Hi all-
Pls correct my last. I mistakenly put an ``==2'' at the end of
the 3rd para of my posting. It's in the wrong place and should be
deleted.
Regards,
Jack
--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley
---------- Forwarded message ----------
Hi all-
I have downloaded John's essay on Entropy. His little execises
implementing information theoretic concepts are fun and amusing; some sowhat
similar exercises may be found in Liu's book <Elements of Discrete Mathematics>
(McGraw-Hill, 2d Ed. 1077) from which I tried to teach a course to
uncomprehending juniors in about 1986, at a place callled Elmhurst C9llece, in
Illinois.
I have a problem with Dr. Denker's discussion of entropy -
(unfortunately, my download of his posting does not contain page numbers). In
his exercise on the ``cup game'' he writes ``where ther are N cups and B
blocks (to be hidden under the cups), there are N^{B} (LaTeX notation) possible
states. ( OK, no problem so far).
Then he writes, under the following para. 2, ``if we are smart, the
number of'' guesses ``is at worst'' (i. e., the minimum number of guesses) is
the smallest exponent E, of 2, such that 2^{E}>=N^{B}=2.
This statement cannot be correct. I there is 1 object and 2 boxes,
then the prediction is 2*{E}>=2^1=2 -> I need two questions to decide which
cup.. But I can make the decision with one question, ~~Is it Box A?''.
Again, if there are 3 cups and one object, then the prediction is that
2^{E}>=3^{1}=3. But if I label the cups ABC, then two questions suffice to
locate the cup holding the object: ``Is the object in one of the cups A or
B?''. In the worst case, the answer is Y, in which case, I ask, ``Is the
object in cup A?" Either answer locates the object.
I haven't thought this through. Maybe the counting ust need a trivial
correction.
Regards,
Jack
--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley