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On stating the obvious (Coseparator)

September 26, 2012

Dear All,

I weigh 100 kg.

My height is 5ft.

I am 50 yrs old.

One question that readily comes to mind: is it true?  Before we burden ourselves with reality-check, let’s look at what’s being said:

I weigh 100 kg.

What does it mean?  Not much really, but if you insist:

My weight is 100 kg.

or

100 kg is how much I weigh.

That’s pretty much all that there is to the statement:

I weigh 100 kg.

Well, there’s more.  The trouble is that it’s all too obvious; it hardly needs to be stated explicitly and hence rarely noted and as a result of which not easy to readily recognize.

Imagine you are looking at me standing on one of those quarter-a-reading weighing machines in the mall.  What you see is ‘me’ looking at an arrow pointing to ‘100 kg.’ Pictorially,

me -> 100 kg

It would be a more closer approximation to reality if the arrow were vertical with ‘me’ at the bottom and weight ‘100 kg’ at the top of the arrow, but [until I figure out how to draw arrows here] fortunately, “like children, I can think things so hard I can see them”.

The situation approximated by

me -> 100 kg

can be thought of as a function weight assigning to me, the only element of the domain set, 100 kg, the only element of the codomain set of the function

weight: me -> 100 kg

What about the ‘obvious’ you mentioned?  Well, I am on my way.

If you bring back the image of me looking at my weight, you notice that there are other weights surrounding my weight 100 kg, which poses no problem in terms of capturing the scenario in terms of functions.  All we have to do is restate the function weight as that which assigns 100 kg of the codomain to the ‘me’ of domain as earlier, but now the codomain has elements other than 100 kg, to keep things simple, let’s say 200 kg.

weight: {me} -> {100 kg, 200 kg}

We need to see that which we don’t see, in order to see the obvious, when we look at me looking at my weight.  One thing we are not seeing is me looking at one arrow pointing to 100 kg and another arrow pointing to 200 kg.  Yes Virginia, there is superposition, but please don’t go quantum on me: not-now & not-here.  Unbeknownst to us, our good friend function took good care of this; for, by definition, function is single-valued, which comports well with physics in the sense that the property weight is single-valued.

weight (me) = 100 kg

or

weight (me) = 200 kg

but not

weight (me) = 100 kg & 200 kg

Let’s sum-up: Things like me have properties like weight to which a value like 100 kg is assigned.

Now let’s switch gears.

If you promise me not to go mystic; we can become different, but first we need to be same.

How do we go about the business of figuring out we (you & me) are different?  Well, going by what you just said, we must be same.

Same what?

Different where?

I weigh 100 kg.

You weigh 100 lb.

Same property weight.

Different values of the property weight at you vs. me.

weight: {you, me} -> {100 kg, 100 lb}

Now, in the above, we defined the function weight with {you, me} as domain set and {100 kg, 100 lb} as codomain set, with the element ‘you’ assigned the value of ‘100 lb’ and with ‘me’ assigned the value of ’100 kg’ as spelled-out below:

weight (you) = 100 lb

weight (me) = 100 kg

To tell the truth we are least interested in how much you weigh or how much I weigh; what we are interested in is ‘how do we tell us (you, me) apart?’

To make our life easy, let’s say both of us have just one property i.e. weight.  We can further imagine being in a black-box and furthermore imagine being pulled-out, one at a time, and placed on a weighing machine and placed back in the box after noting the weight.  One way this mysterious being can fail to realize that there are two people in the box is if we both weigh the same; if the function takes the same value at both ‘you’ and ‘me’: if there is only one element in the codomain of the function weight.  In other words, if both of us weigh the same, then, based on that measurement, our mysterious dude pulling us out of and placing us back in the black-box after weighing might mistakenly think that there is only one person in the black-box.

Thus in order to distinguish elements of a domain set such as {you, me}, we need a codomain of at least two elements (a property such as weight with at least two values such as 100 kg, 100 lb).

This is pretty much all I have as a motivation for our study of Coseparator.

Happy Thursday!

Thank you,

posina

P.S. Yes, VIRGINIA, there is a Santa Claus.  He exists as certainly as love and generosity and devotion exist, and you know that they abound and give to your life its highest beauty and joy.  Alas! how dreary would be the world if there were no Santa Claus.  It would be as dreary as if there were no VIRGINIAS.  There would be no childlike faith then, no poetry, no romance to make tolerable this existence.  We should have no enjoyment, except in sense and sight.  The eternal light with which childhood fills the world would be extinguished.

You may tear apart the baby’s rattle and see what makes the noise inside, but there is a veil covering the unseen world which not the strongest man, nor even the united strength of all the strongest men that ever lived, could tear apart.  Only faith, fancy, poetry, love, romance, can push aside that curtain and view and picture the supernal beauty and glory beyond.  Is it all real?  Ah, VIRGINIA, in all this world there is nothing else real and abiding.

Francis Pharcellus Church

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