| Topic: |
Science > Physics |
| User: |
"Skeptic" |
| Date: |
02 Oct 2006 04:36:30 PM |
| Object: |
Twice as Many Numbers as Numbers |
Remember the incident recounted in "Surely You're Joking Mr. Feynman" in
which Feynman asks a kid if he knew there are twice as many numbers as
numbers? The kid names a number and Feynman responds with a number twice as
large.
I decided to try that with my nine year old daughter. She said 200 so I
said 400. She said 2225 and I said 4450.
"So," I said "whatever number you can name there's always a number twice as
big."
Instantly she said zero.
How can kids that young make you feel so stupid?
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| User: "" |
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| Title: Re: Twice as Many Numbers as Numbers |
03 Oct 2006 04:56:08 AM |
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In article <yDfUg.9159$e66.1839@newssvr13.news.prodigy.com>,
"Skeptic" <jgreimer@sbcglobal.net> wrote:
Remember the incident recounted in "Surely You're Joking Mr. Feynman" in
which Feynman asks a kid if he knew there are twice as many numbers as
numbers? The kid names a number and Feynman responds with a number twice as
large.
I decided to try that with my nine year old daughter. She said 200 so I
said 400. She said 2225 and I said 4450.
"So," I said "whatever number you can name there's always a number twice as
big."
Instantly she said zero.
How can kids that young make you feel so stupid?
ROTFL. Beautiful. If she keeps that kind of thinking up, she
would be able to do software development work. Thinking of
all the possible way Murphy's Law can be invoked is an art
form that only the highest level of bit gods seem to be able
to do.
/BAH
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| User: "kunzmilan" |
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| Title: Re: Twice as Many Numbers as Numbers |
05 Oct 2006 08:29:42 AM |
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All agree that natural numbers exist. The question is, if does natural
space exist. But natural numbers themselves form the one dimensional
space. Is the point with coordinate 0 its part? If you try to construct
the two dimensional space without zeroes, you must left out both axes.
Then you get only a difference of corresponding combinatoric function.
Using the generating function \sum n^m, for n = 1, and m going from 0,
we get points 1, a, aa, aaa... Zero vanishes as the point 1 on the
scale.
The following table is the table of partitions of n into at most n
parts
1 1 1 1 1 1
- 1 1 1 1 1
- 1 2 2 2 2
- 1 2 3 3 3
- 1 3 4 5 5
- 1 3 5 6 7
Both indices start from zero. The difference of this table, obtained by
shifting each column for j rows down, is
1
- 1
- 1 1
- 1 1 1
- 1 2 1 1
- 1 2 2 1 1
- 1 3 3 2 1 1
is the table of partitions of n into exactly n parts. It is simple task
to find both reccurencies.
The lone 1 represents empty space, defined as 0^0. The elements of
tables count the number of orbits of natural spaces.
kunzmilan
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| User: "Cam Jones" |
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| Title: Re: Twice as Many Numbers as Numbers |
02 Oct 2006 05:27:18 PM |
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Skeptic wrote:
Remember the incident recounted in "Surely You're Joking Mr. Feynman" in
which Feynman asks a kid if he knew there are twice as many numbers as
numbers? The kid names a number and Feynman responds with a number twice as
large.
I decided to try that with my nine year old daughter. She said 200 so I
said 400. She said 2225 and I said 4450.
"So," I said "whatever number you can name there's always a number twice as
big."
Instantly she said zero.
How can kids that young make you feel so stupid?
Cute story! I guess us little kids are just smart like that. However,
technically, zero is not an actual number, but a concept, an idea
invented a little while after pi was invented. For many millenia,
numbers were used in ancient civilizations to record the number of
objects, and as one can not own zero hogs, citizens of these
civilizations found no use for the number that was not even known to
exist at the time.
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| User: "Hero" |
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| Title: Re: Twice as Many Numbers as Numbers |
03 Oct 2006 04:17:34 AM |
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Cam Jones schrieb:
Cute story! I guess us little kids are just smart like that. However,
technically, zero is not an actual number, but a concept, an idea
invented a little while after pi was invented. For many millenia,
numbers were used in ancient civilizations to record the number of
objects, and as one can not own zero hogs, citizens of these
civilizations found no use for the number that was not even known to
exist at the time.
Numbers were invented before civilisations and zero was there too. The
only part which came later (Indian; Maya) was to use a symbol or sign
for it.
Proof: The basic concept of number was answering the question "How
many?" (and sometimes "How much?"). What did one answer to "Here are
three birds on a twig. Two are flying away and than an other one. How
many remain?" ?
Answer. " None" or "Not one"
Isn't it alike to what You are formulating in "...zero is not an actual
number..".
For You zero is a number, but a not-actual one.
You underestimate our ancestors.
Friendly greetings
Hero
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| User: "Richard Tobin" |
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| Title: Re: Twice as Many Numbers as Numbers |
03 Oct 2006 05:00:56 AM |
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In article <1159828038.145824.34980@b28g2000cwb.googlegroups.com>,
Cam Jones <onespiritedgal93@bellsouth.net> wrote:
However,
technically, zero is not an actual number,
This must be some new use of the word "technically" that I have not
previously encountered.
but a concept, an idea
Unlike, say, 3?
invented a little while after pi was invented.
How you could possibly know this is a mystery.
For many millenia,
numbers were used in ancient civilizations to record the number of
objects, and as one can not own zero hogs, citizens of these
civilizations found no use for the number that was not even known to
exist at the time.
So because people didn't write down zero when accounting for hogs,
they must not have had the concept?
-- Richard
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| User: "tadchem" |
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| Title: Re: Twice as Many Numbers as Numbers |
03 Oct 2006 04:44:01 AM |
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Skeptic wrote:
Remember the incident recounted in "Surely You're Joking Mr. Feynman" in
which Feynman asks a kid if he knew there are twice as many numbers as
numbers? The kid names a number and Feynman responds with a number twice as
large.
I decided to try that with my nine year old daughter. She said 200 so I
said 400. She said 2225 and I said 4450.
"So," I said "whatever number you can name there's always a number twice as
big."
Instantly she said zero.
How can kids that young make you feel so stupid?
Did you forget about "00" - often found on Roulette wheels?
Tom Davidson
Richmond, VA
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| User: "Sorcerer" |
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| Title: Re: Twice as Many Numbers as Numbers |
03 Oct 2006 05:28:07 AM |
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"tadchem" <tadchem@comcast.net> wrote in message
news:1159868641.056439.19040@e3g2000cwe.googlegroups.com...
|
| Skeptic wrote:
| > Remember the incident recounted in "Surely You're Joking Mr. Feynman" in
| > which Feynman asks a kid if he knew there are twice as many numbers as
| > numbers? The kid names a number and Feynman responds with a number
twice as
| > large.
| >
| > I decided to try that with my nine year old daughter. She said 200 so I
| > said 400. She said 2225 and I said 4450.
| > "So," I said "whatever number you can name there's always a number twice
as
| > big."
| > Instantly she said zero.
| > How can kids that young make you feel so stupid?
|
| Did you forget about "00" - often found on Roulette wheels?
|
| Tom Davidson
| Richmond, VA
That's 10 times bigger.
"0000"
Androcles
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| User: "Cam Jones" |
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| Title: Re: Twice as Many Numbers as Numbers |
03 Oct 2006 04:15:45 PM |
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Thank you for your criticism, however, I was not implying that the idea
of zero was not around, but there was not a written symbol to represent
it. I know when pi was calculated, and later specfied, because I have
done research in that area. Obviously, the individuals present are
scientists, or at least interested in science, as while I was merely
commenting on a subject, several people rushed to debate. Whether that
is a good or a bad thing, we will never know.
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