The Universe of Disco

Hangman's Wages

A few years back I asked on history stackexchange:

Wikipedia's article on the Halifax Gibbet says, with several citations:

…ancient custom and law gave the Lord of the Manor the authority to execute summarily by decapitation any thief caught with stolen goods to the value of 13½d or more…

My question being: why 13½ pence?

This immediately attracted an answer that was no good at all. The author began by giving up:

This question is historically unanswerable.

I've met this guy and probably you have too: he knows everything worth knowing, and therefore what he doesn't know must be completely beyond the reach of mortal ken. But that doesn't mean he will shrug and leave it at that, oh no. Having said nobody could possibly know, he will nevertheless ramble for six or seven decreasingly relevant paragraphs, as he did here.

45 months later, however, a concise and pertinent answer was given by Aaron Brick:

13½d is a historical value called a loonslate. According to William Hone, it has a Scottish origin, being two-thirds of the Scottish pound, as the mark was two-thirds of the English pound. The same value was proposed as coinage for South Carolina in 1700.

This answer makes me happy in several ways, most of them positive. I'm glad to have a lead for where the 13½ pence comes from. I'm glad to learn the odd word “loonslate”. And I'm glad to be introduced to the bizarre world of pre-union Scottish currency, which, in addition to the loonslate, includes the bawbee, the unicorn, the hardhead, the bodle, and the plack.

My pleasure has a bit of evil spice in it too. That fatuous claim that the question was “historically unanswerable” had been bothering me for years, and M. Brick's slam-dunk put it right where it deserved.

I'm still not completely satisfied. The Scottish mark was worth ⅔ of a pound Scots, and the pound Scots, like the English one, was divided not into 12 pence but into 20 shillings of 12 pence each, so that a Scottish mark was worth 160d, not 13½d. Brick cites William Hone, who claims that the pound Scots was divided into twelve pence, rather than twenty shillings, so that a mark was worth 13⅔ pence, but I can't find any other source that agrees with him. Confusing the issue is that starting under the reign of James VI and I in 1606, the Scottish pound was converted to the English at a rate of twelve-to-one, so that a Scottish mark would indeed have been convertible to 13⅔ English pence, except that the English didn't denominate pence in thirds, so perhaps it was legally rounded down to 13½ pence. But this would all have been long after the establishment of the 13½d in the Halifax gibbet law and so unrelated to it.

Or would it? Maybe the 13½d entered popular consciousness in the 17th century, acquired the evocative slang name “hangman’s wages”, and then an urban legend arose about it being the cutoff amount for the Halifax gibbet, long after the gibbet itself was dismantled arond 1650. I haven't found any really convincing connection between the 13½d and the gibbet that dates earlier than 1712. The appearance of the 13½d in the gibbet law could be entirely the invention of Samuel Midgley.

I may dig into this some more. The 1771 Encyclopædia Britannica has a 16-page article on “Money” that I can look at. I may not find out what I want to know, but I will probably find out something.

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Getting Applicatives from Monads and “>>=” from “join”

I complained recently about GHC not being able to infer an Applicative instance from a type that already has a Monad instance, and there is a related complaint that the Monad instance must define >>=. In some type classes, you get a choice about what to define, and then the rest of the functions are built from the ones you provided. To take a particular simple example, with Eq you have the choice of defining == or /=, and if you omit one Haskell will construct the other for you. It could do this with >>= and join, but it doesn't, for technical reasons I don't understand [1] [2] [3].

But both of these problems can be worked around. If I have a Monad instance, it seems to work just fine if I say:

    instance Applicative Tree where
      pure = return
      fs <*> xs = do
          f <- fs
          x <- xs
          return (f x)

Where this code is completely canned, the same for every Monad.

And if I know join but not >>=, it seems to work just fine if I say:

    instance Monad Tree where
      return = ...
      x >>= f  = join (fmap f x) where
        join tt = ...

I suppose these might faul foul of whatever problem is being described in the documents I linked above. But I'll either find out, or I won't, and either way is a good outcome.

[ Addendum: Vaibhav Sagar points out that my definition of <*> above is identical to that of Control.Monad.ap, so that instead of defining <*> from scratch, I could have imported ap and then written <*> = ap. ]

[ Addendum 20221021: There are actually two definitions of <*> that will work. [1] [2] ]

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