Why does everyone disagree with you

I've solved this problem over a cup of tea.

If the point of a pin is of zero area then it ceases to exist as an object in itself. Therefore, no number of angels could dance upon it, even if these angels themselves occupied zero area - in which case they'd also cease to exist.

On the other hand, any number of angels could dance upon the head of a pin, given the right relative scale between the two.

Edited By blowlamp on 29/01/2020 11:21:36

To introduce an engineering slant to the needle's point discussion, when I was a new apprentice three of us were given a project to design and build a balancing machine for car wheels. We decided to go for a cone arrangement balanced on a point, with a spirit bubble to indicate level.

Our instructor told us that it couldn't possibly work because the point, having zero area, would be subject to infinite force which would destroy it. We, being spotty yoofs but lately out of school, couldn't counter his arguments but built it anyway, and it worked as well as any first year apprentice project does.

By the way, Steve, if you're still reading this thread which you started, although it has wandered from your original subject, it is a model of respectful discussion with a modicum of erudite teasing. In my experience this is something this forum does extremely well.

George B.

Well, at least I stirred that Hornet's nest without getting stung too badly! (This time! )

Howard

OK, I'll bite. Some little while ago there was a greek who postulated that matter was not infinitely subdivisible, which at some later date became adopted as one of the founding tenets of physics, namely that all matter is composed of atoms. Needles are thus a pile of atoms (or sometimes molecules) and so the sharpest point on any given pin has the limiting dimensions of the atomic radius of it's particular atomic constituants. The point of the pin thus has a non zero area. The minimum area pin should be composed of carbon (diamond) with an atomic radius of 60 picometers or 0.6 angstroms if you prefer. One could conceive of a pin composed of solid hydrogen which would bring the radius down to 25pm or 0.25 angstroms.

Regarding the angels there are two possibilities. (Ignoring the 3rd case of the non-existance of angels making asking the original question void)

1. Angels are non-matterial entities and are not constrained by atomic dimensions in which case no comment can be offered.

2. Angels are material beings. In which case the smallest form they can take would be a single atom which would not sensibly define them as angels (unless all atoms are angels) and would pose the question what the heck de we mean by dancing. In which case we come up with the answer of one or none.

As someone once said ' ask a silly question' and sometime you get a reasonable answer which is of no help whatsoever.

;0)

Martin

Talking of pins, in a previous employment we made (I say made but two specialist subcontractors were used) pins that had flattened points less than 1um ) 0.001mm in diameter and split down the center like a quill pen. The run-out was <2 um (from memory) and they were supplied as sets with the lengths matched to much less than 1um. The material was tungsten carbide but even so just touching the point was enough to damage them. They were very expensive. Shown as item 21 in this patent that gives an idea of the application.

**LINK**

The pins weren't patented, to do that would have revealed how we made them.

Robert G8RPI

I'm not sure. If an atom has a radius then it's presumably that of the outermost electron shell. If the pointy thing's point comes down to a single atom, then the point must be the point furthest from the point (or head) at t'other end, at the surface of the electron shell that's also furthest from point at t'other end, ie. back to dimensionless point upon a sphere.

Or do needles have flats on the end?

No wonder religion's so contentious.

Robert, how many could sit on your flatted carbide points? Would there be room for more if the points weren't divided, or would some of them fall down the crevasse?

Edited By Mick B1 on 29/01/2020 12:54:10

Well I am following it , albeit dumfounded.

Steve.

This is how discoveries are made!

Edited By blowlamp on 29/01/2020 14:36:43

Possibly the thread is this long and erudite because some of us have too much time on our hands, certainly me.

And that should generate a disagreement!

Howard

Well, (Baby), it's cold outside; I keep getting bored with genealogical research (I find myself going round in circles); most of the goggle box is utter rubbish, indeed I can't even be bothered looking; so what else am I to do? Mind you, my standard of erudition is pretty poor.

Peter G. Shaw,

(who failed English Language, English Literature and French, and dropped aLtin after two years. Which allows me to claim that I have failed anything and everything to do with languages that I have ever attempted.)

.

Great post, Martin

The accepted wisdom is that Angels are non-corporeal, and therefore do not inhabit a dimensional space. [*]

As such: The original question that worried Aquinas is not valid for any ‘real world’ interpretation of a point ... but only for the Euclidean version.

It should now be obvious why the ‘needle’s/needless point’ pun was so clever, and why reference to the head of a pin is crass.

MichaelG.
.

[*] Bazyle’s cuppa got him very near.

.

Edit: It’s getting colder ... so here is Euclid’s succinct definition of a point:

https://mathcs.clarku.edu/~djoyce/java/elements/bookI/defI1.html

Edited By Michael Gilligan on 29/01/2020 16:20:03

Exactly right.. And whether the "point" individual medieval theologians had in mind when they wrangled over this question [assuming we can accept they did] was the real-world point or the geometrical one makes a huge difference to the parameters of the question they were trying fruitlessly to solve.

σημεῖόν ἐστιν, οὗ μέρος οὐθέν - literally [the bit outside the brackets]: "a point is [a thing] of which [there is] part no."

What those medieval theologians needed was a workshop each, then *they* could have had the debates about HSS and carbide, Myford and Boxford, etc and saved us all the bother

Well, 'tain't really Euclid's definition, is it, but David E. Joyce's interpretation of various others' interpretation of it?

Looks to me unfairly insulting to Euclid - 'primitive' definitions and all that. You gotta remember he wasn't standing on shoulders of giants like wot we are today - Euclid's amongst them. He had to work this stuff out from pretty much zilch, and no angels to help him either - they weren't invented till later; and of the gods and goddesses only Athene knew anything about anything, and she was too busy intervening in other affairs most of the time.

.

Please see Bill Phinn’s post

I have no Greek, so must rely upon translations supplied by others.

... but the ones I have seen are pretty consistent.

I would be happy to see your offering.

MichaelG.

.

P.S. ... Try copying Bill’s Greek text into a Google search box

Edited By Michael Gilligan on 29/01/2020 17:22:25

Euclid's genius was his conception of a useful entity# that doesn't exist! He invented the point as 'that which has no part' - meaning something with a location, but no width, breadth or height. Particularly clever because location is also difficult to imagine, because it can only be defined in terms of a reference point. It's conceptually recursive, ie the whole notion disappears up it's own fundament!

Like points, infinity, and the square root of -1, zero doesn't exist in the real world either! It should be complete nonsense. Amazing that all these ideas are so incredibly useful. Unlike angels...

Dave

# Entity is a posh word. It means thingy.

Now that all points are covered, I'm more concerned I've just remembered that angels are men.

So whereas I was considering the idea of Legs & Co frolicking aboot on a pin, I now see an all male dance troupe such as the Chippendales - only with wings.

Thank you for that suggestion MichaelG, a fruitful result.
DaveD

Similar rubbish like" if a tree falls in the forest and nobody hears it, doe's it make any sound?, or something like that. Argument for arguments sake.

People often disagree with me when I'm wrong, and sometimes when I'm right.

I reckon you did the turning on a Myford. The split down the centre was done with a junior hacksaw and - here's the secret - you used Trefolex on the blade.

George B.