Having become somewhat happy with my syntax, I'm now looking into the structure of the lexicon, starting with verb aspect and tense.

Aspect:
There are approximately four aspects, plus a null. The aspects are a perfective, a habitual, a progressive, and an "eternative" aspect.
Since I think of this in terms of subsets of R, let's say that the perfective is a single point, the habitual a set of measure 0, the progressive an interval of positive measure, and the eternative is the entire space. The perfective isn't really just a point, and the habitual is not just a set of discrete points, but the internal temporal structure of verbs with those aspects is unimportant. The precise width and distribution of the habitual and the measure of the progressive are not realized as part of this structure. Also, other aspects are not realized as part of this structure.

The null can be interpreted as a gnomic tense.

Tense:
The tense structure is currently fractal:
We take a map from all time into [-1, 1] and consider binary strings. We translate these strings into points of [-1, -1] as follows:
a_1a_2a_3...a_n -> sum_{i=1}^n ((-1)^a_i)/2^i

If we let in strings of infinite length then we get all of [-1, 1] with some points having multiple representations, but the map is well-defined and that's all I care about.

Tense markers actually occur as strings of [past] and [future] markers, which I'll denote as p and f, so that if we take positive numbers to be in the future and negative numbers to be in the past, we get that an f in the i-th position corresponds to a_i = 0 and a p in the i-th position corresponds to a_i = 1. Hence a string of p and f gives a unique point in [-1, 1], and thus a unique point in all time (I'd say the real numbers, but that's making some assumptions about time that I'm not willing to make).

Note: the point that the string maps to is the point of time corresponding to the temporal position of a perfective action, but also to the average of the habitual and the center of the progressive.


This aspect and tense structure is also applicable to spatial location; Hence we get a subset of R^4, which we'll consider the local tangent space of the spacetime manifold at the point here-now. Note that a point in the tangent space corresponds locally to points on the manifold via the exponential map, but for points outside the neighborhood of definition the notion of tense becomes problematic anyway.

I'll try to get mood and evidentiality later, but those require actual logic and epistemology so they're more difficult than aspect and tense marking.

Analysis of my personal version of English is not a terribly rewarding pastime, usually, as the only interesting pieces of my phonological, morphological, syntactic and semantic individuality tend toward the generation of easily-dispelled local ambiguities.
I have noticed a point of mild interest, however, and would like to note them down before they sneak up on me again:
The different tonality I give to serial elements and apositives when speaking (either physically or mentally). When giving a list, all the elements except perhaps the last one are pronounced in a rising tone, not quite reaching question pitch but definitely above the starting tone. Apositives, however, are pronounced in the rising-falling tone, so as to link them with the antecedent, or in a high-level tone without a significant pause between the antecedent and the apositive. This kind of distinction doesn't make it into writing because English doesn't recognize tonality except with regards to questions. The differences in spacing would perhaps be easier to implement, but would not completely clear up confusion as the end of the apositive clause would not be marked well.
This realization came from reading about the use of the Oxford comma and attempts to create situations where the Oxford comma is misleading.
The example given was a book dedication to "my mother, Ayn Rand(,) and God", with the assumption that Ayn Rand is not the author's mother, and comparing that to "my parents, Ayn Rand(,) and God". (I wish I could parenthesize a lack of a comma), again with the assumption that the author is not the child of Ayn Rand and God.
Focusing on the apositive case, in the case of leaving out the comma for the apositive we'd get "my mother Ayn Rand and God", which works, and "my parents Ayn Rand and God", which works because Ayn Rand is singular. But what about "my friends these people and those people"? The term "my friends" could include both "these people" and "those people", or it could include only "these people" and the actual group mentioned is "my friends and those people"; without apositive markings, this ambiguity cannot be resolved locally.
Perhaps plurality ought to be dealt with separately.

Given that most grammatical structures are morphologically realized in the conlangs I'm building, I don't think I have to worry about this for the conlangs, but it would be nice to have a regular system for written English that I could use.

Apparently while I don't have the patience for dubstep most of the time, I can make it if I simply layer enough stuff. My problem has always been maximalism, whereas dubstep tends to be very minimal. In this case it was quite an obstacle, but apparently four basslines was enough, at least once I stopped trying to simplify the percussion.
Now to add sound effects, because apparently dub does that.
My psytrance/dubstep crossover is going to be a complete mess.

[Edit] Apparently my music program died on me. So all of this is moot, although the lessons learned will be kept.

Moments before the second midterm, waiting for the last stragglers to arrive. Nobody speaks, no rustling of paper or twitching of pens, just waiting, waiting, dreading and hoping and waiting. Anticipation, premonition, the ticking of the clock, minds blank and hearts cold.
And into the silence comes a voice: "Why did the Turing Machine cross the road?"
A pause, baited breath.
"To get more tape."

UPenn it is.

41 pages

Of "vital" importance:

Is there an injection of hom(x^3,x) into (hom(x^2,x))^2? I.e. given a map D(x,y,z), can I decompose this into A(B(x,y),z)? I need to make sure that my conjunctions actually work.
It looks like it should work, but I want to make sure that there isn't something really bizarre lurking around.

Today while teaching section I was really tempted to use the phrase "magic dancing" when describing a point that visits every interval in [0, 1] under iterations of the sawtooth function.
I would have used it, had I not forgotten the origin of the phrase in the context of it being funny to me.

So after years of working on this thing, I've finally gotten the syntactic structure finalized. Both semantics and morphology are essentially nil, but the syntax is done, kinda. I doubt it's going to change significantly.

we have a few important sets to consider:

The set of stems V, the set of cases C and the set of sentences S.

Then there are three operators:

The description operator D, which generates adjectives/adverbs (increments clausal depth)
The conjunction operator +, which generates conjunctions (clausal depth fixed)
The sentence operator T, which sends three stems and a permutation of cases to a sentence

The term "cases" is an abuse, since the three "cases" are subject, object and verb. Note also that C^2 refers to a permutation of 2 distinct cases and C^3 refers to a permutation of the three cases.

D: V^2xC^2 -> hom(V, V)
+: V -> hom(V^2, V)
T: V^3xC^3 -> S

*note: hom probably means homomorphic with regard to semantic structure, whatever semantic structure there may be.

[EDIT]: Made the conjunction operator binary.

I just switched to Chrome. So far, not too bad. The address bar is bigger than I'd like, but the total stuff on top is much smaller, and the status bar only shows up when it means something, which is nice. It makes the pages look bigger. I like the tabs on top thing, and the elimination of the file, edit, view, etc menus.
It's certainly faster than Firefox, although it seems to have some problems with videos.
I've changed the font to something terrible. The fact that I can change the font is fun, but probably more useless/problematic in the end; I can barely read this post as I'm writing it. Also, on my friends page, apparently it only affects my view of Harry's posts. Everything else is in Times New Roman.
The address bar itself has been modified in an interesting manner. When you type a few letters into it, it gives you the page you've visited most that has those letters in the address, then a Google search for those letters, then an address consisting of those few letters, and then some of the pages you've visited with those letters in the address, and then some other random pages that might be popular and contain those letters in the address. I don't really like it, because it returns six results and only six results and only three of them do you care about. Unlike in Firefox, you can't scroll down to see more results, only those six. There is an option to search your history for pages containing those letters, but then you have to go through your entire history. Not fun.

I'll stick with it for a while, but it might end up being a bit too quirky for me.

Gah, I need to think of questions to ask people.
Why am I the only one in charge of this?
Oh, right, I was too lazy to delegate.

So I forgot my gender again today. That is all.

Currently pulling what I consider the other, other, other Altman maneuver, the first three being playing all your 2s early in Chinese poker, that trick for getting generators of unit groups of Z_p, and jumping under a low ceiling with the tubular portion of a giant coke-bottle attached to your head.
There are probably more Altman maneuvers, but those are the ones I consider first.

I'm apparently keeping the wrong part of my New Year's resolution, the one that gets me on Santa's naughty list rather than his nice one.
Ah, well, I was trying to be realistic when I made that resolution; if I can't do it right, I can do it wrong until it breaks.

Props to Aaron Diaz for his translation of a certain commentary on the possible future, readable underneath today's issue of Dresden Codak

I really like 7/4 time. I can't think in it, nor can I really imagine it musically, but it's fun.

I'm going to try the "push all the buttons at once" method, and maybe that will do something interesting.

Watch me
As I fade from your memories
Into the dark of time
Watch me
When I'm the last thing you can find

I'm fine with leaving
I'm fine with knowing
You will not remember me
Even though
My thoughts of you
Could drive me insane
I'm fine with dying
With disappearing
From your life eternally
All I ask
Is if I must go
Bury my remains
When I'm gone

Analytic number theory scares me like little else.

The Fourier transform for general locally-compact abelian groups actually makes more sense than the standard R formulation, mainly because the resulting space isn't actually just the domain. For instance, this would explain the Fourier transform for R/kZ giving functions of Z. Yeah, I'm too lazy to bold things.