That seems like a not very persuasive complaint since even professional mathematicians will “epsilon” to mean a very small difference in an informal setting. To use a recent example from discussing a calculus midterm that we were going to make two versions, one of the professors said something like “the midterms will be within epsilon of each other” and no one batted an eye.
Because professional mathematicians understand and depend on the technical usage, there’s little risk of the technical sense becoming diluted by such quasi-humorous, figurative allusions to the technical jargon, which can serve as a means of in-group bonding. When outsiders do it, hover, it’s no longer clearly an allusion to something else, and risks being mistaken for a distinct technical usage in its own right, in addition to losing the slight humor/bonding value.
Another mathematical in-term that has been subject to similar abuse by outsiders is the word “isomorphic”. When a mathematician speaks to a colleague of all the local cafeterias being isomorphic, this is clearly hyperbole—but it’s only clear if one understands the actual meaning and normal context of the word.
From what I’ve seen of cafeterias on large college campuses, it isn’t actually hyperbole to say that “all the local cafeterias are isomorphic”. They’re technically distinct, but under a transformation that preserves all relevant properties, they can all be mapped to each other; they are the same up to isomorphism.
That seems like a not very persuasive complaint since even professional mathematicians will “epsilon” to mean a very small difference in an informal setting. To use a recent example from discussing a calculus midterm that we were going to make two versions, one of the professors said something like “the midterms will be within epsilon of each other” and no one batted an eye.
Because professional mathematicians understand and depend on the technical usage, there’s little risk of the technical sense becoming diluted by such quasi-humorous, figurative allusions to the technical jargon, which can serve as a means of in-group bonding. When outsiders do it, hover, it’s no longer clearly an allusion to something else, and risks being mistaken for a distinct technical usage in its own right, in addition to losing the slight humor/bonding value.
Another mathematical in-term that has been subject to similar abuse by outsiders is the word “isomorphic”. When a mathematician speaks to a colleague of all the local cafeterias being isomorphic, this is clearly hyperbole—but it’s only clear if one understands the actual meaning and normal context of the word.
From what I’ve seen of cafeterias on large college campuses, it isn’t actually hyperbole to say that “all the local cafeterias are isomorphic”. They’re technically distinct, but under a transformation that preserves all relevant properties, they can all be mapped to each other; they are the same up to isomorphism.
Do you have evidence that people are actually misunderstanding what either of these terms mean?