Speed dating in SoCal

I didn’t know about speed dating until I saw Hitch.  Sometime soon after, unbeknownst to me, I found myself in one of those; scooting over (while being stoned silly) from one chair to the next.

Everybody looks serious—on a mission i.e. purpose-driven: wishing one another the love of a lifetime—lasting forever—in less than 3 or 4 or 5 min… (lost track, I been to sooo many; each with its own idiosyncratically-established duration), which for obvious reasons elicited riotous laughter (accidental pun) from me to the point of being escorted out.  As if this is not enough amusement I had to put up with my date chastising me on the way back to my un-enriched studio for not being able to feign seriousness the way she did: it’s not like you inhaled anymore than I did (gist of her complaint).

Any number of things can happen at these speed dating events.  Usually there is a set

W = {w1, w2…}

of some number of girls and then there is another set

M = {m1, m2…}

of guys waiting to get laid.

One possibility—this is good—is that every girl who showed up is an object of desire of some guy in which case we have an arrow pointing to every element in W (from some element in M).  We call such a scenario

f: M -> W

an onto function.  So when somebody tells me that we have an onto function

f: M -> W

I’m being told something about the codomain set W (of the function f; Conceptual Mathematics, page 59).

It can get better: at the end of the exhausting musical chairs every girl (in the codomain set W) finds her Prince Harry and every guy (in the domain set M) finds his Beyoncé in which case we say that that particular pairing

g: M -> W

is an isomorphism.  Befitting the afore-claimed ‘better,’ isomorphisms are more “informative” than onto functions.  When an event manager tells me that her speed dating event resulted in an isomorphism

g: M -> W

I’m being told something about both the codomain set W and the domain set M (of the function g; Conceptual Mathematics, page 39).

I might add (just for fun; please don’t hate me) that it would be interesting if your speed dating service can pull a 1-1 function

h: M -> W

But then there can be some girls (left out in the codomain set W) that no guy (in the domain set M) wants, the event manager complains.  I know (Conceptual Mathematics, page 340 but, from a guy’s perspective, there’s peace: wars often start[ed] out with two guys fighting over one girl (had not Rama and Ravana liked one and the same Sita we wouldn’t have had the absurd war of Ramayana and all the demonization [of Ravana along with many other similar-hued southern brothers and full-figured sistas who arrived on scene after him] that’s been a fixture-in-time since then).

So to sum up:

1-1 function h: M -> W informs us about the domain set M

onto function f: M -> W informs us about the co-domain set W

(which may be one reason for invoking duality in speaking of 1-1 and onto functions)

isomorphism (which is both 1-1 and onto) g: M -> W informs us about both the domain set M and the co-domain set W.

Thanks to all the fun I had making up all this (i didn’t inhale I’m lost now: let me go figure out how to go from here to the isomorphisms in:

A Unity and Identity of two maps

f: A -> C

g: B -> C

with a common codomain object C

is a map

h: C -> D

with the object C as domain

which composes with the two maps f, g to give two isomorphisms

hf: A -> D

hg: B -> D