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Ed Lake
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Supermassive black hole NGC1277 compared to the size of our solar system

Until now, the galaxy with the largest known fraction of its mass in its central black hole (11 per cent) was the small galaxy NGC 4486B1, 9. Here we report observations of the stellar kinematics of NGC 1277, which is a compact, lenticular galaxy with a mass of 1.2 × 1011 solar masses. From the data, we determine that the mass of the central black hole is 1.7 × 1010 solar masses, or 59 per cent of its bulge mass.

It needs to be noted that there are competing viewpoints on the size of this black hole.

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File under Very Interesting If True.
On Sexual Violence Against Women: Some Numbers Without Suggestions

(1) Either feminism has worked, or leaded gasoline was worse than we thought. The number of rapes is declining rapidly. In 1980, the NCVS -reported rate of rape was 2.4 per 1,000. By 2011, the number had declined to 0.4 per 1,000. This is both (a) in line with the decline in other crime statistics, and (b) despite the broadening of the definition in 1995. 

(2) International statistics demonstrate the possibility of substantial further reduction. The United States still has about double the rate of sexual assault as the European average. One halving should be very possible, and we are in fact on a trajectory which will take us there relatively soon. Two halvings appear to be substantially more difficult. 

Note that, presuming the same distribution of rapes per rapist, a single halving still results in 9% of women having been raped. This will still be a substantial public policy problem at that point.

(3) There is some dispute over whether we have caught a majority of sex offenders. Estimates of offenses per offender differ significantly. If the number based on surveys of sex offenders is correct -- six per offender -- then we have caught about 250,000 sex offenders, and have somewhere between 500,000 and 700,000 left to go. If we assume a single rape per rapist, and based on the reoffense rate we might, then we can have as high as 2,500,000 left to go. 

Note that neither of these numbers requires any conclusions about what the number of rapes is. (I assume a high number.)

(4) The next halving will likely be more difficult. We can expect the  generational effects of sexual assault to continue for some time. There is a reasonably high correlation between propensity to offend and childhood victimization. 30% of sex offenders were victimized as children. If this is an actual correlation, then we will probably see a decline as the people victimized in the 1980s and 1990s enter their 50s. 

(5) The next halving after that will be very, very difficult. It will be very difficult to deter or rehabilitate sex offenders with serious comorbidities. In a fairly large study, 49% of sex offenders had a medical history of moderate to severe neurological insult. 22% had medically recognized neurological sequelae. Add to that the 24% of sex offenders with a history of psychiatric hospitalization, and we find a substantial population of sex offenders with a very low probability of deterrence or rehabilitation.

Watching The Big Bang Theory on the plane back to London yesterday (long flight), I was intrigued to see Sheldon invoke Munchhausen's Trilemma in a slightly peculiar context. Penny had told him a secret about her relationship with Leonard. Unable to trust himself to keep quiet, Sheldon abruptly declared his intention to move out of Leonard's apartment. When Leonard asks why he is moving, he appeals to the trilemma: his motives, qua motives, are not explicable. Studio laughter.

Here's what I found interesting. Munchhausen's Trilemma is usually framed as a problem about knowledge. How do we know each thing that we know? Well, presumably because it is inferred from some other piece of knowledge; but then what justifies that further claim to knowledge? Either we find ourselves in an infinite regress, or the chain of justifications loops back on itself and becomes circular, or it ends on some axiomatic propositions that are not susceptible to questioning. None of these alternatives seem very inviting.

Various things have been written about how to resolve the trilemma as an epistemological question, for example by relaxing the standards of certainty required for knowledge. In addition, it is fairly common for philosophers to bite one or another of the bullets and just say that justification is circular or dogmatic, or whatever it is that they choose.

What interested me, however, was the idea that the trilemma might apply to motives as well as to beliefs; ie, that each thing one wants depends logically on ulterior motives, leading us to the three horns described above. Does it? And has anyone written interestingly about this question?

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