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Butter, yogurt, Digger

I've been buying butter in small tubs, so I can leave it out to get soft, and not mess with sticks in a tray. I'd been buying Plugra. Last time I bought Kerrygold, and after leaving it out it was practically turning into butter soup, in temperatures not as hot as they had been. It claims to be naturally softer, because it's from grass fed cows. It doesn't say that grass means more Omega-3 fats, but that's usually the case, and O-3s have lower melting points than O-6 (maybe why deep sex fish use them.) So, that checks out. And O-3 would mean marginally healthier butter.

Question remains whether it's "naturally softer" enough to not be annoying to spread straight out of the fridge.

***

Yogurt making continues, and my latest batch is like the best-set I've ever made. I went for maximum laziness, simply filling the mason jar with milk and sticking that in the oven (heated by pilot light); no pre-heating of milk, no heating of the oven to get the temperature above 106 F. I did add a bit of yogurt from the Trader Joe's tub, in addition to the yogurt already in the jar. I left it incubating for a while, 13 or 15 hours, I think. Came out not very sour, and a mix of semi-solid and stretchy-goopy, vs. my more common "solid on top, fermented liquid beneath" or the "totally separated curds and sour whey" of previous late-generation attempts. I am pleased, if unsure about being able to replicate this.

***

I re-read the webcomic Digger for the first time, a couple days ago. It really is good! Serious story but also hilarious in many places. Pseudoniece G' seems to be liking it, too.

***

I re-read the webcomic Treading Ground last night, for the second or third time. Much quicker, only 251 strips, vs like 750 pages. It's a lot cruder and I'm not mentioning it to 13 year old pseudonieces. But funny in its own way. It also had advice on cutting meat with dull knives (apply pressure and speed) which has served me well since first reading it.

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On cul-de-sacs

problems of cul-de-sacs
http://www.citylab.com/design/2011/09/street-grids/124/
From the 1950s until the late 1980s, there were almost no new housing developments in the U.S. built on a simple grid.

networks that have 45 intersections per square mile (like Salt Lake City) and others that have as many as 550 (Portland, Ore).

In their California study, Garrick and Marshall eventually realized the safest cities had an element in common: They were all incorporated before 1930.
These cities were built the old way: along those monotonous grids. In general, they didn’t have fewer accidents overall, but they had far fewer deadly ones. Marshall and Garrick figured that cars (and cars with bikes) must be colliding at lower speeds on these types of street networks.

foreclosure hotspots tend to be focused in places with the least location efficiency – in spread-out subdivisions

http://www.npr.org/templates/story/story.php?storyId=5455743
On the other hand, there's the problem of having to drive your car almost everywhere. Or, in Speck's words, the uneasy feeling that "your car is no longer an instrument of freedom but a prosthetic device."

cul-de-sac communities turn out to have some of the highest rates of traffic accidents involving young children.
"The actual research about injuries and deaths to small children under five is that the main cause of death is being backed over, not being driven over forward," he says. "And it would be expected that the main people doing the backing over would in fact be family members, usually the parents."

making walkable cul-de-sacs
http://www.accessmagazine.org/articles/spring-2004/reconsidering-cul-de-sac/

Bit more history, and a schematic diagram of changing patterns: https://www.reddit.com/r/explainlikeimfive/comments/4yfhx9/eli5_why_arent_neighbourhoods_built_gridstyle/d6ngpp4

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Plants: mostly not dead

It's been really hot and humid in Boston the past week. It had been cooler, enough so that I broke down and bought a new box fan, despite the uncertainties of my future, and it did good work in my bedroom. But now the weather has gone the other way, and fanw's donated air conditioner is slaving away not just at cooling my room (which it is good at) but most of my apartment (not so good, given both insufficient power and terrible air circulation... still, it does help, as a few seconds on my "balcony" demonstrate.)

My A/C is not asked to cool my second bedroom, aka storage room, aka solarium for my plants. I checked in on those plants just now, and yeah, I let things go too long; the room is an oven, and the soils are dry. Still, they're holding up:

The spathiphyllum is looking droopy and kind of pale, but most of the leaves are green, or a sunburnt yellow, not dry and brown, which is actually pretty good show for it. It has been watered and put on my desk, where it's only 30 C and the sun is filtered.

The basil is still alive, which is amazing given that I bought the annual last summer; it's rather lanky, as the two living stems are making a show of being beanstalks, but it was even putting forth little flowers earlier. It has been watered and put in my bathroom for now, because hey, humidity? I should probably research what it likes about that.

The jasmine has gone really weird: one half is completely wilted and pale yellow, like ghost leaves, the other half is a vigorous green. I don't remember how it was oriented, maybe one part got too much sun? Or not enough? It is draining in my sink, since it lacks a drainage dish, I'm not sure where I'll put it. Probably in my living room with the others.

And finally, the terrarium. I posted about this last year; time has not been good to it. It did quite well for a while, with the rainbow plant finding its way through one of the wholes and growing outside of it. Finally I cut that off; then, worried about water lost to transpiration, I added some. Then I taped over some or all of the holes, for better recycling, also to keep things from growing through. When I next checked, it had all gone moldy. I untaped the holes but still. :( Then the plants died and the mold dried out. But then, later, something managed to sprout again! So that was cool.

But tonight, even that was dead and brown. I finally opened the terrarium again, for the first time since setup, and the soil/matrix was completely dry. I guess its magic recycling powers were defeated by the sheer heat. But I remembered not using all of the seeds, so I added some water and broke up the soil, then added the seeds... and cuttings of jasmine and spathiphyllum, because I didn't have many seeds, actually. It's now in my living room, closer to light than the spathiphyllum.

The spathi and the jasmine are still looking better than when I first rescued each of them from the garbageway. The jasmine only flowered a bit this year, like three blossoms... which still managed to put out a whole lot of fragrance.

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more on first person narrative

A followup to my previous first person narrative post:

Some of the reddit threads that spawned the previous post:

https://www.reddit.com/r/FanFiction/comments/4incmv/do_you_prefer_fics_that_are_told_from_the_first/
https://www.reddit.com/r/FanFiction/comments/4lau6y/big_nopes_for_writing_in_first_person/?ref=search_posts
https://www.reddit.com/r/FanFiction/comments/4tuawd/what_tropes_make_you_immediately_stop_reading/

I still find the aversion weird. First person is natural for letters, a diary, autobiography, or any other version of someone telling their own story.

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Simplified Shadows of Python

I spent longer than I expected figuring out the problem described in Robbie's Shadows of Python post. I kept revising my e-mail to him: "You're wrong because of X. No, I mean Y. Um, Z?" Eventually I got it, I think, and distilled it to a simpler piece of contrasting code:

x=1

def f():
    print(x)

def g():
    print(x)
    x=2

>>> f()
1
>>> g()
Traceback (most recent call last):
  File "", line 1, in 
  File "r.py", line 8, in g
    print(x)
UnboundLocalError: local variable 'x' referenced before assignment


Simply because we will (or even might, it works if the assignment is in an if clause) assign to x in the future, it becomes a local variable for the scope of the whole function, blocking access to the outer scope definition. This compile-time annoyance from the same language that has no equivalent to Perl's 'use strict;' to stop you from using misspelled variables. Thanks, Python.

Checking against the other big scripting language, Perl:

$x=1;

sub f {
    print $x, "\n";
}
sub g {
    print $x, "\n";
    $x=2;
}

f();
g();
f();

[Zefiris:0] perl r.pl
1
1
2


Happy access to a global variable. If you use 'my $x=2;' in g(), then the change to the global-level variable is avoided, of course.

Python would let you use 'global x' in g(), or 'nonlocal x' for intermediate scopes, but that gives you full access to x. There's no "I'm going to create a new local variable from this point on, while having used an outer variable earlier in the function." And this doesn't work:

x=1
def h():
    x=x
    print(x)
h()


You can do that in Perl, with or without 'my', getting expected behavior in each case.

This is part of the reason I'm willing to work in C++ again; yes, it's annoying, but I've seen no language that doesn't have mindbendingly stupid shit in it somewhere.

Edit: someday I'll remember I want the pre tag, not the code tag, for preserving indentation.

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links: cities, labor, evolution

Discussion of urban taxes, which introduces me to the idea of frontage taxes. My new love, along with land tax. http://urbankchoze.blogspot.com/2016/07/city-taxes-as-urban-growth-policies.html?m=1

GE drops annual employee ratings
http://www.wsj.com/articles/ge-does-away-with-employee-ratings-1469541602?mod=e2fb

Massachusetts bans employers asking for salary history
http://thinkprogress.org/economy/2016/08/01/3803836/massachusetts-equal-pay/

Evolution of urban animals is rapid
http://www.nytimes.com/2016/07/24/opinion/sunday/evolution-is-happening-faster-than-we-thought.html

evolution of Europeans and white skin
http://www.sciencemag.org/news/2015/04/how-europeans-evolved-white-skin

Some friends got really excited by this: library furniture maker http://www.wcheller.com/index.html

convention bumps may be due to changing willingness to talk to pollsters, rather than actual changing opinion. Though I wonder if this year is an exception. http://www.vox.com/2016/8/1/12341802/polling-clinton-trump-winning

Advocacy of backing into perpendicular parking spaces http://www.vox.com/2016/8/1/11926596/safer-back-into-parking-spaces

Feynman wrong about Faraday cages?
https://sinews.siam.org/DetailsPage/TabId/900/ArtMID/2243/ArticleID/757/Surprises-of-the-Faraday-Cage.aspx


(PDF) 21 page article on Greek voting, acclamation vs. counting: https://melissaschwartzberg.files.wordpress.com/2011/07/schwartzberg_shoutsmurmurs.pdf

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links

Time for another dump.

Israel's massive desalination project.

Messing with prices works: 5 cent charge cuts UK plastic bag use by 85%.

Smoking gun found in North Carolina: voter ID laws are explicitly racist in their intent, aimed at disenfranchising black voters.

Long piece on Hillary's climate policy.  The DNC pro-gay rights platform.

Houston Chronicle endorses Hillary, way early. They went for Romney last time.

Story on how Hillary helped a constituent with cancer.

Trump claims a tax exemption for people with income <$500,000.  Bit odd for an alleged billionaire.

Apollo http://observer.com/2016/07/space-radiation-devastated-the-lives-of-apollo-astronauts/observer.com/2016/07/space-radiation-devastated-the-lives-of-apollo-astronauts/ dying off of heart disease.

GOP thinker thinks modern GOP is doomed, by its original sin of Goldwater and racism.

Trump blames GOP for RNC ratings.  What a leader.  Such responsibility.  Wow.

Trump talks about a http://www.ifyouonlynews.com/politics/trump-may-have-just-leaked-classified-info-on-his-first-day-getting-intelligence-briefings/www.ifyouonlynews.com/politics/trump-may-have-just-leaked-classified-info-on-his-first-day-getting-intelligence-briefings/ or secret base in Saudi Arabia.  Neither one reflects well on him.

Hillary's DNC speech, annotated.  Trump's speech, annotated.

Another article arguing dieting doesn't work.

Hillary's paid speeches in context.

"Why should I *like* Hillary, rather than fearing Trump?"  A list.  A similar list -- haven't checked to see if they're kept in sync.  Not included: what she did for trans people.

America's gridlock. "What if D's won every place w/ electorate less than 75% white, lost everywhere else? D's would win 292 EV's but just 36 Sen/191 House seats."

Green Party platform calls for something that was done in 2009.  Such updating.

"what if Hillary accepted the nomination with 5 children by three different men, like Trump?"

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I got into this comic in late May, I don't remember exactly why. In short, I liked it a lot, and have re-read various stories out of it several times, and even sketched a bit of continuation fanfic. So, big hit here.

Why do I like it? I guess the usual for me: interesting and sympathetic characters, funny lines (and images) while having a somewhat serious tone (so, like Bujold and Cherryh at times, though much lighter than either), somewhat interesting stories and worldbuilding.

How to describe it in an interesting way? Eh... Like many other webcomics, it's modern day + weirdness, I guess you could put it under urban fantasy. High school students in this case, dealing with magic, alien tech (also magic) and their lives. The soap opera content is actually pretty low; the kids are pretty sensible, and Shive isn't big on darkness or angst.

Special theme: transformations, especially genderbending ones. This strip argues that if magic were real and general, transformation magic would be huge. I believe it.

Also, the government shown has generally been knowledgeable and helpful, along with having a good excuse for covering up magic.

The title doesn't mean anything really, it's just a title.

As with many webcomics, it starts off pretty rough, in both art and writing. Page #2: "There will be moments in this comic where it will be particularly obvious that I began writing it when I was a young man shortly out of high school. This is one of those comics." I would say the comic has found its voice, though not its art, by the end of "Sister". If you can take a lot of in media res, then you could start at the beginning of that. Further back, 'story' starts happening with 'Goo'.

Reasons not to read it: it's ongoing, and not super fast. I think the last year or two of our time covered a day or two of comic time (granted, very busy days.) There's a reason I got tempted to continuation fanfic, after catching up.

Comic has been going since 2002, but the archives don't feel *that* deep to me. Not like a daily regular such as Sluggy Freelance.

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Turkey context:

Turkey's military is sworn to uphold secular democracy. This might be the sixth coup since 1960.

Turkey joined NATO in 1955: https://en.wikipedia.org/wiki/NATO#Members so being a NATO member with a coup isn't new. For that matter, Portugal joined in 1949, and was run by the dictator Salazar until 1968. Greece was run by a junta of colonels from 1967 to 1974.

Erdogan has been undermining democracy, going after opposition MPs https://www.theguardian.com/world/2016/jun/08/erdogans-draconian-new-law-demolish-turkeys-eu-ambitions and prosecuting more than 1800 people since 2014 for "insulting" him.

And this weirdness, from what I'm told is the third largest newspaper in Turkey and legit: http://www.hurriyetdailynews.com/no-one-should-do-politics-in-turkey-except-erdogan-says-chief-adviser-yigit-bulut.aspx?pageID=238&nID=100501&NewsCatID=338

'With President Recep Tayyip Erdoğan at the helm in Turkey, there’s no need for anyone else in the country to engage in politics, presidential adviser Yiğit Bulut has said.

“There is already a leader in this country and he is engaging in politics. There is no need for anyone else to engage in politics. He is engaging in politics both at home and abroad. Our duty is to support the leader in this country,” Bulut, Erdoğan’s chief economy adviser, said during a program on state television TRT Haber on June 14.'

'Bulut, a former news anchor and editor-in-chief of the private broadcaster 24 TV, was appointed as then-Prime Minister Erdoğan’s chief adviser in July 2013 during which time he unraveled a vast and nefarious international conspiracy to assassinate Erdoğan “using telekinesis.” After Erdoğan’s election as president in August 2014, he was appointed as his chief adviser on economics.'

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foods

I've made my fourth consecutive batch of yogurt! Or some variety of fermented milk product, starting from a yogurt culture. I don't know if the way I heat my milk is "real yogurt" or not. It's varied, anyway, but tend to be mild warming, then a long 'cook' in the oven with the pilot light on. I had one batch I heated to be hot and held that for a while, and it came out much curdier than usual, almost like yogurt cottage cheese especially on top. OTOH this latest batch I just heated mildly, and there was still curds or grains on the surface. I wonder if some yeast got in and I'm making a sort of kefir.

For most of my life, cruciferous vegetables have been broccoli. I gagged on my parents' Brussels sprouts, and never saw the point of cauliflower. A while back I started getting into kale ("so nutritious! superfood!"), either frying it in a pan or heating it in a bit of water in pot (steam-boil?) Occasionally microwave, but ehhh.

This week I finally bought a head of cabbage. ("Cheap! Robust!") Still working on what to do with it; first batch (mostly outer leaves) I did the pot thing to. Second, more chopped up, I fried in olive oil, adding a bit of Worcestershire sauce and sriracha and black pepper. Ended up feeling pseudo-Korean. I liked it.

I've also gotten good at grilled cheese sandwiches. Yes, it's not hard. Still, it's a new thing. Now I wonder if I could make patty melts. (My burgers lean that way anyway, since I never buy buns, but I rarely try grilling the bread or some onions.)

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numeric integrals

So there are the left and right Riemann sums, and the much better midpoint Riemann sum. Recently I wondered about integrals that took the average of the endpoint of each strip: (f(x)+f(x+step))/2. The thing is that most of the halves combine, so you can just add up f(x) for each whole step, plus f(start)/2 and f(end)/2. How's that compare?

Much better than the left and right sums, but not quite as good as the standard midpoint one. E.g. the integrals of sin(x) over 0 to pi/2 are

left_: 0.9992143962198378
right: 1.0007851925466327
mid__: 1.0000001028083885
mine_: 0.9999997943832352

All the other integrals I tried show a similar pattern: x, x^2, x^3, 1/x, e(x)... the two are close, but midpoint is just a bit closer to the correct answer. Or looked at another way, has close to 1/2 the error... hmm, that factor is consistent too. I should look into that.

Or: if I just recalled my terminology correctly, midpoint Riemann sums have half the error of trapezoidal Riemann sums. Which is not what I would have expected.

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AVL tree

For a long time, self-balancing trees had seemed like magic to me. Earlier this year I put my mind to figuring them out, and on my own came up with the idea of a weight-balanced tree. With a bit of peeking, I then moved on to a height-balanced tree, pretty much an AVL tree. Then I started coding one in pure C, for Real Programmer (TM) cred.

Stage one, achieved some months ago, fulfilled the basic criterion: you could feed it an increasing sequence of keys, and get a beautifully balanced tree back out. Woo! It had problems, though. Most obvious, I concentrated on the balancing part firt, so got heights on the fly via a function rather than from cached values. Not exactly computationally efficient. Less obvious, I had a clever-seeming tree-rotation function I'd come up with: "to rotate right: insert tree value to the right, copy rightmost left value into root, delete same value from the left tree." Elegant, but O(log(N)), when there are actually O(1) rotations available.

I went back to the project this evening, and got the faster rotations working. It took longer than I expected, because when you do rotations that way, there's complexity: 1->2->3 can be rotated left, but 1->3->2 needs a rotation right (on 3->2) then left, to come out balanced. Turns out that my slower rotation did the correct thing in both cases, so simply replacing my rotate functions wasn't working until I added more logic. Grumble grumble.

I still don't have heights cached, and the whole thing feels like an unholy mess of pointer manipulations (especially with parent points in the tree.) But, progress!

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_First Contact_

1987 book I just finished, by Bob Connolly and Robin Anderson. It's about the contact between white Australians and highland New Guinea in the 1930s, mostly done by Australian gold prospector Michael Leahy, with Leahy's 1930s photographs (and some 1980s ones, by the book's authors.) It's main sources are Leahy's diaries and 1980s interviews of both surviving Australians and highlanders. So we get views from both sides, though most of the surviving highlanders were teens or kids at the time, naturally.

First half or so of the book is a step-by-step following of the initial expeditions, but it later pans out to further developments and reactions, closing with independence for Papua New Guinea in 1975.

Notes:

* The highlanders seem to have been extremely isolated from the coast. They can't have been entirely so, because shells filtered up as highly valuable prestige/trade/moka items, but OTOH they hadn't heard of the white men who'd been on the coast for 50 years, and on first viewing thought the whites were relatives returned from the dead. The highlanders themselves say that.

* Pretty isolated from each other, it seems, or more accurately a person's radius of experience was pretty short, hemmed in by hostiles tribes.

* Volatile mix of racism, paternalism, and humanity among the whites. Michael could readily go for a lethal show of force to "kill before we're killed" while objecting to the bloodfeud killing of the natives or gratuitous killing by his own coastal native 'gunbois'. One brother went half native, taking two native wives and never leaving; a friend from the Administration went full native, being accepted by the highlanders he lived among; Michael turned into an Angry Old White Man, disappointed at not getting wealthy and ranting to his grave against the independence movement.

* Both major Out Of Context problems and rapid adaptation by the highlanders. Took them a while to figure out if the whites were human and not spirit, but quickly taking advantage of the wealth they offered and assessing the physical danger they posed.

* Highlanders somewhat balking at independence, as they had less negative experience of colonialism than the coastal New Guineans, and feared being dominated by the coastals. A Liberian UN commissioner was really surprised at the feelings he ran into. "Development, then independence." Of course, most of the Australians had no intention of developing NG into economic independence, that's not what colonies are for.

* Examples of both benign and imperial introductions of money and trade. The early prospectors weren't that violently rapacious, though killing a fair number of people to establish "don't mess with our stuff"; they brought in lots of wealth of shells, axes, and other goods to buy food and labor with, but the workers weren't losing their own land, and had a real choice to work. Administration and the coastal colonists didn't like independent labor though, and instituted poll taxes that had to be paid in Australian money.

(The prospectors might have been worse had they ever found major gold prospects to dredge. Happily they didn't, and coffee plantations ended up the main means of wealth extraction.)

* WWII was a push toward independence. No mention of attitudes wearing off from the Japanese or the fact of their pushing out Australia, but the returning US and Australian soldiers are claimed to have been relatively egalitarian, a shocking contrast with the pre-war colonists.

* Colonialism probably really did bring down the violent death rate, here.

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First country to recognize the US

I saw a claim that this was Morocco. On researching, it seems a bit complicated.

* In 1776 some Dutch port gun-saluted a US-flagged warship, so "recognition".
* In 1777 Morocco formally recognized the US
* But we might not have found that out until April 1778, due to communication times, by which time I think we knew France had recognized us.

So Morocco seems to have been the first sovereign government to make the decision to recognize us.

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I was reading about the Darien Gap, nigh-impassable swamp at the south end of Central America. Moderately interesting on its own. But the page ends with "It is also mentioned in John Keats' poem 'On First Looking into Chapman's Homer'"

So I read the latter page, which has not just the poem, a paean to Chapman's translation opening Homer up to those who don't know Greek, but analysis of the poem's allusions.

"Then felt I like some watcher of the skies
When a new planet swims into his ken;
Or like stout Cortez when with eagle eyes
He star'd at the Pacific — and all his men
Look'd at each other with a wild surmise —
Silent, upon a peak in Darien."

new planet -- Uranus
Cortez -- actually Balboa
Darien -- Darien

I'm not new to classic poetry referring to modern (for its time) science; I used to be really into John Donne, who had a lot of this. But I'm still impressed by such things.

I also realized that for all my timeline work, I had no real idea when Keats lived. Connecting him to Chapman and Uranus didn't really help, either, though I would have guessed Uranus discovery to be mid-late 1800s. Nope! Keats 1795-1821, poem 1816, Uranus 1781. Which also sounds familiar, hmm. Clearly my art and history time sense needs work.

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LA in Boston?

Much of this year's spring was in fact springlike, cool and cloudy, reminding me of San Francisco. It was a bit weird, but I was happy.

Recently it has been hot and humid. Today it is hot and dry -- 30 C, 42% humidity, 12 C dew point. It feels a bit like LA. Going for a run had my lungs feeling odd... maybe like LA? And there's an odd slightly burned smell to the air, maybe ozone? Though wunderground says the air quality is good. Fire hazard warning, maybe it's just smoke I'm smelling. Which would also be like LA, much of the time... I haven't heard of any ongoing fires, but an auto shop had "heavy" fire last night.

Also, it's bright. Even when in full building shadow, looking out kind of hurt my eyes, and the shadows themselves don't look that dark. I was reminded of "LA light", a result I think of natural and manmade smog diffusing light around. Granted, I haven't been paying that much attention to noon[1] sun and shadows, so I'm not sure what's normal. But it felt different.

[1] 1:30 actually, but that's 12:30 solar time thanks to DST. So pretty close to zenith.

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What's in the box? part N:

* A bunch of clothes that were probably too small for me when left in that box, let alone now
* My burgundy leather jacket, which seems to still look good despite my rounded belly
* My old everyday light tan corduroy shirt-jacket, which old Caltech friends would recognize, which seems to still hang nicely. It must have been REALLY loose then. Needs stitches and dry-cleaning to not be slobby, but worth it.
* The nicest of my old tie-dyes, which is full of holes beyond reasonable repair, but I should take a photo of it because it was a *nice* tie-dye.

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random math stuff

I've never forgotten how to make a Taylor series, but I did forget why or where it came from. I thought about it a bit in terms of increasingly accurate approximations with derivatives, then gave up and looked it up.

"Assume a function has a power series in (x-x0), then plug in x=x0 and take derivatives to find the coefficients."

Hmmph. It certainly works, but feels kind of out of thin air.

As for what they're for, my first thought was "deriving wacky identities for pi and e". More seriously, calculating transcendental functions. But I'd not learned one twist on the latter: if you have a nasty integral, you can expand the integrand as a Taylor series, integrate *that*, and voila, you can calculate the integral.

***

As hinted at before, I like revisiting fundamentals. Feynman's lectures chapter 1-22 is like the bible of this, where he starts from natural numbers, goes through making log tables, then evaluating complex exponentials, and finally getting to Euler's formula through sheer calculation. But there are basics he doesn't cover, like evaluating trig functions without Taylor series. The obvious thing is to work from known angles with the half-angle and angle-addition formulas. But where do the raw values come from? How do we know what angles go with what side length ratios?

Well, the isosceles right triangle is entirely determined by its name, that one's trivial. But how do we know that 30-60-90 goes with 1-sqrt(3)-2? I came up with one way: cos(30)=sin(60)=2*sin(30)*cos(30) -> sin(30) = 1/2.

I learned just the other day that sin(18) has a fairly simple algebraic value. But if you try a similar approach to the above, cos(18)=sin(72), you end up with a cubic equation in sin(18). Bleah! Instead there's a geometrical approach, which I can't describe well without diagrams, but it starts with assuming there's an isosceles triangle such that bisecting one of the equal angles yields a similar sub-triangle. That quickly gives you a 36-72-72 triangle; more cleverness yields that the side/base is phi (golden ratio), and so sin(18) = 1/(2phi).

Speaking of which, the proof that phi is irrational is simple and neat. The golden ratio is defined by n/m = m/(n-m), n>m. Assume it's a rational, so that m and n are integers, and n/m has been reduced to lowest terms. But the golden ratio definition requires there be a yet smaller m/(n-m), contradicting the lowest terms assumption... There's a related geometrical proof, where you start with a golden rectangle with integer sides, cut out a square with integer sides, and keep going... you run out of integers.

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Distance from a point to a line

This was something covered in pre-calculus, way back in 7th grade. Like most of precalc, it didn't leave a deep conscious impression on me. Or much of any impression, in this case. In my new hobby of revisiting math fundamentals, largely in bed, I tried to figure it out in my head, got annoyed, and looked it up. The formula isn't bad, though not one I was working toward (it uses Ax+By+C=0 lines, I was using y=mx+b), but the proofs I saw were pretty grotty. I came up with a new one I like more.

Simplify! Skipping the *really* simple stages, of horizontal and vertical lines, what's the distance from a line to the origin? Combining the two representations, the line is y=-Ax/B -C/B. A perpendicular line from the origin is y=Bx/A. Via algebra, he point of intersection is x=CA/(A^2+B^2), y=CB/(A^2+B^2). The distance from that to the origin is |C|/sqrt(A^2+B^2). (Adding |absolute value| because distances must be positive, also this C is actually a square root of C^2 from the Euclidean distance formula, so of course pick the positive root.)

Now, given a line and some other point (X,Y), we just have to translate the system so the point coincides with the origin. This turns the line into A(x-(-X))+B(y-(-Y))+C= Ax+AX+By+BY+C=Ax+By+(AX+BY+C)=0 Applying the previous result, the distance is |AX+BY+C|/sqrt(A^2+B^2). Voila!

I need a math icon.

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Fun with timelines, Japan edition

This is largely mnemonic notetaking for myself, no guarantees of interest to others.

Periods of Japanese history, with distinctive features, and all the reliability of "I read Wikipedia pages last night".

Jomon: 14,000-300 BC. Sedentary hunter gatherers. Ainu anatomy. Some of the oldest pottery in the world, pre-dating the Middle East by millennia, recently beaten by 18,000 BC pottery found in China. Named for the cords used to imprint decorations on their pottery. Contemporary with, uh, everything, from the Ice Age through to Hellenistic times or China's Warring States period.

Yayoi: 300 BC-250 AD. Full-scale rice farming, bronze and iron tools, population changes to more like modern Japanese, Koreans, and Chinese; one could reasonably thing most Japanese people are the descendants of Korean farmers from this time. Chinese documents start referring to 'Wa', as a chaos of tribal communities. Contemporary with Alexander, Punic Wars, Rome's height; Warring States, Qin dynasty, Han Dynasty. Named for an archeological site.

Kofun: 250-538 AD. First part of the broader 'Yamato' period. Yamato dynasty ends up with hegemony over Kyushu and much of Honshu by the end. Named for giant 'keyhole' shaped tomb-mounds. Haniwa (clay tomb offerings.) Contemporary with late antiquity and the early Dark Ages of Western Europe, and general chaos in China.

Asuka: 538-710. Second half of Yamato. Buddhism introduced. Country name changed from Wa to Nihon. Lots of Chinese borrowing including writing, Taoism, and models of strong government. Imperial family claims equality with the Emperor of China and the title of Tennou. Named for I can't tell. Contemporary with the Dark Ages, rise of Islam, and beginning of the Tang Dynasty.

Nara: 710-794. Named for the capital being at Nara, Japan's first urban center. Writing spreads, with Kojiki, Nihon Shoki, and waka poetry. More Buddhism, and building of Todaiji.

Heian: 794-1185. Named for its capital, now Kyoto. Peak of Chinese influences, and hyper developed court culture, coupled with shitty popular conditions. Real power largely with the Fujiwara. Rise of the samurai class. Tang Dynasty government model. War against the Emishi of northeast Honshu, probably heirs of the Jomon and parent/cousin to the Ainu. Hiragana and katakana developed. Tale of Genji. Breakdown of strong government and rise of feudalism. Beginning is contemporary with Charlemagne (crowned HRE in 800), Haroun al Raschid, and Tang; period spans 1066, start of the Crusades, much of the High Middle Ages, and rise of the Song Dynasty.

Kamakura: 1185-1333. First shogunate, by the Minamoto family. Named for the de facto shogunate capital. Double figurehead: Minamoto shogun wields power for the emperor, and Hojo regents wielded power for the shogun. Zen Buddhism arises, among many other sects. Mongols invade, kamikaze. Contemporary with High Middle Ages, Black Death, and Mongols.

Muromachi: 1336 [sic]-1573. "It gets its name from the Muromachi district of Kyoto.[3] The third shogun, Ashikaga Yoshimitsu, established his residence on Muromachi Street." Openly military government that was nonetheless weak; things get even more feudal, with rise of the daimyo, passing into the Sengoku (warring states) period. Shinto resurgence, spurred by the kamikaze. Europeans start visiting in 1543, bringing pumpkins and guns. Contemporary with Hundred Year's War, Gutenberg, discovery and conquest of Americas, Yuan and Ming dynasties, War of the Roses, rise of Protestantism, fall of Constantinople, Elizabeth I.

Unification period. Most of Shakespeare's career.

Edo/Tokugawa: 1603-1868. Named for capital or ruling family. Very strong shogunate, "sword hunt" of guns and non-samurai swords, stratifies but peaceful and prosperous society, probably the world's best attempt at autarky. Starts in the same year Elizabeth I dies. North American colonies start. Seclusion (sakoku) starts in 1640s, along with Thirty Year's War and execution of Charles I. Ukiyo-e, kabuki, sushi. Rise of literate and mercantile society. Perry visits in 1853, followed by crisis and opening.

Meiji: 1868-1912. Rapid Westernization, industrialization, nominal democracy, end of formal feudalism. More Shinto resurgence, State Shinto, emphasis on Imperial divinity. Defeats of China and Russia. Named for the Emperor (as will be the rest.)

Taisho: 1912-1926. Democratic peak, in between chaos and militarism. WWI and expansion into Asia. First commoner as prime minister. Fear of Communism. Rise of pan-Asianism.

Showa: 1926-1989. Modern history.

Heisei: 1989-. Starts the same year the Berlin Wall falls. Economic stagnation, worldwide appeal of anime.

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