Re: The Promise of Forth

Jonah Thomas wrote:
John Doty <jpd@xxxxxxxxxxxxxxxxxxxxxxx> wrote:
Jonah Thomas wrote:
John Doty <jpd@xxxxxxxxxxxxxxxxxxxxxxx> wrote:
Jonah Thomas wrote:
What would we do to test which of these was true?

My problem here is that it appears we have only one history to go
by, and we can't do very good statistics on that.
In astronomy we're quite used to using statistics to examine
historical data. We're not the only ones, either: consider
epidemiology. What's needed, though, is a quantitative statistical
theory.
If people at a church picknick get food poisoning and you want to
figure out what did it, you can look at each different food and ask
who ate it. You might get a graph like this

chicken egg salad mashed potatoes waldorf salad

ate&gotsick 56 34 30 55
ate&well 62 37 38 35

none&sick 8 30 27 0
none&well 10 30 31 32
132 131 126 132

You can do statistics on this, or more plausibly you can do logic on
it.

Incidentally, consider what sort of statistics you'd do about this? Lots
of people eat contaminated food and don't get sick, so when you look at
what people ate you don't get a smoking gun. Lots of correlation between
eating the spoiled food and the unspoiled food. Not very good statistics
at all. And the data isn't perfect, either. But if only one kind of food
is spoiled you can look at the people who didn't eat it and who got sick
anyway. This time it's almost certainly the waldorf salad, because all
32 people who didn't eat it didn't get sick.

The table is so scrambled I couldn't see that. But that's perfectly analyzable statistically. Since otherwise it seems to have been about 50/50, the probability of 0/32 is roughly 1 in 4 billion (heads come up 32 times in a row). The null hypothesis is therefore ruled out at that level. This could be done more carefully, but it hardly matters.

It doesn't take much
statistics. When this sort of problem is muddy enough for statistics to
be useful you probably won't find much of an answer.

On the contrary, in real life it's almost always that muddy, and statistics are necessary.


Sometimes logic works.

No professional epidemiologist would use logic here. Believe me, I'm married to one. Logic is the limit of Bayesian statistics when likelihoods are restricted to 0 or 1. But in real life, that never happens.


But what data do we have about Forth to do quantitative statistics
on?
We don't. That's why we can't address a statistical hypothesis.

Then you have no basis to rule out the null hypothesis. You're going on
gut instinct.

No, I'm going by the usual rule that an untestable hypothesis is not admissible in science. Bayes' theorem tells you that, in fact, it's when you admit an untestable hypothesis you're going on gut instinct, because the likelihood you get back simply reflects your "prior" ("prejudice" in more colloquial English).

--
John Doty, Noqsi Aerospace, Ltd.
http://www.noqsi.com/
--
History teaches that logical consistency is neither sufficient nor necessary to establish practical, real world truth. Those who attempt to use logic for that purpose are abusing it.
.

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