How big is the head of a pin?September 8, 2014 1:49 PM   Subscribe

When discussing how many "x" can fit on the head of a pin, are we talking about the pointed end or the end that one would push on?

This has bothered me for sometime, but because I was generally only hearing it in the context of fantastical things like "how many angels can fit on the head of a pin" I figured it didn't really matter.

Then watching Cosmos the other day, NdGT mentioned that some large number of some tiny variety of microbes could fit on the head of a pin, and so now I need context and the Internet is just confusing me more.

On the "head means point" side we have:
• Googling the "how many angels" question brings up "how many angels can dance on the point of a needle" as an alternative form of the same question.
• the non-pointy end of pins is varied in size, based on the pin, so how could you even ponder the angels question if you can't agree on the size of area you're talking about?
• The pointy end is much more interesting to think about because (to the naked eye) it vanishes to infinity small.
On the "head means what you push" side we have:
• Why wouldn't you say "point of a pin"? it's like "point of a needle" but with a nice alliterative bonus.
• We hit nails on their heads, and the head is opposite of the point
• This website (first google result for: "how big is the head of a pin") says that "the head of a pin is about 2mm in diameter".
• Because the point of a pin is vanishingly small, maybe it's not very useful as a comparison for scientific purposes?
posted by sparklemotion to Religion & Philosophy (21 answers total) 5 users marked this as a favorite

We hit nails on their heads, and the head is opposite of the point

Bingo. This is all you need.
posted by feral_goldfish at 1:53 PM on September 8, 2014 [17 favorites]

I've always understood the "head of a pin" as the part you push onto. I do not have any references for this, but it seems logical. The pin is like a tiny person standing on its pointy foot, with a tiny head on top.
posted by mumimor at 1:53 PM on September 8, 2014 [1 favorite]

The size of the point of a pin depends how sharp it is. The size of the head is fairly consistent for a given size of pin, and more importantly is far easier to visualize for most people, which is probably why the expression is "head" rather than "point". And yes, head is most definitely the side you push on.
posted by randomnity at 1:54 PM on September 8, 2014 [1 favorite]

If it were the pointy end, how would one determine where the "head" stopped and the needle began, and why say "on" instead of "along"? The part one pushes has a well-defined edge off of which excess angels/microbes might fall.
posted by teremala at 1:56 PM on September 8, 2014

On the "head means point" side we have: Googling the "how many angels" question brings up...

And, that's where you took the wrong turn. I think the best way to think about this is that, like a structurally-similar nail, the head is the part where you force to make it stick into something; NdGT was simply looking for a convenient reference object that was a few square mm in area, and nothing more. I.e., there was not meant to be any comparison or allusion to the "angels dancing on the head of a pin" koan whatsoever, and so you need not square this particular circle.
posted by Joey Buttafoucault at 2:10 PM on September 8, 2014 [1 favorite]

Response by poster: Ok, consensus seems to be heading in the direction of what my gut tells me, but that just leads to more questions.

Given that the Angel question has been posed both as "the head of a pin" and the "point of a needle," were old-timey philosopher types asking two different questions (and expecting to get different answers)? Because I could see a train of thought that could say that an infinite number of angels could fit on the head of a pin, but zero angels could fit on the point of a needle (because singularity).

Again, if you're talking about angels, why even bother with the "head" question when the "point" question is so much more interesting?

If it were the pointy end, how would one determine where the "head" stopped and the needle began

The "head/point" would the surface, however small, on the very top of the needle with the pointy end facing up. If you were "along" the side of the needle at all, you wouldn't be on the point.
posted by sparklemotion at 2:11 PM on September 8, 2014

Given that the Angel question has been posed both as "the head of a pin" and the "point of a needle," were old-timey philosopher types asking two different questions (and expecting to get different answers)?

I've actually never heard the "angels dancing" phrase using "the point of a needle". The only philosophical/religious reference to needles I've ever heard had to do with a camel passing through a needle's eye. So my money's on....they asked about the head of a pin, and someone else got that confused.

And as to why bother with "head" vs. "point" -- actually, I've always heard that discussion being referred to with mockery - as in, it was a useless thing to be arguing about anyway. Kind of like how we always talk about how "MeFites can overthink a plate of beans"; no one's ever done any kind of statistical analysis of how big a plate or what kind of beans, because it's not the plate of beans that's the point, it's our argumentative nature that's the point. Same too here, how it doesn't really matter whether we're figuring out how many angels dance on either the head OR the point of a pin, because it's a question that has no bearing on practical reality anyway.
posted by EmpressCallipygos at 2:17 PM on September 8, 2014 [7 favorites]

Related:
In modern usage, this question also serves as a metaphor for wasting time debating topics of no practical value, or questions whose answers hold no intellectual consequence.
posted by SLC Mom at 2:18 PM on September 8, 2014 [11 favorites]

It means the enlarged top of the pin.

Your first three arguments don't hold water.

1. It's irrelevant that you can find an alternate expression on the Internet. You can find everything on the Internet. If you want to misspell Arkansas as Arkansaw, you can find thousands examples of that misspelling to bolster your case.

2. Your Google searches brought back pushpins and other relatively recent inventions of consumerist culture. Google Books shows that the expression goes back at least to 1898 (and no doubt much further), when consumer goods had more standard sizes.

3. The pointy end isn't more interesting to think about. The fact that it is an undefined area is a distraction from the key point of that expression, which is the futility of trying to quantify a number of amorphous, spiritual beings. If it was the point of the needle, that would be not just futile but silly.
posted by dontjumplarry at 2:19 PM on September 8, 2014 [2 favorites]

Again, if you're talking about angels, why even bother with the "head" question when the "point" question is so much more interesting?

I think you're glossing over the crux of the issue, which is that debating how many angels can dance on the head of a pin is a waste of time. It's not a pursuit with philosophical, theological, or practical import; it's navel gazing.

You are treating it like it is more than a rhetorical device to describe someone wasting their time, which is, in itself, somewhat sublime.
posted by Admiral Haddock at 2:19 PM on September 8, 2014 [4 favorites]

I've always understood it to refer to the pointy end, as the entire purpose of the thought exercise is to think about an area that is almost impossibly small... and yet no matter how small that area is, some number of angels can still dance on it.

If you read the wikipedia page, it cites the earliest uses of the phrase (1667, 1678) to explicitly talk about the point, not the other, wider side.

Even then, however, those citations set up a straw man of supposed unnamed scholastics spending too much time thinking about a truly trivial question. No one actually tried to think about this question.
posted by lewedswiver at 2:20 PM on September 8, 2014

Given that the Angel question has been posed both as "the head of a pin" and the "point of a needle," were old-timey philosopher types asking two different questions (and expecting to get different answers)?

No. The answer would be the same either way: either "a finite number" or "an infinite number." If I'm remembering right, the purpose of the pin question was to spark discussion about whether or not angels have any corporeal existence in any sense. Either some (or none) can fit on the head or point of a pin (if they do take up space in the physical world), or an infinite number can (if they don't).
posted by FAMOUS MONSTER at 2:28 PM on September 8, 2014 [4 favorites]

SLCmom has it.
posted by notned at 2:31 PM on September 8, 2014

As I understand it (and wikipedia disagrees, so I am probably way off-base here, but I like this answer too much not to share it), the question isn't asking whether the number's seven or seventy, it's asking whether the number is finite or infinite. In other words, is matter infinitely divisible (infinite angels, with infinite places to stand), or is there a point below which you can't subdivide any further (one angel one atom)?

"How many angels" has come down to us as "...not a pursuit with philosophical, theological, or practical import [...] navel gazing", but it's actually a sophisticated question about the nature of matter, asked with the tools those thinkers had available to them.
posted by Leon at 2:31 PM on September 8, 2014 [2 favorites]

Debating the meaning of the debating question. We are truly meta.
posted by Leon at 2:32 PM on September 8, 2014 [1 favorite]

"Again, if you're talking about angels, why even bother with the "head" question when the "point" question is so much more interesting?"

THEY WERE ALL DUDES THEY DIDN'T SEW.

No, but seriously, theological writing sometimes goes off in hilariously bizarre directions while trying to express the inexpressible. Luther had this whole strange point about free will that had to do with playing a flute and riding a horse and turning in upon yourself (donut-style, I always pictured) and it gets his point across in context but makes PRETTY MUCH ZERO SENSE if you know things about horses or flutes. Or Erasmus has this whole extended metaphor about small children trying to get an apple, where if you know anything about child development is either impossible or else really mean to small children. Sometimes you're like, "Dude, it is obvious you have not left the monastery in 40 years, even from a vantage point of 8 centuries." You can get the point (ha ha!) without knowing if they're talking about the ball or the point of the pin.
posted by Eyebrows McGee at 2:45 PM on September 8, 2014 [7 favorites]

If you check out pins for sale on Amazon, they're often described by the shape/color of the head, referring to the end you grasp. Clearly you could fit more angels on the decorative flower-head pins, which is why I use them.
posted by Metroid Baby at 2:49 PM on September 8, 2014 [4 favorites]

The "head/point" would the surface, however small, on the very top of the needle with the pointy end facing up.

If your question is "when NdGT says this, what does he mean?", I would say that he's trying to communicate science, not philosophy, and as such almost certainly isn't intending to bring infinitesimals into the discussion. But is there by chance a transcript of how many microbes and which type? We can solve this with math.
posted by teremala at 3:15 PM on September 8, 2014 [1 favorite]

Then watching Cosmos the other day, NdGT mentioned that some large number of some tiny variety of microbes could fit on the head of a pin, and so now I need context and the Internet is just confusing me more.

This is a deliberate reference to the angels thing, and it's basically a sly jab at religion. It highlights the difference between "unknowable" and merely "invisible". "How many angels can dance on the head of a pin" is a famous example of the unanswerable questions that plague religion, where there's no empirical way to answer them, and no practical consequence for the results. Like angels, we can't directly perceive microbes, but NdGT's point is unlike angels, microbes are real, and thus his question has a meaningful, definitive answer. That answer could even have real consequences, since some microbes affect us in many reasonably well understood, well documented, and most importantly, verifiable ways.

He is talking about the non-pointy end, because that is the head. The pointy end doesn't have as well-defined limits, so for the pointy end, the question would basically boil down to "how much of the pin constitutes the tip" to which the answer is again arbitrary and worthless, but more importantly to his point, that is not a question of science, but one of linguistics or philosophy.

Plus, yeah, the word "head" has meaning and does not refer to the sharp point, but to the round thing that vaguely resembles a head.
posted by aubilenon at 3:31 PM on September 8, 2014 [3 favorites]

I assumed the saying referred to the pointy part of a pin, with the implication being that it's already a very tiny space and so discussing whether one or two or a hundred angels could co-exist on it is especially pointless.
posted by clockzero at 3:58 PM on September 8, 2014 [1 favorite]

As the head/point question has been solved (the head is the part that you push on), I thought I would drop this here, courtesy of Terry Pratchett:
Over the years a huge number of theological manhours have been spent debating the famous question: How Many Angels Can Dance on the Head of a Pin?

In order to arrive at an answer, the following facts must be taken into consideration:

Firstly, angels simply don't dance. It's one of the distinguishing characteristics that mark an angel. They may listen appreciatively to the Music of the Spheres, but they don't feel the urge to get down and boogie to it. So, none.

At least, nearly none. Aziraphale had learned to gavotte in a discreet gentlemen's club in Portland Place, in the late 1880s, and while he had initially taken to it like a duck to merchant banking, after a while he had become quite good at it, and was quite put out when, some decades later, the gavotte went out of style for good.

So providing the dance was a gavotte, and providing that he had a suitable partner (also able, for the sake of argument, both to gavotte, and to dance it on the head of a pin), the answer is a straightforward one.
posted by His thoughts were red thoughts at 4:32 PM on September 8, 2014 [7 favorites]

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