[conspire] (forw) Re: Correction

[Rick Moen]

Quoting Texx (texxgadget at gmail.com):

['Birthday Paradox':]

> For starters, most people (Including me) have NO IDEA how to START on
> this problem.

No, that's demonstrably _not_ true.  I've asked it many times, over long
decades,  to a variety of groups, and intuitive guesses tend to run
to around 100-180 persons in the notional room before there's greater
than even likelihood of a shared birthday.

The correct number is 23.

The interesting bit is to speculate about why most people's intuition is 
so wildly wrong, on that puzzle (as it also was for the pond puzzle).
Here's the best guess, that I've also heard from others who've pondered 
why:

Someone idly pondering the puzzle will tend to imagine himself/herself
entering the room.  Then, a second person enters, and the likelihood of
a shared birthday is really small, 1/365.  The ponderer then pictures 
a second person entering, and guessimates the likelihood of
_imagined-self_ in the room sharing birthdays with either of the other
two, still super-small.  Then, the ponderer extrapolates to the chance
of imagined-self sharing birthdays with any of _three_ random persons,
and so on (still super-small).  And thus you end up with shirtsleeve
guesstimates of 100-180 persons.

The perceptual flaw in such imaginings, as experienced by most people,
is that they are self-focussed.  The ponderer guesstimates likelihood 
of _himself/herself_ sharing a birthday with one of n other people, but
forgets that the question asked was different -- likelihood of _any_ of
the room occupants sharing a birthday with _any_ other occupant.

I should add that this so-called 'Birthday Paradox' is no paradox:
There's no contradiction.  It's just a math problem with a
surprising-to-most but perfectly logical answer.

The easy, if tedious, math-wonk way to calculate the answer is to first
invert the question:  How many people can be in the room before the
chance of them _not_ sharing a birthday drops below 0.5?  
For a single person in the room, the odds are 365/365 = 1.  For two,
it's 365/365 * 364/365 = 0.9972.  For three, 365/365 * 364/365 * 363/365 
= 0.9917.  Keep going (if you have nothing better to do with your time),
and you find that at 23 occupants, the odds drop below 0.5.



> I believe I have read about this, and while I dont remember the
> solution, I do remember that its counter intuitive.

*ding*

And thus my point -- but, again, the interesting bit is _why_.


> (Ricks hint about backwards backs me up on the non intuition)

No, it very much doesn't.  My hint merely suggests a much easier way of
grinding out the answer than if it doesn't occur to you to invert the
question.



> Of course, the un asked question is why are otherwise intelligent
> people wasting time with pond scum?  (snicker)

Oh, maybe because developing a gut-understanding of exponential growth 
might motivate a person to take a pandemic caused by a 'novel' virus
very seriously?


> If one has the symptoms, can we just accept that as the positive
> rather than waiting for the lab?

For purposes of scientific understanding and public health, no, we
cannot.

> If they have the symptoms and they are severe, they need to be treated
> anyway and will have the same load on healthcare.

But not the same _risk to_ healthcare and to everyone else.


> It would be great to have good numbers like S Korea, but we dont and I
> doubt we ever will.  That horse has gone.

Not correct.  Many things that South Korea did correctly starting in
January are no longer possible (note that South Korea and the USA had
their first confirmed cases the same day, Jan. 20th), but
mass-deployment of good, effective, quick testing kits is still possible
and should be a top priority.


> The negatives are nice, but if you only test once, how do you detect
> whether that person gets it later without repeated testing of the negatives?

Obviously, it's highly desirable to have ample testing kits so that 
anyone can, if there's a medical reason, be tested at any time including
(if prudent) repeatedly.


> People being people, the lockdown will eventually end and as soon as it
> ends, bad behaviour will return, feeding a 2nd bounce and
> likely a 3rd.

It's not inevitable that people will be people.  Sometimes, particularly 
after Darwin Club behaviour, they become dead people.

> I was expecting Trump to lose if this thing keeps going into fall now Im
> not sure.

Magic 8-ball says:

o  Reply hazy, try again.
o  Ask again later.
o  Better not tell you now
o  Cannot predict now.
o  Concentrate and ask again.


> Its looking like he can use legal action to prevent stations from
> airing video of things he REALLY SAID.

No, he cannot.  Haven't you learned, yet?  The Toddler has 
bullshit-bluster people on speed-dial.