Axiomatization

Axiomatization, or development of a set of ideas from first principles, is certainly a popular technique in mathematics and to some extent in areas like physics, etc. The irony is that across my humanities classes, few want it in any of them, even philosophy.

It is true some fields of endeavor don't lend themselves to it particularly well (the study of natural languages comes to mind--most languages have rules but they also have exceptions, etc). On the other hand, an axiom by definition is something which is true by assertion and so whenever something is simply asserted as true, that is an axiom. At the same time, whenever one says "these are the conclusions desired", it automatically forces them to build an argument in support of them with certain premises which in term have premises and sooner or later one hits axioms. The difference is merely they are enumerated last.

Meaningful discourse can certainly be had without explicit axiomatization, but axioms are the logical foundation of discourse (along with a specified system of logic which is itself axiomatic). Thus to fully understand the other and the foundation of their argument, one must understand--at least implicitly--their axioms.

Coding Irony

I went through the part of the code which was most suspect vis-a-vis the errors I was getting and found the flaw: a typo. The irony of this situation is not to be underestimated. Insofar as I can tell, all the algorithmic stuff is right, and in fact everything else is right, but this little tiny thing in wrong.

I'm just hoping it doesn't unveil some larger flaw lurking in the shadows, obscured by the heinous nature of what I found.

My Little Coding Nightmare Revisited

It's even worse than I thought initially. It turns out that the error is systematic and not sporadic (as I should have immediately guessed from its repeatability). It turns out that there is always a sort of inflation of the values of the sum of squared differences coming from somewhere.

This means that while the script looks like it is working great and doing what it should, it is completely bunk and will need to somehow be fixed to avoid this issue. I am thinking about trying to put a series of commands in to reset the values of different variables to zero in hopes of clearing out whatever error is compounding on me.

The next option if that fails it to post the relevant files to the R mailing list and hope someone is kind enough to tell me where I went wrong . . . which I somehow doubt.

A Difference Between Friends and Acquaintances

I have had reason within my own personal life to ponder the difference between being friends with someone and being merely acquainted with them. One major difference can be summarized as follows:

• Friend: Someone you want to spend time with and are willing to actively work to make time for as it is possible to do so.
• Acquaintance: Someone who you spend time with incidentally, not intentionally or with whom you are not willing to make time for beyond the incidental. People you only see in class or at work would could as such.
  

The sticky bits are with respect to

1. a person you simply do not have time for regardless of whether or not you would work to make time if you had any. I would say this is more a friend than an acquaintance.
2. People you have been acquainted with over an extended period. Then this could be said to have grown into friendship.
3. People you were friends with but now no longer spend time with.

So as even I must admit, the above distinction leaves something to be desired. But I never said it was the whole definition.

Playing with Knives

I'll admit I ha five stitches put in today after doing just that while working on my sailboat. Rather embarrassing really, it's a knife I carry on a daily basis. I'm starting to hypothesize that any tool you haven't hurt yourself with recently you don't sufficiently respect.

Thanksgiving Meals

While I live in Minnesota, I'm originally from parts farther south and am amused by the seemingly monolithic nature of traditions surrounding the Thanksgiving meal. It seems to go something on the order of:

1. Turkey (or ham)
2. Sweet Potatoes
3. Stuffing
4. Mashed potatoes
5. gravy
6. bread
7. pumpkin pie
8. various fruit pies
9. salad
10. Cranberries

While such a meal is certainly good, I find it amusing that the list is so rigid and so seemingly widespread. Everyone seems to do some subset of it (and in some cases superset).

Here I am wishing for ribs, cornbread, gumbo, barbecue, seafood . . .

Coding Nightmares

My coding nightmare tonight has been discovering an error in the way a piece of code executes I can't duplicate outside it's native environment, but I can repeat natively.

Here I am, working on an R script to do some (rather elementary) computational geometry and I want it to compute $(a-c)^2 + (b-d)^2$ (to use the TeX notation) where $a,b,c,d \in \[-2,2\]$. A little examination shows that the sum should always be less than or equal to 16. I was getting 16.8. Not good.

The problem is that while I can duplicate this kind of MAJOR error when computing this number as part of the script, I can't get it by starting R up cleanly and manually imputing one example. Then it works fine. I have to wonder what in the world is going on.

The worst part is most likely the solution is simple and would be obvious to a professional programmer but to me, an amateur, is far from it.

Grrrr . . .