Abstract Algebra, Abstraction, Addition, Algebra, Algebra of Parts, And, Categorical Product, Category, Category Theory, Choice, Concept, Conceptual Mathematics, Conjunction, Disjunction, Element, Exponent, Exponential Law, Exponentiation, Higher Universal Mapping Property, Map, Map Object, Math, Menu, Multiplication, Name, Naming Elements, Object, Or, Part, Product, Product Set, Reality, Reflection, Set, Space, Sum, Theory, Transformation, Universal Mapping Property

# On choosing from a menu

Dear All,

I like choices—lots, Big Lots—but I’m not big on having to choose. Then again not choosing, I am told, is a choice-made (for all intensive purposes), provided it [not-choosing] is on the menu. I can have coffee *or* tea if and only if both coffee *and* tea are on menu. This is when I ceased to think that the owner of the Chinese restaurant advertising

Take out

Dine in

had issues with conjunctions.

Happy Conjunctions!

posina

Lil bird story

Starbucks is—thanks in large part to our Prime Minister’s enlightenment embodied in his recent prophecy (Money doesn’t grow on trees.)—setting shop in India. You have no idea how ecstatic I am—after all these years the trauma of having to smell chai every time I lift a cup of coffee to my lips in north India is going to end. (I thought of blogging to make some new friends, but with all these pungent cartoons it’s beginning to feel a lot like pipe-dream ;-)

In any case, I spend a substantial amount (you pick a metric) of my life at Starbucks watching people. They have lots of hard to pronounce (forget spelling) items on the menu. Many people get their coffee to go in paper cups or yucky plastic. Some join me (not necessarily at my table) in enjoying their coffee while nibbling on stone-sized pastries while reading New York Times or Wall Street Journal exuding an aura of intellectual. So what we have here is a menu M of items and each customer, in addition to choosing items from the menu on the wall, chooses—take out or eat in—from a verbal menu consisting of 2 items. The invariably pleasant person behind the counter somehow keeps track of all the combinatorial explosion barely a feet away from the face. How do you do it, I ask during one of those rare moments when nobody is around. It’s simple, she says.

Let’s say M = {coffee, tea, OJ}. Furthermore, let’s say each order can be to go (0) or eat in (1). The sum total of all the bewildering possibilities boils down to

M^{a + b} = M^{a} x M^{b}

3^{1 + 1} = 3^{1} x 3^{1}

Of course you have to subscribe to the somewhat startling idea of the primacy of AND (x) over OR (+), she added, which had an undesirable effect of sobering me to my senses like a scare out of nowhere.

Having thus returned to ground state, I grudgingly copy a paragraph from the Conceptual Mathematics textbook (page 356).

The fact that disjunction (‘or’) must be explained in terms of conjunction (‘and’) and not in terms of ‘or’ gave pause to many people meeting it for the first time. Indeed, there are often situations in daily life where the transformation from ‘or’ to ‘and’ can be puzzling if we try to explain it. Perhaps the following exercises (Exercises 7 and 8) will help illuminate what is behind such a transformation. The algebra of parts (to which Article VI with Sessions 32 and 33 is a brief introduction) is useful for illuminating relations of actual spaces and transformations as they occur in mathematics. Conversely, the interplay of actual spaces and transformations can help to clarify the more abstract algebra of parts which is its reflection.

From → Note to self

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