Did this occur naturally? What’s the source? I suppose that some human error has switched the fonts in some way so that the unlikely characters appeared there, right?

Yes, it occurred naturally. I had a formula with a calligraphic object, and I closed the bracket at the end of the formula, rather than at the end of the object. Everything in the middle also became calligraphic. There are no small caps objects in that font set, instead there are symbols stored in that part of the table. Same with numbers.

If you really twisted your brain around, it might be possible to give a meaning to the altered formula.

The first step would be to interpret the backslash as a set-theoretic complement, and the Xs and Ys as something like models in the sense of model theory, defined by a set of concepts which are meaningful within the model. Thus X \ epsilon might mean “model X without the concept of set-membership”, and so on.

Then, the trace of a product of “models” could conceivably mean something, at some high, category-like level of abstraction. Ultimately, I suppose that we are summing some numerical quantities which abstractly characterize the concatenated models appearing in the trace formula.

The reverse turnstile symbol (T on its side) has a meaning in category theory (though there it normally stands for a dyadic relationship); and I imagine one could come up with some meaning for that superscript, that is also serving as the index of summation. The art of doing it well would be to come up with an interpretation which both has continuity with known uses of the symbols, and which defines a concept that isn’t ridiculously contrived (isn’t something that no-one would ever care about).

on June 13, 2013 at 5:00 amLuboš MotlDid this occur naturally? What’s the source? I suppose that some human error has switched the fonts in some way so that the unlikely characters appeared there, right?

on June 13, 2013 at 4:25 pmdberensteinYes, it occurred naturally. I had a formula with a calligraphic object, and I closed the bracket at the end of the formula, rather than at the end of the object. Everything in the middle also became calligraphic. There are no small caps objects in that font set, instead there are symbols stored in that part of the table. Same with numbers.

on June 15, 2013 at 9:15 amMitchell PorterIf you really twisted your brain around, it might be possible to give a meaning to the altered formula.

The first step would be to interpret the backslash as a set-theoretic complement, and the Xs and Ys as something like models in the sense of model theory, defined by a set of concepts which are meaningful within the model. Thus X \ epsilon might mean “model X without the concept of set-membership”, and so on.

Then, the trace of a product of “models” could conceivably mean something, at some high, category-like level of abstraction. Ultimately, I suppose that we are summing some numerical quantities which abstractly characterize the concatenated models appearing in the trace formula.

The reverse turnstile symbol (T on its side) has a meaning in category theory (though there it normally stands for a dyadic relationship); and I imagine one could come up with some meaning for that superscript, that is also serving as the index of summation. The art of doing it well would be to come up with an interpretation which both has continuity with known uses of the symbols, and which defines a concept that isn’t ridiculously contrived (isn’t something that no-one would ever care about).

on June 18, 2013 at 9:03 pmdberensteinOne could also take Hilbert’s point of view: mathematics is just symbol manipulation where one symbol can substitute for another. 😉