Penney's Game puzzle

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Penney's Game is a non-transitive probability game involving coin tosses. You invite your friend to name a sequence of coin tosses (at least three long), and you can always name a sequence that is more likely to come up first.

See this link which suggests a card-game variant for a good explanation and a diagram.

Now, what happens if you have five players. Player 1 names HTT as his sequence. Player 2 names HHT in order to beat Player 1. Player 3 names THH to beat Player 1. So Player 4 names TTH to beat Player 3. Player 5 now names HTT to beat Player 4.

If Player 2 usually beats P1, P3 usually beats P2, and P4 usually beats P3, then how does P5 - equivalently P1 usually beat P4? P1 < P2 < P3 < P4 < P1 ??

Bit baffling at first, but I think it's fairly easy to figure out what I've partly neglected to point out.

All this comes from a discussion on the JREF forums of this vos Savant column - which prompts an entirely separate discussion of random strings and probability...

On academic publishing

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There's been substantial discussion lately over academic publishing. Most recently, George Monbiot put out this on Comment Is Free, to be followed by this response on the Scholarly Kitchen (a blog from the Society of Scholarly Publishers). I can't remember where I saw many other discussions of this - if you know any feel free to comment (edit: Ahah - the ever excellent Peter Coles had this blog).

Let me say first I find both a little aggressive in tone, but there's important points raised by Monbiot, and some sensible responses by Kent Anderson at the Scholarly Kitchen.

First off I do want to say that frequently individual article prices are absurd and I've often been put off dismantling what I suspect is very dodgy research because I'd have to pay some crazy price to read it (and I have access to most major journals through the subscriptions of my employers). I can't expect my employer to pay for it (or a more expensive full subscription) if it's outside my field and I'm just making some comment beyond the remit of my work. I end up just not looking.

Secondly, us physicists make great use of the arXiv, but that is much more expensive to run than people realise and it takes something like half a million dollars a year of public funding of various sources to support, and it does no peer review or any of the other functions publishers directly perform.

On to Anderson's post though. He argues early on that most papers are inaccessible to anyone but specialists anyway, because they're too technical. He searches PubMed for 'cardiac', picks the first paper and points out its unparseable to most people. The bit he quotes is 
Intrathoracic herniation of the liver ("liver-up") is associated with predominant left heart hypoplasia in left diaphragmatic hernia but not right fetal diaphragmatic hernia. Our observations indicate that this difference may result from different ductus venosus streaming sites in these conditions.
Now, I haven't done biology since double science at GCSE, but I broadly get the gist of 'intrathoracic herniation of the liver', 'predominant left heart hypoplasia', 'left diaphragmatic hernia' (and naturally the right version), although I'd have to Google ductus venosus streaming sites. I bet if I wanted to actually read this paper I'd have more clue about it, and there's no reason to think that a well-motivated reasonably intelligent amateur couldn't manage that. Admittedly I'm one person and a bit of an oddball in this sense but then...

... then there's the fact this is a randomly selected paper, and only one randomly selected paper. If I was trying to find out something about hearts, maybe my grandfather was started on some new medication I wanted to find out more about, I'd be doing a more detailed search, and even then if this cropped up I'd skip it in favour for something more obviously up my street. This single example of a mildly difficult to parse abstract is in no way an indication that most papers published are going to offer no value to people outside the immediate specialisation.

Anderson says
Let's assume I can read the whole paper. Like 99.9% of the population, I'm not going to know what to make of it.
Well over two million people in the UK have some kind of science, technology or engineering degree, and are probably going to be able to make a reasonable stab at parsing a lot of the essentials of a paper they are interested in. A not insignificant minority of these are going to have the skills in statistics to make reasonable criticisms of some papers from that angle without even knowing anything about a subject. If you gave a statistician a paper on a drugs trial they don't need to know anything about pharmaceuticals to critique the analysis. Many will be able to offer criticism of experimental design too.

This is particularly important for the kind of paper many will want to know about - e.g. a new cancer drug has come on the market and your mother has the cancer in question, and you want to know what justification the NHS has for saying it's not effective enough and they're not paying for it.

Anderson says
To chart a useful course forward, we need accurate information, rational thought, and reasonable plans. Monbiot provides none of these in his inflammatory, off-base, and ultimately unfair rant.
I find this a mildly baffling statement. Monbiot supplies quite a number of figures and accurate information, he certainly provides some rational thought (maybe not all though) and offers reasonable plans. I think Anderson is making something of an unfair rant himself.

There's a real absurdity in expecting certain private individuals (I can think of several excellent bloggers) to stump up tens of dollars for a single paper which they probably already think is a bit shit, or they wouldn't be wanting to download it to criticise it. And being able to criticise scientific publications is pretty crucial, even if you're not a specialist, especially when it has either been funded by public money or is about to lead to public money being spent.

Surprise!

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I've recently been reading Stephen Law's new book - Believing Bullshit (do check out the Amazon link if only for the comedy review Stephen mentions on his blog).

I'm only about a quarter of the way in, and finding it enjoyable, but I thought I'd pick up on one bit of the text I'm not completely sure I agree with. It's about what makes a scientific theory that is well supported by evidence.

Bad physics demonstrations

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Yes, I know. I've not blogged for ages. Anyway, I'm blogging again, and then will probably fall silent for months again.

Two things have inspired me to write today, both physics demonstrations or analogies.

Gravity

The first is a very common description of gravity as described by Einstein's Theory of General Relativity (GR). GR essentially describes gravity as due to the curvature of spacetime, and that curvature as being due to matter. Almost as soon as someone starts to try to explain it they use the rubber sheet analogy. Now I link to that page to describe the analogy, but that page does not do a bad job of using it. Essentially the analogy is that you have a rubber sheet, and a ball on that sheet curves it, and the curvature of the sheet affects the motion of other objects upon it. Now, I've no criticism of that page. There are two major problems with this analogy.

  • The ball deforms the sheet - why? It's because the weight of the ball is pushing down upon that sheet. What gives the ball weight? Gravity, which is the thing this analogy is trying to describe. Now that's not too serious, you can simply point that out and say that the mechanism by which mass curves spacetime is not described - it simply does so.
  • If you roll a small ball slowly past the larger ball it curves in and rolls toward the big ball. This is because the small ball rolls downhill. Why does it do this? Because of gravity. This is a serious problem. There's a path deflection due to the geometry of the sheet, but there's also a path deflection because of a preexisting downward force upon the ball. This is almost never pointed out, and most worryingly the effect exactly looks like what people generally think of as a gravitational attraction - a movement towards rather than a deflection of a path from what would naively be considered straight.

Professor Brian Cox, using this description in this week's Wonders of the Universe, I'm looking at you.

Magnetism

When you first studied magnetism at school, what demonstrations of it do you recall? I bet that a very early one was putting a sheet of paper over a magnet and sprinkling iron filings over it. You get something like this image - iron filings lining up upon field lines. You're then also shown a diagram like this showing discrete field lines.

What's wrong with this? Well, field lines don't come in discrete chunks. They're continuous. Every point in space has a magnetic field line passing through it, and the field lines do not vary in strength in some onion-skin like way. There's nothing special about where those iron filings are lining up. The field lines are no more existing in a particular number than the field lines of Earth's gravitational pull exist in particular places, rather than smoothly over the entire surface. I bet you that every kid comes out of that lesson thinking magnetic fields look something like an onion. I did, and it took me a disturbingly long time to figure out that they weren't, and why, because noone ever corrected that misconception.

What is actually happening is that every iron filing is itself becoming magnetised and is drawing adjacent filings towards itself. It's like they're concentrating the field where they are. The filings are an active part of the field - they're not what a physicist might call a 'test particle' that doesn't affect the things around it and only traces out some physical phenomenon.

This is really problematic. People come away from seeing this thinking that magnetic fields are hairy.

Better ideas

Now both these demonstrations are actually useful if explained properly, and I honestly have no idea if there's a better demonstration of these physics concepts. Do you have one? Or do you have a pet hate amongst common physics demonstrations yourself?

A problem of unstated data

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In The Guardian's ongoing series of science questions posed to major political parties, the Green Party's response to the question
Is animal testing necessary? Are the ethical concerns outweighed by the benefits? How would you like to see regulations on animal testing change under your government, if at all?
states that

We agree with the independent patient safely organisation, the Safer Medicines Trust, that animal testing may be more harmful than helpful.

The Safer Medicines Campaign, previously known as Europeans for Medical Progress, has a habit of using arguments like the following:

  1. Results from other species simply do not reliably translate to the clinic, as evidenced by the 92% failure rate of potential new drugs in clinical trials. [1]
  2. That must include animal data, since crucial decisions, such as whether to proceed to clinical trials and whether the drug might cause cancer or birth defects are based on demonstrated safety in animals. Yet, as we know from Northwick Park, even safety in monkeys at enormous doses does not guarantee safety in humans. [1]
  3. A large systematic survey published in November 2009 found serious omissions in reporting of data and in strategies to reduce bias in results. Only 12% of the animal studies used randomisation, only 14% used blinding and only 8% gave the raw data. [1]
  4. The best way to evaluate the effectiveness of animal tests for drug safety is to compare their results with subsequent real- world outcomes in patients and consumers. [1]
  5. Aids is another: while at least 80 vaccines work in animals, all 80 have failed in human trials. Similarly, every one of more than 150 stroke treatments successful in animals has failed in human testing. A study in the British Medical Journal found that animal tests accurately predict human response less than 50% of the time. [2]

[1] Safer Medicines Campaign Spring 2010 Newsletter http://www.safermedicines.org/newsletters/newsletter_spring_10.pdf
[2] "The dead end of animal research", Comment is Free (Guardian), August 2009 http://www.guardian.co.uk/commentisfree/2009/aug/07/animal-testing-medical-research

I've previously argued that their arguments are weak. Take the first. We're told 92% of the drugs tested that pass animal tests fail in later human clinical trials (the phrasing is mildly ambiguous but I believe that is what is meant). While that might look like a problematic figure, I would think that any competent scientist would also want to know:

  1. The proportion of drugs that failed animal tests but would pass a later human clinical trial.
  2. The proportion of drugs that failed animal tests but would also fail a later human clinical trial.
  3. The proportion of drugs overall that fail animal tests

In other words, we ideally want a test for drugs that perfectly predicts the results of human clinical trials, as we don't want to do clinical trials that needlessly endanger people or might unacceptably delay them getting the best treatment. In the event we don't have that, we need to know four numbers to get a good picture of things - how many drugs failing one test would fail the other (which is a good thing), how many would pass one but fail the other (which would mean we are maybe giving those in clinical trial dangerous substances), how many would fail one but pass the other (meaning we've missed out on a potential cure) and how many pass both (which again is a good thing - these are the drugs that will go into common usage).

Similarly, other quotes above give one piece of information without giving corresponding pieces of information that are crucial in assessing the best options in pharmaceutical testing, and I would argue that "The best way to evaluate the effectiveness of animal tests for drug safety" is not "to compare their results with subsequent real- world outcomes in patients and consumers" but "to compare their results with other potential testing techniques".

I'm continually disturbed by the fact that the Safer Medicines Trust, which says "We focus on evidence based analysis of animal experimentation to assess the balance of help or harm to human health", so frequently writes pieces of publicity that fail to give all the necessary information to do this.

If you think animal testing is morally wrong, that's not something I can really argue with you about, but if you want to make a case it's outdated and there are better options I'd love to hear about them, but I'm usually disappointed by how the case is presented.

The Science Vote

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Recently, Michael Brooks, a journalist and author with a background in quantum physics, announced he will stand against David Tredinnick in the Bosworth constituency in the general election. This is because David Tredinnick has such famously irrational beliefs.

This has caused some controversy, as it may split the vote and so on, and Brooks is not a man local to Bosworth.

On astrology

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I appear to have found myself engaged with @angelneptustar, an astrology fan and also a Boris Johnson fan.

This came about through Marsh's post at the Mersyside Skeptics site. I read through the HuffPo article in question (I refuse to link to that rag, but you can follow through to it if you really wish) where angelneptustar comments on Boris Johnson's astrology chart and how it shows he is very talented.

Not a blog post

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This is not a blog post. It is an instruction to anyone self-identifying as a skeptic to read this.

To Columbo's Rescue

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Browsing my arxiv feeds this morning, I picked up this post - "A defense of Columbo (and of the use of Bayesian inference in forensics): A multilevel introduction to probabilistic reasoning" by G. D'Agostini.

Considering the topic, it's an enjoyable read. It's motivated by this NewScientist article from late last year. I criticised that article myself but did not touch upon the incident with Columbo. D'Agostini provides a fairly clear if mildly technical explanation of the mathematics behind the problem expressed - of the strength of the evidence against the killer Columbo caught when he picked one of thirteen (or twelve, as the NewScientist article says, but that's a minor niggle) cameras off a shelf, taking the one involved in the crime. As NewScientist says:

If only it were that simple. Killer or not, anyone would have a 1 in 12 chance of picking the same camera at random. That kind of evidence would never stand up in court.

Pascal's Wager

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I've long held that Pascal's Wager is a completely absurd argument. Most people will know what Pascal's Wager is, but it's loosely speaking the argument that you should believe in God because doing so offers the possibility of infinite reward, whereas not doing so offers no reward at all.

There are obvious flaws in it, which apparently even Pascal recognised. The primary one I think, is that the reward for believing something does not lead to a mechanism by which you can genuinely accept that belief. If you offer me a £10,000,000 to believe that pigs can fly, I will not be able to start believing that pigs can fly just to gain a benefit.

For this obvious reason, if anyone mentions the Wager in any context other than an example of dubious logic, treat anything else they say with caution.

However, Pascal's Wager is not really the object of this post. What I'm going to discuss is instead (despite the blog title) Pascal's Mugging.

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Edd works somewhere between astronomy and computing and has a general interest in science, skepticism and other related topics.

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