Wednesday, March 26, 2014

The Definition of Insanity

From Landscape Urbanism and its Discontents, courtesy Envision Baltimore:
Rather than having an urban fabric based on spatial definition by buildings, landscape would be the 'structuring medium.' The 'look and shape of the city' was to be a matter of 'open space within which buildings are set'.
It didn't work the first time; it's not going to work again.

Monday, March 24, 2014

Bouncing around my mind

Pertinent to this post:

Since the PPA has no inkling of what the actual supply of any of their permit zones actually is, they routinely issue far more permits than spaces that can possibly handle those permits. Anecdotal evidence (courtesy a certain foulmouthed blogger) suggests, for example, that PPA Zone 4 currently has ~2x the permits its physical constraints can possibly handle.

Their ignorance--abetted by the fact that one has ever found a way to assess onstreet supply (until now)--is the only way they can get away with this. The implicit guarantee of a permit is that you are entitled to a place to park in the area where it's issued; if you have more outstanding residential permits than residential spaces, you've reneged on that implicit guarantee. Hint hint.

Wednesday, March 19, 2014

That Eureka Moment

One of my long-term projects has been developing a mathematical model for scheduling in Jarrett Walker-type transit systems. Today, I made a breakthrough--

I had previously realized that a model of such a system would yield two intersecting planes in my defined 3-space, and that desired overall frequencies could be model by stacking instances of these planes atop each other. But I'd been at a loss as to how to model the routes within the planes (other than the fact that they were vectors).

What I realized today, however, is that the planes are actually a set of null space vectors; this means that a prescribed eigenvalue in the null space will seed an eigenvector that corresponds to that value. What that means is that the entire system can be modeled with nothing more than the equations of the two intersecting planes, and the set of eigenvalues that yield the eigenvectors corresponding to the known bus routes.

Fortunately, we remain in vector space so far, but it appears the apparatus I'm constructing will wind up generalizing into a differential equation, to accommodate "gridlike" systems which attempt to install a mass transit grid even over non-grid street networks.

Friday, March 14, 2014

Dominion

I've been playing a lot of Skyrim lately, and ruminating on Elder Scrolls lore, so if you pardon this nerding-out, I'd like to offer my opinions on what will happen in the next game.

1. It will be called Dominion, and be based in the heartland of the Aldmeri Dominion (Summerset Isle).

2. No matter how you play Skyrim, things turn out for the Dominion's benefit. Canonized lore will have it that the Dragonborn completed the Assassin's Guild questline (ends with the assassination of Emperor Titus Mede II), whose end results in the fragmentation and collapse of the Tamrielic Empire. The whole civil war questline ends up in the dustbin of history; in a certain sense, it does not matter whether or not the Empire or Ulfric wins, as the whole of Tamriel splits into a bevy of statelets which the Dominion then vacuums up.

3. Thalmor religious persecution has developed into full-blown genocide. And Mundus is worse off for it; in fact, it's buckling.

4. It will be the Hero's job to assume Talos' divinity and stabilize Nirn and the firmament. The second-most-important task is destabilization of the Dominion, by now roundly considered evil. 

Of course, this doesn't undermine the ability to make moral choices--an Elder Scrolls staple--any more than the Empire's overarching existence's does Daggerfall. It's likely that Dominion's principal moral hazard lies in how the Hero goes about unifying the resistance, and be informed by various groups having different degrees of moral rectitude and likelihood of carrying out their resistance.

5. Freedom of movement--to a significant degree--will be curtailed, especially in the early game. (Full freedom of movement occurs in the late game.) No matter how you go about it, the Hero will quickly be branded an enemy of the Thalmor state, and so will need to get quite good at avoiding Justiciars, at least until you're powerful enough to take them head-on. Much of the early game will thus take on elements of getting from Place A to Place B without attracting authorities' interest, and creating and inculcating friendly bases throughout Summerset. The Dragonborn you ain't.

Coll. Incidentally, the Shouts mechanic will be implemented here, but in a vastly different way. It's likely that, in the lore, under the Last Dragonborn's influence, Shouting was developed from a "special skill" to a school of magic built on the Greybeards' teachings.

Coll 2. It's likely that Summerset's traditional joinable factions will be closed to non-Altmer (particularly if they keep this Nazi thing going). I'd bet that the "real" joinable factions will involve some combination of hidden factions and under-the-table dealings with traditional ones closely associated with the Thalmor, and relative freedom for the ones that aren't. So, for example, the Assassins' and Thieves' Guilds will be significantly easier to join than the Fighters' Guild or local Mages' Guild variant (unless that turns out to be the Psijic Order, which has zero known relations with the Thalmor overlords).

I don't really know what's on Bethesda's storyboards, but these ideas seem like they'd make the best possible Elder Scrolls game to me. Certainly, gameplay mechanics in Dominion will have a very different, unique, and interesting twist to them, particularly since what we know of the Thalmor implies that the next game will have to encourage stealth-based gameplay to a far greater extent than previous installments ever did.

Thursday, March 13, 2014

A Sample Program

Some notes on what a sample elhi math program would look like...

Grades 1-3: Introducing Relations
  • What are relations?
  • What are operators?
  • What are numbers?*
  • Numbers in real life
  • Telling Time, Counting Money
  • Relations Between Numbers
  • Operators Symbolize Relations
  • Simple Arithmetical Operations
  • Add and Subtract any Pair of Numbers
  • Simple Multiplication and Division (to 10)
Grades 3-6: Greek Math, Intermediate Arithmetic
  • Geometry and Ratios
  • Plato's Meno
  • Archimedes and the Method of Exhaustion
  • Multiplying and Dividing Larger Numbers
  • Multiplying and Dividing Fractions
  • Decimals, Zeros, Negative Numbers
  • How to Use an Abacus
  • Pythagorean Theorem
  • etc. 
Grade 7: Geometry. Elements. Euclid.
Grade 8: Algebra. The Compendious Book. al-Khwarizmi.
Grade 9: Analytic Geometry. La géométrie, Descartes.
Grade 10a: Trigonometry.
Grade 10b: Calculus.
Grade 11: Discrete Math.
Grade 12: Elective (if so chosen)
  • Combinatorics
  • Boolean algebras (logic, set theory, etc.)
  • Linear algebra
  • Multivariable calculus
  • Graph theory
  • etc.
___________
*Note order. The relations are more important than the numbers. For example, a first-grade project could be to make a family tree (create a statement of relations), and then a way to link any two members of the tree together without long text block or, well, the tree (that is, create operations). We then introduce the standard operators (perhaps in the context of the family tree project). Numbers also have to be introduced early, but teaching relations and operations needs to be separate than numbers for a while because (1) we want students to have a major aha! moment when we merge the two together, and (2) by teaching the relational/operational aspects separately from numbers, we can focus students' attention on the fact that mathematics is really relational in nature.