From Derb's Email Bag: Virtuous Pagans, Fired For Apprehending A Thief, And Benford's Law, Etc.
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Just a few:

Brainteaser solution.  There's a worked solution to the brainteaser in my October Diary here

Virtuous pagans.  In my October 23rd podcast I passed comment on the defacing and pulling-down of statues of historical figures, persons judged by the zealots of Wokeness to have been insufficiently antiracist. I suggested a parallel with the "virtuous pagans" that medieval Christian theologians had issues with: people like Aristotle and Cicero, who lived virtuous lives before the coming of Christ.

A Mormon friend emailed in about that.

Regarding your comments on "virtuous pagans,"  the Church of Jesus Christ of Latter Day Saints is the only Christian church, or any religion I'm aware of, that addresses this issue in doctrine and practice.

"The ministry of Christ was not confined to the few who lived on the earth in the meridian of time, and it is not confined only to those living now. The apostle Peter made it clear that those who do not have the opportunity to hear the gospel on this earth will have such an opportunity in the spirit world (see 1 Pet. 3:18–20; 1 Pet. 4:6). And the apostle Paul in writing to the Corinthians asked: 'Else what shall they do which are baptized for the dead, if the dead rise not at all? why are they then baptized for the dead?'” (1 Cor. 15:29)." — Elder Franklin D. Richards.

So Mormons believe that those who lived without hearing the gospel in this life will be given the chance in the next world. Living Latter Day Saints are given the duty of performing ordinances (like baptism) by proxy for the dead, in Temples. Searching out the dead via genealogy and organizing the records are key parts of this effort. That's why Mormons are often the best genealogists around.

The LDS Temple baptismal font, where baptisms for the dead are performed, rests on twelve oxen, signifying the twelve tribes of Israel. 

There are numerous references here: just do a site search for "Redemption of the Dead."

The moral case for Trump.  In that same podcast I made the moral case for Trump (got rich by building stuff, with a starting boost from his Dad) over Biden (got rich from politics).

A friend emailed in with this:

You may not be aware of it but for decades Freddie Trump [i.e. the president's father] was a hero among NY Jews for building first-rate affordable apartments. My aunt and uncle lived in one in Brooklyn and spoke highly of Freddie. That business model ended with civil rights litigation and Donald has admitted this. No wonder today's building boom focuses on luxury. No landlord can possibly make money from underclass black tenants without tax subsidies.

Fired for apprehending a thief.  In my September 25th podcast I told the story of the supermarket employee who was fired for apprehending a thief. I remarked on how odd this was, and wondered if the thief was black. The news story of course didn't say, and had no pictures, only gave the thief's name as Adrian Moore.

A listener:

I think this is (actually was) your manBurlington Free Press has a memorial tribute here, with picture.

Moore actually was black, though not very.

Benford's Law.  On November 6th I mentioned the geek website, who were applying Benford's Law to vote counts by precinct in select cities and counties. Did the numbers follow Benford's Law? Where they didn't, were there benign explanations for their not doing so?

A listener emailed in with far, far more than you wanted to know about this. Short answer: Yes, there are benign explanations. Long answer (edited down some, believe it or not):

When you partition the data in a way that groups related values together (like precincts within a single county, which usually have similar populations), the Law is likely to be broken due to those values' similarity. You need a large evenly distributed range, over something like three orders of magnitude or more, to reliably expect Benford's law to apply. In contrast, the data coming from Miami-Dade county, for example, is very clustered around 1.5 orders of magnitude.

If the distribution isn't spanning orders of magnitude, Benford's test is just going to favor whatever the peak of the distribution is.

You can adjust for this by changing the base you use from base 10 to a smaller value.  For example, if we change to base 3, I believe the digit distribution will spread out by a little over 2x (3^2 is a little under 10).  That doesn't give us much room to apply Benford's law to Biden's
votes and see a pattern though, with only 2 options for starting digits. We get 523 "1" values and 295 "2" values, which is a pretty reasonable 50 percent drop.  

If we compromise and go to base 4, we get 417 for "1", 203 for "2", and 198 for "3", which is not the smoothest distribution, but the values are very clustered on 5 orders of magnitude, with over 50 percent of them being there.

So that basically ensures that Benford's law will not consistently work on a dataset this narrow.  Now as for why it's "consistently inconsistent" within each county—that is, why Biden's graph looks one way while Trump's looks a different way ... well, they're all counties that Biden beat Trump in.

If Biden gets 2x the vote that Trump gets, the peak of his distribution will likely be in the same order of magnitude but with a different peak, and therefore (as explained above) a different favored starting number in Benford's test.  It's basically impossible to do this test, this way, with candidates who are not tied, and see similar results.  

In Miami-Dade county, where Trump got 46 percent and Biden got 53 percent, the 7 percent difference is not enough to shift the peak vote count away from the 1000's to the 2000's. 

But in a county like Milwaukee, where Biden got 69 percent and Trump got 29 percent, that 40 percent difference is certainly enough to change the peak and the most popular leading digits.  

Without doing a full analysis, I can see that the website you shared [i.e.,] shows that Trump has "1", "2", and "3" being popular, while Biden has "1", "4", and "5" being popular, which would make sense if the "1" counts increased to be split between "1" and "2" counts, the "2" counts increased to "3" and "4" counts, the "3" counts increased to be "4" and "5" counts, and some tail-end "8" and "9" counts increased to wrap around and become additional "1" counts again.

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