I don’t know how to answer your question as you have posed it after the …, but if you let pi(x) = # of primes less than or equal to x, then the Prime Number Theorem says pi(x) ~ x/log(x) –i.e., the limit as x goes to infinity of pi(x)/(x/log(x)) is 1.

]]>what’s the density of primes do for large x… let’s say the kernel density using a unit normal kernel of the indicator fuction of the primes for large x.

]]>Phil said,

“there’s an infinite number of primes, but there can only be a small number of large primes.”

Uhh … If we’re talking about prime numbers, the cardinality of the set of primes greater than the integer N is independent of N.

Quote from above: “The cannibal interpretation implies they all eat each other and the effect dies out. I don’t think that is really correct.”

From a bigger picture perspective this may actually be correct in some way.

We’ve had decades of (ever increasingly silly?) “priming” research that (with a lot of other things) culminated to a point where a lot of this stuff is now viewed very, very critically (and perhaps even suspiciously).

“Priming” was hip and happening for about 10-20 (?) years, where everyone jumped on board the hype-train. But now, all the “seminal findings” are sort of laughed at, and “the big names” of this field are looked at with pity (if nothing else).

In this sense, perhaps “priming” research sort of ate itself and died.

]]>Right. That is the other explanation for what we observe, that all the effects are negatively correlated in some weird way that they almost exactly cancel out.

]]>To readers who don’t know: giving people some seemingly irrelevant experience or information before they do something is called ‘priming’ them.

]]>Terry:

Interesting point. To clarify: the piranha argument is a reductio ad absurdum: *if* these large and persistent effects all existed, *then* they’d interfere with each other in a way that such large and persistent effects would not be observed, *hence* they don’t exist.

Your bowling ball analogy is better in that it works without the absurdum part being required.

]]>But, does the cannibal interpretation really make sense? Wouldn’t a Brownian motion interpretation make more sense? Perhaps call it “Brownian Bowling Balls”. If people are bombarded by strong psych influences, they should bounce all over the place continually. This is what standard Brownian motion theory predicts, that an object bombarded by bowling balls will follow a wildly fluctuating random walk. The fact that we do not see this huge volatility means the effects of each individual influence must be small. We can then infer the effect of each individual influence from the volatility of the overall random walk. (You can run the math in either direction. The math is about a hundred years old.)

The cannibal interpretation implies they all eat each other and the effect dies out. I don’t think that is really correct. The individual effects don’t necessarily cancel, they cancel somewhat, but there is always some motion and there is some net drift in one direction or the other. That is standard Brownian motion theory too.

]]>Anon said,

“I thought the goal of psychological science is to explain, predict, understand behaviour and/or phenomena, etc. I reason a tremendousely important part of this might be to compare theories, compare variables, compare constructs, etc. to see which one best explains, predicts, and helps in understanding, things.”

I would hope that the goal is “… to see which one best explains, predicts, and helps in understanding things, under what circumstances,” but my impression is (sadly) that there is little of what Anon suggests, and even less of my amended version.

]]>Shecky:

No, there really are some piranha theorems, formalizations of the idea described in my quoted paragraphs. A couple of mathematicians at Columbia are working on it.

]]>Perhaps (the gist, and/or implications, of) this reasoning allows me to point to yet another one of my annoyances concerning current day psychological science.

I thought the goal of psychological science is to explain, predict, understand behaviour and/or phenomena, etc. I reason a tremendousely important part of this might be to compare theories, compare variables, compare constructs, etc. to see which one best explains, predicts, and helps in understanding, things.

If this makes (any) sense, i reason this 1) might deserve some more acknowledgement, and 2) could be relevant (in some way or form) for the “piranha project” mentioned above.

]]>Our general rule is, make the titles as boring as possible, then anyone who clicks through to read the post will be pleasantly surprised by all the entertainment value we offer.

The one quick trick that improves your blog comment section 100x!

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