Social constructs are social constructs

Noah Smith stepped into a bit of a minefield with his "scientific facts are social constructs" thread — making fun of the idea here [tweet seems to be deleted; it was referring to this tweet], attempting to get a handle on the utter philosophical mess that followed here. With the latter tweet, he illustrates that there are many different things "scientific facts are social constructs" could mean. We have no idea of the original context of the statement, except that it was in an anthropology class [0].

Clearly on some level, scientific facts are not social constructs in the sense that they fail to exist or function differently in a different society. My computer and the network it is attached to functions in exactly the way it is supposed to based on scientific facts in order for me to deliver this text to you via http. This is the universe of physics, computer science, and engineering. We are crossing model levels and scales here — from the human to the electron. As Erik Hoel shows, it is entirely possible that you cannot begin to even formulate what you mean by "social construct" and "electric current" at sufficient fidelity simultaneously (one is a description of macro states and the other is a description of micro states).

But this was an anthropology class. In anthropology, the process of science and the social constructs of society (including the process of science) are in a sense at the same level. It is entirely possible for the social process of science to interact with the anthropological states. Think of this as a "quantum uncertainty principle" for social theories. The process of measuring anthropological states depends on the social scientific process measuring it in the metaphorical sense that measuring the position of an electron depends on the momentum of the photon measuring it. It's a good thing to keep in mind.

However, in a sense, we have no possible logical understanding of what is a social construct and what isn't because we have empirical evidence of exactly one human species on one planet. You need a second independent society to even have a chance at observing something that gives you insight as to how it could be different. Is an electron a social construct? Maybe an alien society kind of bypassed the whole "particle" stage and think of electrons instead as spin-1/2 representations of the Poincare group with non-zero rest mass. The whole particle-wave duality and Hydrogen atom orbitals would be seen as a weird socially constructed view of what this alien society views as simply a set of quantum numbers.

But that's the key: we don't have that alien society, so there's no way to know. Let's designate the scientific process by an operator P = Σ |p⟩ ⟨p|. We have one human society state |s⟩, so we can't really know anything about the decomposition of our operator in terms of all possible societies s':

P = Σ Σ ⟨s'|p⟩ |s'⟩ ⟨p|

We have exactly one of those matrix elements ⟨s'|p⟩, i.e. s' = s for ⟨s|p⟩. Saying scientific facts are social constructs is basically an assumption about the entire space spanned by societies |s'⟩ based on its projection in a single dimension.

If you project a circle onto a single dimension, you get a line segment. You can easily say that the line segment could be the projection of some complex shape. It could also be a projection of a circle. Saying scientific facts are social constructs in general is saying that the shape is definitely very complex based on zero information at all, only the possibility that it could be. And yes, that is good to keep in mind. It should be part of Feynman's "leaning over backwards" advice, and has in fact been useful at certain points in history. One of my favorites is the aether. That was a "scientific fact" that was a "social construct": humans thought "waves" traveled in "a medium", and therefore needed a medium for light waves to travel in. This turned out to be unnecessary, and it is possible that someone reading a power point slide that said "scientific facts are social constructs" might have gotten from the aether to special relativity a bit faster [1].

However, the other thing that anthropology tries to do is tease out these social constructs by considering the various human societies on Earth as sufficiently different that they represent a decent sampling of those matrix elements ⟨s|p⟩. And it is true that random projections can yield sufficient information to extract the underlying fundamental signal behind the observations (i.e. the different scientific facts in different sociological bases).

But! All of these societies evolved on Earth from a limited set of human ancestors [2]. Can we really say our measurements of possible human societies are sufficiently diverse to extract information [3] about the invariant scientific truths in all possible societies including alien societies? Do we really have "random projections"? Aren't they going to be correlated?

So effectively we have come to the point where "scientific facts are social constructs" is either vacuous (we can't be sure that alien societies wouldn't have completely different sets of scientific facts) or hubris (you know for certain alien societies that have never been observed have different scientific facts [4]). At best, we have a warning: be aware that you may exhibit biases due to the fact that you are a social being embedded in society. But as a scientist, you're supposed to be listing these anyway. Are anthropologists just now recognizing they are potentially biased humans and in their surprise and horror (like fresh graduate students being told every theory in physics is an effective theory) they over-compensate by fascistically dictating other fields see their light?

Yes, anthropology: 

Anthropologists can affect, and in fact are a part of, the system they're studying. We've been here for awhile. 

xoxo, physics.

Now, can we get back to the search for some useful empirical regularities, and away from the philosophical argy-bargy?

...

Footnotes:

[0] Everyone was listing unpopular opinions the other day and I thought about putting mine up: It is impossible understand even non-mathematical things without understanding math because you have no idea whether or not what you are trying to understand has a mathematical description of which you are unaware. This post represents a bit of that put into practice.

[1] Funny enough, per [0], Einstein's "power point slide" was instead math. His teacher Minkowski showed him how to put space and time into a single spacetime manifold mathematically.

[2] Whether or not evolution itself is a social construct, you still must consider the possibility that evolution could have in fact happened in which case we just turn this definitive absolute statement into a Bayesian probability.

[3] At some point, someone might point out that the math behind these abstract state spaces is itself a social construct and therefore powerless to yield this socially invariant information. However, at that point we've now effectively questioned what knowledge is and whether it exists at all. Which is fine.

[4] I find the fact that you could list "scientific facts are social constructs" as a "scientific fact" (in anthropology) that is itself a social construct to be a bit of delicious irony if not an outright Epimenides paradox.