How many grains of sand?

[HRM Resident]

If you remove a single grain from a pile of sand, it
remains a pile. At what point does it stop being a pile
of sand?

--
HRM Resident

[James Warren]

On 2024-01-19 8:46 p.m., HRM Resident wrote:
> If you remove a single grain from a pile of sand, it
> remains a pile. At what point does it stop being a pile
> of sand?
>

When you remove the last grain.

[lucr...@florence.it]

I'd have thought second to last :)

[HRM Resident]

So 1 or 2 grains of sand constitute a pile?

--
HRM Resident

[James Warren]

Yes, a small pile. 1 might be a degenerate pile.

If you wish to define a pile you will have your answer.

[HRM Resident]

James Warren <jwwar...@gmail.com> writes:
>
>> So 1 or 2 grains of sand constitute a pile?
>>
>
> Yes, a small pile. 1 might be a degenerate pile.
>
> If you wish to define a pile you will have your answer.
>

You provide no context. In a construction site, a few
grains might never be considered a pile, whereas in a precision
laboratory, even a small number might.

I don't think it's possible to nail down a definition of a
pile. What you are doing is akin to asking me to explain when a
cup of coffee becomes too diluted to be considered coffee.

Or were you thinking of a pile that requires Preparation H
to no longer be a pile?

--
HRM Resident

[axemen99]

David Joyce
Professor of Mathematics and Computer Science at Clark University

Science replaces vague terms by precise ones. This has been going on
since the Greek mathematicians formalized geometry about the same time
as Eubulides proposed the sorties paradox.

Eubulides’ paradox argued that a single grain of sand isn’t a heap and
adding a single grain won’t change a nonheap into a heap, yet there are
heaps of sand.

One can simply say that a single grain of sand by itself is a one-grain
heap of sand, and the paradox goes away. Alternatively, you could define
a single grain of sand as a nonheap, but define two grains of sand as a
two-grain heap.

Which definition, whether it be one of the two above or some other
definition, depends on the application in mind and the elegance of the
resulting language. If you’re investigating how heaps of sand collapse,
you might require at least two sand grains with one atop another, since
one by itself can’t collapse. On the other hand, if you’re thinking of a
heap of sand being much the same as a set of sand grains, you might
require only one. That could make a more elegant theory: given a pile of
sand, if you remove one grain of sand at a time, it remains a pile of
sand until there is no sand left.

There are other solutions to this question that are more complicated.
You could change your logic. Deny the law of the excluded middle. Use
fuzzy logic. Or you could keep to classical logic but make “heapiness” a
function with a numerical value rather than a predicate.

https://www.quora.com/If-you-keep-removing-a-grain-of-sand-from-a-pile-till-what-point-does-it-remain-a-pile

(I did not do well in my Computational Logic in my younger days.)

[James Warren]

A pile on a construction site is a pile to some but not necessarily to
all. It is subjective.

[James Warren]

Well said! :)

[James Warren]

On 2024-01-20 9:43 a.m., HRM Resident wrote:

[HRM Resident]

James Warren <jwwar...@gmail.com> writes:
>
> A pile on a construction site is a pile to some but not necessarily to
> all. It is subjective.
>

So you don't know. Why not say so? I say "I don't know" often,
when I do not know. Perhaps you should look up to me as a role model.

--
HRM Resident

[James Warren]

I don't know because it is not well defined. I offered that any number
of grains greater than zero is a pile. That is my definition. Yours?

[HRM Resident]

James Warren <jwwar...@gmail.com> writes:
>
> I don't know because it is not well defined.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

That is the right answer. Picking any number from 0 to infinity is
just an opinion. There is no point debating opinions when we both say
we don't know.

--
HRM Resident

[lucr...@florence.it]

On Sat, 20 Jan 2024 08:53:37 -0500, axemen99 <axem...@gmail.com>
wrote:

Yabbut, now we have google lol

[Mike Spencer]

1. Start with a grain in your prospective "pile".

2. Measure the angle of repose.

3. Add one grain to the "pile".

4. Go to 2.

We expect the angle of repose measurements to converge. When repeated
cycles through 2.-3.-4. produce the same value at whatever degree of
precision you're using, the size of the "pile" that produced the first
convergent value is the minimum size of a pile.



--
Mike Spencer Nova Scotia, Canada

[HRM Resident]

Mike Spencer <m...@bogus.nodomain.nowhere> wrote:
>
> 1. Start with a grain in your prospective "pile".
>
> 2. Measure the angle of repose.
>
> 3. Add one grain to the "pile".
>
> 4. Go to 2.
>
> We expect the angle of repose measurements to converge. When repeated
> cycles through 2.-3.-4. produce the same value at whatever degree of
> precision you're using, the size of the "pile" that produced the first
> convergent value is the minimum size of a pile.
>

This offers a blend of scientific measurement and philosophical
inquiry. It provides a novel way to tackle the question, turning it into a
scientific experiment. This offers a blend of scientific measurement and
philosophical
inquiry. It provides a neat way to tackle the question
by turning it into a scientific experiment.


--
HRM Resident

[James Warren]

This value will not be the same for every pile. It will have a Gaussian
type of distribution. The mean will be the mean pile size, not THE pile
size.

[James Warren]

Not an opinion, but an operational definition.