Interesting Links for 09-10-2018

[andrewducker]

Saudi Arabia arrests economist after he criticises Crown Prince's plans

(tags: saudiarabia OhForFucksSake )

Doctor Who: Jodie Whittaker's debut is most watched launch for 10 years

(tags: drwho bbc tv )

How Flocking works

(tags: birds fish behaviour )

A cartography of consciousness – researchers map where subjective feelings are located in the body

(tags: psychology visualisation bodies emotion )

Are super-cheap solar fields in the Middle East just loss-leaders?

(tags: solarpower economics middle_east )

Tricky question here about male musicians. Anyone got any suggestions? (Although the existing comments are great)

(tags: music men satire viaElfy )

The truth about traditional JavaScript Benchmarks

(tags: javascript benchmark fail )

The majority of people do not understand consent

(tags: consent sex society OhForFucksSake )

Doctor Who's viewing figures - boy's down 31%, girls up 264%

Hopefully, given time, those boys come back.
(tags: gender drwho girls GoodNews )

Council cuts due to austerity twice as deep in England as rest of Britain

(tags: austerity UK )

China has designs on Europe. Here is how Europe should respond

(tags: china europe politics )

Why Mathematicians Can’t Find the Hay in a Haystack

(tags: mathematics )

Comments

[simont]

Why Mathematicians Can’t Find the Hay in a Haystack

Perhaps even more counterintuitively, that phenomenon can happen in purely finite situations, as well.

An example is a graph theory problem I encountered a couple of years ago. In graph theory, a tournament is defined to consist of a set of players, and for each pair of distinct players, a choice of one of them to be the winner. (So it's specifically referring to the everyone-plays-everyone format out of the various options for real-world tournaments. And no draws.)

The problem is: given a positive integer k, show that it's always possible to construct a tournament with the property that for any subset of up to k of the players, you can find another player who beat all of them.

It turns out that this is indeed possible for all k, and moreover, the larger you make the tournament, it becomes more and more likely. More precisely, for a fixed k, the proportion of tournaments with n players that don't have that property tends to zero as n increases.

So in one sense, it's trivial to actually construct a tournament with this property. Simply pick n to be large enough that, say, 99% of all tournaments that size have the property we want (which is an easy calculation), and then make up a tournament of that size by choosing every match outcome at random. If a check reveals that you've found one of the 1% of tournaments in which some set of k players is not dominated by anyone, just try again; the expected number of attempts until you don't get unlucky is fractionally over 1.

And yet, if you try to explicitly describe a tournament with this property – or, better still, describe a deterministic procedure that will guarantee to construct one for any k – then that's a much harder problem than merely proving their existence. Which feels bizarre given that the random approach works so readily in practice – if 99% or 99.999% of all tournaments of a given size work, how can it be hard to specify a particular one of those?! – but it's true nonetheless.

The reason, I think, is much the same as the phenomenon described in that article, where it's surprisingly hard to specify a transcendental number or a 'typical' geometric shape, and outright impossible to write down more exotic things like a non-computable real or a non-principal ultrafilter. The point is that you have a gigantic search space, and a tiny subset of it that you don't want – but that tiny subset happens to have a near-total overlap with the set of things that can be described concisely, so it takes some work to find something that's in the concisely-describable subset but not in the unwanted one.

[andrewducker]

Fascinating!

Is there much research into "describability"?

[simont]

I don't know of any myself, but that doesn't mean a great deal. Off the top of my head it feels like a bit of a vague concept, perhaps heading in the direction of 'philosophy of mathematics' rather than mathematics proper (in that it's not the kind of question you can answer conclusively by proving a theorem, but one where you argue vague and woolly concepts back and forth and expect to be disagreed with).

Solar Panels

[danieldwilliam]

I think the cost of installing solar panels is going to be pretty contingent on local factors.

Thinking about the cost components

Cost of the panels - raw materials

Cost of the panels - manufacturing equipment and labour

Cost of the panels - energy for production

Land

Installation

Maintenance

Grid connection

Finance and interest costs

Net of subsidies and taxes

Land and installation are going to be locally driven costs. Some of the grid connection costs are local. Some of the maintenance costs are local. Subsidies and taxes are mostly local.

(I'm also not sure that the concept of a loss-leader exactly applies to large infrastructure projects.)

Doctor Who Viewing Figures

[danieldwilliam]

My guess is that the boys who didn't watch the opening episode of Doctor Who largely won't come back. I think once you've stopped watching a series you've stay stopped watching it. If the reason you stopped watching it is Get Rid Of Slimy girlS then you might have to do some difficult mental replumbing in order to return to watching the programme.

As for Doctor Who

[dewline]

I stuck around. I had fun. I plan to keep sticking around. I get rewarded with such Pavlovian ease this way, you know?

Dr Who

[anef]

I thought Jodie Whittaker was excellent in the first ep, but I wish they'd lay off the emotional manipulation. This is what makes me not want to watch it! (But I dare say I'll carry on)