Love it :~)
I have nothing but respect for the greats that came before me, without them I wouldn't be where I am today. I firmly believe a solid foundation is the cornerstone in becoming a chef. By the same token I don't hold much to the notion of there being only one "the" way to do any thing under the culinary sun. Even the classical French chefs of past years don't agree among themselves.
Bechamel, mornay, and hollandaise are three sauces that are perfect examples. Hollandaise/ clarified butter or no?/ melted butter or softened?/ vinegar at the start or to finish?/ etc. etc. etc.
The vast majority of facts, aren't.
At my present employment, I am called upon to make a thickened milk sauce with a scant touch of nutmeg on a fairly regular basis. Due to the popularity of gluten free at the moment, we thicken it with rice flour. When I make it, I start off with melted butter that I stir rice flour into and then cook on low heat for 7 minutes (hesitant to call it roux due to the possibilty of being pulled over to the curb by "the" police.) A younger sous chef asked me why I bother to make a butter/rice flour concoction first because a slurry would work just fine. My reply was that the mouth feel wouldn't be the same without the butter and I feel that using it delivers a closer flavor profile to the way I was originally shown to make the sauce 30+? years ago. I am just glad that I don't have the burden of having to come up with our public description or name for the final sauce because it keeps me from facing liability, lawsuit, or derision issues.
An interview question that I have been known to ask is "What numbers between 1 and 10 when multiplied will give you 21?" the standard answer is 3x7. I then ask " What about 5.25x4?" I don't do this to be a wise ass (although I am), I am looking at the reaction because it gives me a glimpse into how open the mind is.
Some great points here.
For the classifications of the sauce, I think that if you were to make a bechamel sauce, you are making a sauce that is thickened milk flavoured with onions, bay leaves, and cloves. If you thicken it with a rice "roux" what's the difference? The classification calls for a roux but the definition of a roux can change. It doesn't have to be wheat flour, it has to be starch.
Thing is, that's mother sauces. I agree that there are numerous ways to go about making the mother sauces (Sauce aux tomates Is a great example. In Escoffier time it was made with a roux, but today it's agreed that it's not.)
But one thing they are all in agreement in is the garnishes for classical dishes. There's a reason you memorize them, because that standard doesn't change.
As for the numbers question... I like the smart ass aspect of it. A smart ass reply to they answer you gave is that the question is misleading. You said "numbers" but does that imply rational numbers, whole numbers, etc? LOL Would an answer of 2i=21 be correct?
I'm not saying we need a straight jacket or anything. What I am saying is that when you are talking about garnishes for classical dishes, that's where things get sticky.
How you make your mother sauces is another issue altogether. For instance, I've seen a hollandaise thickened that doesn't need butter, but is that a hollandaise?
On the other hand, if you tell me a sauce robert is a brown sauce with mushrooms and ham, with a bit of yellow mustard whisked in, would we agree that it's no longer a Robert Sauce?
Then I guess the question is really, at which point do we change the classification of a classical standards and/or garnish? In the case of the original question, demiglace (which literally means "half glaze") isn't currently a demi by the name status but more of a glace. (glace if I remember correctly is 1/10th)