The Square Root of W

 

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 FIFTEEN HUNDRED red molecules

In EACH glass-full  !

[well –  let’s just round that off to 1,000;  then we can  later  round it back up    by adding  “half again”]

 

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.  [plus ‘half again’

 

They are little.   INCONCEIVABLY small.

 

Well, recently  I got to thinking –

If a drinking glass   is too big

(by more than a factor of a Thousand:  3 +      orders of magnitude)

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     and listing three meaningful digits.

 

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 we 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 above number     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 the one written out, above,   with nearly four dozen zeros.       Too unwieldy.

Because a single molecule is so small,     it does us little good   to look at whatever numbers (accurately) describe its size.

But

What if   we knew   the middle size?    A container    maybe      (like a small glass)

— ‘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)

You see     – once you  learn/know   that the square root  (say)  of 81   is    9         you can get back the original number (81)

in two EQUAL jumps:    1 X 9  =  9              &      (using the same factor,  once again):     9 X 9  =  81.    [And you can use this same exact process   with ANY number (however big)    once you know its square root.

So  (if we can determine the square root of W)   we can use it as a   a   middle point  on our “table”  (at the left end of which is   a single water molecule;     and at the right end:   all the water on the Earth)

That middle point     then    can serve as a sort of  Teaching Tool.      A Philosophical / cognitive  assistor.

You see ~

While we HAVE  (some    vague) notion  as to the size of the ocean,  but

a SINGLE WATER MOLECULE  is  just   WAY too SMALL !

Many of us have been to the ocean;  but

none of us have visited a MOLECULE.

So  –

it might  be helpful  –  to have in front of us     an object,    a container  maybe         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.

 

Let’s call this “middle size”:    M

 

You will remember that  w   is small … but it is NOT  Zero.    It is ONE.     It’s a   single  water molecule.

So

(the first jump):   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   the size   of  M.

 

              [taking the square root of a number   which is  in Std. Scientific Notation]:    4.63 × 10⁴⁶

 

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.”

 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  (Addemdum,   12 July 2026):

If I had my way  –   every child  would, while growing up,  have ready access to a decent binocularscope     like I did.

 

In the house I grew up in  (in northwest Ohio)  there was   such a device    in its own wooden case,  in the back corner of the hall closet.    And when we wanted to use it, we did not need to ask permission to do so,  we would simply get it out  and use it.          We would look at     our finger,   at a strand of hair,    some table salt,   maybe a bug,    flower parts  …  anything.

Such a device is typically  low-power,   but  even so  –  very entertaining.      If, for example,   you look at a hair,   you can still recognize it as a hair,  but   you can see things about it   that you simply can NOT see with the naked eye.        It EXTENDS one’s ability to see.

It teaches you   –   that  the far end  of perception    is NOT  the far end of  reality.      (Just because  you cannot perceive something,   that does not necessarilly mean   that  it does not exist.)      {John Muir  says  ~  “Nature  will bear the closest inspection.” }

 

 

Now,  it COULD be   (of course)    that I learned more from  the above essay    than you did.     In any case    I find it has had a fairly profound effect on me.

What the essay does  (or, at least  –  what it trying to do)     is to  make the ‘inconceivable’  conceivable.     It   (schematically)   puts forward    three things (of different sizes,  but  the SAME SUBSTANCE)   onto  our mind’s  “table”.     And  only the MIDDLE  one:    (M)   is every-day   and  relatable.      The far  right  one  (W)   is only BARELY relatable.     And the far  left  one  (w)    near-zero  relatable.     So  –

What one is left with  –  to contemplate  –   is only the middle size    and the (right end / very big) size   …   coupled with the belief   that   the middle size (M)    really  IS    the MIDDLE  size:   (that the  factor of increase    that gets you from the  far left: (w)     to the  “middle”:  (M)       is exactly  the  same  factor of increase    that gets you from  the middle      to the  far  right end.

So  –  even though   my  notion  of   “how big  the  Earth’s  hydrosphere  is”    is probably as much  emotional   as it is  cognitive,    still  –  I find I get  something   out  of  contemplating   the comparison of these two sizes.      [&     I can believe   that the same jump  exists   on  the left side of the table      as on the right]

 

And so  –   now,   when I look at  even a very small object  (such as a small crystal)  –   I find   I now apply this  (square root of W  /   the “middle size”)  notion       and am able to “see”   what an  enormous   object  (& structure)    this ‘tiny crystal’  is !

 

And THIS  means     that  ‘Big’   &   ‘Little’    are not  Simple Opposites   in the way we had thought.     They are NOT mutually exclusive.      Even something which  is  “Small”    is  also  Gigantic.

 

When we were very young     we learned:    up & down,    left & right,   black & white,   big & little    and so on.

Now  –  I don’t think  we should say   that  such notions  are “wrong”  exactly.   But surely   it’s okay  to see  that they are (in fact)  “childish”.     Only  “first approximations”.    NOT  the end of the story.

 

In 1916  Don Marquis  began publishing material  (in New York city’s   Evening Sun newspaper)  allegedly written by a cockroach (Archy)  who lived in his apartment.   Archy claimed   that before the last Transmigration of Souls   that   HIS  soul  inhabited the body of a free-verse poet,  and that he was  really    a writer of some renown.    He said   that even though he was barely recognized  here on Earth,  that he had quite (large & enthusiastic) following on Mars,  being able to communicate with his Martian friends / fans  via wireless technology.  (radio).    Well  –  one day one of his fans (on Mars)  asked Archy    what the main Life-Form  on the Earth was like.    And Archy told him   that  ‘the dominant life form here   is a peculiar creature   who is genuinely confused   as to whether his grandfather  was God   or a monkey’.

I would like  (discreetly)   to suggest    that such (mutually exclusive) thinking    is really   a (thoughtless)  hold-over  from early childhood.   [ surely  (for example)  the notions of Creationism  and  Evolution  are NOT  really  Mutually Exclusive.   We are just predisposed toward simplistic ways of thinking. ]     We would LIKE things to be simple:    Right and wrong.   Black and white.   Good and bad.      (YOU know …)

 

As Solzhenitsyn  tells us:        “The battleline between good and evil runs through the heart of every man.”        And Mister Rogers  has tried to teach us:    “The same people  who are good  sometimes     are the  very same people    who are bad  sometimes.”

And  (of course)   one of the problems with grown-ups    is that they tend to think that they are done learning.      But –

I used to hear my grandpa say    –    “When you think you’re green, you’ll ripen.       And  when you think you’re ripe,  you’ll rot.”

 

Life    is a  Great Mystery.             And  we’re still trying to figure it out.