There's something about "3"

Perhaps a little numerology. This is an exploration—something I’m trying to figure out, not something I’m proposing.

What is it about “3?”

  • Three points define a plane
  • Three legs make a stable stool
  • At least three data points are needed to perform meaningful statistics
  • Songs should have at least three verses
  • At least three elevation measurements are needed to draw a contour map
  • Thesis, antithesis, synthesis
  • Three dimensions of space
  • Sign, object, interpretant
  • Father, Son, Holy Ghost
  • Chemicals, cells, organisms

I acknowledge this list is impressionistic, idiosyncratic, and personal, but I think there may be a common theme or intuition that connects them. Three in gives a sense of stability, settledness, resolution.

What leads me here is a struggle of sorts to figure out what Charles Peirce was describing when he discussed triadic logic. That’s something that has been discussed on the forum in the past. It started out with his theory of signs with the ideas of sign, object, and interpretant. I won’t go into it in any depth because I don’t get it. Beyond that though, growing out of that I guess, he developed his ideas about a general triadic logic as opposed to our normal dyadic, i.e. two factor, logic.

Peirce is identified as a pragmatist and a colleague of William James, whose ideas I find satisfying and helpful, so it seems like there must be something there. Here’s what Peirce wrote about his triadic system:

Firstness is the mode of being that of which is such as it is, positively and without reference to anything else.

Secondness is the mode of being that which is such as it is, with respect to a second but regardless of any third.

Thirdness is the mode of being that which is such as it is, in bringing a second and third into relation to each other.

This is from the Stanford Encyclopedia of Philosophy’s entry on Peirce:

Merely to say that Peirce was extremely fond of placing things into groups of three, of trichotomies, and of triadic relations, would fail miserably to do justice to the overwhelming obtrusiveness in his philosophy of the number three. Indeed, he made the most fundamental categories of all “things” of any sort whatsoever the categories of “Firstness,” “Secondness,” and “Thirdness,” and he often described “things” as being “firsts” or “seconds” or “thirds.” For example, with regard to the trichotomy “possibility,” “actuality,” and “necessity,” possibility he called a first, actuality he called a second, and necessity he called a third. Again: quality was a first, fact was a second, and habit (or rule or law) was a third. Again: entity was a first, relation was a second, and representation was a third. Again: rheme (by which Peirce meant a relation of arbitrary adicity or arity) was a first, proposition was a second, and argument was a third. The list goes on and on…

…If Peirce had a general technical rationale for his triadism, Peirce scholars have not yet made it abundantly clear what this rationale might be. He seemed to base his triadism on what he called “phaneroscopy,” by which word he meant the mere observation of phenomenal appearances. He regularly commented that the phenomena in the phaneron just do fall into three groups and that they just do display irreducibly triadic relations. He seemed to regard this matter as simply open for verification by direct inspection.

Although there are many examples of phenomena that do seem more or less naturally to divide into three groups, Peirce seems to have been driven by something more than mere examples in his insistence on applying his categories to almost everything imaginable…

…It is difficult to imagine even the most fervently devout of the passionate admirers of Peirce, of which there are many, saying that his account (or, more accurately, his various accounts) of the three universal categories is (or are) absolutely clear and compelling.

As usual in my discussions, soon enough I get around to bringing the Tao Te Ching into the discussion. This is from Verse 42, Paul Lin’s translation.

Tao begets One.
One begets Two.
Two begets Three.
Three begets all things.

This is a verse I’ve wrestled with too. This is what Wang Bi, a Chinese commentator from about 250 CE wrote about it. It’s also translated by Lin.

Myriad things have myriad shapes but return to the One. How can they become One? Because they are from nothingness. From nothingness comes One; this One may be called nothingness. Once it is called “One,” how can it not be described? Having One and describing it, are there not two? Having One and two, then there is three. From non-being to being, the numbers end here. From this point on, nothing flows from Tao.

Therefore regarding the birth of myriad things, I know their master [Tao]. Though with myriad shapes, they blend breaths into one. People have their hearts, different states have different customs, but One is obtained so kings and dukes become their masters. With One as their master, how can it be forsaken? The more One multiplies, the further are the people from it: to be diminished is to be near the One; to be diminished to the utmost is to reach the ultimate. Though it has been called “One,” it adds up to three. Those whose roots are more than One, can they be close to Tao? “To diminish it in order to augment it.” Are these merely words?

I recognize this post is somewhat scattershot, but that just reflects my own thinking on the issue. There is something about “3” that I’ve always felt and that I’m interested in beyond any specific philosophical purpose. Somehow I keep thinking it comes back to the three-legged stool.

Swirls are a 3.

3 is the number I’d attribute to consciousness. I am studying swirling power and consciousness.

If I’m correct there, perhaps that’s why it intrigues you.

I’m not familiar with this. Please expand.

Well consciousness is a kind of ‘play’(as in ‘go’ with a VHS or CD). A type of play that fits in the ‘I’ position, is a swirl, swirling.

Change your disc- change your swirl.

Don’t forget about Valentine Michael Smith!

I understand the reference, but not it’s significance.

Martians are weird about 3.

I’m not sure the last example is actually an example of a triplet, as I believe you can add atoms on the one end and populations on the other.

In human pursuits like literature, poetry, rhetoric, and comedy, it does seem like the number three has a certain draw and pleasing-ness to it when compared to other numbers. As far as the occurrence of threes in nature, I suspect you could be experiencing confirmation bias and failing to notice the repeat occurrence of other numbers, though I’d have to give some thought as to where we see numbers like 2, 7, 10 etc. repeating in nature.

We think that there’s only one way to count, but it’s not true.
One way is 1, 2, some, lots, all. 3 is the minimal quantity of some in this counting, which makes it interesting. If it weren’t for the number of fingers and toes we have, it’s a far more useful number than 10, and only slightly less useful than 1 and 2. I’d suggest actually that the usefulness of a number (in general, outside of specific context) is directly correlated with how far removed it is from 1 on a number scale.

Actually, it’s probably the best example in the list. It’s one we’ve discussed on the forum previously, back when @apokrisis was around. It’s from hierarchy theory. In this case, cells are the focus level, chemicals are the impetus, and organisms are the constraints. It’s an example, at least according to @akokrisis, of a Percian triad.

I don’t think so. I’ll stick with my intuition that there is something special.

7 is the true enigma. It’s a questionable number. It even teaches us a lesson about the number 3.

I think 1-10 are equally ‘something’- which is why base 10 works.

Can you explain? ***

Apophenia? Pareidolia? Someone who knows math should be able to adjudicate on the matter. I’m not much of a book person but from what I’ve set eyes on, no such thing - 3-ness - has been reported. The golden ratio (\varphi = 1.618033989...) however, now that’s a real pattern: nautilus, sunflower seeds, pine cones, multiplying lagomorphs, the pyramid of Giza, etc.

A trivial mathematical fact is \lfloor \pi \rfloor = 3 = \lceil e \rceil. People are purposeful animals.

I don’t think it’s really a math question. It more likely says something about human cognition.

That’s not true. I gave two examples in my OP.

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The ‘something-ness’ of 1-10, I think, is a more proper topic suited for serious discussion.

When counting, we need to use the number 3 more often than the number 10 for two reasons.

First and most obviously, we need to account for 3 when we count to 10, but not vice versa. We can simply count to 3 and stop.

Secondly, often it is sufficient to refer to some generalized quantity like “many”. While I don’t think this is a logical necessity, I think it happens to be the case that we to need to be specific with smaller quantities more frequently than larger ones.

To suggest the something-ness of ‘3’ is less or more than all 1-10, I propose, is wrong. Different- maybe.

I argue there is equality between the something-ness of 1-10.

What 3 belongs to, is likely equal to what 10 belongs to.

On Topic: what kind of things, in a single sentence answer, does 3 belong to?

I don’t understand the question.

In your original post, you claimed 3 has the following relationships:

  • Three points define a plane
  • Three legs make a stable stool
  • At least three data points are needed to perform meaningful statistics
  • Songs should have at least three verses
  • At least three elevation measurements are needed to draw a contour map
  • Thesis, antithesis, synthesis
  • Three dimensions of space
  • Sign, object, interpretant
  • Father, Son, Holy Ghost
  • Chemicals, cells, organisms

Is there a single sentence description you can give to categorize these things(under the something-ness of the number 3)?.

That’s sort of the purpose for this discussion—to characterize the phenomena I’m describing.