Disturbingly delightful

TIME

In Indo-European languages “time” is not just an abstract one-dimensional continuum; the abstract time is a dialectical negation of the idea of time as the rich environment of external conditions that may influence us, but which we can influence only negligibly… the whole tempestuous march of events (e.g. these blog-posts)  over which the reader (and, for that matter, this author has little control… something a mere smooth line (often used to think about time) cannot be or do.

ORIGIN

There could be no science or technology without something like this ‘origin’:

All the laws (actions of time on states) constitute an infinite-dimensional affine space which is not a vector space, but the specification of the inertial law (“which would be if there were no forces”, as Newton put it) provides an origin in this space.  It is the specification of the inertial law as a zero in the affine space of all laws which permits the vectorial addition of individual simplified laws (or rather of their corresponding forces; we define a specific force to be the difference between the actual law and the inertial law, and the forces are added vectorially).

Dialogues Concerning Two New Sciences

Having thus made contact with dizzying sensibility (it is not that sensibility is dizzying but the dearth of sense in the ivory-clad detritus [aka academia] entrusted with education is what makes encounters with sense and sensibility scary, threatening, politically-incorrect, offending-the-sentiments…) let us now touch the ground—one rock-solid constancy that’s always there to embrace your foot every time you step on it.  Well, it’s not the only one; there are many constants… I’ll return with few definitions in a min., in the meantime here’s Bob for your auditory pleasure:

times are a-changin

CONSTANT

There are things out-there

A = {table, chair, beer bottle, money…}

and then there is a constant

c: B -> A

enabling us to speak of our universal love – of money as a constant map with

B = {me, you…}

and with arrows from each one of us in B—all pointing (invariably) to the ‘money’ in A.

Definition: A map that can be factored through 1 is called a constant map.

–Conceptual Mathematics, page 71

 

In terms of the above definition, we say the map

c: A -> B

where A = {you, me} and B = {table, chair, money} with

c (you) = money

c (me) = money

is a constant map because the map c: A -> B can be factored through the singleton set

1 = {money}

as follows:

A –c–> B = A –r–> 1 –s–> B

i.e.

c = sr (read as ‘s after r’)

where

r: A -> 1

is taking both ‘you’ and ‘me’ (in A) to the ‘money’ in 1

and

s: 1 -> B

is taking the ‘money’ in 1 to the ‘money’ in B.

 

Moving along, given a bunch of people that we can readily think of such as

P = {Tom, Dick, Harry}

we can, equally readily, think of a function

f: P -> B

assigning to each person in P her / his significant other in B (the set of people in, say, this world).  We can, once we get to B from P via this map f (of ‘significant other’), go to A via our earlier constant map c (of ‘universal love of money’) as in

P –f–> B –c–> A

Stated succinctly

cf = g (read ‘cf’ as ‘c after f’)

with g: P -> A, which simply says that all three (Tom, Dick, and Harry) love money just as you suspected.  What’s worth noting is that this ‘love of money’ is pretty much all that we need to satisfy

cf = g

and that ‘significant other’ barely matters in that they all can go out with any one in B they like, which occasions another definition.

Definition 10.2: In a category (not necessarily a monoid), the notion of constant map c: B -> A can be defined as follows: for every object P there is a map g: P -> A such that for all f: P -> B, cf = g.

–Sets for Mathematics, page 168

I’m still debating whether to vent on economists (I have some choice words for them) in the guise of talking about constants in monoids (Conceptual Mathematics, page 366)… see you as soon as I settle that inner-conflict

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