I planned some time ago to start sharing my thoughts on a blog but procrastinated with excellence. Why was this? I realised that I was struggling with the mental challenge of finding a starting point to an essentially random set of future posts. But without a starting point, future posts can never arrive in the present. Fortunately I have resolved this impasse: where better to begin than a disclaimer whence all subsequent posts can be disclaimed? Here are my thoughts on this matter.
BLOG DISCLAIMER – To be applied to this and all subsequent posts
Any comments or implied opinions on this blog may or may not actually be my opinion. It might be the case that they were my opinion and are no longer so. It might be the case that they were not my opinion but have become so since the appearance of the entry. Or, it might be some other possibility: perhaps they have fluctuated in and out of opinion, or will do so in the future. It’s really quite hard to say. Opinion is such a volatile thing. I suppose the most important thing to do as a reader is to determine whether comments are something you choose to form opinions about: in the case of a binary agree/disagree opinion, either way is fine by me; in the case of a more complex opinion spectrum, any point on the spectrum is also fine by me. Of course, this doesn’t mean that I won’t vigorously disagree with you, subject to the disclaimer about which I now write. (Note, as a point of interest, that this disclaimer is now defined in a recursive fashion. I’ll assume that the disclaimer is somehow well-defined, subject to the vague and ad-hoc construction of the English language)
I might also refer to mathematicians and/or their actions from time to time. I think that it is wise to assume that I refer to mathematicians like me. Moreover, I will assume that such a set is not empty by adopting the convention that if two things are identical then they are also like each other: as I am identical to myself, I am like myself; thus, the set of mathematicians like me does, in fact, contain at least one mathematician (the wise reader may also choose to make the default assumption that there is exactly one member in that set, due to the diversity of characteristics of mathematicians). Getting back on track. in order to determine some notion of like-ness, there seem to be two obvious ways forward: I could choose to define likeness in terms of matching characteristics; alternatively, I could proceed along the route of similarity.
Matching Characteristics Approach: Here we choose some well-defined characteristics, such as located in the Northern Hemisphere, or Male which an entity either possesses or does not. Two entities are ‘like’ according to a particular characteristic if they each possess that characteristic. Sometimes we might well be able to infer ‘likeness’ according to another characteristic if neither of two entities possess a given characteristic, but sometimes not. However, I digress somewhat. We might say that two entities are similar if they share enough characteristics. However, since there are so many possible characteristics out there, and there is always a sense of grey-ness in any physically-based characteristics (e.g. hermaphrodites; someone with one foot in the Northern Hemisphere and one foot in the Southern Hemisphere and the connecting parts of the body variously split between equator and the hemispheres) this is all just too confusing. Also, for any set of similar characteristics, I would likely be able to find an entity with whom I match on each characteristic in the set with whom I feel that I am less similar than another entity with whom I do not match on all of the characteristics in the same set. An obvious point being that I feel that I am more similar to some females that I know than to many males that I know (Is it really necessary to warn you to take care against any unfounded inference based on this point? Is it really necessary to warn you to take care against any unfounded inference based on the purpose of including the previous sentence? The few people who make any inference, founded or otherwise, beyond the previous sentence will doubtless understand the point of the sentence before that, so I’ll say no more here). Since a decent definition must suitably represent the underlying point, I am going to abandon the Matching Characteristics Approach to ‘similarity’. (Which, presumably, is also abandoned in the standard disclaimer ‘Any similarity to any persons living or dead is entirely coincidental’: it is not a coincidence that Jack Bauer is similar to many people on the characteristic of Male. In fact, that is expected and not coincidental. Perhaps on the matching characteristics definition I would be able to accept this version of the standard disclaimer: ‘It is coincidental that we can choose a large set of characteristics of a character in this piece of fiction such that were there is a single factual person on the planet who matches the fictitious character on all of those characteristics’. Mmm, despite the obvious flaws at present, this certainly has some merit, but I won’t pursue it here.)
Similarity Approach: We have abandoned, with good reason, the TRUE/FALSE approach to similarity. We (why have I now become ‘we’ instead of ‘I’? Force of habit, I suppose. Since it is intended to refer to My blog, We will revert to I) I think that a scale of similarity will work better (N.B.: logically, the crossing out of the word ‘We’ should happen here. I’d never considered the limitations associated with the linearity of meaning permitted by the written word). For this there is a scale of matching from ‘totally identical’ to ‘no possible match’ on such and such a characteristic. Perhaps we need a metric of sorts, although this would require the quantification of a given characteristics. Could be done, of course. But hopefully this won’t be required, and the quantification would need to be done on a characteristic-by-characteristic basis. Interesting stuff to think about. However, I can’t think of an example where this scale of similarity fails to make sense, incorporating naturally, as it happens, binary characteristics.
So, where were we? I’ve forgotten what I was actually talking about. Ah, scanning back up this entry reminds me that the purpose of this was to define a notion of similarity which arose as I attempted to disclaim anything and everything that might arise in my blog, and to indicate that all contained might or might not be my opinion.
And we recurse again.
Confused? Welcome to the world of mathematicians like me.
[NEXT TIME: Due to the number of asides which seemed to occur in this post, I ought next time to talk about the value of parentheses (which are brackets ((no offense to anyone who knew that!)(which can also be nested (fewer people know that (but maybe not, on reflection))))).]