Website activity diary 2018

This page details what I've been working on lately, so that you can find recent changes to my site. It's entirely possible that some links on this page shall fail to work, or fail to live up to their descriptions: that just means I haven't checked in (recent changes to) the pages they referred to as recently as I've updated this page. This page omits things separately covered by the thoughts of the moment section of this site, unless I update one after its moment: this page is about on-going development on the rest of this site.

Differentiate polynomials

Explored the gradients of chords to show how an algebraically formulated deriviative matches my latest reformulation of how to do differentiation. Explored several other details (e.g. multinomials, particularly homogenous ones) in support of that.


Began describing one of the tools that shows up repeatedly all over mathematics.

Natural arithmetic
I began examining the consequences of applying general arithmetic to the natural numbers, starting with a look at unique prime factorisation.
Another look at polynomials
Now contrasting their formal treatment, as lists of coefficients under a contrived arithmetic, with their interpretation as functions from a ringlet to itself.
Began describing differentiation
Introducing it in the context of linear spaces, rather than reals, using simplices to generalise chords and provide gradients. I've had this in mind for many years.
Reworked positive ordering
A clarification of earlier work on when arithmetic itself induces order on its values.
Earlier history
2017, 2016, 2011–2015, 2010, 2009, 2008, 2007, 2006.

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