Lemmas

A lot of my blog posts seem to be about cryptography, or at least mention issues related to it, and I am aware that this may make my posts harder to understand. I am also aware that there do not appear to be any helpful introductions to cryptography out there, or rather none which is accessible to the non-expert but still gives a sense of the underlying mathematics. In my mind I have often imagined that I could write such an introduction, and recently I have been motivated to do so after discussion with a school-age relative who said “Cryptography sounds really interesting”. She may not think that way after she’s read all this, but I hope to at least convince myself that a relatively concise explanation of cryptography, from the ground up, is possible. As cryptography is a rather large field, though, I will only cover RSA public key cryptography.

Since my liturgical one-liner 2 years ago, I have not read much discussion of the connections between the worlds of Free software and religion. For instance, both these worlds have a concept of a chain of trust and the concept of forking / schism. A chain of trust in the software world is based on public key cryptography, allowing one developer to sign the public key of another developer, who can then sign a piece of software, whereas in the religious world there are chains of reincarnation or succession. Similarly, forks can arise in software projects when there are two or more groups with differing visions for the future of a project, and schisms can happen within religions when groups disagree on matters of doctrine. The purpose of this blog post, though, is to prove (or at least put forward some interesting reasoning in support of) a lemma, which is that the “true” Christian Church is continuous with regards to two chains, starting from Christ: a chain of apostolic succession and a chain of communion (which follows the line of doctrinal accuracy in the event of schism).

Yes, I have a new mobile phone. The word “new” is redundant, however, as it is the only mobile phone I own, or have ever owned. To give a full record, I should mention the times I borrowed an old family mobile while away at university, but as I didn’t use it between terms, and didn’t pay the bill on it, and didn’t carry it around with me, I don’t think that counts.

I suppose this raises the obvious question of “Why not earlier?” or “Why now?”. Well, to some extent, the longer you go without a mobile, the easier it is, but those occasional moments where owning a phone would prevent one from having to wait around somewhere, or would enable one to do the polite thing of passing on useful information, start to add up. The more general principle, however, is that, when faced with accelerating change, with technology being out of date before you even get it home, the most sensible policy I have for making buying decisions is:

“Decide what the perfect form of this product is, then wait for it to exist.”

Optionally one can add:

“Then wait for the price to go down.”

which is an almost inevitable occurence. There is also a corollary to this:

“Then when you get it, keep telling yourself you don’t need anything else.”

Motivation

We are currently at a critical stage in the development of computer technology, and our choices now affect the sort of world we are going to live in. People are having to make choices about products and services, and often the information they need to make informed choices is not widely available. Over the course of writing this blog I have seen many examples of people making these choices, some poorly, some wisely, in the news and in real life, and have been at a loss for a complete and hopefully compelling commentary on the issues involved. The following, then, is my attempt at such a piece, which should also serve as a lemma for future posts I have in mind.

It’s been a while since I contributed to this thing, but I haven’t run out of things to say. The main reasons for the delay is waiting to hear back from an email and talk to my hosting admin to get a setting or two changed. For that reason I thought it was time for another Lemma post, where I explain something which I might later rely on in another post. Alternatively, these Lemmas may actually be “proto-categories”; that is, discussion on a subject which I think is important enough for a one-off post, but, until amassing some undetermined number of posts on the subject, not worthy of a category of its own.

Helpfully, that introduces an important concept: the balance between creating structure (like categories for blog posts) and the distraction that unnecessary structure can produce. Another example would be how directory trees or menus should be structured. Clearly a directory containing a single file makes it harder to navigate to that file (in some circumstances), but I don’t think there is a mathematically derivable value which is ideal for all directories. This minor uncertainty is perhaps what makes good design and good structure so hard to achieve: on the surface there is no clear distinction between right and wrong, as every person using a system will have a different approach or different strengths.

Acknowledging that, though, I have come to appreciate that there is a valid methodology which can be applied to design decisions, based on the principles of usability. For simplicity and hopefully relevance, I am mostly talking about computer software and website usability, such as is worked on by Open Usability and Jakob Nielsen respectively, but my eye for usability has stretched far beyond that as I will discuss later.

I have realised the potential need for a new category of blog post, or at least a new purpose for the blog, namely being an online source of stock answers to common questions. While I should not be intending for people to come here for my opinion on the latest [Slashdot] article, I do occasionally (in IM / IRC conversations) find myself at a loss for the sources or analogies that would make my position more cogent. Particularly in blogging it would be helpful if I could link to something which explains some basic principle I have without having to go off at a tangent to explain it. For that reason I expect to occasionally write little “lemma” blog posts, which can be used later to prove greater theorems.

The most notable issue to speak on so far is that of security. Everyone who uses the net will presumably be somewhat aware of security (or their lack of it, at least in terms of its symptoms). Moreover, anyone who takes their own security seriously should be aware of at least the principles of security, even if they do not follow individual issues. It is also worth noting that security and privacy are closely linked; as the fourth amendment of the Constitution of the United States of America puts it “The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated…”. As a case in point, I think most people would have a view on the “The innocent have nothing to hide” debate.