Subject: Re-inventing the Wheel

From: Shlomi Fish <[email-masked]>
Date: Tue, 11 Dec 2001 15:07:13 +0200 (IST)

I said it to Muli, but here goes:

He who re-invents the wheel has a much better understanding of how a wheel
works.

Another option is:

He who re-invents the wheel sometimes invent a much better wheel.

:-)

Regards,

	Shlomi Fish

----------------------------------------------------------------------
Shlomi Fish        [email-masked]
Home Page:         http://t2.technion.ac.il/~shlomif/
Home E-mail:       [email-masked]

"Let's suppose you have a table with 2^n cups..."
"Wait a second - is n a natural number?"

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From: "Nadav Har'El" <[email-masked]>
Date: Tue, 11 Dec 2001 15:25:00 +0200

On Tue, Dec 11, 2001, Shlomi Fish wrote about "[hackers-il] Re-inventing the Wheel":
>...

How about:

   He who re-invents the wheel will likely design a square wheel and spend a
   year trying to figure out why it doesn't work properly.

Your first sentence is true, but only if you do actually manage to re-invent
the wheel. Humans have existed for thousands of years without having wheels
(let alone wheels on axes). Millions of humans needed them, and yet no-one
was able to invent them - until someone came along and invented it. If you
were in the stoneage, are you so sure you'd be the one inventing the wheel -
and not the millions who didn't? Isn't it a whole lot easier to use an
existing wheel design (which looks trivial once you know the idea)?

-- 
Nadav Har'El                        |     Tuesday, Dec 11 2001, 26 Kislev 5762
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |I have a great signature, but it won't
http://nadav.harel.org.il           |fit at the end of this message -- Fermat

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From: Shlomi Fish <[email-masked]>
Date: Tue, 11 Dec 2001 16:09:46 +0200 (IST)

>    year trying to figure out why it doesn't work properly.

Cute. But I did mean that you actually invent a good wheel.

> existing wheel design (which looks trivial once you know the idea)?

You are assuming two things:

1. That Humans needed wheels. Before Civlization, Humans travelled from
place to place over unmarked trails and rough terrain. Wheels would be
useless without good roads.

After Civilization was founded, the wheel was invented shortly afterwards.
I believe the wheel was invented in Ur at 2000 or 4000 BC. (can't
remember) Most people believe that the wheel was invented during the Stone
Age which is entirely non-factual.

2. You assume that those people had the cognitive tools necessary to
invent the wheel. Like I said in a very early post, there is evidence that
spoken language was invented 70,000 years ago, and writing much further
down the road. It is possible that humans did not possess conceptual
thinking without language. (but let's not start a flame war about it,
again).

--

Quoting Ovid: "Let others praise ancient times; I am glad I was born in
these."

Regards,

	Shlomi Fish

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From: Oleg Goldshmidt <[email-masked]>
Date: 11 Dec 2001 16:51:17 +0200

> He who re-invents the wheel sometimes invent a much better wheel.

Sometimes is the operative word here. It is probably very interesting
to explore the necessary and sufficient conditions for success in this
endeavor.

Richard Feynman discusses different ways of learning/understanding
things, in particular, in his "Lectures on Computation" (trying to
bring things on topic here, and succeeding marginally :-). He himself
usually tried to re-invent the wheel (i.e. to work things out) in
order to understand how things worked. However, even he consulted the
accumulated knowledge often in order not to go too far sideways in the
process. He is wise enough not to disparage other ways of learning and
understanding.

And yes, he managed to invent a better wheel on a couple of
occasions. What does this prove? Feynmans are few and far between...

-- 
Oleg Goldshmidt | [email-masked] 
"If it ain't broken, it has not got enough features yet."

---

From: "Nadav Har'El" <[email-masked]>
Date: Tue, 11 Dec 2001 17:59:40 +0200

> process. He is wise enough not to disparage other ways of learning and

I'm reading now a biography of the mathematician Paul Erdos, called "The
Man Who Loved Only Numbers". It's a very non-traditional biography, filled
with funny stories, anecdotes, and stuff like that.

One of the anecdotes is about the Indian (I mean, from India) Mathematician
Ramanujan (if I remember his name accurately). This guy was a genius and
an autodidact. After he finished school and some very basic training in
arithmetic and such, he decided that he loved Mathematics. He had no money,
and couldn't afford a university or books (I'm talking about the beginning of
this century, by the way), but he managed to find one book about mathematics:
a "formula" book (for using in tests), filled with several thousands of
correct mathematical formulas, without proof.

Ramanujan, who never saw a proof in his life, wanted to know why these
formulas are correct. So he set out to convince himself that they were.
He invented weird notations for ideas he never saw printed, but most of
the "proofs" remained in his head (he viewed them as "enlightenment" more
than as proofs - he somehow "realized" that something was correct).

He then set out to invent new formulas, and found what he thought was an
interesting one regarding the density of prime numbers. He sent it (without
proof) to several known mathematicians, but they all ignored him. Finally,
one famous English mathematician (Hardy) read his mail, and was amazed.
Ramanujan, some uneducated Indian, seemed to have come by himself to an
improvement on a theorem of Gauss (of whom Ramanujan has obviously never
heard of). He invited Ramanujan to London, where they started to do research
together. Hardy liked to give "scores" to mathematicians. He (humbly) gave
himself the score of 25 (I hope I'm remembering this correctly), and one
of his colleagues in Cambridge a 30. He gave the great Hilbert an 80. And
he gave Ramanujan a 100.

Ramanujan was amazing. He came up with correct mathematical ideas and
formulas, which he knew were correct, but he didn't know how to prove it
in that strange formal way those Europeans used. He wasn't used to the common
notations either. Some people described Ramanujan as having direct access
to God's book of truths. But what despaired Ramanujan the most was the
fact that he repeatedly came up with theorems that were actually known
for a long time before him. Anybody doing a masters or doctorate knows how
disappointing it feels to discover something amazing, only to realize that
it was already known for 100 years, so imagine how it feels for this to
happen every day! Ramanujan became depressed, and tried to kill himself by
jumping in front of a train. Luckily, the train stopped in time and
Ramanujan lived (though he was hurt). Shortly after, he caught TB and a
couple of years later, he died.

Besides being a very touching story, it also has a moral. Someone doesn't
need formal training to be a genius. He doesn't even need to have access
to good books to be one. But if you don't do either of those, and try to
"reinvent the wheel" all the time, to make up the theory of your profession
on your own instead of trying to read or hear about it from other sources,
you'll end up very disappointed. In the real world, you need to cooperate
with people, and you expect to get acknowledged by them. You can't do that
unless you play by other people's rules, follow the accepted notations, and
so on.

Imagine you re-inventing on your own the concept of quick-sort, and calling
it Wawawiwa-order. Then you call its performance Z(a*hello(a)), not knowing
that people usually say O(n*log(n)). This will frustrate both you and the
people who will need to listen to you (to the point where unless you're a
one-in-a-billion genius, no-one will even bother to listen to you).

-- 
Nadav Har'El                        |     Tuesday, Dec 11 2001, 26 Kislev 5762
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |Don't accept your dog's admiration as
http://nadav.harel.org.il           |conclusive evidence that you're wonderful

---

From: Shlomi Fish <[email-masked]>
Date: Tue, 11 Dec 2001 20:11:47 +0200 (IST)

> Long story about Ramanujan (or whatever his name was) snipped.

I personally don't feel depressed when I discover that something I thought
about myself was already discovered before me (even very long). For
instance, when I thought about my algorithm for determining if two graphs
were isomorphic, I felt good that I managed to get close to the one
proposed about 30 years ago by myself. (and with a small amount of
input from Prof. Even's help - analyze what was wrong with the first
versions of the algorithm)

What makes me feel good is that _I_ came up with it myself, without having
read the proof or the algorithm or whatever. I consider this as an
exercise to my brain to "re-invent the wheel", so to speak. In the same
vain, one can claim that thinking about mathematical or logical puzzles is
useless because you can look up their solution in the answers section.

I realize most of the things I came up with were already thought about and
documented. But I live with this fact very well, without any frustration.

If Ramanujan was frustrated because of that - so be it. I'm not.

Regards,

	Shlomi Fish

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From: Gilad Ben-Yossef <[email-masked]>
Date: 11 Dec 2001 21:59:36 +0200

> with funny stories, anecdotes, and stuff like that.

So, anyone here has a non infinite Erdos number or know one who does?
( http://www.oakland.edu/~grossman/readme.html for those unfamilier with
the concept)

Gilad.

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From: mulix <[email-masked]>
Date: Tue, 11 Dec 2001 21:55:32 +0200 (IST)

> ( http://www.oakland.edu/~grossman/readme.html for those unfamilier with

unless i'm mistaken, orrd, one of haifux's founders has a pretty high
erdos number (through eli biham, i believe). orr?
-- 
mulix

http://vipe.technion.ac.il/~mulix/
http://syscalltrack.sf.net/

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From: "Nadav Har'El" <[email-masked]>
Date: Tue, 11 Dec 2001 22:34:26 +0200

> ( http://www.oakland.edu/~grossman/readme.html for those unfamilier with

Oh, I know several people with Erdos number "1" (the best possible).
Looking at http://www.oakland.edu/~grossman/Erdos0, I've seen (but not
more than that - it's not like I talked much to any of them, and certainly
haven't written any papers with them) the following people:

	Graham, Ronald L. (Mathematical Sciences department, AT&T Bell Labs)
	Aharoni, Ron (Math Department, Technion)
	Holzman, Ron (Math Department, Technion)
	Pinkus, Allan M. (Math Department, Technion)
	Zaks, * (the 3 brothers from the Technion)

Come to think of it, I also saw Erdos himself in person (I heard him
lecture)...

I wonder if I have an Erdos number... The most known Mathematician I
coauthored a paper with is Matania Ben-Artzi (from HUJI). I have no
idea what his Erdos number is... Anyway, I'm not a prolific paper
writer, so I bet I have some crappy Erdos number :)

-- 
Nadav Har'El                        |     Tuesday, Dec 11 2001, 27 Kislev 5762
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |I don't eat snails. I prefer fast food.
http://nadav.harel.org.il           |

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From: Omer Zak <[email-masked]>
Date: Wed, 12 Dec 2001 00:00:46 +0200 (IST)

I put forth my claim to having complex Erdos number 1 + 1i.

My justification.
When I was student in the Technion, there was this guy by the name Juliusz
Reichenbach(SP?).  He had a brother who was professor in the Technion, but
he himself was in the world of crackpoint math, if you get my meaning.

After coming to the Technion and doing whatever he needed to do, he would
in the evening go to the Students' dormitories, find a room with empty bed
and understanding(?) student and sleep there.  Thus I got to know him.

He self-published some sort of mathematical journal, which is hard (to
someone without deep Math training) to tell whether it was serious or
crackpot; and claimed that Erdos is an honorary editor.  So he had the
Erdos number 1i (the i is for his imagination).  Therefore I can claim to
have the complex Erdos number 1 + 1i.

> ( http://www.oakland.edu/~grossman/readme.html for those unfamilier with

                                             --- Omer
There is no IGLU Cabal.  However, the world is full with iGLU Cabals
(imaginary GLU Cabals).
WARNING TO SPAMMERS:  see at http://www.zak.co.il/spamwarning.html

---

From: Alon Altman <[email-masked]>
Date: Wed, 12 Dec 2001 02:41:10 +0200 (IST)

> existing wheel design (which looks trivial once you know the idea)?

  Re-inveting the wheel is ont thing... patenting it in 2001 will grant you
the Iggnobel prize :)

  Alon

-- 
This message was sent by Alon Altman ([email-masked]) ICQ:1366540
The RIGHT way to contact me is by e-mail. I am otherwise nonexistent :)
--------------------------------------------------------------------------
Only God can make random selections.

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From: Alon Altman <[email-masked]>
Date: Wed, 12 Dec 2001 02:51:17 +0200 (IST)

> erdos number (through eli biham, i believe). orr?

  I have the same Erdos number as Orr (through Alon Itai). I'm 3 Erdos and
so is Orr.

  Alon

-- 
This message was sent by Alon Altman ([email-masked]) ICQ:1366540
The RIGHT way to contact me is by e-mail. I am otherwise nonexistent :)
--------------------------------------------------------------------------
No amount of genius can overcome a preoccupation with detail.

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From: Shlomi Fish <[email-masked]>
Date: Wed, 12 Dec 2001 06:40:37 +0200 (IST)

> I put forth my claim to having complex Erdos number 1 + 1i.

Actually, I take claim to be the first person to come up with this joke.
Here is an excerpt from the "Pope Died on Sunday":

<<<
"You know," said Rachel "Your character does not add up to a whole
number."

"You are wrong." answered Rudolf, "My character adds up to a hyper-complex
number which is 100% whole."

"The question is whether its absolute value is whole."

"I did not think about it, but I think it is."

The question is whether hyper-complex numbers have absolute values. And it
sounds a little better in Hebrew.

This excerpt was not integrated into the main storyline yet. But it is
still on my homepage, assuming it will be back online.

Regards,

	Shlomi Fish

---

From: "Nadav Har'El" <[email-masked]>
Date: Wed, 12 Dec 2001 14:37:03 +0200

>   I have the same Erdos number as Orr (through Alon Itai). I'm 3 Erdos and

I gave up finding my Erdos number. It is probably more than 3, if finite
at all. There are plenty of 1 Erdos people in the Technion, so if it's very
important to someone he can become a 2 Erdos (becoming a new 1 Erdos is
impossible, for obvious reasons ;) ).

The page http://www.oakland.edu/~grossman/compute.html says the following
interesting thing about Erdos number 3:

   "Remember, the distribution of Erdצs numbers is such that almost every
    mathematician with a finite Erdצs number has a number of less than 8 --
    only about 2% are higher, and none is more than 15. See our facts page
    for more details. People in other sciences or even social sciences may
    also have small Erdצs numbers. We've even heard about a horse who claimed
    to have an Erdצs number of 3."

-- 
Nadav Har'El                        |   Wednesday, Dec 12 2001, 27 Kislev 5762
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |Hospitality: Making your guests feel at
http://nadav.harel.org.il           |home, even if you wish they were.

---

From: Oleg Goldshmidt <[email-masked]>
Date: 12 Dec 2001 21:23:06 -0500

Oleg Goldshmidt <[email-masked]> writes:

> [Feynman] himself usually tried to re-invent the wheel (i.e. to work
> things out) in order to understand how things worked. 

I took the book off the shelf and found the passage. Here is a quote:

"Finally, after you've figured out how to do it you read how they did
it and find out how dumb your solution is and how much more clever and
efficient theirs is!"

And that's Feynman...

-- 
Oleg Goldshmidt | [email-masked] 
If it aint't broken it hasn't got enough features yet.

---

From: Shlomi Fish <[email-masked]>
Date: Wed, 12 Dec 2001 21:30:08 +0200 (IST)

> it and find out how dumb your solution is and how much more clever and

From which book it is taken? It rings a bell from "Surely you're joking
Mr. Feynman". I'd like to have the complete context.

Regards,

	Shlomi Fish

---

From: Oleg Goldshmidt <[email-masked]>
Date: 12 Dec 2001 21:45:23 -0500

> Mr. Feynman". I'd like to have the complete context.

Go up the thread ;-) It's "Feynman Lectures on Computation".