Re: Me and David C. Ullrich


Elmo wrote:
> sugnaboris@xxxxxxxxx wrote:
> > Elmo wrote:
> > > sugnaboris@xxxxxxxxx wrote:
> > > > Elmo wrote:
> > > > > On this forum I have argued the question, "Two coins were flipped and
> > > > > at least one is a head. What are the chances that there are two heads?"
> >
> > <snip>
> >
> > > > If you accept that this meets your criteria, then it will be very easy
> > > > to settle the discussion with a real-coin or computerized simulation;
> > > > if you don't accept it, could you please propose your own experiment in
> > >
> > > > equivalent terms?
> > > If you will read a little further, we are examining the difference
> > > between, "Two coins were flipped and at least one is a head", and "Two
> > > coins were flipped, given that there is at least one head." I will
> > > accept your program for "given at least one head." It's easy to see
> > > that it will give 1/3.
> >
> > <snip>
> >
> > Yes, but the point of my proposing an experiment, then asking you to
> > propose your own experiment in equivalent terms, was to give you an
> > opportunity to define *exactly* what you mean in unambiguous terms that
> > can be checked experimentally. If you can't describe an experiment in
> > this way, then it seems to me that you have no proper definition of
> > what you mean.
> >
> > Can you describe the experiment that would give a probability of 1/2 in
> > the same sort of detail that I gave for the 1/3 case? If you can, I am
> > happy to run a simulation for you. However, as you are no doubt aware,
> > setting up an experiment of this sort requires all steps to be
> > described completely unambiguously, and in an imperaitve/procedural
> > fashion.
> >
> > Look forward to seeing your experiment proposal.
>
> We need two computer programs.
> Call them P1 and P2.
>
> P1 randomizes the coins, and color codes the outcomes.
> P1 passes the color code to P2.
> P1 shows us two colors.
> We see two colors, for example, red and green.
> We can say, "at least one is red", or "at least one is green".
> P2 has the color code, takes our "at least one is" choice, and
> announces the outcome, in terms of, "at least one is a head", or "at
> least one is a tail".
>
> Eldon

It sounds like you aren't able to specify an experiment that could be
carried out that would give the probability of 1/2. You can forget all
about the details of the implementation, because that's completely
trivial (OK, RNG isn't trivial - but all we're trying to do is
discriminate between 1/2 & 1/3). It makes no odds as to whether two
programs are used, really it doesn't. Generating the trials and
checking them can be done independently of each other, within a single
program, just by separating the concerns.

So, again: are you able to write down a set of logical steps such as
"flip this number of pairs, discard these pairs, count these
occurences, divide this number by that number"? If you can do that,
it's very easy to test your hypothesis; but if you can't identify how
to gather the data for such a simple test, then it's very likely that
you don't have a concept that really represents a probability. All we
need is for you to identify the "successful" outcomes, then we can run
a large number of trials, and divide the successful ones by the total
(as I described in my example experiment, a few posts ago).

Would you like to define a proper experiment, or do you think that
there is no real experiment that would give the result that you claim
(or is there a 3rd option)?

.