Re: Infinitesimals

On Dec 7, 2:17 pm, Jason Simons <Sim...@xxxxxxxxxxx> wrote:
John Jones <jonescard...@xxxxxxx> wrote innews:309fb09d-d438-40e9-b006-759d325d14bc@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:





On Dec 6, 8:50�am, herbzet <herb...@xxxxxxxxx> wrote:
John Jones wrote:

Infinitesimals - are objects that cannot be observed by any direct
means, but merely talked about... they are not so much a hidden
object but an inaccesible object, yet still supposedly inhabiting
the world of objects.

But I would have to know what makes the infinitesimal object
inaccesible before accepting the idea of one. It is not their size
that makes them inaccesible, for if we should shrink down to their
level we would still not see one or point one out.

We don't need to "shrink down to their size" to observe them.
Suppose I to be an infinitesismal less than any real number but
greater than zero. �Then 100 + I is an infinitesimal, but is
"large" enough to "see".

I guess what you mean is that the difference between 100 and
100 + I is not distinguishable "to the eye".

So the
inaccesibility of infinitesimals refers to an accessibility of an
unknown type. This is a good enough reason to reject the
infinitesimal as an object, or as descriptive of the world of
objects.

I don't think anyone has observed a quark either. �They are a hand
y
mental construct. �It is possible, of course, that there are, in f
act,
objects that meet the description of "quark".

What are the criteria for object-hood?

--
hz

Yes, shrinking down to 100 would mean avoiding the awkwardness of
shrinking down to zero and then trying to work my way up. But if I
have the ability to shrink (an ability borne by some of the Celtic
heroes of old), I could equally shrink to 100+I, but I would have the
same problem. I would still not be able to identify an infinitesimal.
In fact, no sizing variable, like shrinking ability, could get me to
meet an infinitesimal.

So, an infinitesimal is not characterized by size, and if size is
necessarily represented by sequence, then an infinitesimal is NOT in
the sequence. Quarks also, may not be physical objects, if all
physical objects can be sized. If they are not physical objects, then
I am thrown into a fog of my own making if I claim that 'the quark'
physically exists.

I have put myself into circles thinking about infinitesimals for years.
I suspect that 'infinitesimal names numbers' (yeah no different than any
other) that under certain circumstances (which becomes the new problem)
become irrelevant.

Did Newton observe that the distances got so small so quickly that in
one sense the order of magnitude (needs to be defined) difference
becomes unimportant in one sense, but remains important in the other?

In the differential the measurement would be invisible (because our
instrument for viewing would always miss it), but it isn't zero either.
If we change our instrument of measure to be smaller, the difference
would again be an order of magnitude smaller so as to be unmeasruable.

The problem now is to define "order of magnitude."

I don't know if this is helpful or not, just thought I'd add where I've
been on this.- Hide quoted text -

- Show quoted text -

You might want to follow the rest of the discussion on infinitesimals
because some ideas are chucked about there.
.

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