Someone over at Metafilter had a great question: What syntactic category are mathematical operands? (Their username is notsnot, in case this needs to go in a dissertation someday.)

Let’s start with something like

Three plus four is seven.

For now, we’ll say the numerals are NPs.  In a construction NP <word> NP, the <word> could be various things: a verb, a conjunction, a preposition. We can immediately rule out verbs, since plus and its friends (minus, times, over, etc.) are not conjugated.

We should also look at non-mathematical sentences, like

Determination plus luck means victory.

Let’s do some syntax. There are some standard though fallible tests for prepositions.  For instance, they can usually be modified by right:

He fell right in the river.
She lives right down the street.
Go to the cave right in the forest.

*Determination right plus luck means victory.
*Three right plus four is seven.

Prepositional phrases (PP) can often be fronted:

Up the hill she walked.
*Plus four three is seven.

You can front a PP and replace the NP with an interrogative, or front just the questioned element:

Sam is the king of England.  Seven is three plus four.
Of what is Sam the king? *Plus what is seven three?
What is Sam king of?  *What is seven three plus?

PPs allow gapping:

Sam is king of England, and Joe, of France.
*Seven is three plus four, and eight, plus five.

These tests aren’t definitive, but plus is failing every one of them. A better match might be conjunctions. Plus, like and, can link NPs or sentences, and can be used multiple times:

Bill and Anne and Rahesh came.  Two plus two plus one make five.
Bill came, and Anne left.  Bill came, plus Anne left.

On the other hand, this transformation sure doesn’t work:

Sam is a king and Sam is a dancer.  >> Sam is a king and a dancer.
X is 4, plus X is sin θ >> *X is 4 plus sin θ.

It looks like the construction S, plus S isn’t really the same plus as in two plus two.  And other operators don’t allow it at all:

*Bill left, minus Anne stayed.
*Bill left, over Anne stayed.

A bigger problem is that English sentences allow literally infinite amounts of inserted material.

Sam and Alice are nobles.
Sam and Alice are fine, just nobles.
Sam and Alice are still nobles.
Sam, prince of Florin, and Alice, duchess of Guilder, are nobles of Sylvania.
Sam and possibly Alice are, as of Tuesday, nobles.

How much of this can we do with mathematical expressions?

Three plus four is seven.
Three plus lovely four is seven.
Three plus four is still seven.
Three, square root of nine, plus four, half of eight, are seven.
Three and possibly four are, as of Tuesday, seven.

These are not impossible, but at best they sound jocular.  The additions are not math; they’re intrusions of ordinary English.

There’s also the complication that mathematical plus and minus can be unary: you can say Minus three plus four is one. You can have a conjunction beginning a sentence (And the Lord said to Moses…), but that’s not how minus is working here; it’s obviously a modifier for three.

Not to belabor the obvious, but many of the basic things we can do with a sentence don’t really work in mathematics.  You can’t really put a mathematical expression in the past tense, or use the present perfect, or use pronouns, or passivize, or insert a relative clause, or nominalize, or cleft, or topicalize.

And all this is looking at a very basic expression that probably did arise out of normal syntax.  It’s even harder to apply our notions of normal English syntax to something like

x equals minus b plus or minus square root of b squared minus four a c over two a.

or

e to the i n equals cosine of n plus i times sine of n.

I’ve gone into this much detail to convince you (and myself) that ordinary English syntax doesn’t really explain mathematical expressions.  I hope my conclusion doesn’t shock or appall you: mathematical expressions don’t follow English syntactic rules; they follow mathematical rules.

Now, maybe you could shoehorn the quadratic formula or Euler’s formula into the syntactic framework of your choice. I will bet you, however, that you’ll end up with a pile of very idiosyncratic special rules and special syntactic categories, and a bunch of ad hoc exclusions of normal English rules.

And there’s an alternative formulation that would end up far simpler than that: mathematical expressions have their own cross-linguistic syntax, based on their written form, and languages have conventions on how to say them aloud.

I don’t think this is terribly surprising… it’s like discovering that the Russian of Tolstoy’s War and Peace contains a number of passages which are written in the Roman alphabet and don’t follow ordinary Russian syntax.  Is this a revolutionary discovery about weird undercurrents of Russian?  No, it’s just that Tolstoy included quite a bit of French in the text.  Similarly, English sentences can have embedded mathematics.

Still, I hadn’t thought about it this way, and I find it interesting that a pretty ordinary part of English turns out to be, well, not really English at all.

Now, for historical and practical reasons, there’s a certain overlap, especially with basic arithmetic. People undoubtedly said “Two and two are four” (or “twá and twá sind féower”) long before international mathematics was formalized. So these behave more like ordinary English than the quadratic formula does.

Plus, the conventions for speaking math out loud were, of course, invented by speakers of the language out of existing (or newly borrowed) words, and follow ordinary language conventions– where possible.  So you can read cos (2θ) as “cosine of two times theta”.  On the other hand you can just read it as “cos two theta”, which probably has no non-math analogue in English.

(I should add that programmers are very familiar with the idea that math expressions have a particular syntax.  They don’t bother with linguistic categories at all; they define their own, such as operators, variables, constants, functions, and statements.)

 

 

Advertisements

I’ve basically redone the Almeopedia. You can find it here.  The help page is here.

ticai-alchemy-shop

The old version (which is still up, for now) has had a speed problem for a long time. Just loading a page took 40 seconds, which made browsing painful and editing almost impossible.

I’ve been redoing pages (like the numbers page) by using Javascript to process big raw text files, and I used the same method here. It runs lightning-fast on my computer. The first few links may be slow when you try the above link, but it should speed up once the files are in your cache.

Since it’s now my code, I was able to do some side features:

  • shortcuts for the Unicode letters I use
  • changes to facilitate the historical atlases
  • SFW mode (makes the pictures tiny and adds business-friendly nonsense titles)
  • improvements to the choose-your-own-adventure section
  • customizations to the Wiki markup to eliminate busywork

There’s about 3 meg of raw text.  I’m amazed at how fast Javascript can plow through it (e.g. if you do a text search).  I skipped some optimizations I could have done simply because it’s good enough as it is.

I also took the opportunity to put the Historical Atlas of Skouras into Almeopedia. The old version was in Flash, which is deprecated these days.

Unfortunately, the new version isn’t externally editable.  Still, if you find errors or think something should be added, shoot me an e-mail.

There are undoubtedly errors and bugs… I copied all the text by hand, but I haven’t yet checked each page.  But, one of the purposes of the project was to make it easy to revise what’s there and put out lots of new material.

 

 

I came across this interview with Eric Weinstein, and it got me thinking. Weinstein is an advisor to Peter Thiel, and– wait, come back!  I know Thiel is the embodiment of everything wrong with late capitalism, but the article is only half that. It’s deeply weird and doesn’t quite know what it wants, but it does have some interesting things to say about the frivolity economy.

Candy_LargeWide

His thesis, more or less, is that capitalism should be more disruptive, and also combined with socialism. But let’s start out with the strong bit: his critique of American education.

The problem is that we have an educational system that’s based on taking our natural penchant for exploration and fashioning it into a willingness to take on mind-numbing routine. This is because our educational system was designed to produce employable products suitable for jobs, but it is jobs that are precisely going to give way to an economy increasingly based on one-off opportunities.

Now, this isn’t entirely right. It’s not that routine is the goal of education; it’s that mass education in any form involves teaching things the kids don’t care to learn at that moment. Kids actually learn quite readily if they happen to love the subject.  Plus, sometimes you can’t get to the good parts without mastering the boring bits. You can’t learn quantum mechanics without learning calculus; you can’t read Sanskrit literature without mastering Sanskrit morphology.

But Weinstein has a point.  Traditional societies didn’t educate the majority at all.  Industrial society educates everyone because manufacturing and service jobs require a high level of literacy, and jobs will resemble school in many respects… often, the unattractive respects: lots of routine and rules; mindless obedience; doing things you are not personally interested in because it’s Your Job.

You can see how this sort of education and a certain sort of society fit together nicely in the career of … my Dad.  He was bright and did well in school, though he never went to college.  He started as an assistant pressman at a major printing company, rose through the ranks to management, and ended up as an executive, an expert on technical printing problems.  He not only stayed in one industry, he stayed in one company. It was a pretty good life for him, and a definite step up from his father, who was a carpenter.

Now, late capitalism has nearly destroyed that sort of career– especially for those who never make it to management.  Weinstein takes the view that predictable, medium-affluent working class jobs are over, presumably because those are ripe to be automated.

At this point many give up and conclude that humans are worthless, or at best should just be given a stipend while the robots do all the work.  Weinstein says instead that humans should do what they’re best at: handling one-time events. Or with less jargon: doing things that aren’t easily automated, because they require adaptability and creativity.  For him this means technologists and finance people, but also inventors, artists, and writers.

I’d actually make this category far broader– see my list of professions unlikely to be taken over by AIs. It’s interesting to speculate what sort of education would focus on these skills, rather than those required to be an accountant or an assistant pressman.

This is also about the point where Weinstein dissolves into a messy set of contradictions. He’s obviously been talking to too many venture capitalists: he tells us “certain fields will need to undergo a process of radical deregulation to give the minority of minds that are capable of our greatest feats of creation the leeway to experiment and to play.”  Unreflective Thiel-worship, in other words.  Haven’t those people done enough damage?  But!  He also thinks we need to recognize the “dignity, well-being, and health” of the 90%.  He mentions a universal basic income, but so far as I can see, his bright idea is that this is tied to having jobs that aren’t necessarily marketable.  So, you can be a playwright or something, and still get paid enough to live on, and this is somehow valuable dignified recompense but it’s not, y’know, welfare.

The interview ends with Weinstein’s assurances that the Very Powerful are thinking very hard about inequality these days. And this of course is complete nonsense.  His boss, Thiel, supports the GOP, whose first order of business right now is not subsidizing playwrights, but handing the super-rich another five trillion dollars.  Whatever the super-rich say to Weinstein at cocktail parties is not the truth of their secret benevolent hearts; it’s the bullshit they tell the 10% to hide what they are really doing to the rest of us.

(As a side point, I’m not saying that the super-rich are all evil plutocrats.  Only half of them are!  Once they have all the money, quite a few rich men develop other interests, including improving the world. The class to be terrified of is the moderately rich: the mere millionaire.  They’re the ones who need more money and can’t understand any value but money and vote consistently Republican.)

What’s interesting is that there’s a bright future we could have— if we chose to pursue it. Thinkers of the early 20th century couldn’t see past the mass of uneducated peasants in their societies.  Aldous Huxley couldn’t see any alternative to keeping around a class of “Epsilon Semi-Morons”; Orwell couldn’t imagine anything nicer than spreading around the wealth such that everyone could eat but no one could go to a restaurant.  But postwar America and Europe turned out very differently from either vision.  It turned out that everyone could have a way better job than peasant, and everyone could go to restaurants.

And similarly, lots of people can’t see a future right now that doesn’t include masses of factory jobs.  They fixate on what ex-factory workers could do, and all that comes to mind is, well, factory work.  But the world is actually quite rich, and AI could make it far richer.  You really could put everyone to work doing things that are today only open to the 10%.

The thing is, you don’t do this by deregulation, disruption, and giving the super-rich more money.  Weinstein’s bosses won’t give us that bright future: no ruling class voluntarily disinherits itself.  They won’t even give us a UBI, because it would cost money.

The tricky bit is, of course, how do we get there from here? Well, it’s not going to be a quick process.  But we can’t even start on it till we 1) shut down the current wave of downright reactionaries; and 2) get rid of plutocracy.

(If you want an idea to rally around, though: UBI isn’t a bad idea, but combine it with Piketty’s 0.5% tax on wealth. You can’t get to the bright future and also keep increasing inequality.)

 

 

I picked this up and zipped through it tonight. It’s by the same people who did Gone Home. It’s similar in gameplay, only it’s set in spaaaaaaace.

20171027025708_1

So: It’s 2088.  You’re Ami Ferrier, who’s been sent to grab the AI data from the unoccupied Tacoma space station.  It’s soon clear that something bad happened here, and you can snoop around to see what it was.

You can look at physical clues, but you also look at virtual clues: the AI kept recordings of significant crew interactions, in the form of augmented reality recordings. These are color-coded ghosts (with full audio). The clever bit is that you can’t just stand there gawking at them– the characters move around, and you have to decide which ones to follow. You can then rewind and follow someone else.

All this makes two big improvements over Gone Home:

  • The futuristic setting, which allows the art and story people a good deal more creativity.
  • The AR recordings, which just feel more involving and interactive than a straight audio.

But the overall method and even the story structure are similar.  You can root around offices and personal quarters, look in drawers and trash bins, solve a few simple puzzles to gain access to additional areas.  You don’t have to do any of this, but you’d might as well, because that’s the game… you don’t get to shoot anyone at all. You’ll very soon get to know each of the six residents of the station.

The story has been described as cyberpunkish, or Late Capitalism in Spaaace.  Let’s just say that you won’t be surprised to find corporate shenanigans going on, and some inscrutable and possibly dangerous AIs.

Gone Home had the advantage of being a low-key domestic story; it was unusual because we almost never see something like that made into a game. But I think Tacoma is a step forward in storytelling; without losing the interest in everyday personal interactions, it’s more streamlined and dramatic.  Rather than slowly leafing through a couple decades of family life, it focuses on a very stressful period of days, with a few key flashbacks. (I think there are fewer items to look at, but that’s because they rely on the AR for so much of the storytelling.  The games each take about 2 hours to play.)

The ending is also a lot more satisfying.  (Mouse over to read if you aren’t worried about spoilers.)  One, Ami actually does something, unlike the entirely passive PC in Gone Home. And two, the story manages to not replay every AI story ever told, which is refreshing.

One minor complaint: the low-detail ghosts. When they’ve obviously gone to the trouble of motion-capturing the performances and building 3-D models, I don’t get why they didn’t just show the characters’ faces.  It’s not like they were trying to hide them– there are pictures of each one.

Anyway, it’s a really interesting exercise in storytelling.  It could have been told as a movie or a comic, but the interactivity adds something, though that something is hard to explain. Perhaps it’s that it requires active curiosity, rather than passive acceptance. A lot of far fancier games could learn the lesson that it’s kind of annoying to grab the camera away from the player and just show them cutscenes.

I was thinking about some games I’ve started and not finished, and I think I’ve figured out why: there’s too much to do.

ME-quests

Your to-do list

These games include Rise of the Tomb Raider and Mirror’s Edge Catalyst.  I loved the games they’re sequels to, I’ve started them, got some distance into them, and just never seem to start them up again. What I realized today is that the original games were mostly linear, and the new games are far more open-world.

And it makes me anxious. I feel like I have to find everything in an area before moving on.  I know I could skip most of the stuff, but then I worry that I won’t have mastered all the skills needed for the main quest.  I have other complaints– e.g. Faith and Merc in the original Mirror’s Edge were far more likeable characters than Faith and Noah in Catalyst— but I think it’s the size of the game that bothers me.

The irony is, I’ve put an ungodly number of hours into Mirror’s Edge. But part of that it is because it’s in nice digestible chunks. I will replay the game occasionally, or I’ll spend time on the time trials.  The game is so focused that there’s no paralysis of choice.

Dishonored and Dishonored 2 hit the sweet spot of “mostly linear, but with side stuff to make it fun to explore.” There are just enough runes and lore drops.  Arkham City is also well balanced.  (I did get all the Riddler trophies– once. If I just want to mess around as Batman or Catwoman, I’ll play the challenge maps.) Saints Row 4 has a nice approach: it’s sprawling, and yet the game will lead you through all the activities if you let it.

So if you’re a developer, I’d suggest that making an open world is not something you have to do, and can even make your game worse.  Embrace linearity.  I’d rather have a solid main quest to do than a huge number of fairly shallow activities, where it’s not clear what I should be doing.  (On the other hand, a good place for those shallow activities is in a separate challenge mode.)

If you’re Bethesda, however, you should just carry on. Fallout 3 and Oblivion, for me, did open-world in just the right way. Although I completed the main story in both, I appreciated the fact that I didn’t really have to. Plus these games, and Saints Row 3/4, are great at making so much of the world interactive. That is: an open world goes well with multiple playstyles and playthroughs: if you can be a hero one time and a rogue another, if you can wander down the road and find a new story, if you can make a home and find shops to customize your character.  Neither Faith nor Lara really have the opportunity to put the main quest aside for a few months, maybe buying a house or playing as a rogue.

All this is entirely subjective (it’s quite all right if you play games very differently), and it’s not intended as the last word on these particular games.

Edit: So why do publishers insist on making games open-world?  According to this scary article, it’s because they can monetize them better. Ugh.

 

 

The most important thing is done, I think: the cover!

India-Cover-Front

Who are these people?  Once you read the book, you will know!  Also the answer is on the back cover, but you won’t even need that clue.

The text is about done— I have at least one more book I want to read, but it’s about time to order the proof copy. I’m hoping to make the book available by the end of November. Make your family buy you a copy!

I could probably use another couple of readers for this draft. E-mail me if  you’re interested and you are pretty sure you can read it and make comments within the next 3-4 weeks. (Sorry for the rush… some other stuff has needed dealing with.)

By the way, does anyone know what that big tree in the center is?  The fruits look like mangos, but the leaves are nothing like mango leaves. Perhaps an Indian tulip tree?

This turned into a mini-research project… The chart below shows who had the majority in the Senate and House, and who held the White House, for each of the 115 Congresses of the United States. The main point is to examine when a party has been able to do what it wants in government.

Congress

The colors: beige is “Pro-Administration” (not an actual party); green is Federalist; orange is Democratic-Republican; purple is Whig; blue is Democratic; red is Republican. (White can be taken as “the opposition”— except in 1881, when it means that both parties had the same number of Senate seats.)

The number gives the percentage of seats in the Senate and House held by the majority party.

For Democrats and Republicans, I’ve used two colors: dark when the party can do what it wants; light when it can’t.  The general rule is that it’s light when not all three columns match— that is, government is divided.

However, I’ve modified this for the period 1953-1988.  With Eisenhower and Nixon, this is largely because neither tried to govern in conflict with Congress, at least by today’s standards. With Reagan, I’ve shown Congress as stymied, but not Reagan himself: he was able to implement the major policy shift from liberalism to plutocracy without serious setbacks.

I haven’t tried to graphically depict cases where a party was too divided to get much done— e.g under Carter and Trump.

What emerges, I think, are a number of periods with very different overall structures.

  • 1789-1800: the early years. I don’t know much about the politics of the time, but it’s probably not worth drawing lessons from it as everyone was trying to figure out how things worked and what their disagreements were.
  • 1801-1830: the Era of  Good Feelings.  Well, no wonder things went pretty smoothly: the Democratic-Republicans had a lock on government.
  • 1830-1860: the pre-Civil-war period. A lot more contentious, as a Democratic/Whig system developed. The second half of the period, dominated by the slavery question, shows a high degree of contention.
  • 1860-1932: overall, the Republican Period. This was the old style GOP, of course— the party of Northern business above all. There are a few contentious periods, but overall the number of strong GOP years is striking. Only Cleveland and Wilson had strong Democratic years.
  • 1933-1979: the liberal period. This period was dominated almost as strongly by the Democrats.Congress was so reliably Democratic that GOP presidents had to work with it.
  • 1980 on: the plutocratic period. Very largely a return to Republican rule, but much less solidly. Compare the majorities: where the 19C GOP often had numbers in the 60s or higher, the present-day GOP hasn’t risen above 57%. Divided government is the norm rather than the exception.

The reason I looked at all this was because I was curious how often we’ve had divided government, and the bipartisan courtesies that used to accompany it: infrequent filibusters, accommodating confirmation hearings, a collegial Senate, etc. We often hear people bemoaning increased polarization and wishing that people would just work together somehow across party lines. It’s said that the parties used to be miscellaneous coalitions so that they could pretty easily work together.

I think the general answer can be read from the chat: bipartisanship usually isn’t necessary. In 76 out of 115 Congresses— two-thirds of the time— we’ve had undivided government. That means that one party held the presidency and Congress, and could pretty much do as it wanted. (Again, we’re ignoring intra-party fights for now.) In such times you could be bipartisan if events warranted, but you could also pretty much ignore the other party.

Of course, that leaves another third of the time when we have divided government. Then, of course, it’s useful if both parties can work together. On the other hand, at least two of these periods were highly polarized times when being “moderate” arguably meant being a piece of jelly-like protoplasm:

  • The pre-Civil War period. People looked for decades, but there was really no moral or pragmatic compromise to be found between slavery and abolition.  The compromisers of the time aren’t exactly highly regarded today.
  • The present day, which is a lower-key but just as polarized debate on whether the country should be run for the benefit of its richest 10%, or for everyone. And some other issues, like whether or not we’d like to preserve the planet’s ecosphere and avoid nuclear annihilation. I sympathize with those who “hate politics” and wish that everyone would just get along. But you can’t wish the issues away, and “moderates” are usually deeply delusional about what’s actually happening in the country.

(What happened in the 1875-96 period?  I really don’t know, though now I’m curious. This was the Gilded Age, when the preoccupation was making money. The party lines seem baffling today: the Republicans were protectionist and pro-industry; the Democrats were laissez-faire, anti-tariffs, and associated with small farmers, immigrants, and Southerners. Neither seems to map to todays’ liberal/conservative divide.)

So, when you hear that (say) filibusters used to be uncommon— sure, they were, but look at those majority numbers. Majorities over 60 used to be common. This isn’t to say that the abuse of the filibuster isn’t a problem; the point is that periods of amiable divided government really haven’t ever been the norm.