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From: hanson on 14 May 2010 20:30
---- . about the Size of Avogadro's number, N_A... ----
THE MOST POWERFUL & FAR-REACHING # IN PHYSICS
:>
In other posts the general questions about the history, the
definition & use of Avogadro's number, N_A, are discussed
and stop at the SI mode that says: N_A, =~ 6.022x10^23
atoms or molecules per mol(e), referring to the number (N_A)
of C12 atoms that are contained in 12 gr of C12, (1 mole)
>
But rarely is the size of N_A, [6E23] given any attention &
discussed in relation to our normal day to day experience.
>
So, let's have some fun with that mol or N_A, in which 6E23
atoms happen to be in ~2.5 table-spoons full of soot. Right...
yeah, so what, BFD.... until you contemplate & realize that
the size of
>
== 6E23 miles happens to be ~ 3 times the diameter of the
accessible universe.
== 6E23 football fields will stretch from here out to some
farthest galaxies we have observed.
== 6E23 people would need ~ 85 Million Million or
85'000 Billion Earths to house them.
== 6E23 Years is 4'000 Billion times longer then the age of
the universe since the Big Bang.
== 6E23 kilograms is one tenth of the mass of Earth
>
So, if what I penciled/estimated above, about the immensity
of the size of N_A, has not yet grabbed your attention yet then,
all you beat-off artists & fornicators, estimate how many times
you, or to make you feel less guilty, how many eons it will take,
if all the "active" males of the entire earth get at it, to ejaculate
== 6E23 individual sperms.- Give yourself some self-satisfaction
for a scientific reason for a change.... ahahahaha... AHAHAHA...
>
This truly gigantic, cosmic sized number N_A, or 1 mole, works
the other way and shows how incredibly SMALL items can be,
i.e. :
== 6E23 atoms are present in 1 iron marble, only 2 oz heavy.
== 6E23 molecules of C2H5OH are in ~ 1 single shot of Booze.
== 6E23 molecules of Helium are in one ~5 gallon Balloon.
== 6E23 molecules of sugar are situated in 1 cup of it and
== 6E23 molecules of H2O go down your gullet with very
gulp of water that you swallow.
>
Rem: 6E23 is the same # that reaches yondern cosmic limits.
In the above iron marble example you'll have to chop it into
6E23 = 602 000 000 000 000 000 000 000 individual pieces
to pick up 1 of it up as a single iron atom. Very small boogers.
>
This diminutive extent of the particles in the atomic world was
suspected since antiquity but it was only some 80 years ago
with the Nobel prize to Perrin in 1926, for his work on N_A, that
the existence of atoms was *officially* accepted and adopted.
>
There are 2 widely used equations which connect our day to
day experience with the micro/atomic world, namely:
>
N_A = F/e ---> 6E23 elem.el charges per Faraday unit, and
N_A = R/k ---> 6E23 Boltzmann units for the univ. Gas constant.
>
And there are still more such N_A connections on the other
side of the scale of human experience, in the cosmic realm,
where the Hubble constant and the Cosmic background temp,
Tb, can be expressed by using or needing N_A, when looked
at it thru the prism of the Finestructure const, [a], Boltzmann's
constant [k], and the Lyman series limit freq. fL, as in
>
H = (1/2) * [(a^2)/2]^2 * fL / N_A ����Hubble,
H = (3/2)* k * Tb * ((a^2)/4) / (N_A * h). �Tb ~ 2.7..K.
>
So, there is an interesting concept emerging here:
|||| It appears that there are N_A sized steps that nature takes
|||| in its manifestations... from the cosmic realm, which when
|||| sliced into N_A segments does arrive at the day to day
|||| human domain experience, which wherein when events
|||| are subdivided again into still N_A smaller fragments we
||||| experience them as the particles in the atomic world....
||||| Surprisingly if we chop these atomic events/particles yet
||||| one more time by another N_A sized step further down,
||||| we arrive at the **** Domain of the NATURAL UNITS****.
>
These profound notions go back to Max Planck's time ca.
1899 when he first proposed NATURAL units for L, M & T
(instead of our arbitrary cultural ones like gr, cm & sec) as
follows:
>
m_pl = sqrt (hbar*c/G) -- l_pl = sqrt (hbar&G/c^3) & t_pl = l_pl/c
>
The inter-relationship of/between these units simply states that
1 Planck mass, m_pl, unit has the size of 1 Planck length , l_pl,
and it exists for the duration of only 1 Planck time unit , t_pl.
See more in http://en.wikipedia.org/wiki/Planck_units
>
These Planck units are so small that they seems to have only
academic interest. But when they are seen as an entire mole
size set, (N_A times larger), then they represent familiar values
of physically existing M,T, & L values in the atomic world:
>
|||| m_pl / m_e = a^(1) * (N_A*pi*sqrt3)
|||| 1 mole of electron masses = 1 Planck mass
or conversly
|||| r_H / l_pl = a^(0) * (N_A*pi*sqrt3)
|||| 1 mole of Planck length units = 1 H-Bohr radius
or
|||| r_e / l_pl = a ^(2) * (N_A*pi*sqrt3)
|||| 1 mole of Plank length units = 1 classical el-radius
or
|||| tau / t_pl = a^(-1) * (N_A*pi*sqrt3) ****
|||| 1 mole of Planck time units = 1 atomic time unit
>
So, it appears, or at least one cam make a case that
|||| Nature is Self-Similar over all scale domains & in all
|||| events & processes to which we humans have access to
>
N_A, the mole, that humble and indispensable number
for the dudes at the chem lab bench, is much more far
reaching then physicists have given it credit for. Unfortunately
N_A's use for the development of **fundamental experimental
physics*** was stopped, a few years after Max Planck
introduced his natural units, by the stream rollers of Einstein's
relativity which looked for illusions and lunatic apparition that
are never there when you probe'm close-up in the real world.
>
So, Einstein, his Zios and his Goyim Dingleberries have
effectively derailed fundamental physics for over a century.
It basically shows that even physics is, like all other science
endeavors, also just another social enterprise...ahahaha....
>
Now sports fans, carry on with your self-manipulation to prove
to yourself that N_A is indeed useful for all natural events.
Till then, thanks for the laughs, guys... ahahahanson

From: rabid_fan on 15 May 2010 11:55
On Fri, 14 May 2010 17:30:40 -0700, hanson wrote:

> But rarely is the size of N_A, [6E23] given any attention & discussed in
> relation to our normal day to day experience.
>>
> So, let's have some fun with that mol or N_A, in which 6E23 atoms happen
> to be in ~2.5 table-spoons full of soot. Right... yeah, so what,
> BFD.... until you contemplate & realize that the size of
>>

Contemplate and realize?

The magnitude of Avogadro's Number is well beyond the ability
of the human nervous system to grasp. Comprehension is impossible.
Comparisons may be "fun" but they are quite useless.

"One, two, three, infinity." This phrase is taken from the title
of a popular science book by George Gamov. It refers to the
counting system of some primitive tribe. Anything beyond a quantity
of "three" is beyond the reach of human imagination and therefore
relegated to the concept of "infinity."

Indeed, the human mind has serious problems grappling with quantities
that exceed about five or six. We cannot visually recognize (i.e. without
counting) any assemblage that exceeds about five or six in size.

The solution is not to deal with them at all using our innate
mental capacity. The solution is mathematics.

Mathematics is a tool to extend our limited mental abilities
in the same way that a wrench (lever) is able to extend our
limited physical abilities. Our positional number system
allows us to express and compute using virtually any magnitude,
even if that magnitude is incomprehensible to our innate
mental sense.

But even our current mathematics fails when we need to consider
the exceedingly exceedingly (sic) large. [Maybe exceedingly^n ?]
Such quantities make Avogadro's Number seem sub-microscopic.

There have been attempts to grapple with hyper-large numbers
through several different notations. Check out:

Knuth's up-arrow notation
Ackerman's function
Conway's chained arrow notation
Moser's polygon notation
Hyperpowers
Hyperfactorials

Essentially, to allow human beings to effectively and consistently
deal with hyper-large quantities (which do emerge in many practical
situations), a new kind of mathematics needs to be developed.

From: Uncle Al on 15 May 2010 12:44
rabid_fan wrote:
>
> On Fri, 14 May 2010 17:30:40 -0700, hanson wrote:
>
> > But rarely is the size of N_A, [6E23] given any attention & discussed in
> > relation to our normal day to day experience.
> >>
> > So, let's have some fun with that mol or N_A, in which 6E23 atoms happen
> > to be in ~2.5 table-spoons full of soot. Right... yeah, so what,
> > BFD.... until you contemplate & realize that the size of
> >>
>
> Contemplate and realize?
>
> The magnitude of Avogadro's Number is well beyond the ability
> of the human nervous system to grasp. Comprehension is impossible.
> Comparisons may be "fun" but they are quite useless.
[snip]

12.0107 grams of graphite.

The US national debt in unreconstructed zimbabs. The number of angels
that fit on the head of a pin (assuming bosonic angels composed of
religium). The number of avocados in a guacamole.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz4.htm
From: rabid_fan on 15 May 2010 13:16
On Sat, 15 May 2010 09:44:04 -0700, Uncle Al wrote:

>
> 12.0107 grams of graphite.
>
> The US national debt in unreconstructed zimbabs. The number of angels
> that fit on the head of a pin (assuming bosonic angels composed of
> religium). The number of avocados in a guacamole.

No matter what you choose to call them, absolute numbers
are in reality quite unnecessary. Ordinary physical and
chemical change are statistical phenomena. The only significance
of large magnitudes such as Avogadro's Number is to insure
that statistical interpretations achieve a new kind of
absolute determinism.

From: rabid_fan on 15 May 2010 15:02
On Sat, 15 May 2010 19:10:14 +0100, Androcles wrote:

>>
> My father was a human calculator, he could add a column of figures
> faster than you can say "column of figures". He could also play the
> piano; both activities can be improved with practice. I could once play
> my way through the first movement of Beethoven's Moonlight Sonata after
> six months practice, but the second movement was too difficult for me
> and when I realised it would take me a year or more I gave up.
>

Both the ability to mentally calculate and to perform a musical
instrument are now completely passe.

I do not possess any recording of the Moonlight Sonata, but
using the information for this composition, as digitized MIDI
data, I can recreate a perfect rendition of it at anytime and
anyplace.

Many diehards and purists will disagree, but in the future,
if it has not already, the profession of the human musician
will succumb to the same digital forces that have destroyed
the occupation of the human calculator.

(When's the last time a human being performed in the pit on
Broadway?)

Human beings should busy themselves with the intellectual activity
of musical composition and not with the ridiculous task of physical
actuation. The latter is for monkeys and machines.

> Human beings are exceptionally good at pattern recognition, we recognise
> faces because we practice looking at faces.

Not quite. The ability to recognize faces is hard-wired into
the human brain. In fact, a surgeon (or accidents) can ablate
certain regions of the cortex to induce prosopagnosia, or face
blindness.

Similar techniques (or acts of nature) can produce acalculia,
or the inability to perform any mental arithmetic.


> We are also good at seeing
> things that are not there,

Well, the brain completes the visual pattern for us,
just as it is able to create aural frequencies that are
"not there."

But the sapient man always consciously overrides such
innate completions because the expected pattern may not
always be the actual pattern. To be so easily deluded
can be dangerous and deadly.


>
> I remember pi = 3.14159265379.
> Let me check with the calculator.
>
> 3.1415926535897932384626433832795
> I was wrong, I'm out of practice, it is ....359, not ....379. That is
> known as "forgetting".

Actually, pi is pi (insert unicode character). The symbol for
pi denotes the exact value of pi. There is no other way to specify
it.

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