A Tale of X Colleges

Well, X is more or less a Roman numeral, right? For the remainder of this post, I’ll just anonymize their names as College 1, 2, etc. in rough order of preference.

 

If you’ve been reading my previous posts, you probably know that the college admissions process was not as simple as “apply to college 1 and be done with it since you had a 100% chance”. I knew for a fact that it was not a 100% chance. The only trouble was that my resume was impressive enough to warrant applying to college 1, yet had fairly obvious flaws that forced me to apply to college 10. Nevertheless, I apply to college 1 anyway early. I was going to apply to college 4 as well but I didn’t finish before the early deadline oops. The early thing was supposed to facilitate the college 1/4 combo, although from what I hear there were people who got into college 1 and outright rejected from college 4. Overqualification much?

The deferral from college 1 wasn’t TOO surprising although it did elicit a rather irate response by various people, including the person who got rejected from college 4. I subsequently dropped colleges 7 and 8 for having annoying essays. (Incidentally, I had written an essay for college 8, but then when I checked some other box on the Common App, it gave me another essay to write. At this point, there were about 3 days remaining so I decided to just drop it. I also applied to the public school “chain” which I’ll call college 6, 6.1, 6.2, …, 6.5 for ease of identification even though certainly I would not put college 6.5 over college 7 or 8 (College 6 is more or less well-placed, however.) It was essentially all one big combined app for that school, so no matter.

Oh, and I guess I don’t apply to college 13 because who would ever want to go to college 13, right?

So ultimately I applied to: college 1 (defer), colleges 2, 3, 4, 5, 6-6.5, 9, 10, 11, 12. 10 apps!

The first good news comes in around February, where college 9 decides to accept me with a scholarship thing, on condition of interview. This is interesting since apparently nobody in a particular linear algebra class (our highest math level, which means that they all skipped 1+ grade in math) got such a scholarship, although other people not in linear algebra got the offer. So I take off two days to go to the college, which was a pretty decent facility, I must comment. The guest wifi was pretty terrible though.

Then the acceptances and rejections came rolling in. First was college 1. Reject. Whoops. More irateness. [Though I note that the guy who got rejected by college 4 may in fact go to college 5 due to a full ride scholarship there, NOT college 1 (which is notorious for not being a college that gives scholarships since they’re so top-caliber). Maybe their decision regarding me was a factor for him, I don’t know.] I get some pity acceptances from college 12 and 6.5 (which remember is pretty much college 12-level), and college 4 waitlists me. Well that’s better than a rejection I suppose. The next batch came, and I start going up the 6-ladder: first an acceptance to 6.4, then 6.3, then 6.2 (which an unusual number of people are going to apparently – like people who I consider GOOD at our school o_o). I also get an acceptance from college 10.

More rejections: college 2 and 3 pretty much at the same time. College 5 accepts me, although they’re really expensive. Time to hope for a scholarship. College 6.1 accepts, and whoa college 6 accepts, even though they’re a college that traditionally does not accept my type of profile since they pretty much only look at the area where I was quite weak at. I guess I’ll count my blessings.

Financial stuff! I was basically banking (aha pun right?) my chance at college 5 based on whether they give me a full ride (apparently only two were given this year, unlike in previous years where there were maybe 3 or 4). Being a public school, college 6 of course was relatively affordable, and college 9 (the early interview college) was very costly as well without the scholarship. At this point, I go check college 11, and it turns out I forgot to give them some form or another and they canceled my application. Enjoy my $70, I guess.

So I thought I did pretty decently at the interview but maybe they realized that I thought that they were around college 9 so they gave me only some scholarship, more or less a “quarter ride”. (To be fair, even if it were a half ride it would more or less be on par with college 6’s cost (public schools op) so why bother.) College 5 ends up giving their scholarship to 1) a guy who’s fairly crucial to their startup and 2) a Saudi Arabian IMO gold medalist. I guess I can’t compete with that, though it does make my college decision a lot easier.

So here we are. College 6 it is.

 

(To be fair, college 6 is pretty good; my college list is a bit top heavy.)

Post-mortem

Big things happened. I won’t actually complain about the workload; in reality it wasn’t that much, and I still managed to keep my sanity and my life. And… a lot of things ended. I’m going to reflect upon these:

HOMECOMING (b. October? 2010; d. 10/18/2013)

My last homecoming ever. As you might know, my traditional homecoming convention is the “coming home” part, and I invite my friends because going home by myself makes me look like a loner. (Maybe I am. Whatever. (Maybe they are too. Whatever.)) If I can hear homecoming from 100 meters away from my home, you know it’s REALLY loud. Noise is… well, unpleasant. And dances, unless impressive, aren’t very impressive.

I like displays of skill. I do appreciate the amount of time spent making intricate choreography but in the end it’s just a memorized set of moves. (If it syncs up with the music, say, that’s a skill of timing.) But things that don’t time with the music properly and don’t show some skill (I say TKD falls under this category) feel rather lacking to me.

Plot is probably the “interesting” part of homecoming, at least to me. I admit – with just about an hour to spare, you can’t develop it much, and obviously you need to include a bunch of dances. But I feel that the dances were either explained in a way that the plot seemed contrived, or the dances weren’t even explained at all. I know, putting dances where dances actually make sense is kinda tough, but surely it must be possible? It’s even worse if you start a dance without doing any explanation. Then I get confused.

Anyway, what happened… CaML conflicts homecoming again, which spells a dearth of contestants, and a very good average overall. During lunch on Monday and Wednesday (not CaML tuesday) duoed with Epixyl live. We’re both support mains but I decided to give him the support role. Monday I played ADC (Miss Fortune, first time playing her) and Wednesday I went top (Malphite). Surprisingly, did very well on MF (10/2/6 I think?) but I always canceled my ult by moving… Something to fix eventually.  Wednesday I went mostly even – slightly negative in lane but Malphite’s obviously a team-fight champ that doesn’t really need to get fed (besides, I just stacked armor and the enemy laner eventually did no damage at the end). We won both games. Tuesday there wasn’t very much time to play LoL so I completed my physics lab instead. Thursday I actually went to homecoming. It’s the last senior day, so why not. I started wearing red on Wednesday and Thursday, since I legitimately only actually have one red sweater.

Assemblies were very meh. They’re very scripted and overall I felt they were kinda lame. Activites were a one-sided stomp for the students this time – volleyball despite the huge ball size is always a physical sport. Also, the wifi REALLY sucks in the gym. My laptop’s faulty wifi card (I suspect, at least) doesn’t help the situation.

DAWNGATE BETA (b. 10/09/2013; d. 10/20/2013)

Technically, not dead, just very, very, starved and floundering. I got my beta-key on 10/9, after signing up near the end of August, if my memory serves me correctly. Initially, it looked like an interesting perspective of MOBA’s, incorporating RTS elements like actual drones complementing your gold income. Kill these wells, get more gold income.

It actually turned out pretty close to expectation, really. My winrate is not particularly high, and it seems that not having a jungler at all is a terrible idea (it is with LoL, at least). I don’t think the team without a jungler ever lost, really. This explains probably half of my losses. I wanted to try something new, since I had always mained support in League, and decided to try my hand at ADC – that is to say, Varion. Nearly all of my wins come from Varion (though I think I have a Mikella win) and it’s probably my most competent hero. Champion? Shaper.

My perspective on this game: there’s a lot to take in. But mechanically, it somehow ends up even simpler than LoL. You can think of DotA as a really mechanically challenging game (think heroes like Invoker or Meepo; couriers; denying; runes; the list goes on) with tons of quirks. The difficulty curve is high. I probably will never actually be able to start. LoL is a lot simpler in most ways: hero control is actually intuitive, always locked on your character (this makes multi-unit control somewhat weird though). None of those micro-intensive mechanics that DotA has.

And Dawngate takes this a step further. No more item actives – some of them get relegated to “summoner spells” that you acquire as you level up. (For instance, Zhonya’s Hourglass is now Stasis in Dawngate.) And – this is a big one – most shapers have no resource system. None at all! Whereas in LoL, mana is the standard, with a few exiles such as Riven (ahaha) not needing this resource, and others using energy, and a few using rage or metal or heat or whatever, in Dawngate, apparently Pure Shaping (i.e. nothing but cooldowns) is the standard. That includes all of the ADC’s (except possibly Nissa, I think) so I wasn’t given the option here. Also, itemization has been greatly consolidated, with the array of stats being compacted to a very few numbers. Movement Speed, Cooldown Reduction, and Attack Speed have been reduced to a single stat Haste. Power dictates both your Attack Damage and your Ability Power. How do they ensure certain characters are in their certain roles? Every shaper has its own Attack Damage multiplier. The ADC standard is 1.0, meaning every point of Power equates to one point of damage. Haste also reduces cooldowns for each shaper individually. I like a minimalist design but it appears to have forced them into using such gimmicks to solidify champs into their individual roles.

And yes, no more item actives, except arguably health potions and consumables of the like. Items are differentiated by their passives mainly. One grants additional attack range (I usually beeline for this item as an ADC – it grants Haste too), another acts like an Aura item, giving everyone defensive stats. And a fair few reduce armor. Another acts like Statikk Shiv, and yet another was Runaan’s Hurricane. They weren’t very creative when making these items, it is very evident.

But actually, it’s not that bad of a game. I should probably explain Varion’s toolkit briefly. The Q is an 8-second cooldown straight damage ability linear skillshot, doing pretty serious damage at higher levels. There’s no damage falloff, which means nobody is safe! The W is a teleport ability of sorts: you make a warp, and recast to actually warp to your warp. Very useful ability, which I don’t think anyone in League has yet. (LeBlanc? I never understood that champion. I guess it can be paralleled with Lissandra, to an extent.) And E buffs your autoattacks whenever you cast an ability, along with a free vision toolkit. R is just a lot more damage. And yes, you don’t need any mana to cast any of these. That’s the broken part.

Wards! Everyone gets one ward that expires and you can then place another ward. It’s a step that Riot definitely took in their changes towards Season 4. Gold abilities are somewhat replicated by Riot as well: now there are items in League S4 that grant you gold when creeps around you die. Very good for supports.

But here’s the thing that ultimately caused me to stop playing: the graphics settings, even at Low, are way too high. I mean, I got around 7 fps on this computer, which is pretty new. It’s running Windows 7, ok? (Meanwhile, my laptop is fine, though since I have limited access to it usually, I can’t really test Dawngate to any formal capacity. For some reason, matchmaking is blocked by the school wifi, despite the main game not being blocked. Strange quirk that doesn’t happen with LoL)

LEAGUE OF LEGENDS (b. January 2013 d. 10/22/2013)

The birthdate represents when I believe I started to play ranked, that is to say, immediately when I hit level 30. And the death date represents the death of a dream for gold… at least in season 3. People always say that’s (that is, playing ranked immediately after hitting level 30) a bad idea. But well, it wasn’t THAT bad.

It was right before the League system came out, so I actually got to experience the joys of ELO. And tank it I did. The standard 1200 ELO quickly dropped to about 1038, and I was looming in the low 1100’s by the end of my placement matches (I think I went 3-7). Then the League system approached.

I definitely sought to at least get placed into silver, which I knew required getting back on track to 1200. And, well, the last recorded ELO I had was 1258, winning the next 5 games.

Silver 5 was achieved.

Silver 5 would be where I would reside for nearly the rest of the year, sometimes peeking into Silver 4. My maximum win deficit would be around 16 more losses than wins. But it would eventually rise, after an extremely awesome win record with Sona, going 27-4 with her in a week. My best is Silver 3, promo series, but well life started to kick in.

It’s unfortunate really. I could easily have a positive win record were my computer’s internet to be actually operational, not getting disconnected due to outside forces or inside forces. You know when they say that oh, statistically you should have less afkers, trolls, and ragers because you aren’t one? You should win 5 games for every 4 lost? Well sadly, my afk rate is not very enviable.

But there’s always next season. One at the clearing of college apps.

I’ll be there.

That said, I was also accepted to PBE. I feel a sort of moral obligation to test it out every once in awhile. Some Season 4 core changes have already been implemented such as the trinket system and new support items. They seem quite interesting, actually. And one thing that I might experiment is going Executioner’s Emblem on the ADC, which helps the support out a lot. I don’t know.

On PBE, I believe I was one of the first to find out a Lissandra bug (she feels quite playable actually, might pick her up next season). So yeah. Next season sounds like a good time. Also, one for all is a ridiculously fun gamemode.

Now, I only play LoL proper (i.e. my main account) to maintain first-win (150 IP is strong), by playing Coop-vs-AI. I’m looking at Kha’Zix and Tryndamere, partially because they pwn bots and partially they’re champs I don’t usually play (now that I think of it, I really don’t play very assassin-y or allin champs)

CANDY BOX 2 (b. 10/23/2013 d. 10/25/2013)

Candy Box was an internet sensation. It was one of the first “idle HTML5” games to come out. Then came other spinoffs of the trope – A Dark Room, Cookie Clicker.

But Candy Box is back with a vengeance! Welcome to Candy Box 2.

However CB2 is pretty short actually. There are already videos of a full speedrun in 30 minutes or so. It simply doesn’t feel the same way as Candy Box 1. Graphics are greatly improved – enemies are now more well-endowed than a three-character string. There’s healthbars as well. Really, I was not compelled to keep playing once I finished the game (obviously, not as fast as 30 minutes, but still). The same could be said to Candy Box 1, I guess. Unlocking the computer spoils everything. Although, I did play this game completely spoiler free. So it was fun for awhile.

OMO (d. 10/29/2013)

Solo OMO! Too many things going on at once, checking was fairly limited. In the end, got a 26/30 when I’m certain I could’ve gotten around a 29/30 with proper checking. Meh.

Let’s break things down one problem at a time. I’ll rate things 1-10 by difficulty, 1-10 by work required

1) Um. Well. Yeah. Let’s make sure that all the digits are correct… Don’t try to pull a fast one on me. I mean, for crying out loud, a 4-function calculator is allowed on this test. So… really now? Whatever. [D1 / W2]

2) Wait, we’re done already? Next. (Ok, I guess if you don’t know how to rotate things by 45 degrees for easy viewing it might take about 15 seconds longer). Should’ve made it bigger, maybe. [D1 / W1]

3) Meh easy combo 2^4 done kthxbai [D1 / W1]

4) This actually required a little bit of work, that is to say write an equation and stuff dies. [D2 / W3]

5) 11 is prime this problem = wat [D1 / W1]

6) GG my casework sucks. but well casework = win [D2 / W3]

7) Area ratios, still an easy problem [D1 / W2]

8) Very easy to see what’s going on [D2 / W2]

9) lolwat [D1 / W1]

10) I don’t actually remember solving this problem. [D3 / W4] projected

11) I swear this was on the OMO before… [D2 / W2]

12) Telescopes after a bit. [D3 / W3]

13) So you’re like, clearly you want to nom an antidiagonal, and that’s like the pascal’s triangle [D4 / W2]

14) This problem is very meh [D2 / W3]

15) OFF BY ONE HELP (I see pattern, it works) [D3 / W3]

16) Meh, if you work backwards (which is what you’re supposed to do with these types of problems) you win instantly [D4 / W2]

17) This was an ok problem. [D5 / W4]

18) The hard part was convincing myself it was constructible. [D3 / W5]

19) OMG THIS PROBLEM LOOKS BAD…

Wait never mind, it’s like the cube of pi^2/6.

[D4 / W3]

20) This problem is great. Too bad it can never be used ever again 😦 [D6 / W4]

21) meh [D5 / W6]

22) SADFACE MUCH (Fine, I probably wouldn’t have solved this during the contest) [D8 / W6?]

23) meh [D6 / W7]

24) Super easy telescope thank you very much (Spotting the telescope took one problem’s worth of subconscious thought) [D4 / W4]

25) omg the coincidences! [D6  / W6]

26) meh [D7 / W8]

27) fun problem, sort of [D7 / W7]

28) wow u srs (mischecked that 31 satisfies condition) [D9 / W8]

29) yay linearity of expectation [D8 / W7]

30) Algebra pls [D9 / W10]

So, by my perceived difficulty (D10 would be problems like OMO #30-Fall or #50-Winter, I guess)

10: None!

9: 28, 30 (2)

8: 22, 29 (2)

7: 26, 27 (2)

6: 20, 23, 25 (3)

5: 17, 21 (2)

4: 13, 16, 19, 24 (4)

3: 10, 12, 15, 18 (4)

2: 4, 6, 8, 11, 14 (5)

1: 1, 2, 3, 5, 7, 9 (6)

—-

And by work done:

10: 30 (1)

9: None!

8: 26, 28 (2)

7: 23, 27, 29 (3)

6: 21, 22, 25 (3)

5: 18 (1)

4: 10, 17, 20, 24 (4)

3: 4, 6, 12, 14, 15, 19 (6)

2: 1, 7, 8, 11, 13, 16 (6)

1: 2, 3, 5, 9 (4)

MOCKCON (d. 10/30/2013)

It was an interesting experience.

Becoming a candidate was probably a viable option, given how Je.Wu. successfully won the nomination. But the entry bar was high enough – to produce some video – that I decided against this route. Then I saw the candidates.

Of course I’m going to vote for Je.Wu.

I do not say this unconditionally, but the other candidates I really did not have any motivation to vote for. For our convention, we have four parties: Radical, Liberal, Conservative, and Reactionary. This is the Bay Area, so we’re an extremely liberal bunch. The Reactionary party is basically out, and the Conservatives will have a hard time (although since I suppose they’re more moderate, it won’t be nearly as bad.) I mean, there’s also various fiscal conservatives as the Silicon Valley is job central. So we’ll see.

Various position papers, nothing really surprising. Je.Wu. probably promises more than he can actually do, I disagree with a lot of the Conservative/Reactionary stuff (yeah, I guess I’m a liberal too). The liberal party papers aren’t really that exciting either. It could be a lot closer.

My analysis of the situation: Je.Wu. has the upper hand with the intellectuals at our school, and by that I’ll put an estimate of maybe 25% of the electorate. Unfortunately I’m not sure he has enough name recognition with the rest of the school, so this is not nearly enough; he’ll need quite a bit more than 33% in order to get into the next round, and if he’s going against the Liberals, he loses because the Conservatives would rather vote a moderate position over the radical one.

Debates. Apparently they’re debating on abortion in our period. I remember a particular anecdote in Freakonomics about a Romanian leader Ceausescu who enacted some anti-abortion thing and ultimately (Freakonomics claims) these children that would have been aborted instead overthrow his regime some 22 years later. What irony. The argument is that these children are aborted for a reason; they’re basically unwanted for whatever reason – rape, limited finance, safety, some other ideological reason (I don’t actually know of very many valid reasons to be honest, but that’s a different discussion). We can assume that the mother has a valid reason for abortion, unless you’re some sort of sadist who likes killing unborn babies, but that’s an exceedingly small fraction of the population.

So it would be clear that abortion should be made available end of story right? Well of course the right-wing puts up a religion argument and stuff. Je.Wu. did not perform very well, and despite me telling him the anecdote he didn’t really execute it correctly. For shame. I thought the Liberals did better.

And then more stuff happens. I go ahead and “advertise” which amounts to telling people to vote Je.Wu. here have a tag as well, you already have a tag? well have another tag to give to your friends. This probably improves his chances by maybe 3-4%, and there’s obviously other advertisers other than me, so he gets some popularity boost. No other candidate goes nearly as far with their campaign. I guess the Reactionaries already gave up/mounted a troll campaign, the Conservatives and the Liberals are banking on their relative strength in popularity, with each representing the “main” parties.

Mockcon actually happens, and I’m not sure what most of the stuff goes on. We talk about various issues, and I figure I might as well participate at some point to keep that participation part of Mockcon up. So I go ahead and properly execute that Romanian anecdote. I also talk about how gun control is really awesome.

My stance (and this is pretty much my real stance and not a roleplayed stance) on gun control is that people should not be able to own any guns outright. Legitimate uses of guns – hunting and rifling – will be given on a rental basis; you borrow a gun from whatever hunting ground you want to hunt at, and you return on your departure. Protection is not a valid claim: if you look at many mass shootings, they ended in suicide, so what makes people think that putting a gun to an assailant’s face will deter them? You would also have to actually train people to use guns, and if too many people have this skill it really makes an extremely unsafe community. Law enforcement would not be able to use guns with actual bullets; perhaps they can use tranquilizers or tasers or something. You probably don’t want to actually kill your target, just subdue them.

Then the actual voting of stuff happened after each discussion period. Apparently we sided with the majority (that is to say, the Radical party) each time, although I dissented with one of the issues, I believe foreign policy. We were basically the swing voters, although the only time we deviated from the Liberal party platform was regarding healthcare (on the grounds that the Liberal plan was not good enough). However, that was the closest issue, which probably caused some worry to the Radical campaign. (In reality, probably most of the parties were split on the issue).

The actual election: I know that facing against the Liberal campaign would be suicidal, since they would simply capture the Conservative votes. So the ideal strategy would be to get a Radical/Conservative victory into the runoffs. For some reason Aa.Li. wanted a Liberal/Conservative tie; while this is amusing, it would most likely not work. In the event that this would be resolved by tiebreaking, most Radicals would probably go to the Liberals (and NOT the Conservatives) which would ultimately lead to the Radicals getting quashed. So instead of treading over risky ground, our state (Wyoming) decided to play it safe. (One guy was in the Conservative inner circle though, so his vote was effectively lost). Wyoming is powerful sometimes, in swing situations. We can pretty much fine-tune the results to our liking 😀

Then the runoffs occur, and not completely surprisingly, many Liberals came over to our side, although a fair few did jump to the Conservatives. We win a pretty convincing victory there. GG

COLLEGE EA, OR APPS IN GENERAL (d. 10/31/2013)

Deadlines appear farther than they actually are.

I guess that pretty much sums it up. I relegate Caltech to Regular Decision due to my apparent failure at finishing my apps to an acceptable level by the deadline. (In other words, the only early college that I submit is MIT.)

One more app left, Princeton (as of 12-05)

WMTC (d. 12/01/2013)

WMTC Postmortem

It was a complete surprise; that’s all I’m willing to qualify it, not putting any positive or negative connotations on this word. So, one day, I was called up to the office. This was expected; I had applied to be a TA (anyone can, really – even my godawful GPA (by MSJ standards, of course) was met by the counselor as “great! You can become a TA”). I was expecting a schedule change, as I had had every single year before that (for different reasons than being a TA). But what was to come was very different.

“Congratulations!”

“Huh?”

“You were selected to be on a math team!”

“Wait, what? I never even applied…” (and this is true)

Apparently, one of the people on their team decided to drop out pretty late in the process, and I was one of the early candidates to be selected. Why me, I don’t know. I’m definitely not on the top of the pecking order in Olympiad math, never having been selected to the top 17 (although it’s not a strict top 17, more like a top 9-10 with leeway afterwards) to take the tests after TSTST. (I assume that this is the case since I’m mostly a one trick pony with my combo skills (…formerly?)) And while I suppose my ARML performances peaking at 3rd and 5th are pretty decent, that just means there are people who did even better than me. As I would later learn, ARML performance probably was the more relevant metric, as WMTC is indeed heavily modeled after ARML despite their claims otherwise.

Ok, so I’ve been considered to be on a math team, and all that’s left is my approval. I definitely cannot make a fully reasoned decision in 5 minutes without even knowing what the competition is like, so I defer this until later. Apparently my parents were also contacted during this process as well.

I look at the competition problems, and it’s a mire of computational algebra, computational geometry, and computational trigonometry (geo and algebra at the same time!). The other half of the competition is filled with inequalities and range problems (basically inequality problems rephrased). It didn’t really look very nice, especially with combinatorics historically being my strong point.

Add that to a rather hefty price tag, mostly the plane ticket both ways. But the administration, being woefully ignorant about many things, loves it. Something apparently caught my parents’ eyes as well: apparently if you get a gold medal, you get an invitation to UC Berkeley. I’m not sure what this entails to. Does that mean you get automatic entry? That would be pretty cool; I have a feeling that otherwise getting into Berkeley might be sort of hard due to… a godawful GPA!

Yes, by MSJ standards. But isn’t Berkeley basically MSJ version 2?

Berkeley is at least semi-high on my preference list. Probably even before a few semi-big name privates like Cornell. (It loses to MIT (I want to hope/think that I get in), Caltech (lol oops forgot to early), Stanford (LOL), CMU (dependent on financial package, somewhat), and Princeton (because Princeton))

It probably could mean a lot of other things too. But at any rate, my parents sent me off. It was Thanksgiving break anyway, I was probably going to play video games, sleep in, and maybe do some college apps. (That’s not an entirely wrong analysis.)

So I replied the next day with an affirmative response. The clueless administration was so happy that they called me into the office again to congratulate me. (And then again to finally change my schedule.)

A few months pass.

It is now Veteran’s Day. I do a few practice problems. I don’t like these problems; they’re about as non-kosher from “elementary competitive mathematics” as you can get without directly introducing calculus. A lot of these problems can be “solved” by simply plugging in a random value if a problem asks what the integer part of a particular expression with a variable is. For instance, xsin(x)+cos(x)^2 [with x between 0 and pi/2 exclusive]. The intended solution is probably to note that x > sin(x) always and then it results in 1. But you can simply plug in whatever you feel convenient, whether that be pi/3, pi/6, pi/4, even the endpoints, for god’s sake. [I accept the expression; I’m still agnostic ok?] Yes, nothing suddenly breaks down if you use the endpoints (that said, going negative is fine too). It’s a pretty smooth formula, and you won’t suddenly have random discontinuities.

I do decently well , and I would’ve gotten more or less gold medal range. I make a mental note to be careful, though. Not careful as in other competitions, of course; this is no SMT, PUMaC, HMMT, or even ARML. I’m talking careful as in taking a math test, which I sort of lack. Forget a +C on an indefinite integral? DELETED. Use the wrong bound brackets, or a plus minus sign? DELETED!

This occurs in other contests too, but when you’re relying on the entire contest on a test as to whether you’ve remembered every single last solution, or a test on how fast you can evaluate stuff, it’s no surprise that China always wins. They love this stuff, man. It totally explains how they bombed IMO 2011 #2 far worse than everyone else, and yet still came back with all the other problems. They are masters of mass production, mass calculation, mass precision.

But no ingenuity. No, definitely none of that! I mean, WMTC’s format is more or less ARML except three of the individual rounds have become time trials, with 10 minutes to do 4 problems (it’s doable, but uncomfortable even for me – typically I finish a middle round (5/6 and 7/8) with 3 or 4  minutes to spare, not enough for another two problems.

Back to the post-mortem of the competition itself. I go to SFO, and check in my luggage accidentally. Apparently I wasn’t supposed to do that and carry it onboard. It felt pretty free, to be honest. Security goes without a hitch, and I go to the place. Apparently there’s a lower deck where the flight actually happens. I go there after a bit. I start writing some of my essays for Stanford, and do that general checkin stuff.

On the flight, I finish another Stanford essay, although I’ll still have to fix it a bit. The cool thing is that nobody’s sitting in the middle and I have a window seat, so that’s a bit of extra legroom. What is possibly odd is that there was a woman on the isle seat who was watching Chinese dramas (I think) on an iPad and then a few hours later (I slept for a bit) it was a man playing a card game on the same iPad. I think it looked like Big 2, and then he went on to play Plants vs Zombies and some random missile game. They were spouses; I suppose he was uncomfortable with me sitting alone in a row with his wife? I don’t know, whatever.

I watch a movie to adjust myself to China time. Then I listen to music listlessly on their radio stations; my laptop battery’s out of power. Unlike in the flight to PUMaC there are no AC adapters… except a few in the lavatory, what. What would people do with that anyway, use an electric razor? That said, are electric razors even allowed on the flight?

International flights offer food, apparently. Substantial food, for free. Or rather not free but subsidized by the big plane ticket. On the way there: rice and chicken, with the texture of rice being quite crumbly (BAD) and the chicken being a lump of meat with barbeque sauce pasted on it. In the middle, we get a random sandwich (it was decent, although the plastic wrapping reeked of whatever it was afterwards) and some ice cream (actually quite good!). Then the next meal came and I got eggs. Terrible mistake.

For some reason, I decided to eat the entire thing, including the potatoes. The potatoes were congealed into some cakelike thing. I swear, I got a fit of indigestion when I left the plane, so I suppose that wasn’t the best of plans.

It appears as if I got the worse of options, the other being curried rice (the curry looking quite pungent and the rice actually looking like rice) instead of chicken, and noodles instead of eggs. Oh well.

We wait a very long time, about an hour, before we decide that nobody new would show up. Then another hour at the shuttle. My cellphone runs out of battery so no gratuitous pictures of the airport. Security is annoying. Customs and all. But that goes fine.

We arrive at the hotel. Not really much happens, although this place is very very big. There’s a full-fledged indoor arcade/carnival/amusement park, and an indoor badminton complex of about 20-30 courts. And this is just a single building: our competition site is somewhere else, about 10 minutes away by walking. There’s even a rather dilapidated monorail thing. I try to acquire internet and get a Chinese screen that I can only partially read. After much deliberation, I gather that I need to enter my cell-phone number and some random PIN. Then it appears that the cell-phone number has to be from China. There goes that plan.

And then Ke.Li. says that there should be an Ethernet cable. I ask him for one; I definitely didn’t bring one. I go back to my room, and look where an Ethernet cable should be. OOPS there’s an Ethernet socket… with a complimentary Ethernet cable. Ok, that basically solves things. The ping to League is bad here but that’s expected with a whole ocean to cross (200 to be precise). (PROTIP: Riven is pretty bad with high ping.) I just play for my first win of the day for LoL and smurf a bunch of One for Alls. I also check in on Cybernations and Kingdom of Loathing, as well as more mundane things like emails and Facebook. Yay, my proxy solution works (Psiphon).

I’m rooming with Da.St. and a really short guy called Ma.Li. (and despite the truncation of the name, not Asian). Ma.Mu. (Yes, Je.Wu., your roommate from MOP) would’ve been in our dorm as well but apparently he’s staying with his parents.

The discussion focuses at first on a combinatorial game that Da.St. made up, or more accurately an automaton. I quickly come up with a stable configuration that he was searching for k=3. Why is there no combo in the contest, why!?

Fun puzzle! Figure out the rules of this automaton.

K=3 stable configuration:

X11X

1221

1221

X11X

(X is just a placeholder)

We then explore exploding patterns and I quickly write up a program in C++ on the most excellent IDE ideone.com.  (Sure, a metahint for people figuring out the rules of the automaton)

Next the discussion turns to OP DotA abilities (i.e. everything), between Ma.Mu. and I. Yeah… basically everything.

The actual competition happens. I have a bunch of pencils and pens, as well as water. I don’t end up using more than one pencil and more than zero pens. The team next to up is absent, which leads to a somewhat funny yet awkward moment when they’re called to stand up. Oops no Indonesian team.

I feel that I pretty much got the problems that I would’ve gotten on a pretty much ideal day, including a few tricky curveballs (by that I mean careful curveballs) and a Chebyshev polynomial that I could derive on the spot. (STILL not a good problem to put on a test, but it was sort of fun to find at least!) Despite not getting anywhere near perfect, I feel as if nobody else is going to either. Planar angles suck. See what I mean by a non-kosher competition?

Also, combo! Yay? Nah just kidding, just a VERY standard balls and urns problem and a conditional probability problem that I could do because I simply glazed over the problem that said planar angle. Well, it’s a start, I suppose. I hear that WMTC might be held at somewhere not at China for the first time next year, and I hope the Koreans can show how combo is really done.

(This general lack of combo and overboarding of algebra seems quite the par for the course for China, really. I’m also saddened that there were not one but two planar angle problems.)

The problems, in detail:

Set 1: something / something / something / trig

Set 2: Balls and urns… / Easy range problem / Annoying shoelace problem involving solving three sets of simultaneous equations / Our Russian Comrade Chebyshev

Set 3: Another range problem / “Find x” when there’s a lot of x that could satisfy the given thing / PLANAR ANGLES WHY / Something that looks like an inequality but doesn’t really ask anything

Set 4: Easy range problem / Trick problem involving zeroes of a random function

Set 5: MOAR PLANAR ANGLES / Conditional probability!

So I believe I missed #4 (1.4), #11 (3.3), and #15 (5.1), and gave the best possible answer for everything that wasn’t actually a question…

So 32? Then I give maybe a -4 leeway just in case some other things I missed. Decent I suppose.

Relays are mostly good, our component of Ma.Mu. and I (I’m in position 1 to hopefully give tons of time for Ma.Mu.) gets 2/3. Allegedly Da.St. and Ke.Li. get a perfect, and I don’t know the other two guys (Bi.Su. and Ma.Li.). Team round seems to go quite decently.

Also: WTF BCA (AAST basically) is here wat!

There’s a talk by a Bulgarian guy. Cool, I think I solved this IMO #1. (It’s a freaking geometry ok! I’m definitely qualified to go to IMO!) He talks about generalizations of this, which I’m not entirely certain what he’s actually getting at (other than a possible extremely deep generalization about generalization other than generalizations on problems). Like, I don’t really understand how noting that some 6 points are always on a single conic (better than 5, at least) is useful. Mathematics is supposed to be beautiful and ellipses are pretty ugly and contrived. It strongly compromises the problem fatally. WMTC could use a lesson in how ellipses are contrived as well.

Then the rest of the days are for excursions. I had bad battery rationing the first day and was unable to get much footage from anywhere but the Forbidden City. So instead, we (me, Ma.Mu., Da.St.) play some Ghost on the bus after hearing about other BCA people playing the same. We start off with a simple game of putting a letter in the front or in the end. Then it escalated into putting letters in between as well, then it became an anagram game. The last word for that was UNCOPYRIGHTABLES. Looking for other interesting ways to play Ghost, we try a variant where your final word must have one letter mutated into an adjacent letter (e.g. RUS could become RUT). I suggested a keyboard variant but apparently Da.St. wasn’t very familiar with the QWERTY keyboard off the top of his head.

Then I had another crazy idea, so crazy that it might work. Multi-Ghost. After banning four rare letters of JXQZ, play 22 simultaneous games of Ghost. The catch? You must use a distinct letter on every game. Here are the rules codified:

–          22 simultaneous games.

–          You start off with a letter pool of ABCDEFGHIKLMNOPRSTUVWY (i.e. every letter but JQXZ)

–          You must use your entire pool every turn. (The Ghost rule of insertion is in effect)

–          When a game is lost by someone, either by challenging and failing or completing a word, everyone burns a letter from their pool, in play order starting from the player whose turn is currently happening.

–          Score is added up at the end of the game.

Game 1 started off with a rather quick challenge on QUW (not a word, even from Zyzzyva – sorry Ma.Mu.!), and then things were pretty smooth-sailing, with notable moments being CRANKSHAFTS being challenged (NKHS, which was aimed towards “ANKHS”, became NKHFS). Zyzzyva tells me that HANDKERCHIEFS would be another possible word. I was bluffing on a different word though.

Then at the endgame, two words were transposing into PERFORATED (although at PFORTE it could actually have become PIANOFORTE!) except one of them was misspelled, and the last word to be “completed” was UNCOPYRIGHTABLES (though by that time we did not have enough letters to finish). Yep, that word again. Final score: 5-5-12 losses, me tying Da.St.

The once innocent game with short 3-4 minute rounds became a 4-5 hour behemoth. We played another game, which ended up with 5 turns of peace, until I decided to massively challenge to my failure in each of them as I pulled into a very quick early anti-lead of 0-0-6, either because the words were heading towards my loss (FANATICISM), the words I had nothing to complete with (DEMOCRATICALLY) or the words just escaped my mind (MOTORBIKERS) or I had no idea at all what it was (CUMBERBUND). Fortunately this positioned me very well, with me losing out on another challenge next turn (but winning on a different one), and the score went from 0-0-6 to 0-1-7 to 5-5-7. And we were unsure about the status on the remaining words, but I was only up for one possible word (problematicised that I challenged) while Ma.Mu. and Da.St. had a far more contentious rivalry with four undecideds (showviewing, among others). So I actually had the lowest “maximum score” of 8, compared to 9 and 10. But we don’t know completely for sure as of now.

Assuming problematicised doesn’t go through I should not be able to get dead last :P, though I’m already out of the running for an uncontested first place.

Bluffing is a very interesting part of the game now. I was not actually bluffing on CHSKRS, while I claimed that my only word was “CHESSKERS”, a portmanteau of Chess and Checkers (my word was actually CORNHUSKERS), but I was on GALWIG (Zyzzyva informs me that GLASSBLOWING would have worked – GALIG apparently was going for GALVANISING). We did a triple bluff on HYPERGNT (Da.St. starting with HYPERGENERATION, me adding HYPERGNTM (for HYPERMAGNETISM) and finally Ma.Mu. thinking of HYPERGIANTISM for HYPERGINTM which was challenged.) (It’s also one of our undecideds)

After the second game, I decided that the game ran too short as vowels were certainly in short supply. But how would we fix this? For this came the next step of the game: everyone would come up with their own custom deck of letters, with the current stipulation that there are no JXQZ, and there were at most 6 of any letter (nobody came close to this limit). We also added a cycling mechanic, where everyone would start off with a deck size of 21, and each turn 7 letters are deployed.  (every three rounds the set is regenerated)

The game started much more smoothly, with the first challenge coming in at EEEEI (BEEKEEPING, REENGINEERING), but things mostly smooth sailing. Turn 7 had to be adjourned due to light issues, and the game is still unfortunately on hold.

This would make a good forum game, or even a flash game or full-fledged game. I don’t know.

Awards! The ceremony was really quite hectic, with the powerpoint massively out of sync from the rest of the ceremony, and the silver medals for advanced were leaked – Da.St. and Ke.Li. The powerpoint was hastily rewound back to the title page, and the whole thing was pretty disorganized. Apparently my name was called a few times saying “Get ready to come up!”. Well, that totally doesn’t spoil anything does it?

Yeah, I got a gold medal, the highest ranked U.S. member. I suspect that the top score was only 2 higher (explaining the tiebreaker for top 3), and I tied with about 3 other people for whatever score that I got. It looks pretty consistent with everything that I had heard from before.

Our team was beaten by one of the BCA teams? Darn. Wait how, they got only 1 silver medalist, we got 2 silver and a gold…

The ceremony lasts a very long time of calling people up.

Then a pretty standard bus ride back to the airport, and then airport security stuff.

I should brush up on my Chinese. I almost had the impulse to say “Los Angeles” when the checkin guy asked me where I was going, and I spent a very long time indeed remembering that San Francisco was actually Old Gold Mountain.

More customs / immigration stuff!

I lost my first thing at the airport: my boarding pass. That was a fun run back to the information desk and back.

On the airplane now. With such close quarters, it’s impossible to not see, accidentally or otherwise, what other people around are doing. I guess that really can be self-confirming. There was a flight attendant earlier discussing how life was like to the people in the row in front of us, supposedly after the talk about how to operate an emergency exit. The guy next to me talked to the other guy next to me about introductory stuff. So the guy next to me is a college student (mistaken initially as a high school student?) and the other guy next to me is doing some startup thing. The guy next to me seems to maintain a journal (I suppose the paper forces you to write the more important stuff, rather than the relative “cheapness” of blogging). He indeed talks about the flight attendant. And I open up my Stanford essays and he talks about that too (“the guy next to me is doing Stanford apps”). Yes, eavesdropping is super easy. (Wow, you’re also from Fremont!) The other guy sees my notebook filled with numbers and I guess that elicits a small conversation. Now, he confuses me as a college student initially? Oh, the irony. (I suppose he could assume that the guy and I are of comparable ages, and changed his frame of reference when the guy said he was in college, not high school.) I quickly talk about NIMO and then finish up with my relatively standard combo problem. (and by relatively I mean not very standard. Hopefully!) I’m still trying to make this into a presentable form.

Yay combo problems.

I guess writing a post-mortem is a good idea, so I begin doing so. The guy and the other guy initially sleep for a few hours, and then wake up. Now, there are three laptops in this row: both the guy and the other guy have Macs and I have a Windows. At least one additional laptop exists in front of us. The guy is writing a novel, it appears, and the other guy is watching a movie. I’m eating my stuff, this time careful to pick beef and not chicken. The rice already tastes like rice and the beef I guess is of passable quality and texture.  I might save the salad this time.

Anything further would probably be taking it far too meta, not that the above isn’t already so. I guess I’m running out of battery life to continue this much further. I suppose after this I’ll go sleep at around 3 AM Pacific time, and perhaps wake up at 10 when the flight ends. LOL college apps. Whatever, I don’t really have very good ideas right now for that roommate letter. Maybe the airplane flight. Just maybe…

Two laptops. And when I woke up, one. It appears as if I was surreptitiously given an ice cream thing and a sandwich while I was asleep, and when I woke up the ice cream had transmuted into yogurt. The sandwich was pretty good, and the edges were a nice spicy feeling. Breakfast I guess I skipped (it’s ok, the two options were the same this time, and you know what happened there) but I got a coke to wake me up. I played some Osu!droid to further stimulate my fingers. Apparently, I did significantly better on one of the songs without music, as the music no longer offset me…

Then I opened up this laptop again, intending to finish this post. There was an announcement about WMTC on the intercom, apparently. Hm ok.

I exit the plane, bid farewell to the team, go through customs and security (making that three times), get my luggage, go to my parents, and go home.

And another 4100 words, (or maybe still counting!) to concatenate onto my post-mortem post.

THIS POSTMORTEM POST (b. 10/20-ish, d.12/09)

I suppose this concludes the postmortem post, and as you can see I tend to not really finish stuff that I start until quite a long time later. Oh well. That could be a blogpost in its own right. (It does conveniently attach the WMTC postmortem in the same post though.) And incidentally that postmortem is over half this blogpost. Ah well. Publish time.

Grades

This is a post mostly directed at my parents, who probably don’t even read this blog. You could sort of call it a rant, I guess.

I have never been a particularly studious person, at least in relatively mundane subjects in school. Of course, I do my homework and stuff partly to learn the material as I go and of course to get the points, because grades obviously matter to some extent. You could guess that my grades are not all A’s at this very moment, or else there probably wouldn’t be anything to write about.

But there have been various accusations that have caused plenty of arguments around my house. I address them as follows:

1) YES, I know about my grades too. I get emails from Schoolloop every weekday. I usually don’t check the progress reports unless something major has changed. But when something major has changed, I will want to see what happened for the better or for the worse. And many precipitous drops can be explained by…

2) Ok, it’s a zero. Wait… I turned in this assignment! But of course, you’re going to call me a liar because the teacher knows more about me than I do myself. Please note that teachers have a fairly large latency period and I communicate to them about grades in the following manner:

a) The day after I see that the grade dropped, I’ll go contact them. Of course it’s patently ridiculous to expect instant gratification. But my parents expect it anyway.

b) I’ll then probably wait a day or two to see if the issue resolves. No, I won’t ask them every single day. Teachers in my opinion are people and are not machines that do things instantly. 

c) I ask people relatively non-intrusively. This is to add on to the unspoken politeness I guess. MAYBE it lowers the chance of it actually getting changed, but I think cordiality is an asset that is realized in better subjectivity.

3) Maybe the zero is actually a zero. Well, ok I admit that I forgot to do the assignment. I can’t remember everything. Of course you can tell me to organize better, but I’ve done that before. It doesn’t help that significantly and I believe it poses a significant burden. That is to say, yes, still zeros exist. Yes, I write assignments down if I feel that there’s a lot of things to do for the next day. 

That said, I believe the number of legitimate zeroes that I have had has sharply declined in the past few years.

4) It’s near the beginning of the school year! The teacher decided to change the point system into a category-based one. (or conceivably the other way around but I don’t think that has ever happened) This can wildly affect grades and clearly it’s something to comment on. NOT. I really don’t want to spend another half hour explaining what actually changed, so stop getting onto my nerves about this issue.

5) The grade has still been [insert not that good of a grade] for the past week! Yeah, as if it’s my fault that the teacher either doesn’t update much (Bellotti updates, what, once a month?), or there really wasn’t much to add. I really can’t affect the updates if there are no updates.

6) YES, I do care about my grades. Maybe not with the same enthusiasm as you, but I recognize that an A is better than a B. I will attempt to get an A without spending an overly large amount of effort doing so. 

7) While I appreciate you caring about my grades, and I guess your possible stress over the grade rollercoaster is possibly justified, please note that this stress is entirely optional. If you need to relieve yourself of this stress by ignoring the grades for awhile, DO SO! I actually encourage you to do so. I look at the grades every day, so I know about my situation already.  I think I can handle this “stress” relatively well, but it seems by your outbursts that you guys might not take stress nearly as well. So… yeah. You don’t have to be a proxy for me, especially if it leaves your health/emotional stability in the worse. 

kthxbai.

Research Complete 2 – A design philosophy

I really hope that this idea eventually gets implemented someday (also hopefully by me). This would be for a computer version as a forum really wouldn’t do the calculations justice. It’s sort of my idealized vision of what a civilization-building game would go like, and I’ve played quite a few civilization games (and even their modded counterparts) – Civilization 3, 4, 5, Rise of Nations, Age of Empires 2, 3, Europa Universalis 3, Victoria I and II, ostensibly Starcraft, Starcraft II (to a very limited extent), Warcraft III, and a bunch of mods for Civilization 4. I particularly enjoyed Civilization 4 and Rise of Nations. Of course, I like the Blizzard crafts as well, but they’re less related to a semihistorical context.

EDIT: I forgot to mention Sins of a Solar Empire (not relevant here) and Galciv 2 (very relevant to some of the ideas).

I would suggest at least getting a feel for Research Complete (1) which can be found in the AoPS forums. It was designed to have a heavy emphasis for research with a branching out as enabled by tech.

RESEARCH

Not much I would change here. It would probably have to be a tree-like structure with some techs unlocking other techs. Since I probably want an RTS feel, I would have to ensure that the time standards are reasonable. Early techs would take a few minutes to maybe half an hour, and later techs may take a few days. That would be if the game is persistent multiplayer, which is probably the most reasonable genre to host such a game. (that said, I’ve played quite a few persistent multiplayer games (tribalwars, ikariam, civworld) and they all seem to play the same way. I want to break out of this mold).

I like to keep a mystery of exploration. The first time RC was created, nobody knew what was the best thing to maximize, and this mystique keeps the game interesting. If things are consistent and never-changing, people quickly determine the best possible way to do things, the fastest way to do things, and do them. They make guides: “oh, do this and that and then that for the fastest possible victory” and the game becomes boring and solved. Randomness is one way to do so, but it has to be implemented in an interesting fashion. AI would be one (although the investment to make a worthwhile AI is probably too much to ask for). However, I believe that it may be worthwhile pursuing RANDOMIZED TECH TREES!

They would still make sense, and the gameplay would still have to be viable – core gameplay function should still be intact, although some secondary modules could probably be done away with as an interesting twist. A game without most military function would certainly change some warmongers’ strategies. Also, you would not be able to see most of the tech tree until you unlock them – this is an important characteristic of RC which largely prevented such tunneling.

However, people largely adopted strategies from other people because it was too tedious to copy-paste everyone individual data every day. So people would know what everyone was doing very quickly on. This can be mitigated with a computer version, a persistent multiplayer online game. Collaboration to explore the tech tree is definitely a possibility and I would encourage such alliances. But to prevent large alliances from fully traversing the tree the tree would have to be somewhat big.

(New!) TOOLS

This would play out similarly to Doodle God. It’s a simple minigame to pass the time, and this time there are actual effects. You can unlock more starting items with more techs, of course. Timesinks like these can reward active players. Of course, Doodle God is also susceptible to walkthrough-ization, but hopefully randomized tech trees mitigates this (so random items). This provides a crafting aspect to the game, and perhaps this can be an itemsink: you might damage a resource beyond use if you try to combine things incorrectly, and it might take time before you get good at combining even correct recipes (think of it as learning)

(Sort of new!) LAND

In RC1, this manifested itself as the construction module, but now I’ve split this up into two modules: the use of open land for raw resources (such as metals, rocks, trees) and expansive plots (like farms), and the urban center filled with lots of buildings. I neglected the land aspect in RC1; I hope to include it in RC2. Notably, you will need lots of resources to fund your little city, which comes from the use of land. You can apportion a certain number of people to farm, others to mine, and so on, and in the land module you do not make buildings but rather improve infrastructure. (maybe improve your mining capability or something). Land will have some sort of terrain modifier that makes certain lands more conducive to mining and others for farming or quarrying. With that said, food is important for growing your population which is important for the workforce.

CONSTRUCTION

And this is the building part of things. Buildings will involve the conversion of lower resources into bigger and better resources.  They require people to operate (of course (ok, maybe until you get robots to operate the buildings for you)). You have a lot more control here: you can set the number of people in each building which affects the efficiency of each building.

I like the construction space gating mechanism as much as the next person, but it makes less conceptual sense if we are operating on the premise of such expansive lands. While there will still be a land cost, it will be rather minor. The real cost comes from the construction costs, and the costs to house people into these buildings. Efficiency will operate on sort of a logistic curve: it takes a critical mass of people for a building to become effective, but stuffing too many people into a building and you run into diminishing returns (and perhaps people might die due to bad conditions, etc.). So one would need to create duplicates of the same building, i.e. expanding the building outwards. Food will be a more relevant concern.

MILITARY

I had a dream last night. It would make the game rather simple, really. And that is to create the concept of NEIGHBORS. What I didn’t really like was the monotony of the maps found in Tribal Wars and Ikariam. Each island looked the same, every village was so perfectly aligned to a grid. I get rid of the map, at least partially. Everybody, upon starting the game, is assigned a few (perhaps 6-10) neighbors. These neighbors are not all neighbors with each other though! Instead of a cluster system, there is an abstract map where you have neighbors, which is probably assigned partially based on your join time (so that your neighbors should be of approximately the same relative strength). You can only perform your military exploits on your neighbors (although you can resort to more peaceful measures such as trading and such). However, the catch is this: when you inevitably try to expand your land area via military exploits by carving out land from other people, you might acquire additional neighbors, who could possibly be quite large! The number of neighbors you have should roughly be proportional to the perimeter of your empire, which can either be well-managed or perhaps less well-managed.

Military actions are still much of the same: raid for resources, conquer for some lands, attack for actual military conflict, etcetera.

ESPIONAGE

This was a thorn in the foot in RC1. But with an online interface (and with an actual need for espionage with hidden values and such) espionage might actually work well here. With more powerful spies you can get more information from your neighbors.

MARKET

Another painful aspect of RC1. You can offer resource trading between neighbors and probably a range around them (so perhaps a 4-5 neighbor range). It won’t be a stock market implementation (until perhaps later with stock markets). It could also function in that you have a certain resource that someone else doesn’t have, and a trade could occur.

INVENTIONS

Now, inventions are tied to technologies, so you won’t get irrelevant inventions or anachronistic inventions. You can only invent things that you have already researched. I think Victoria II does a good job exemplifying this aspect.

OTHER MODULES

May add later.

English Homework

PRETEXT: There’s English HW and I decided it might be a good idea to post something after a ton of time of not posting. This is not the longpost, by the way. This is probably very cynical, sort of irrelevant to the prompt, perhaps grammatically incorrect, and I did no planning or editing (other than this PRETEXT) although I did backspace a few times to actually make sentences or catch spelling mistakes (which I habitually do, although this was discouraged in the context of the assignment). Hence, no closure. And stream of consciousness.

 

Are you prepared for the next step? (20 min)

In this essay-thingy, I will attempt to answer a question in 20 minutes. This is for English homework, by the way. The question is as stated, “Are you prepared for the next step?” No planning or editing whatsoever (although my pride sort of cheats this by backspacing quickly) But I digress. One minute in. The real world seems like a whole new world. There is no obvious shelter that is provided, and you need to provide it yourself with your own hands and labor. It is this that this is very different from the circumstances that I face today. Of course, there is college to bridge the gap.

Bridging the gap is a very overused expression. In 3rd grade, I’m pretty sure they said that 4th, 5th, and 6th would be used to bridge the gap to junior high, and in 6th grade they said that junior high was the bridge to high school. In a sense, yes. In a sense, no. I did not really feel the accomplishment of actually crossing the bridge – it was so streamlined. It feels rather as if instead of crossing a discrete gap, a river to cross, I was seamlessly moving from one to the next. I’m pretty sure the bridge is supposed to have this effect. But I never actually feel as if I actually crossed this bridge.

School has been much the same for all these years. While the addition of the period system introduced a variety of teachers that I hold a varied amount of respect to, it really wasn’t so different from before. After all, in elementary school we had to go to different “labs” every week or so for “specialized activities”, and inclass we definitely did a whole host of things each day. It’s basically a schedule. Scheduling appears to be a very integral part of college and beyond as well.

The commitments were basically the same as well. There are school assignments to do each day, and there are extracurriculars. However, testing largely phases out in college, with just a final (which of course has been introduced in junior high, since I don’t remember having to test for finals in elementary school). The claim is that grades now count for high school instead of junior high, which is in a sense true (after all it dictates which college you go to to some extent) but these grades are essentially thrown out in college, and life starts anew. Then college grades are thrown out after you get your second job. These grades are really quite transient, and nine minutes.

It feels as if the world doesn’t really need any given person. And in a sense, this is true as well. Your achievements are essentially for naught after a while, and as the ages pass, you die. Those lucky enough to be an impact to society pass on their legacy. But this is such a chancey thing. How will I know that my legacy will carry on hundreds of years from now? Science is probably the best way to get “immortalized”, and even we don’t know how immortal this is, as science (at least renaissance and beyond) is such a new concept, it’s only about 500 years old. But other things of relative time have mostly faded away. I wouldn’t be able to name most of the Renaissance leaders of the time, for instance. But in their time, I’m sure they felt a lot more important than the scientists did.

So there is the question of how to get a good legacy. Perhaps science will go out of vogue in another few centuries, but who am I to judge? I’m sure people will forget of basically everything in the event of a post-apocalyptic society. They will remember those who brought back any semblance of civilization, and clearly I should try to initiate an apocalypse and save a small collective of people (I’M JUST KIDDING). But really, does it matter what we do? Of course, our hivemind would completely collapse if everyone had this mindset.

If nobody thought they had any commitments, then modern society would probably collapse within a few weeks, if not days. It’s really quite scary how we, who aren’t hardwired to be excessively social (of course, more social than lone warriors like tigers, but I’m talking social at the level of ants or bees) manage to live in such a fragile weave of society. We do have primal, hardwired tendencies – greed, for instance, but society has managed to utilize these tendencies to incentivize stability to a sense. Money is definitely something to go after – the embodiment of wealth. But nothing in our minds has the inherent desire to become intellectual, and it appears as if this value is declining with the rise of the corporate world.

War – it comes up, and this is mainly due to our primal warlike tendencies. We were not meant to live harmoniously as a society of seven billion. But we somehow managed to do so, albeit quite shakily. And this is why war happens.

But back to the question, as I have like two minutes left. Am I prepared to enter this extremely unstable world? Yes and no. Of course, the phrasing “unstable world” should already sound warning bells, and of course I am probably not ready to handle such a thing. But in the end, does it even matter?

There are a few things that would indeed transform this mentality. Immortality would be something that changes the legacy problem on its head, and even the small changes that you make over time would add up to a large amount when you multiply this by an infinite value. But it might eradicate desire, as people lose motivation. But time is up.

 

A Quantum Leap

What an oxymoron. You know, how “quantum leap” in colloquial speech means “lots of progress” but quantum actually means small. Heh.

For those of you still eagerly awaiting for the post with a word count perhaps exceeding the total verbiage of the rest of my blog combined, this is unfortunately not that post. Notably, it is a more quantum post, both in size and by content. The longpost does not have significant quantum mechanics material.

Also, post restriction broken.

Disclaimer: I don’t claim to actually have formal knowledge of quantum mechanics. I won’t even claim to have any knowledge of quantum mechanics! So please be aware of any ramifications in using this potentially inaccurate information in serious applications, such as studying for a test, writing a research paper, or other life-changing events. Notably, much of this stuff was derived from a combination of websites and personal intuition.

Disclaimer 2: A lot of this stuff is review if you’ve already taken some sort of chemistry class. I’m sorry for giving you potentially inaccurate or redundant information. In addition, a lot of this stuff may be more focused on competitive-math-oriented subjects, so I’m going to repeat that information too. So that might be redundant as well.

It was a cool and rainy (if my memory holds on the weather that day) afternoon, about one year ago. In Honors Chemistry, we had been learning about orbitals. Now, the most important part about electron orbitals is not the naming. In fact, that probably holds for 90% of everything else, in that naming is generally not terribly important.

However, naming can be interesting, despite its lack of importance. In this case, orbital naming. No, not the s-orbitalp-orbitald-orbitalf-orbital naming (or else this blog post would be: sharp, principal, diffuse, fundamental. Ok this blogpost is done.), but the naming of each individual orbital.

We start with the s-orbital. I’m actually unsure what it’s named. Probably the 1-orbital. Since the names tend to be subscripts below the s/p/d/f designation, I think the only shape – that is, a sphere – would merely be an s orbital, sans subscript. Well, that was boring.

We could enlarge our orbital shell. The nth orbital shell can hold n supertypes (supertype being each individual letter/block) of orbitals. Yes, I’m being really nonrigorous with my naming. And that’s because naming is not important.

We call the s-orbital in shell number #2 the s2 orbital, the s-orbital in shell number #7 the s7 orbital, and so on. It turns out these orbitals are just larger spheres, with a bunch of inner spheres inside them. In a similar vein other larger orbitals are merely simple expansions, so I won’t delve too deeply into that subject.

The next one, the p-orbitals, is pretty straightforward as well. There are three types, the x, y and z. They are shaped like two-lobed thingies. I will now proceed to add a picture to this blog. This is unprecedented. Wow!

See? I was right about the s-orbital.

In other words, the p_x points in the x direction, the p_y points in the y direction, and the p_z points in the z direction. So far, pretty intuitive.

It’s interesting too, as all the p orbitals fit into a nice little compartament, along with the (not shown) s2 orbital.

Next, with some theory-crafting, although I’m guessing it’s well-explained already. Electrons, as you probably know, have several quantum numbers:

The principal quantum number, n, dictates the shell number.

The orbital quantum number, l, dictates what type of orbital it is. You know, the s, p, d, f, g, h, i, j, k, l, m, n, o, etc. thing.

The magnetic quantum number, m_l, dictates what shape of orbital it is. For instance, p -> p_x, p_z, p_y.

The spin quantum number, m_s, dictates which spin the electron is. As electrons are fermions, they have half-integer spins, i.e. either +1/2 or -1/2.

They are constrained by the following:

n≥l≥|m_l|

|m_s|=1/2

Notably, this gives us 2l-1 total orbital types per orbital. Moreover, this also produces the fact that there are 2n^2 electrons maximum in each electron shell. This also furthermore explains why the periodic table has 2 elements, 8, 8, 18, 18, 32, 32, … elements per row, in conjunction with the Aufbau principle. I always thought it was “Aufbau’s principle” but “Aufbau” means “filling-up” in German and therefore cannot really be in possession of a principle.

When l=0, we get the p_z orbital. When l=1, we get the p_x orbital. Or the p_y orbital. I’m not sure. The other one would be l=-1.

At this point, you ask yourself: why is p_z in the middle? Let’s keep going on.
D ORBITALS!

Come on, it’s not that complicated… yet.

We have five orbitals: d_xy, d_xz, d_yz all look like they have four lobes.

But what’s this? There’s ANOTHER d-orbital with four lobes? Yeah, d_(x^2-y^2). Are you even allowed to put such an expression in the subscript? Oh well.

Then there’s this fifth d-orbital that doesn’t have four lobes. Instead it has three balls stacked on top of each other, d_(z^2). Yay complications.

First, can you see any patterns? Unless you’re ridiculously good at inference, probably not. It took me up to the f-orbitals to figure out some meaningful trend. Why is this? Technically, I cheated here. The groups I picked are rather misleadingly grouped. As hinted in the earlier section, something is special with the z-direction. It becomes even more painfully obvious with the d_(z^2) somewhat sticking out. A few trends that you may notice, on the other hand: all subscripts are of degree l, so they’re all quadratic terms here.

Let’s reorganize the d-orbitals by the z-exponent.

5 d-orbitals and how they fit

I guess it might be somewhat a stretch to say that these clouds easily fit, along with s and p orbitals it would share. Although, I suppose the picture itself definitely does not fit the margins set by my blog. Darn.

So I’ll give instructions, by request, on how to view these oversized images. Open a new tab or window. Right-click the picture and copy the URL, and then paste it onto the tab. Your browser may have more functionality like “open image in new tab” when you right-click, so there may be more direct alternatives.

 

Yeah, d_(z^2) looks kinda like a normal p_z orbital with a donut in the middle. How confusing. Also, d_xy isn’t aligned to axes unlike p_x or p_y (while d_(x^2-y^2) is!) What gives?

At this point, the “Modern Chemistry” book stops here, leaving most students content and happy that they don’t have to learn more in chemistry. But this is rather unsatisfying. Exactly what causes this sort of behavior? What would the f-orbitals look like, and for that matter, the g-orbitals and beyond? How are they named, because they sure don’t look too consistent to me.

tada

Fun news! For the f-orbitals, two of them are named f_(x^3-3xy^2) and f_(y^3-3yx^2)! This obviously suggests some sort of pairing mechanism, and indeed this is the basis of the m_l being positive or negative. The other orbitals are named:

f_(zx^2-zy^2), f_(xyz), f(xz^2), f(yz^2), and f(z^3). The homogeneity condition still holds. The z-exponent thing also holds. (2 per z-exponent except when there’s only z^l.) Let’s try dividing out all the z’s and see what we get:

s: “1”

p: “1”, x, y

d: 1, x, y, xy, x^2-y^2

f: 1,x,y,xy,x^2-y^2,x^3-3xy^2, y^3-3yx^2

The pattern is pretty clear now, no?

Meanwhile, I’ll also try to describe the f-orbitals:

The two new f-orbitals have six lobes each. The ones with z^1 exponent have 8 lobes each, the ones with z^2 exponent have 6 lobes each, and the ones (or rather, I should say, one) with z^3 exponent has 4 lobes, all stacked on top of each other.

Since tabling seems to be a useful idea, we perform this again:

s: 1

p: 2 / 2

d: 3 / 4 / 4

f: 4 / 6 / 8 / 6

We know that those z^n orbitals all seem to have balls stacked on top of each other; it seems rather logical that the next one will have n+1 lobes, preserving the pattern.

But if we investigate the xz^(n-1) orbitals, for instance, we see that ALL of these double-lobes are stacked together. We can see the same thing start to form in the xyz^(n-2) and (x^2-y^2)z^(n-2) orbitals as well, with quad-lobes stacked instead.

And all of this stacking is iterated every time we multiply by z. With induction, we can probably name every single orbital…

Except for the orbitals with no z exponent to begin with.

Let’s take a look:

badly ms-painted work

They all have one layer, unsurprisingly (given that their z-exponent is zero). Starting from the p, d, f, orbitals, we see that the number of lobes increases by 2. They are equally spaced; anyone with decent math contest exposure should probably think about roots of unity at this point. [Root of unity: any complex number x satisfying the equation x^n=1 is known as a nth root of unity]  In fact, out of curiosity, let’s factor the d and f orbitals:

x^2-y^2 = (x-y)(x+y)

y(3x^2-y^2)=y*(rt(3)x-y)(rt(3)x+y)

When are these equations zero? For the former, (x-y)(x+y)=0 => x=y or x=-y. Look at the gaps between the lobes. Sure enough, these gaps exactly correspond with the zeroes! So the lobes can be seen as when the equation of the orbital is not zero. In fact, if we use the definition that these electron clouds are merely probability distributions (it could be possible that an errant electron is somewhere else; it’s just very unlikely), then we can see that the regions where the equation has a high magnitude exactly correspond with the regions where the electrons are “likely” to be found. I would also guess that this is how two electrons can share the same orbital, with such parity.

This makes naming future orbitals rather simple. We’re looking at every other root of unity of the 2(m_l) roots of unity. You may have noticed, especially with the f-orbitals, that the coefficients somewhat follow the binomial theorem. And this is no coincidence; if you are somewhat familiar with math contests, root of unity filters can easily kill certain problems. For example, this one:

What is nC0+nC2+nC4+…+nCn? (n is even)

If n were odd, that would be strange as 0,2,4… tends to not have any odd numbers in this sequence. It would also be easier, assuming that I typoed nCn as “nC(n-1)”, where you could easily invoke a symmetry argument.

However, there is another way.

Recall that the Binomial Theorem states that (x+y)^n = nC0 * x^n + nC1 * x^(n-1)y + … nCn * y^n. By plugging in (1+1)^n, we get the well-known fact that nC0+nC1+nC2+…+nCn = 2^n.

However, how would we extract out every other term? We can experiment and try (1-1)^n. Ok, that’s pretty obviously 0, but what exactly is it by the Binomial Theorem? It is equal to nC0-nC1+nC2-…+nCn. Still not quite there yet, but if we add the two up we get

2(nC0+nC2+…+nCn) = 2^n so our desired result is 2^(n-1).

It is a more complicated path to compute nC0+nC3+nC6+…+nCn (n is divisible by 3). Sure, you could do so combinatorially (really!) but it’s not much fun. Roots-of-unity filters are better in this case. If you don’t do math contests regularly, try this exercise out first. It’s admittedly quite hard if you haven’t seen this before.

[hide=Solution]

[SPOILER]

Darn this isn’t a forum.

Ok, so let the two roots of x^2+x+1=0 be w0 and w1. (They should be omega’s but oh well.) One property that you might notice is that w0^2=w1 and viceversa (w1^2=w0). You might think that property, that two numbers are squares of each other, is rather weird (or you may point out 0 and 1 being squares of themselves, but that’s slightly different), but it’s easily seen:

w0=w1^2=w0^4 => w0^4-w0 = w0*(w0-1)(w0^2+w0+1). So if w0^2+w0+1=0, it satisfies that property. Yes, w0 and w1 are complex numbers, easily seen with the discriminant of x^2+x+1 being negative.

The insight: Consider (1+w0)^n and (1+w1)^n, along with (1+1)^n. By the Binomial Theorem, only the terms divisible by 3 align with each other (giving you 1+1+1), while everything else cancels out, as x^2+x+1=0.

You get something like (2^n+(1+w0)^n+(1+w1)^n)/3 as your final answer. In fact, the fact that n is divisible by 3 was not even necessary for this problem. You could clean up 1+w0 and 1+w1 in this case (they turn out to become sixth roots of unity) but I’ll leave the algebra for later.

[/SPOILER]

[/hide]

That was somewhat of a tangent, sorry.

At any rate, what do the formulas remind you of? We have x^2-y^2, and xy. We have x^3-3xy^2 and 3x^2y-y^3. (If you think I’m scaling up and down arbitrarily, you’d be right, because as it turns out constant multiples don’t really affect anything.) Notably, they appear to “look” like expansions of (x+y)^n. However, there’s a catch. Both (x+y)^n and (x-y)^n have positive coefficients of x^2 and y^2 for instance. We wouldn’t expect x^3 and 3xy^2 to alternate signs either.

Insight: Expand out (x+iy)^n. The real part spits out one part of the orbital, and the imaginary part spits out the other. I guess motivation for this could be wanting to get opposite signs for x^2 and y^2 😛

However, it doesn’t answer a few important questions:

Question 1: How does this factor out into alternating roots of unity?

First, if you didn’t know, the n roots of unity have the form cis(2pi*k/n), because x^n=1 =>(r*cis(th))^n=r^n*cis(th*n)=cis(0)

cis(th*n)=cis(0) only when th*n=2k*pi => th = 2k*pi/n.

[cis notation: cos theta + i sin theta, i.e. polarizing rectangular complex numbers. Polar coordinates are easy to multiply as it’s just multiplying magnitudes and adding angles. Thus, [r*cis(t1)]*[s*cis(t2)]=rs*cis(t1+t2).]

So, this is equivalent to either Re((x+iy)^n)=0 or Im((x+iy)^n)=0. It may be more useful to convert x+iy into r*cis notation here (r^n doesn’t really affect things to be honest).

Re(r^n*cis(n*theta))=0 => cos(n*theta)=0 => n*theta = pi/2, 3pi/2, 5pi/2, …

In other words, theta should equal to (2k-1)*pi/2n, i.e. the odd 2nth roots of unity. Similar logic for Im, just use sin instead. Therefore, (x+iy) must have an angle measure equal to the 2nth roots of unity, so it must be a scalar multiple of a root of unity. Hence the gaps are where they are supposed to be. Yay.

Question 2: But I want a nicer formula!

Well, that’s not a question.

But sure. Do note that the polynomial looks like normal binomial expansion, except with every other term…

Wait this sounds like that root of unity filter I talked about earlier! It might not be so tangential of a tangent after all!

But wait. It’s alternating signs! Let’s root of unity filter again, with different filters.

(1+i)^n => 1 i -1 -i 1…

(1-i)^n => 1 -i -1 i 1…

This seems to work; the i’s cancel out, and every other term alternate signs as we want.

So, the proper polynomial would be ((x+iy)^n+(x-iy)^n)/2.

———————————

Now, this explanation is only satisfactory to a certain extent. For instance, it still doesn’t explain why the d_(z^2) orbital has that strange donut in the middle. Well, now is the time.

Actually, pop quiz because I feel like giving a pop quiz. And “since I’m such a nice person”* (*cue Bellotti) this pop quiz is entirely optional!

Here are some g-orbitals. Please name them, and give the magnetic quantum numbers of each. Have a nice day.

A

B

C

D

(Note: the weird gray sphere is the atom itself.)

[Answers:

a: z^4, m_l=0

b: z(x^3-3xy^2) OR z(y^3-3yx^2), m_l=+/-3

c:  z^2(x^2-y^2) OR xyz^2, m_l = +/-2

d: x^4-6x^2y^2+y^4 OR xy(x^2-y^2), m_l = +/-4]

It was a fine day, knowing what was the approximate shape of the orbitals and knowing every single name of every orbital! But then I stumbled upon this site http://www.uky.edu/~holler/html/equations.html and it was once again a state of agony. (As it turns out, the functions on the right are the wavefunctions themselves. I suppose armed with that information one could accurately construct models for all of the orbitals. However, the associated text to these equations, http://archive.org/stream/introductiontoqu031712mbp#page/n141/mode/2up, is supposedly an “Introduction to Quantum Mechanics”. It was also written in 1935, perhaps a decade after the leading scientists formulated quantum mechanics itself :P)

I have no idea how that’s an introduction. Either they had really smart people back then where even the average layperson knew triple integrals, or I guess it’s not really an introduction. But I digress.

Let’s try to tackle the donut problem. Why would there be a donut there? My best guess is that it’s sort of like a standing wave. You have positive and negative regions, but they just swap with each other, over and over again.

I’m out of witty captions today.

More f-orbitals

The gold regions represent positive and the red regions represent negative. Or maybe it’s the other way around. Either way, they alternate ad nauseum.

Also, there appears to be a sort of rotational effect as well, centered on the z-axis (of course, what other axis is so special?). Meh time to learn about sigma pi delta phi bonding.

I guess I’ll end this post with an anticlimactic link: http://www.falstad.com/qmatom/

Enjoy playing with that app.

Restriction

of the post variety.

 

It’s a subtle one, but it exists. Mostly occured from a rather “coincidental” observation from somebody when this blog was 3 posts long. So I decided to “retcon” (probably misusing the word here) my posting schedule to fit this one. Some of you already know about this, but to those of you who don’t, I’ll just say that a) it leads to somewhat long posting breaks and b) I can’t just publish whenever I feel like it.

 

Also, while I do queue up posts, my queue of completed posts is stunningly small (read: queue size = 0). I do have half-complete posts though. As of last count, four.

 

This post will be fairly short, because I need to finish typing this post in around 3 minutes. Now 2 minutes. Also, I guess the previous post was unjustifiably long, and way too personal and nobody should care about that stuff. Although I suppose this post is as well. (although not “unjustifiably long”. Unjustifiably short?)