Subject: RE: [hackers-il] Interesting time_t :)

From: Chen Shapira <[email-masked]>
Date: Thu, 19 Apr 2001 15:43:02 +0200

> P.S. Now that I so absentmindedly missed time 987654321, I'm 
> eagerly waiting
> to September, to see time 999999999 :)

This reminds me when I was about 5 y/o, and just got my first digital watch.

At first I spent some time trying to see how minutes and hours look when
they change.
Then I was trying to see "interesting" times (4:44:44 etc.)

Then (being me) I tried to decide what is an "interesting time", I thought
that a time is interesting if a digit appears twice in a row, more than 4
times at all, and consequtive numbers are also interesting (12:34:56).

Then me and daddy sat down and calculated how many interesting times there
are in a day.

Later, I got my first credit-card my number was very easy to remember
(8005), and then I lost it and got a diffrent card and that number was also
cool (6769) and then I moved a bank...

Anyway, I quickly came to the conclusion, that being a pattern-seeking
creature we are, almost any 4 digit number we try to remember will look
"interesting" to us.

Thanks,
Chen.

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From: "Nadav Har'El" <[email-masked]>
Date: Thu, 19 Apr 2001 15:58:18 +0300

> creature we are, almost any 4 digit number we try to remember will look

These are interesting observations. Richard Dawkins expands on it in his
interesting book "Unweaving the Rainbow: Science, Delusion, and the Appetite
for Wonder" [1]. Richard Dawkins, a well-known zoologist and author of "The
Selfish Gene", now heads some "Understanding of Science" deparment (or
something like that) in Oxford, and this book is about how people fail to
see the beauty of science, and how they prefer "wonders", "coincidences",
superstition, as stuff like that, and why. He has a whole discussion on
"interesting" events and coincidences, and how tricks like Ury Geller's
watch-fixing can be attributed solely to human's attention to "interesting"
coincidences, while forgetting non-interesting events (like the time being
984471241).

[1] http://www.amazon.com/exec/obidos/ASIN/0618056734/thealmostcomplet/

-- 
Nadav Har'El                        |     Thursday, Apr 19 2001, 26 Nisan 5761
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |The 3 stages of sex: Tri-weekly, try
http://nadav.harel.org.il           |weekly, try weakly.

---

From: Gaal Yahas <[email-masked]>
Date: Thu, 19 Apr 2001 18:48:45 +0300

On Thu, Apr 19, 2001 at 03:58:18PM +0300, Nadav Har'El wrote:
> These are interesting observations.

The following is certainly not mine, but here's proof that all numbers
are interesting, with interesting defined as having some nontrivial
property, and triviality not defined. Suppose there are uninteresting
numbers. Sort them. Remove the first uninteresting number from the set,
because it has the profound quality of being the *first* noninteresting
number. Repeat the last step until there are no uninteresting numbers
left.

(Could this be due to Smullyan?)

-- 
Gaal Yahas <[email-masked]>
http://www.forum2.org/gaal/

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From: "Nadav Har'El" <[email-masked]>
Date: Fri, 20 Apr 2001 11:38:27 +0300

> (Could this be due to Smullyan?)

But this proof hinges on the fact that being "the first noninteresting number"
is in fact interesting. If you consider define interesting numbers by
their having an interesting combinations of digits, for example, then this
assumption is not necessarily true - the first noninteresting number might
indeed have a really non-interesting combination of digits.

$ textmode silly
svgalib: Cannot get I/O permissions.
$

If you stretch the definition of "interesting" you can have many proofs
that all natural numbers are interesting. For example, 1 is interesting
(of course) because it is the first number. Now, 2 is interesting because
it is the first number after the (already interesting) 1. And so on by
induction: if N is interesting, then so is N+1 because it is the very first
number after the interesting N.

I wonder what can be said about interesting real numbers. Real numbers are
not countable (i.e., cannot be ordered in a sequence with natural-number
indexes) so you don't always have the notion of "the first non-interesting
number", so your proof can't say that they are all interesting.
But my "proof" above can also be extended to prove that all real numbers
are interesting: we already proved that all natural numbers are interesting
(the proof for negative numbers and zero are similar to what I said). Now
all multiples of 1/2 are interesting, because these come exactly half way
between the interesting natural numbers! Now, similarly, all multiples of
1/4 are interesting, and so on for any 1/2^N. Now, if you take any random
real number (whether rational or irrational) it is the limit of a sequence
of interesting numbers we already seen, so it must be interesting too!

-- 
Nadav Har'El                        |       Friday, Apr 20 2001, 27 Nisan 5761
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |A conscience does not prevent sin. It
http://nadav.harel.org.il           |only prevents you from enjoying it.

---

From: Omer Zak <[email-masked]>
Date: Fri, 20 Apr 2001 12:00:31 +0300 (EET DST)

> of interesting numbers we already seen, so it must be interesting too!

Non sequiteur!
Let's consider a sequence of real numbers having the property P.
Then it is not always true that the limit of this sequence has this
property, too.

Counterexample:
Let the property P be x>0, and let all the members of this sequence have
this property.  However, if the sequence is monotonically decreasing, then
its limit is 0, and 0 does not have the above property.
                                             --- Omer
There is no IGLU cabal.  The limit of the number of its members as
function of t was found to be zero, for large values of t.
WARNING TO SPAMMERS:  at http://www.zak.co.il/spamwarning.html

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From: "Nadav Har'El" <[email-masked]>
Date: Fri, 20 Apr 2001 12:11:38 +0300

> Then it is not always true that the limit of this sequence has this

Of course this is not true for a general property! But for our (very broad)
"interesting-ness" property, you must agree that if a whole sequence is
interesting, then so is its limit? If you knew an interesting sequence,
wouldn't you be interested in its limit?

Quad erat demonstrandum.

Of course, this entire discussion is rather silly as I tried to imply in
my previous posting. Some people might even say that this thread is not
interesting (pun intended).

Pax vobiscum,
	Nadav.

-- 
Nadav Har'El                        |       Friday, Apr 20 2001, 27 Nisan 5761
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |If Windows is the answer, you didn't
http://nadav.harel.org.il           |understand the question.

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From: Oleg Goldshmidt <[email-masked]>
Date: 20 Apr 2001 12:49:09 -0400

> (Could this be due to Smullyan?)

I believe it is due to Littlewood, actually.

-- 
Oleg Goldshmidt | [email-masked] 
"I'd rather write programs to write programs than write programs."

---

From: Omer Zak <[email-masked]>
Date: Fri, 20 Apr 2001 12:56:22 +0300 (EET DST)

> wouldn't you be interested in its limit?

Back to definition of "interesting-ness".
How about trying to define it, and seeing whether it satisfies the
property that: the limit of a sequence of elements, satisfying property P,
also satisfies property P?

One possible way to try to define it:
Expose the possibly-interesting object to the sense organs of N persons,
and determine their reactions by means of a polygraph.
If at least M (M <= N) subjects exhibit responses higher than a certain
threshold, then the object is deemed to be interesting.

From the above empirical and physical definition, the next step is to
abstract a mathematical definition (such as one using the value of a
cross-correlation between the subject and sexually explicit material of
the same dimensionality), and henceforth use it as the mathematical
definition of "interesting-ness".
                                             --- Omer
There is no IGLU cabal.  It has abysmally low "interesting-ness" score.
WARNING TO SPAMMERS:  at http://www.zak.co.il/spamwarning.html