You can watch a bird fly by and not even hear the stuff gurgling in its stomach. How can you be so dead?
— R. A. Lafferty, Through Other Eyes
In modern usage, a shibboleth is a custom, tradition or speech pattern that can be used to distinguish one group of people from another.
The literal meaning of the original Hebrew word shibbólet is an ear of corn. However, in about 1200 BCE, the word was used by the victorious Gileadites to identify the defeated Ephraimites as they attempted to cross the river Jordan. The Ephraimites could not pronounce the “sh” sound and thus said “sibboleth” instead of “shibboleth”.
As the King James Bible puts it:
And the Gileadites took the passages of Jordan before the Ephraimites: and it was so, that when those Ephraimites which were escaped said, Let me go over; that the men of Gilead said unto him, Art thou an Ephraimite? If he said, Nay; Then said they unto him, Say now Shibboleth: and he said Sibboleth: for he could not frame to pronounce it right.
The same story is featured in the irresistible (but slightly weird) Brick Testament through the more prosaic medium of Lego:
Sadly, the story did not end well for the Ephraimites:
Then they took him, and slew him at the passages of Jordan: and there fell at that time of the Ephraimites forty and two thousand.
This leads us to Corinne’s Shibboleth: a question which, according to Dray and Manogoue 2002, can help us separate physicists from mathematicians, but with fewer deleterious effects for both parties than the original shibboleth.
Mathematicians answer mainly B. Physicists answer mainly A.
This is because (according to Dray and Manogoue) mathematicians “view functions as maps, taking a given input to a prescribed output. The symbols are just placeholders, with no significance.” However, physicists “view functions as physical quantities. T is the temperature here; it’s a function of location, not of any arbitrary labels used to describe the location.”
Redish and Kuo 2015 comment further on this
[P]hysicists tend to answer that T(r,θ)=kr2 because they interpret x2+ y2 physically as the square of the distance from the origin. If r and θ are the polar coordinates corresponding to the rectangular coordinates x and y, the physicists’ answer yields the same value for the temperature at the same physical point in both representations. In other words, physicists assign meaning to the variables x, y, r, and θ — the geometry of the physical situation relating the variables to one another.
Mathematicians, on the other hand, may regard x, y, r, and θ as dummy variables denoting two arbitrary independent variables. The variables (r, θ) or (x, y) do not have any meaning constraining their relationship.
I agree with the argument put forward by Redish and Kuo that the foundation for understanding Physics is embodied cognition; in other words, that meaning is grounded in our physical experience.
Equations are not always enough. To use R. A Lafferty’s picturesque phraseology, ideally physicists should be able to hear “the stuff gurgling” in the stomach of the universe as it flies by….
Dray, T. & Manogoue, C. (2002). Vector calculus bridge project website, http://www.math.oregonstate.edu/bridge/ideas/functions
Redish, E. F., & Kuo, E. (2015). Language of physics, language of math: Disciplinary culture and dynamic epistemology. Science & Education, 24(5-6), 561-590.