Summa minutiae

“A facility for quotation covers the absence of original thought.” —Lord Peter Wimsey

Testing for 2020

Pellentesque dapibus suscipit ligula. Donec posuere augue in quam. Etiam vel tortor sodales tellus ultricies commodo. Suspendisse potenti. Aenean in sem ac leo mollis blandit. Donec neque quam, dignissim in, mollis nec, sagittis eu, wisi. Phasellus lacus. Etiam laoreet quam sed arcu. Phasellus at dui in ligula mollis ultricies. Integer placerat tristique nisl. Praesent augue. Fusce commodo. Vestibulum convallis, lorem a tempus semper, dui dui euismod elit, vitae placerat urna tortor vitae lacus. Nullam libero mauris, consequat quis, varius et, dictum id, arcu. Mauris mollis tincidunt felis. Aliquam feugiat tellus ut neque. Nulla facilisis, risus a rhoncus fermentum, tellus tellus lacinia purus, et dictum nunc justo sit amet elit.

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Roseate blood

In his Medieval Hymns and Sequences, John Mason Neale identifies roseate as the pale color of the last drainings of life-blood (“as everyone knows”, he says) since though one drop would suffice, Christ shed all.

An 1895 agricultural bulletin from the University of Michigan defines roseate, rosaceous as “rose-red; a pale blood-red”.

From Harry Irving Greene, a popular novelist and short-story writer in the early 1900s, here's another reference associating roseate with blood. It reads like a fictional vignette designed to tickle all the sentimental reflexes in the folks “back home.” It appeared in newspapers in May 1918.

Father: This wonderful letter that I am writing you - a miracle letter. I was hurt, badly, but I am going to get well. It happened like this — you know I am I an not allowed to name place or date.

No Man's Land! We were raiding it by night, three of us — scouting, prowling. It was as dark as the dungeons of inferno, but often they sent up signal shells — roseate, bursting things that bathed all that evil land in a blood-red light. When their glare flared over us we had to stand as we were caught, hand or foot upraised — moveless objects in the red glow until the light snuffed out and all was dark once more.

A cyanotype of Cystoseira fibrosa

anna-atkins.jpg

From Anna Atkins' 1843 "Photographs of British Algae" using cyanotypes (the blueprint process). There's more at https://publicdomainreview.org/collections/cyanotypes-of-british-algae-by-anna-atkins-1843/

The fundamental laws of ordinary algebra

Continuing with George Chrystal's Algebra: An Elementary Text-Book [archive, google], the 1904 Adam & Charles Black edition.

Chrystal's Algebra, chapter 1, section 2.

The operations of algebra are just the consequences of a very small number of fundamental principles found in arithmetic.

Ordinary algebra is simply the general theory of those operations with quantity of which the operations of ordinary abstract arithmetic are a particular case.

The fundamental laws of this algebra are therefore to be sought for in ordinary arithmetic.

However various and complex the operations of arithmetic may seem, it appears on consideration that they are merely the result of the application of a very small number of fundamental principles. To make this plain we return for a little to the very elements of arithmetic

Fear not, O student - there's nothing scary coming up…

Conservation of meaning

So I'm considering going back and working through all the math that I zipped through in school but never deeply understood. Act 1: the start of George Chrystal's Algebra: An Elementary Text-Book, the 1904 Adam & Charles Black edition.

My comments and notes are in quotation blocks, like this.

Chrystal's Algebra, chapter 1, section 1.

The student is already familiar with the distinction between abstract and concrete arithmetic.

I don't have a syllogism handy, but if you run something past me I can probably figure out how to agree with it since that's how this whole textbook idea works.

The former is concerned with those laws of, and operations with, numbers that are independent of the things numbered; the latter is taken up with applications of the former to the numeration of various classes of things.

concrete arithmetic: regards the numeration of actual specific things; application of the laws of number and operations performed on numbers. Use of numbers to count things.

abstract arithmetic: the same laws and operations as they concern numbers themselves. Use of numbers in and of themselves.

It's been a long time since arithmetic and I don't recall that particular distinction, but OK.

In the spectrum of math from "lower" to "higher":

number -> concrete arithmetic -> abstract arithmetic

Confining ourselves for the present to abstract arithmetic, let us consider the following series of equalities :—

\[\begin{align} \frac{2623}{61} + \frac{1023}{3} &= \frac{2623 \times 3 + 1023 \times 61}{61 \times 3} \\ &= \frac{70272}{183}\\ &=384.\\ \end{align}\]

The first step is merely the assertion of the equivalence of two different sets of operations with the same numbers. The second and third steps, though doubtless based on certain simple laws from which also the first is a consequence, nevertheless require for their direct execution the application of certain rules, of a kind to which the name arithmetical is appropriated.

Step 1: we've thrown numbers and operators around in a particular way and then we claim (assert?) that the two piles of rearranged stuff have the same meaning.

Steps 2 and 3: whoa - mysterious rules of the operators were applied to transmogrify these piles of stuff into entirely different things, and then we assert that they all have exactly the same meaning. The visible forms of these things were changed radically, but their meanings were left perfectly untouched.

So we're given a thing, and we want to change it into something easier to understand or easier to work with, but there is a limited menu of possible changes.

The artistry lies in knowing the menu, selecting the right items from it, and using them in just the right way to change the appearance of the thing without changing its meaning. Maybe you could see it as a law of "conservation of meaning" that must be obeyed at every step. If applying a menu item would result in a different meaning, then you can't use it. Unless you're fluent enough to then select another item from the menu that will save the meaning.

We have thus shadowed forth two great branches of the higher mathematics:—- one, algebra, strictly so called, that is, the theory of operation with numbers, or, more generally speaking, with quantities; the other, the higher arithmetic, or theory of numbers. These two sciences are identical as to their fundamental laws, but differ widely in their derived processes. As is usual in elementary text-books, the elements of both will be treated in this work.

Note the dog's bollocks that were commonly used in British typography way back when. For more information:– wikipedia, stackexchange, Nick Martens (who cites hellbox.org).