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Finite Factored Sets

Cool topic!
Here are some critiques on part 1 of your presentation: Short Combinatorial Talk

1 Colour coding slides by content is a nifty idea. I hadn't seen this before. Unfortunately, even with as little as five headings it is difficult to recall the correspondence between colours and content. Why not try something else. Maybe a designation in the upper right hand corner of each slide?

2. That looks like an interesting diagram on slide 4. Why didn't you explain it?

3. You tend to introduce succinct definitions first, motivating examples later. This worked all right for the fairly simple concepts on page 4, but you started to lose your audience once you reached factorisations on page 5. (By the you get to the bottom of page 5 your audience is becoming anxious you may never introduce any examples and we are starting to feel lost). So, why not reverse the order? Work through an example (page 6), then formalise the notion into a definition? Then, spend some time illustrating how the definition matches the intuitive concept.

4. Slides 4 and 5 contain too much material. Best split each into two slides.

Thanks a lot for your presentation. I am enjoying it!  

Some criticisms of polling

Thanks, betulaster, 

Since you address "how likely meeting a certain politically charged event would be", I assume your question is focussed on what I've called "Polling 2", which concerns itself with predicting future events. These tend to be less politically charged than than "Polling 1", but I agree you are right in pointing out the need to relativise respondents answers. People who identify strongly with a cause, especially if they are not used to dealing with probability, might confuse a question about an event likelihood with the strength of their allegiance. Thus "How likely do you think the Dodgers are to win the World Series?" might be met with "I'd bet my life on it", which is not very helpful for computing statistics :-)

The best way to put the matter into quantitative terms may be to ask the interviewee what odds he would give in a bet on the event occuring. It may seem redundant, but I would also ask the odds they'd give on a non-occurence. (People's grasp on probability is shaky, so overdeterminining their perception helps to reduce error). 

You will notice that for Polling 1 type questions I avoided the natural step of asking people to say how much money it would take to get them to change their mind. For one thing, it would be tasteless to appear to be offering money to get someone to change a vote (for instance). Another reason is that people's perceptions of money vary widely, injecting a confounding variable. The rather convoluted question I came up with to assess an interviewee's resistance to chance of intent has the disadvantage of generating a discreet (non-continuous) answer. and I worry it might also confuse some interviewees, but at least it makes a quantification in terms of a comparable quantity. 

Is there a scientific method? Physics, Biology and Beyond

You make a good point, namely that my article would be improved with an example. I don't have one at hand, although I think this behaviour comes up rather frequently in attacks on climate change deniers. I'll see what I can do to find an example.

Perhaps I should write an article about the more general problem of journalists and politicians selectively using specious, (often pseudo-) scientific claims to attack their opponents? This originates mostly from the left. The right has long since accepted the idea that science arguments will always be against them, and whenever they hear "the scientific method.." they know they are about to be knocked in the head, and mentially prepare some ad hominem attack against some straw man figure of a scientist.

I don't doubt the right could summon the intellectual resources to challenge instances of sciencism. Only it would all go over the heads of the average voter. Such is the level of and the motivating forces behind our political discourse.

Sometimes I feel sympathy for Plato's critique of democracy.

Is there a scientific method? Physics, Biology and Beyond

But this is not what is done. Instead, journalists write, pretty much universally, about "the scientific method", which is supposed to be an iterative procedure made up of observation, hypothesising and testing. This raises two questions:

1) Why don't journalists instead write about the life or physical or social science method? I suppose this is one of the widespread misunderstandings about science. There is also a gross public misperception about the validity that can be to attribute to scientific results. It is true that some of these points are subject to disagreement among philosophers of science, but I think all would agree that the public notions, upheld by journalists, is lazy, naive and incorrect.

2) You could also say, Ok, so there are multiple approaches taken in the various scientific disciplines. But what is wrong with iterative application of observation, hypothesising and testing as a truth finding method? Well, I'd argue, this isn't a method at all. Instead it's a description. I.e., it is not an approach that can be set into operation to uncover the truth.

In case that is confusing, I'll make the point in another way. Let's say you are interviewing the manager of a sports team and you ask him what is his strategy for defeating another team. Suppose he were to answer: "My strategy is to outscore my opponent". This is not a strategy at all. It is merely a restatement of the victory condition.


Hey unreal!

I came to your article never having heard of circling before, and your first iteration at describing put me into the mind: "well, it's just another name for a party". But later you explained how the group gives explicit attention to feelings, especially feelings of the moment. This bring to mind and experience I would like to share with you.

I typically operate in a very masculine oriented environment and I've sometimes heard women complain they find the approaches taken, say, to reaching a decision, are unnatural for them. This worried me. I'm a man and I'm aware of the danger that as a member of the dominant group I might have uncritically accepted the standard approach as the only viable approach. But I didn't really understand the complaint until years later, upon finding myself in an all female environment. How different the woman's way of dealing with problems! Whereas the male approach is to present possible solutions, weighing their likely impact in terms of company objectives, the women hardly confronted the problem at all. Instead they spoke at great length about their feelings; then closed discussion (seemingly without resolution) by performing some joint activity reinforcing group solidarity.

At first, this feminine approach struck me as childish. But then, I began considering the drawbacks of the approach I had been used to. The masculine approach eschewed any discussion of personal feelings: possible solutions were supposed to be judged solely against the criteria of company objectives, although what really went on was a competition to disguise personal interests in the cover of company goals. At the end of the discussion some approach would be agreed upon. But, since the selection was determined by power, it was rarely the best either from either the company or personal standpoints. And, inevitably, there would be losers who, by the ethos of the group were forbidden from expressing their feelings. No thought at all was given to group solidarity, and the participants left the meeting bitter or intent on "getting even" next time.

So now, which of these two approaches is really the most childish?

The impression I get from your article of circling is that it is aimed at correcting some of the defects of what I have been calling the masculine approach to decision making. Not everyone needs this equally (my woman's group certainly didn't) but for some people, if they went into it with an open mind, could certainly benefit.

As for how a group can best reach business decisions, I see advantages in combining the two approaches. We need the rationality of what I've been calling the masculine approach, but (in the masculine environment) it should be up to the leader to explicitly adopt behaviours enforcing the notion that personal feelings are a legitimate concern for expression and consideration as part of the chosen solution.

The Virtue of Silence

Hmm. I suppose the NY Times could run a column on the ethics of open discussion of violating medical confidentiality. No?

Certainly this sequence can be continued. With each new meta-iteration we are further removed from the original issue but might hope to benefit (?) from the silence-equivalent effect of increased incomprehensibility.

Intellectual Hipsters and Meta-Contrarianism

1. The average IQ of visitors to this site is 145 squared? Impressive!

2. Are you trying to be subtly meta-contrarian with your idiosyncratic orthography, or are you just really glad to see me?

Why so much variance in human intelligence?
the question I want to ask about is what is it about humans, culture and brains that allows for such high variance within the species, that isn't true about mice and chimps?

Some points to consider:

1. Has it been demonstrated that variations in intelligence is that much greater for humans than for mice or chimps? This may be true, but you didn't indicate any references.

Whereas I could imagine a test for chimp intelligence, and even timed maze experiments on mice, the concept of what we mean by intelligence becomes increasingly attenuated as we deal with ever simpler life forms; so that, at some point, and maybe even quite early, experts will begin disagreeing on what they are trying to measure.

2. Modern day humans have a big advantage not only over other animals, but also over our cognitively equivalent ancestors of 12+ thousand years ago. Thanks to the invention of culture, we pass knowledge to our offspring, meaning that knowledge can be accumulated from generation to generation. Variations in cognitive performance isn't only a consequence in variations in intelligence, but also reflects large differences in the quality of acculturation.

3. I wonder if your decision to compare interspecies variations in intelligence follows from a mistaken analogy. Consider, that intelligence is a human specialty. Other species have their own specialities. For instance, maybe we should be comparing variations in human intelligence with variations in the maximum speed of healthy, adult cheetahs. (I wonder, whether anyone has ever done this?)

4. The idea that we can assign a number to the variation in human intelligence is suspect. True, we can claim that the standard deviation in IQ is 15% of average IQ value. But it doesn't follow that a +1 sigma individual is 15% smarter than an average individual, because the IQ scale itself is arbitrary and intelligence has never been defined apart from performance on the test. To make the point in another way, 1-sigma variations in intelligence was arbitrarily set to 15 IQ points purely for convenience. We might just as well have set the mark at 900 IQ points. But that wouldn't mean that the +1-sigma individual was then ten times as intelligent as average.

Compare the situation with the cheetahs, where a statement like: "the ratio between the standard deviation in maximum running speeds and the average individual's maximum running speed is .15", really means something in terms of performance that can be measured with a metre and stopwatch.

What would be wanted to put IQ and maximum speed on par, would be credible results showing that a certain superiority in IQ is closely connected with a certain improved ability in raising fertile offspring to maturity, which is the definition of evolutionary success.

Schelling fences on slippery slopes

I think your idea about a Schelling point deserves further thought. But, why (and how) select the point arbitrarily? Why now presume that rational 100% Gandhi would perform an optimisation, according to his personal utility function, calculating the good the offered money could do against the harm done to the world by becoming less pacific?

Since you've already posited a third party, in your example, engaged to destroy Gandhi's prized possessions for deviations, why not just have Gandhi charge the man to shoot him as soon as he shows any sign of going on a murderous rampage? That sounds pretty 100%-Gandhi-like to me.

In fact, it is never hard to boost global utility by engaging an robot enforcer. The trick is to do without or, sometimes, to include the enforcer's own utility function (can he be subverted?) into the calculation!

Occam's Razor: In need of sharpening?

I have the impression that Solomonoff Induction provides a precise procedure to a very narrow set of problems with little practical applicability elsewhere.

How would you use Solomonoff Induction to choose between the two alternative theories mentioned in the article: one based on Newton's Force Laws, the other based on the principle of least action. (Both theories have the same range of validity and produce the identical results).

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