How do you represent what can’t be represented? (Painfully inadequate metaphors, duh.)
Then, the Symbolic Real.
It’s simply, for example, scientific discourse, scientific formulas, like quantum physics. Why is this Real? For a simple reason: the minimum definition of the Real, for Lacan, is that which resists symbolization, inclusion into our universe of meaning. And isn’t that precisely which happens for example with quantum physics? What is quantum physics? Formulas which work — experimentally confirmed and so on and so on — but we cannot translate them into our daily experience of ordinary reality. As we all know, this is what is so traumatic about quantum physics. We literally cannot understand it. Not in the sense that we, common people, cannot understand it, only a couple of scientists can — even they cannot. In what sense? In the sense that it just works, but if you tried to build a consistent ontology out of it, again, you get meaningless results. You get time running backwards, you get parallel universes, or whatever. In other words you get things which simply are meaningless with regard to our ordinary notion of reality. So this would be Symbolic Real. Symbolic, obviously it is Symbolic: formulas, pure signifiers. They function, it’s a functioning machine, but, meaningless. We cannot make any sense out of it. We cannot relate it to our experience. Which is why we try so desperately to do it, which is why we try to invent metaphors to imagine quantum universe. But, it cannot be done.
— Slavoj Žižek The Reality of the Virtual (2004) (my transcription)
(awkwardly writing formulas on the board)
Okay. So. This part is exciting. So. Am I right? So, okay. So, if that’s that, then we can do this. And that’s Shrodinger’s paradox, right? Is the cat dead? Or is the cat… not dead?
(Shortly thereafter, in Larry’s office.)
So, uh, what can I do for you?
Uh, Doctor Gopnik. I believe the results of the physic midterm were unjust.
Uh huh. How so?
I received unsatisfactory grade. In fact, ‘F,’ the failing grade.
Uh, yes. You failed the midterm. That’s accurate.
Yes, but that is not just. I was unaware to be examined on the mathematics.
Well, you can’t do physics without mathematics, really, can you?
If I received a failing grade, I lose my scholarship. And I feel shame! I understand the physics! I understand the dead cat!
But y-you can’t really understand the physics without understanding the math. The math tells how it really works. That’s the real thing. The stories I give in class are just illustrative. They’re like fables, say, to help give you a picture. I mean… even I don’t understand the dead cat. The math is how it really works.
Very difficult. Very difficult.
— A Serious Man (2009) (my transcription)
Thus, an algebraic formula is an icon [i.e. a type of sign which shares some similar property with its object], rendered such by the rules of commutation, association, and distribution of the symbols. It may seem at first glance that it is an arbitrary classification to call an algebraic expression an icon; that it might as well, or better, be regarded as a compound conventional sign. But it is not so. For a great distinguishing property of the icon is that by the direct observation of it other truths concerning its object can be discovered than those which suffice to determine its construction. [par. 279]
Many diagrams [i.e. the second type of “hypoicon”] resemble their objects not at all in looks; it is only in respect to the relations of their parts that their likeness consists. [par. 282]
— Charles Sanders Peirce, Collected Papers Vol. 2