Subject: Re: Card trick
Date: Wed, 01 Nov 2000 08:35:19 EST
From: BRamelson@aol.com
To: <shai@stonehill.edu>

I guess you can use a technique like this to compress an image but JPEG does
a much better job. It also takes into account that small distortions of the
image will not alter its appearance.

What is interesting here is that all the standard compression algorithms
assume that the data needs to be reconstructed in order. Is there ever a
case when order doesn't matter? I still haven't thought of one.

- Brian.

In a message dated Tue, 31 Oct 2000 9:39:32 AM Eastern Standard Time, Shai
Simonson <shai@stonehill.edu> writes:

<<

BRamelson@aol.com wrote:

> Here are a couple of variations that I thought of:
> 1. Instead of revealing n-1 cards, reveal p cards and the magician must
> determine the hidden n-p cards.
>
> 2. Allow for duplicates. This problem is like having N decks of cards with
M
> cards each and one card is chosen from each of the N decks. N-1 cards are
> revealed and the magician must figure out the remaining concealed card.
This
> one is particularly interesting for your class since it gets into
> combinations with replacement.

Sometimes you think more like a mathematician than an engineer.

These are both good natural generalizations opening up lots of new
questions.

>
>
> One of the reasons this problem is so interesting to me is that it is a form
> of compression. Essentially, we are taking advantage of the fact that the
> encoding can be ordered and the information being trasnferred does not need
> to be ordered. I've been trying to think if there is an application of this
> type of compression in the real world but I haven't thought of one yet.
>

You mean the idea of "compressing" unordered chunks of M items into
ordered
chunks of N items, where N<M?

I thought about this on the train to work today. There was a mural on
the
wall of South Station made out of tiny little blurs, which close up look like
nothing and farther away look like a clear picture. It seemed to me that if
you
wanted to transfer this picture over a wire, you could break it up into small
enough chunks so that the order of the blurs wouldnt matter within that chunk
--
that is you could reconstruct them in any order and not ruin the big picture
in a
noticable way. Then we could use this scheme to send chunks of 5 by an
ordered
set of 4... a 20% compression and we pay virtually nothing.... some "blur"
perhaps that no one will notice...

What do you think of this?

>
> - Brian.

--
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Shai Simonson, Professor
ArsDigita University
141 Portland St. (Use 80 Prospect St. for mailing)
Cambridge, MA 02139

Voice Mail: (617) 386-4236
Fax: (617) 494-8174
Email: shai@stonehill.edu
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