Remember “The Powers of Ten”?
(a nine-minute film from 1977
showing the scale & structure of Reality)
Ever see it?
When I was a youth, a book came to our house
a Time-Life book on The Seas. Well
Here’s what I found out from that book ~
If you were to take a glass full of water from the ocean
and then mark all the molecules in that glass – say
you somehow colored them red.
And then you poured it back into the ocean
and stirred it up
or waited
until all those red molecules
were evenly distributed throughout the entire hydrosphere.
And then you again scooped a glass from the ocean –
what, do you suppose, would be the chances of capturing a red water molecule?
It seems a bit unlikely, don’t you think?
Nope !
You would, on the average, find ELEVEN HUNDRED red molecules
In EACH glass-full !
[well – let’s just round that off to 1,000]
This means that you could count how many water molecules are in one glass
by using your glass and the ocean :
Imagine you are sitting in a canoe
With a big trash bag hooked to your port gunwale
(and this bag had the property of being able to stretch infinitely
And yet not break or tear.
It has a built-in funnel at its opening
and this is securely tied to your gunwale
So – while the bag itself is in the water
the only water inside it
is what you pour into it.
And you start –
dipping from the right
and pouring into the funnel on the left.
And each time you do this you count –
“One thousand”; “Two thousand”, and so on.
And you keep doing that
till all the water in the ocean
is inside your bag.
THAT’S how many water molecules
are in a single glass.
They are little. INCONCEIVABLY small.
Well, recently I got to thinking –
If a drinking glass is too big
(by a factor of a Thousand)
What WOULD be the right size?
The Middle Size ?
I have heard that our oceans are 90% still unexplored.
But by now someone will have calculated how much water
Is on the Earth.
So –
I consulted ChatGBT.
I asked – “How many water molecules are on the earth? Please include the oceans, fresh water (including all frozen water / glacial ice, ground water) and bio-mass / water that’s part of living organisms. EVERYTHING.)”
ChatGPT said:
Let’s answer this with a total Earth-scale estimate.
…
{I won’t drag you through the whole response, but
here’s how it shakes out:}
🌊 There are approximately 4.63 × 10⁴⁶ water molecules on Earth, including oceans, freshwater (ice, lakes, rivers, groundwater), and all living biomass.
This is a big number
and is, of course, written in Standard Scientific Notation ~
(which is what you want, when dealing with numbers
that are very large or very small)
The second part tells you the Order of Magnitude;
and the first part (the coefficient) will be some normal number between 1 and 10.
This does not trouble me much, as I was born in 1946.
So – by the time I took high school Chemistry and Physics
working engineers still carried a slide-rule in their shirt pocket. Their ‘calculator’.
We students each had (and used) a slide rule.
Besides that there was a BIG slide rule hanging up in the front of our class room.
This big slide rule was fully functional; and (being nearly a foot high, and 7 feet long) it was easy to see.
Our teacher would often use the big one to work through some of the calculations pertinent to our current work.
Anyway – a slide rule does NOT deal in Orders of Magnitude;
It deals only in Raw Numbers – (both input AND output)
YOU must know the correct order of magnitude
Anyway I know enough Math to understand
that I needed the square root of 4.63 × 10⁴⁶
And, by the way : 10⁴⁶ is simply a short-hand way of telling you how many times 10 is to be taken as a factor:
(10 X 10 X 10 … forty six times [forty-six factors of 10 , not just three] ) : 46,300,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
{ This is 4.63 after the decimal point has been moved one place to the right 46 times }
No one wants to work with numbers that look like that. Too unwieldy.
We are after the MIDDLE Size. A container (like a small glass)
that will be ‘midway’ in size between a single water molecule on the small end; [let’s call this ‘ w ‘]
and the volume of all the water on the earth on the big end; [let’s call this (Upper Case) ‘ W ‘]
We need the Square Root of W.
(And ~ when I say : the ‘mid size’ I do NOT mean “half the size” of the full amount)
Normally, you see – once you determine that the square root (say) of 81 is 9 you can get back the original number (81)
in a SINGLE (multiplicative) transaction – you simply multiply the square root (9) by itself and you’re done.
But
the REASON we’re after the square root of W ( that is – ‘all the water on earth’) is to find the MIDDLE SIZE.
As sort of Teaching Tool.
You see ~
While we HAVE a (vague) notion as to the size of the ocean,
a SINGLE WATER MOLECULE is (it turns out) WAY too SMALL !
Well, to be fair – here’s the problem: Many of us have been to the ocean; but
none of us have visited a MOLECULE.
So –
Maybe it would be helpful – to have in front of us an object, a container something with an EVERY-DAY size,
a size we can RELATE to which shows us the MIDDLE Size. Half-way between a single molecule and the Whole Ocean.
Eventhough we still use the square root (of W – which is ‘all the water on the earth’)
we want to get there (to the ‘big end’ ) in TWO jumps not ONE. So that we can see where we’ve got to, (where we are) when we’re HALF-WAY there.
I mean that —
applying it (the square root of W) the first time (as a factor of increase, applied to w) will get us half way …
{let’s call this M for Mid-size }
and applying it AGAIN (the same factor of increase) will get us the rest of the way … to W.
You will remember that w is small … but it is NOT Zero. It is ONE. It’s a single water molecule.
So
w X M = M or (1 X the square root of W) = M Then: M X M = W or (the Middle size X the square root of W = all the water on the earth)
So
Let’s find M.
[taking the square root of a number that’s in Std. Scientific Notation]
Since the order of magnitude is 46 (an even number)
we can simply allocate half (of these 46 Powers of 10) to each of the two times we multiply ;
and then simply take the square root of the coefficient : (4.63)
Thus
The Square Root of W = 2.15 X 10-to-the-23rd
(which equals about 6.4 cubic centimeters / or 1.3 teaspoons, or about ⅕ oz.)
A miniature shot glass.
A cylindrical container with a diameter of 1.71 cm, and with a height of 2.77 cm would do.
[this is about 11/16” in diameter X about 1 ⅛” high] – inside measurements.
A small shot glass indeed. It’s about the size of the end of one of your fingers (beyond the last joint).
Our hydrosphere is bigger than M
by the same factor that M is bigger than a water molecule.
M compared to w is the same as W compared to M
M/w = W/M ( = 2.15 X 10-to-the-23rd = Square Root of W )
Every time we have a drink of water even a little drink
we drink at least that much.
Every time we wash our hands or face
we use more than that.
Our bodies are mostly water.
And then ~
What if water is sentient ?
I see that Masaru Emoto
wrote a number of books on water.
and/or
Have a look at some video clips
on the sentience of water.
https://www.youtube.com/watch?v=OeeAMNxuqio (Speaking to the Water with Pat McCabe 5:07)
https://www.youtube.com/watch?v=vmUk-gDfZA0 (Water Is ALIVE & RESPONDS to Human Emotion 10:19)
https://www.youtube.com/watch?v=SDNhH8deZPg (Masaru Emoto’s Experiment in Gratitude 1:30)
~~~~~~~~~~~~
If we translate ONE teaspoon of honey into HOW FAR the bees must fly in order to produce it that distance would be about the distance from the earth to the moon. – One teaspoon !
We should learn to distinguish between what something costs (that is – how much we have to pay for it) and its VALUE.
And it probably wouldn’t hurt us if we considered what others have had to do to make it available to us.
It’s as though we’re born and raised to be brats.
But should we live out our whole lives like that?
“Businessmen – they drink my wine
Plowmen dig my earth.
Not a one of them down the line
Knows what any of it is worth.”