer is that actually, they generally don’t. But if they did, I like Maria’s theory: “Maybe it is a Hollywood conspiracy. Think of the lack of plots if people didn’t get stuck inside a walk-in freezer.” Hollywood manipulating real life to make convenient tropes seem more plausible sounds like a fun premise for a film…