"Gosh" Numbers
John
I found three contexts but no attribution.
1. A number that makes someone say "Gosh!"
The nearest star is trillions of miles away? Gosh!
2. A wild-ass-guess number
The car mechanic tells you your car repairs
will be, "Gosh, I'd say $500."
3. Certain consants, for instance pi.
Someone said she had found "gosh number" in a sci-fi book but can't
find the source any more.
I'm wondering what the history of the phrase may be.
Regards,
John
Mark Wallace
None of the above is right.
What a 'gosh number' is can be best explained by an example:
When I say the temperature is 40 below zero, am I using Celsius or
Fahrenheit?
Gosh!
There are several other numbers, particularly in particle Physics,
which do the same thing and are not so arbitrary (Celsius and
Fahrenheit are, after all, extremely artificial measuring systems).
Don't ask me to recall what they are, because I can't (if any come
to me, over the next few days, I'll post them); but I do remember
that the ratio 1:1.6 features large in the biochemical field.
--
Mark Wallace
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M.J.Powell
>When I say the temperature is 40 below zero, am I using Celsius or
>Fahrenheit?
>Gosh!
>
>There are several other numbers, particularly in particle Physics,
>which do the same thing and are not so arbitrary (Celsius and
>Fahrenheit are, after all, extremely artificial measuring systems).
>
>Don't ask me to recall what they are, because I can't (if any come
>to me, over the next few days, I'll post them); but I do remember
>that the ratio 1:1.6 features large in the biochemical field.
Isn't that the 'Golden Ratio'?
Mike
--
M.J.Powell
Odysseus
>
> snip
> >
> >Don't ask me to recall what they are, because I can't (if any come
> >to me, over the next few days, I'll post them); but I do remember
> >that the ratio 1:1.6 features large in the biochemical field.
>
> Isn't that the 'Golden Ratio'?
>
; it can be expressed in many interesting ways. Two of my favourites are
1 + 1/(1 + 1/(1 + 1/(1 + ...))) and
sqrt(1 + sqrt(1 + sqrt(1 + ...))).
--Odysseus
Mark Wallace
That's the one. It turns up all over the place in carbon compounds
and biological matter. It's a better example of a 'gosh number'
than the temperature one, because it's independent of numbering
systems.
As for the Sci-fi book, I have a feeling Fred Pohl wrote something
about gosh numbers in one of his Heechee tales.
--
Mark Wallace
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John
<mwallace...@dse.nl> wrote:
>Odysseus wrote:
>> "M.J.Powell" wrote:
>>>
>>> snip
>>>>
>>>> Don't ask me to recall what they are, because I can't (if any
>>>> come to me, over the next few days, I'll post them); but I do
>>>> remember that the ratio 1:1.6 features large in the biochemical
>>>> field.
>>>
>>> Isn't that the 'Golden Ratio'?
>>>
>> An approximation thereto. If anyone cares the exact value is
>> (1+sqrt5)/2 ; it can be expressed in many interesting ways. Two
>> of my favourites are
>>
>> 1 + 1/(1 + 1/(1 + 1/(1 + ...))) and
>>
>> sqrt(1 + sqrt(1 + sqrt(1 + ...))).
>
>That's the one. It turns up all over the place in carbon compounds
>and biological matter. It's a better example of a 'gosh number'
>than the temperature one, because it's independent of numbering
>systems.
>
>As for the Sci-fi book, I have a feeling Fred Pohl wrote something
>about gosh numbers in one of his Heechee tales.
That's the book. I just found the quote.
"Beyond The Blue Event Horizon", Frederic Pool, Del Rey, NY, 1980,
ISBN 0-345-32067-0, kg 251
Then I turned to the tapes. I let the semi-Albert, the rigid
half-animated caricatures of the program I knew and loved,
lecture me on Mach's Principle and gosh numbers and more
curious forms of astrophysical speculation than I had ever
dreamed of.
Now I still wonder who coined the phrase, Shakespeare or Arthur
Clarke????
Regards,
John
John
Regards,
John
John Dawkins
Odysseus <odysseu...@yahoo-dot.ca> wrote:
Another: Start with Fibonacci's sequence
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...
in which each new term is gotten by adding the previous two terms.
The ratio between consecutive terms settles down to a limit as we go
further and further out in the sequence. The limit is precisely the
Golden Ratio.
In fact, term number n of Fibonacci's sequence is the whole number
closest to the result of raising the Golden Ratio to the nth power and
then dividing by the square root of 5. Example: for term number 11
(that is, 89) take GR^11 = 199.005024999..., divide by sqrt{5} to get
88.997752752...
--
J.
John
wrote:
Sunflowers and other flowers have their seeds arranged in spirals
built by a Fibonacci series.
I can see that these are Gosh! numbers.
Regards,
John
Mark Wallace
Odysseus
>
> Another: Start with Fibonacci's sequence
>
> 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...
>
> in which each new term is gotten by adding the previous two terms.
> The ratio between consecutive terms settles down to a limit as we go
> further and further out in the sequence. The limit is precisely the
> Golden Ratio.
>
is constructed on the same principle, but starting with the 'seed' 1,3
instead of 1,1. It converges very rapidly on successive powers of the
golden ratio. Another curious property of the Fibonacci series is its
appearance in the sums of successive diagonals of Pascal's Triangle, a
table of the binomial coefficients that contains many further wonders.
The golden section itself is just the first in a sequence of interesting
irrational numbers; the next is sometimes called the "sacred cut" and
evaluates to 1 + sqrt(2). Like the golden ratio this number's reciprocal
is equal to its 'fractional' part, and it appears ubiquitously in the
unicursal octagram in similar fashion to the golden ratio in the pentagram.
--Odysseus
John
Function.
***
<http://pw1.netcom.com/~hjsmith/Ackerman/AckeWhat.html>
The Ackermann function is the simplest example of a well-defined
total function which is computable but not primitive recursive. See
the article "A function to end all functions" by Gunter Dötzel,
Algorithm 2.4, Oct 1991, Pg 16. The function f(x) = A(x, x) grows much
faster than polynomials or exponentials. The definition is:
1. If x = 0 then A(x, y) = y + 1
2. If y = 0 then A(x, y) = A(x-1, 1)
3. Otherwise, A(x, y) = A(x-1, A(x, y-1))
***
To get a feel for what makes this an Interesting Function, try doing
A(3,3) by hand.
That the Ackerman's Function, which I always thought was of academic
interest only, models internet denial-of-service attacks transformed
it from an Interesting Number into a Gosh Function (at least in my
mind).
Regards,
John B. Grosh
BTW The definition of "Gosh Numbers" is becoming clearer to me but
the etymology is still missing.
Peter Duncanson
"Gosh" is an interjection which expresses surprise - often
pleasurable. It is a euphemism for "God".
--
Peter D.
UK
(posting from a.e.u)
Lisa Lundgren
>
> Sunflowers and other flowers have their seeds arranged in spirals
> built by a Fibonacci series.
>
I'd say "described" rather than "built," but I get your meaning. It's
any naturally occurring spiral, evidently. Not just flowers. Spiral
galaxies included.
YIC,
Lisa Lundgren
Matti Lamprhey
> >John <jbg...@mindspring.com> wrote...
> >
> > Sunflowers and other flowers have their seeds arranged in spirals
> > built by a Fibonacci series.
>
> I'd say "described" rather than "built," but I get your meaning. It's
> any naturally occurring spiral, evidently. Not just flowers. Spiral
> galaxies included. > YIC, > Lisa Lundgren
Let's assume that nature has a development mechanism along the lines of "the
number of items I can put in this twig/arm/whatever is the sum of the items
in the pair of twigs/arms/whatevers from which it springs". This is the
generation rule of the Fibonacci series, and hence "built" is more
appropriate than the mere "described".
Yours in Mother Nature,
Matti
Mark Wallace
It's a toss-up between the two (I'm assuming 'described' as in drawn
or extended). How about 'constructed'?
Matti Lamprhey
> Matti Lamprhey wrote:
> > "Lisa Lundgren" <tolepai...@yahoo.com> wrote...
> >>> John <jbg...@mindspring.com> wrote...
> >>>
> >>> Sunflowers and other flowers have their seeds arranged in
> >>> spirals built by a Fibonacci series.
> >>
> >> I'd say "described" rather than "built," but I get your meaning.
> >> It's any naturally occurring spiral, evidently. Not just
> >> flowers. Spiral galaxies included. > YIC, > Lisa Lundgren
> >
> > Let's assume that nature has a development mechanism along the
> > lines of "the number of items I can put in this twig/arm/whatever
> > is the sum of the items in the pair of twigs/arms/whatevers from
> > which it springs". This is the generation rule of the Fibonacci
> > series, and hence "built" is more appropriate than the mere
> > "described".
>
> It's a toss-up between the two (I'm assuming 'described' as in drawn
> or extended). How about 'constructed'?
Accreted?
Matti
John
<mwallace...@dse.nl> wrote:
>Matti Lamprhey wrote:
>> "Lisa Lundgren" <tolepai...@yahoo.com> wrote...
>>>> John <jbg...@mindspring.com> wrote...
>>>>
>>>> Sunflowers and other flowers have their seeds arranged in
>>>> spirals built by a Fibonacci series.
>>>
>>> I'd say "described" rather than "built," but I get your meaning.
>>> It's any naturally occurring spiral, evidently. Not just
>>> flowers. Spiral galaxies included. > YIC, > Lisa Lundgren
>>
>> Let's assume that nature has a development mechanism along the
>> lines of "the number of items I can put in this twig/arm/whatever
>> is the sum of the items in the pair of twigs/arms/whatevers from
>> which it springs". This is the generation rule of the Fibonacci
>> series, and hence "built" is more appropriate than the mere
>> "described".
>
>It's a toss-up between the two (I'm assuming 'described' as in drawn
>or extended). How about 'constructed'?
'Built by' was a sloppy construction. I apologize.
I don't think 'constructed' is not an improvement. The problem may be
with my use of 'by'.
How about this.
Sunflower seeds are arranged in a Fibonacci series.
By a simple statement of fact we avoid all theosophical arguments.
(Well, maybe not.)
Regards,
jbg
Odysseus
>
> I'd say "described" rather than "built," but I get your meaning. It's
> any naturally occurring spiral, evidently. Not just flowers. Spiral
> galaxies included.
>
painted nautilus does; the arms look more like linear spirals -- and of
course they aren't a consequence of exponential growth like the organic
ones. In the case of sunflowers, pinecones and pineapples it's not just
that they have a spiral shape: the actual number of seeds, bracts (?) or
whatever in each curving row may be found in the Fibonacci series, and
counting in a different direction will yield its predecessor or successor.
Does anyone know the proper term for the 'plates' forming the outer
surface of a pinecone or pineapple?
--Odysseus
Howard Tuckey
"Odysseus" <odysseu...@yahoo-dot.ca> wrote in message
news:3D6E3341...@yahoo-dot.ca...
They're scales
howard
Mark Wallace
Cool. Gets my vote.
Howard Tuckey
"Howard Tuckey" <htu...@stny.rr.com> wrote in message
news:xfrb9.279620$8M1.43...@twister.nyroc.rr.com...
The pineapple's scales are aka bracts.
hjt
>
>
