[HN Gopher] The Shape of Information
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The Shape of Information
Author : effect
Score : 52 points
Date : 2024-06-18 23:05 UTC (1 days ago)
(HTM) web link (kucharski.substack.com)
(TXT) w3m dump (kucharski.substack.com)
| yu3zhou4 wrote:
| We can also open first 50 bottles, mix drops of each, use test,
| if positive then we know that one of them is poisoned, if not
| then we know that one of the other 50 is poisoned. So we take the
| poisoned 50, split on two brackets and repeat. With 7 tests, we
| can narrow down to a single poisoned bottle (50, 25, 12/13, 6/7,
| 3/4, 2, 1)
| The28thDuck wrote:
| Binary search strikes again!
| yu3zhou4 wrote:
| Nothing clever, I know :p
| selimthegrim wrote:
| Maybe so, but pooled testing as they refer to in the
| article involves using Lambert W function to solve for
| optimal size of individuals tested.
| photochemsyn wrote:
| The limit of detection of the test comes into play; detecting
| poison at a 1:50 dilution might be impossible with that test.
| TeMPOraL wrote:
| But then, if that test _can_ detect poison at 1:50 dilution,
| it means it probably has enough reagent to detect poison at
| 1:25 _twice_ , if you're clever about it. Done well, you may
| end up with a single bottle identified and a bunch of unused
| tests to sell.
| ubittibu wrote:
| I hate when riddles are told badly and ruined. I remember the
| original one which was not solvable this way and really puzzled
| me. When resolving the one in the article I asked myself why I
| had found this to be much more complicated, and it was beacuse
| the number of bottles was 128 in the original.
| Chinjut wrote:
| What do you mean? It works the exact same way for 128
| bottles. 64, 32, 16, 8, 4, 2, 1.
| Chinjut wrote:
| This is essentially the same approach as the solution described
| in the article. You are observing the bits of the poisoned
| bottle number in binary, bit by bit. The only difference is
| that you avoid retesting any bottles once they have been ruled
| out by previous tests, whereas the fixed design in the article
| does not bother with this.
| ReleaseCandidat wrote:
| The answer is easy: by his way of testing exactly one bottle
| won't be opened and of course that's the one that contains the
| poison. Drinking 99 bottles of wine before they go stale isn't
| too healthy either, I'd guess.
| mirekrusin wrote:
| Exactly better to keep 7 with scotch taped test and sell the
| rest on amazon, call it a day.
| photochemsyn wrote:
| When faced with incomplete data, it's really always better to go
| back and get a more complete and reliable dataset than to apply a
| host of statistical tools to that poor data in the hopes of
| extracting some trend or meaning from it.
|
| > "Fortunately, you have a test that can detect poison very
| accurately, even among a large volume of liquid. Unfortunately,
| you have only 7 of these tests available. What should you do?"
|
| You should estimate the cost of getting another 93 tests,
| consider if a cheaper method is plausible and could be developed
| at lower cost, then compare that to the value of the wine
| bottles.
|
| With infectious disease, this is problematic as putting a cost on
| every individual human life is tricky, even if that's the life
| insurance business model. As a practical example, the cost of
| running the CDC's malaria detection program (captures some
| 2,000-3,000 cases a year from incoming travellers) in the USA is
| considered worth the benefit of not allowing malaria to become
| endemic again across the Southeastern US.
| Nevermark wrote:
| The puzzle fails spectacularly.
|
| Without additional action all that wine will go bad.
|
| Important detail is one must recork each bottle immediately after
| sampling & refrigerate. Now the wine will be preserved, and the
| very slight pre-drinking oxygen bump is likely to improve it over
| first corking.
|
| A little overlooked & underrated trick.
|
| (Remember to decant reds and allow them to reach room temp before
| drinking.)
|
| Also left out is value/opportunity maximization, which is a
| crucial implicit factor in any gamed, especially adversarial,
| situation.
|
| Math & algorithm problems without complete context value
| optimization are just ivory tower toys!
|
| The real world, Machiavelli, your ancestors, and your
| shareholders demand better!
|
| The poisoned bottle, once identified, is worth a great deal.
| Minimum value realization is obtained by rebottling, and re-
| gifting it to its original source. Anonymously. Of course!
|
| Or you can save it for a special occasion! Sometimes the best
| move is no move. Accumulate optionality.
| esafak wrote:
| To paraphrase Crocodile Dundee; that's not the shape of
| information, this is:
| https://en.wikipedia.org/wiki/Information_geometry
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