Latest Posts by middlering - Page 2

AU where the odyssey takes place entirely in ikea

I have a new post up on my blog, continuing the Fictional History of Numbers series. In part 1 we built on the natural numbers using algebraic operations, and got the algebraic numbers. In part 2 and part 3 we used geometric and analytic arguments to build up the real numbers.

These two sets of numbers overlap, but aren't the same; there are real numbers that aren't algebraic (as we saw in part 3) but also algebraic numbers that aren't real. So what happens if we combine the two? We get the complex numbers, which are complete and also algebraically closed. But proving this is a little tricky, and touches on the deep strangeness of complex analysis.

And in the process of adding algebraic closure to the real numbers, we lose the ability to order them, which has its own consequences.

It’s impossible to give directions in Boston. Nothing makes sense. There are inexplicable one way streets, there are streets that change their names as you move from one area to another. There’s a road in my area where the gps literally tells you to take TWO full right turns to “stay on” the same road which is at a right angle to the original. There’s like four different Massachusetts Avenues. Sometimes you have to be in the left lane to turn right. The gps can’t even get directions to my workplace correct; it tells me to take a left on a road where lefts are not allowed, and the only way to not have to go across the river and take 15 minutes to turn around is to remember this shit one block early and make the left THERE. Recently, they’ve restricted 1 of 2 lanes on each side of major thoroughfares to only allow bikes and buses, and the government officials seemed to genuinely believe that would somehow EASE traffic. Oh and don't try to drive on Memorial Drive on Sundays; they close it for pedestrians. Just because. And when you DO drive on Memorial, there's one exit that will make your gps lose its mind and start chanting random sequences of numbers for four minutes straight. You can't take a Uhaul on Storrow Drive because the bridges that go over it are too short, and every year some doofus college student ignores this rule and proceeds to "get Storrowed" when they shave off the top of the truck on the overpass and get stuck. I-93 turns into I-95 and makes a big circle around the city, so a lot of the time you'll be on I-95 north but driving east or west.

It’s not limited to driving either. The Arlington train station is not in Arlington, it’s in the middle of downtown. Harvard Square is not a square, it’s more like a pentagon. There are four different green line train routes, and they’re labeled B for Boston College, C for Cleveland Circle, D for… Riverside, and E for… Heath Street. The Silver line is listed on the train map but is entirely run on buses which have to be connected and disconnected from power lines every time you go through the route. The Blue line goes to (and I’m not joking) Wonderland. The two red lines are labeled for their southern points: Braintree line goes to Braintree, and the Ashmont line goes to… Mattapan. To be fair, the train itself stops in Ashmont and you continue to Mattapan on a trolley, but that doesn't make it better. South Station and North Station are 1 mile apart and the easiest way to get from one to the other is just to walk it because otherwise you have to travel through 4 or 5 train stops on two different lines. But make sure you memorize the route because there's a good chance your gps will lose signal in the Financial district because it can't get through the buildings. In Boston Commons there are two train stops within line of sight of each other, on the same street, and one of them screams. To get to the trains at Porter Square, you have to ride down escalators 105 feet below street level, or you could just take the 3 flights of stairs totaling 199 steps (presumably because the engineers had something against nice even numbers). The North End is south of East Boston. Castle Island is part of the mainland.

No matter where you're going or how you're getting there, it takes 45 minutes (no wrong turns) or an hour and a half (one wrong turn). It doesn't matter if you're going one stop on a train; it will take 45 minutes. If it's summer, there's a better than 50% chance you'll be in the train car that lost it's AC; if it's winter, you're guaranteed to be in the car where the heat has it up to 80 degrees and the inside of your winter coat will be a sauna. Check the Red Sox schedule before you go south of the river, or you'll be trapped in the waves of baseball fans flooding the streets and days will go by before you're found again. And just... don't go outside on September 1.

If you're thinking that this sounds eldritch as shit, you're right. The entire city is an arcane lock keeping the ghoulies and ghosties from haunting the rest of the nation. We charge it with every "fuck" we utter while we travel our labyrinthine paths and drink our Dunks. You're welcome.

I have a new post up on my blog, continuing the Fictional History of Numbers series. In part 1 we started with the natural numbers and built up the algebraics, which let us solve equations. In part 2 we started asking geometric questions, and constructed the real numbers.

But the real numbers are weird and hard to define. In part 3 we see one way they're extremely strange, and then talk about why we want them anyway. In the end, we shouldn't worry about the definition of the reals; we should worry about what they allow us to do. And it turns out they're exactly what we need to make calculus function as it should.

His Famous Last Words: Billy Joel’s River of Dreams

From the first few chords of “No Man’s Land” to the fade-out at the end of “Famous Last Words”, this album is entirely unlike anything else I’ve ever heard. Heck, it’s unlike Billy Joel. He made a name for himself as the Piano Man—twenty years after that iconic breakout single, he made an album with barely a hint of piano on it and pretty much disappeared so that he could give new musicians a chance to be heard. And he didn’t come back until he had a truly worthwhile song to share.

Now, he’d seen his share of style changes over the years—look at Glass Houses or even The Bridge. But if those albums were a slow shuffle away from his piano-oriented roots, River of Dreams was a flying leap as he traded his trademark baby grand for overdriven guitars. But under this grittier rock sound, it really still feels like a Billy Joel album.

In my mind, no song handles better this fusion of the new sound with Billy’s signature lyrical style and themes than “No Man’s Land”. Despite its obviously rock sound, it is in many ways a thematic successor to The Stranger’s opening track, “Movin’ Out (Anthony’s Song)”. The two songs handle the a very similar sense of disillusionment and uncertainty, as well as the idea that you shouldn’t take what you’re told at face value. To the average listener, this is a shockingly punk rock sentiment to hear from a pop-oriented singer-songwriter, especially as blatant as it is in “No Man’s Land”. But I feel like this theme returning is a wonderful way to close the book on his career as a (probably unintentional) callback.

But that’s just it—this is his final album. He stepped back from music after River of Dreams. This whole album has a sense of finality about it; Billy has always been a storyteller more than just about any songwriter I’ve ever seen, and he seems to have done everything in his power to make his last big story (at least for now) great. For that reason, I find this album thematically akin to Turnstiles. Both deal with moving on and change, though in very different ways. That’s why—to me, anyway—this album seems so fitting as a goodbye. The drastically different styles present here fit and compliment the overall theme of change.

This is all pulled together by the final track, “Famous Last Words”. It’s a slow-paced, easygoing song exploring the prospect of change through the shift from summer into fall, ultimately using this as a metaphor for the end of Billy’s musical career. But it looks to this uncertain future with a feeling of safety and contentment, secure in the knowledge that good things must be somewhere up the road. It’s similar to “Vienna” in that way, as it’s also about accepting the future not with dread but with a willingness to go at your own speed and enjoy the scenery while you’re there.

I’d consider “Famous Last Words” to be among the greatest closing tracks ever—probably topped only by “The Long One” on the Beatles’ Abbey Road. It closes the record with every bit of strength with which “No Man’s Land” opened it, though in an entirely different way. With a track like this as his last true song for so many years, I think “Turn the Lights Back On” wasn’t the perfect single to release; it was the only one that could follow this song in theme, quality, and lyrics. In fact, I would count “Turn the Lights Back On” as almost a coda to River of Dreams because of this.

In the end, though, I think what River of Dreams represents most to me is an artist who wanted to leave a good legacy in terms of his work. From start to finish, it feels like Billy gave this record his all, and I have nothing but respect for any musician who decides to step back when they feel they have nothing left to say at the moment. Not to mention the fact that his decision to stop making new albums every few years most likely gave him time to really buckle down and get to breaking that record for longest residency at Madison Square Garden. Between the aforementioned residency and the clear care and effort put into both River of Dreams and “Turn the Lights Back On”, it seems that Billy Joel has a level of dedication to both his music and his fans that I greatly respect. If he were to make another full-length record, this precedent is enough to show me that it would very likely be a worthwhile one.

A new post up on my blog!  Last time we talked about the algebraic numbers, and how just wanting to solve simple equations can create a ton of different numbers.  But they don’t get us everything.

So this time we start off with the idea of measurement, and wind up inventing the real numbers.  The real numbers are weird.  Real weird.  But they show up when we start asking questions about size or measurement.  And in part 3, we’ll see they’re exactly the right way to do calculus.

Tentative Timeline for the Jeeves Stories

Note: This is almost impossible to get exactly accurate and should be viewed as hypothetical. Wodehouse himself seemed to pay little attention to chronology and consistency of cultural references, so the best I can do is guess. The novels in particular are difficult to arrange, since they are supposed to take place in such a short time period, yet seem to require more time if they are to occur as described.

According to this hypothetical timeline, Bertie Wooster was born around 1901. If so, he would have been seventeen when World War I ended and so could not have participated. If we suppose Jeeves to be ten to twenty years older, he would have been born around 1881-1891, making him between twenty-three and thirty-three when WWI began and ensuring that he would definitely have “dabbled in it to a certain extent,” as he tells Lord Rowcester in Ring for Jeeves.

“Jeeves Takes Charge” – Summer 1925 (Bertie is twenty-four, and the narration is taking place six years in the future, presumably 1931.)

“Extricating Young Gussie” – September 1925 (This story isn’t usually included in the series, but its events are referred to in later stories and so it’s clearly part of the timeline.)

“The Artistic Career of Corky”- Autumn 1925-sometime in 1926 (Necessarily takes place over a long period of time, possibly the entire New York trip.)

“Jeeves and the Hard-boiled Egg” – Autumn 1925 (A few months into the NY stay.)

“Jeeves and the Chump Cyril” – 1925 or 1926

 “Jeeves and the Unbidden Guest” – Autumn 1926 (Set during Coolidge’s presidency (1923-1929), about a year into the stay in NY, “about the time of the year when New York is at its best.”)

“The Aunt and the Sluggard” – Spring 1927

“Jeeves in the Springtime” – April/May 1927

“Scoring off Jeeves” – Summer 1927

“Sir Roderick Comes to Lunch” – Summer 1927

“Aunt Agatha Takes the Count” – Summer 1927

 “Comrade Bingo” – Late July or early August 1927 (Around the time of the Goodwood Cup.)

“The Great Sermon Handicap” – August 1927

“The Purity of the Turf” – August or September 1927 (Three weeks into the stay at Twing.)

“Bertie Changes His Mind” –

“The Metropolitan Touch” – November-December 1927 (A Friday, December 23 is mentioned, making the only possible years in the right range 1921, 1927, or 1932. In light of information in later stories, 1927 seemed the most plausible option.)

“The Delayed Exit of Claude and Eustace” – Probably early in 1928 (Set during the time of an unspecified Oxford term. Bertie’s age is given as around twenty-five or –six.)

“Bingo and the Little Woman” – Between October 1927 and February 1928 (Invitation received to go shooting in Norfolk indicates that it’s sometime during the hunting season.)

“Without the Option” – March or April 1928 (Boat Race Night is usually the last weekend in March or the first weekend in April.)

 “Clustering Round Young Bingo” – Sometime in 1928

“Jeeves and the Impending Doom” – Spring[?] 1928

“The Inferiority Complex of Old Sippy” – Spring[?] 1928 (Takes place sometime before June 1.)

[“The Rummy Affair of Old Biffy” – The mention of the British Empire Exhibition at Wembley would set it around April-October 1924 or 1925. However, this does not fit the timeline as I’ve guessed at it, because it’s clearly set after Bertie’s brief engagement to Honoria Glossop. Adjusting the timeline to fit around this date would cause other problems, so I’ll call this an anomaly.]

“Fixing It for Freddie” – Summer[?] 1928

 “Jeeves and the Yule-tide Spirit” – December 1928

“Jeeves and the Song of Songs” – Sometime in 1929

“Episode of the Dog McIntosh” – Spring[?] 1929

“The Spot of Art” – Summer[?] 1929

“Jeeves and the Kid Clementina” – Summer[?] 1929

“The Love that Purifies” – August 1929

“Jeeves and the Old School Chum” – Autumn 1929

“Indian Summer of an Uncle” – Sometime in 1929

“The Ordeal of Young Tuppy” – November 1929

“Jeeves Makes an Omelette” – Winter 1929 or 1930

Thank You, Jeeves – July 1930

Right Ho, Jeeves – July 29-31, 1931 (Cannot take place the same year as Thank You, Jeeves, because TYJ begins around July 15 after a three-month trip to America, while RHJ opens around July 25 after a trip to Cannes that started at the beginning of June.)

The Code of the Woosters – Autumn 1931

“Jeeves and the Greasy Bird” – December 1931 (It’s said to be more than a year after Sir Roderick’s engagement in Thank You, Jeeves, and Bertie’s awareness of the Junior Ganymede Club suggests that it’s after The Code of the Woosters.)

The Mating Season – April 1932 (The events of Right Ho, Jeeves occurred the previous summer, while the mention of Boat Race Night and Bertie’s cousin Thomas returning to school—presumably for the summer term—suggest an early April date.)

Joy in the Morning – Summer 1932

Jeeves and the Feudal Spirit – July 1932 (Aunt Dahlia is said to have been running Milady’s Boudoir, first mentioned in “Clustering Round Young Bingo,” for three years.)

How Right You Are, Jeeves – Summer 1933 (Jeeves goes on holiday, not the same one mentioned in Jeeves and the Feudal Spirit. Bertie’s moustache from the previous book is mentioned as having occurred a year ago. Aunt Dahlia is said to have run her journal for four years. The one thing I can’t account for is the claim that the events of Right Ho, Jeeves occurred the previous summer, so for purposes of expediency I will consider it an error.)

Stiff Upper Lip, Jeeves – Fall[?] 1933

Jeeves and the Tie That Binds – Fall[?] 1933 (Tuppy and Angela have been engaged for two years.)

Aunts Aren’t Gentlemen – Spring or summer 1934

Ring for Jeeves – June, sometime between 1946-1953 (Set explicitly post-World War II, with an emphasis on societal changes in the UK. Television is mentioned.)

Today on the blog I start a new project: where do numbers come from?

By which I mean, mathematicians deal with lots of weird kinds of numbers. Real numbers, complex numbers, p-adic numbers, quaternions, surreal numbers, and more. And if you try to describe the more abstract types of "numbers" you sound completely incomprehensible.

But these numbers all come from somewhere. So I'm going to take you through a fictional history of numbers. Not the real history of the actual people who developed these concepts, but the way they could have developed them, cleaned up and organized. So in the end you can see how you, too, could have developed all these seemingly strange and abstract concepts.

This week in part 1, we cover the most sensible numbers. We start with the basic ability to count, and invent negative numbers, fractions, square roots, and more.

But that will still leave some important questions open—like, what is π? So we'll have to come back for that in part 2.

I learned today that the International Baccalaureate organization (the ones who run the IB tests) consider the topics lists for their courses to be copyrighted and confidential. They won't share them without a signed release.

I'm genuinely offended by this. I don't know how the fuck you're supposed to evaluate or understand the program without knowing what topics it covers! (They'll share the topics list with me, specifically, in the course of evaluating the test for my university; but I have to sign a release, and have to promise not to share them with colleagues, because they want my colleagues to sign the same release.)

And there's, like, no point to this. It's not a major secret what the topics a calculus course should cover are. (And sure, they do some stats and matrices or something too, and that's all the added info.) I think you can't even legally "copyright" the contents of these lists, because it's factual information and that's not copyrightable.

I'm really seriously tempted to issue an official recommendation to my university to stop giving any credit for IB tests until this policy gets reversed. If they won't freely share information on the program and the test, we'll have to assume that it's valueless and shouldn't earn credit.

(My only hesitation to that is it's probably a quixotic quest that would just hassle some innocent IB students. But if I can get a bunch of other departments to sign on I'll absolutely do it; IB can't sustain that policy if universities stop rolling over for it.)

fields of mathematics

number theory: The Queen of Mathematics, in that it takes a lot from other fields and provides little in return, and people are weirdly sentimental about it.

combinatorics: Somehow simultaneously the kind of people who get really excited about Martin Gardner puzzles and very serious no-nonsense types who don’t care about understanding why something is true as long as they can prove that it’s true.

algebraic geometry: Here’s an interesting metaphor, and here’s several thousand pages of work fleshing it out.

differential geometry: There’s a lot of really cool stuff built on top of a lot of boring technical details, but they frequently fill entire textbooks or courses full of just the boring stuff, and they seem to think students will find this interesting in itself rather than as a necessary prerequisite to something better. So there’s definitely something wrong with them.

category theory: They don’t really seem to understand that the point of generalizing a result is so that you can apply it to other situations.

differential equations: physicists

real analysis: What if we took the most boring parts of a proof and just spent all our time studying those?

point-set topology: See real analysis, but less relevant to the real world.

complex analysis: Sorcery. I thought it seemed like sorcery because I didn’t know much about it, but then I learned more, and now the stuff I learned just seems like sorcery that I know how to do.

algebraic topology: Some of them are part of a conspiracy with category theorists to take over mathematics. I’m pretty sure that most algebraic topologists aren’t involved in that, but I don’t really know what else they’re up to.

functional analysis: Like real analysis but with category theorists’ generalization fetish.

group theory: Probably masochists? It’s hard to imagine how else someone could be motivated to read a thousand-page paper, let alone write one.

operator algebras: Seems cool but I can’t understand a word of it, so I can’t be sure they’re not just bullshitting the whole thing.

commutative/homological algebra: Diagram chases are of the devil, and these people are his worshipers.

wanted to experiment with some brushes on csp so i just sacrificed Regan from @zzztlk and doodled her

Tag yourself I’m Aled’s iPad

Word rhyming is an equivalence relation

Take the definition that two words rhyme if and only if they end with the same sound.

Reflexive: Every word rhymes with itself.

Well, if two words are the same, all their sounds have to match, including the final one, so this point holds.

Symmetric: If A rhymes with B, B rhymes with A.

This one’s really hard to prove, because it’s so obvious. If A rhymes with B, then the final sounds of A and B are the same. They will still be the same if we swap the words around. Please don’t make me explain it more, I’ll cry.

Transitive: If A rhymes with B and B rhymes with C, then A rhymes with C.

Call the sound at the end of word A ‘&’. If A rhymes with B, then B also has to end with ‘&’. If B rhymes with C, and B ends with ‘&’, then C also has to end with ‘&’. This means that both A and C end with ‘&’, and so A rhymes with C.

There we go. The argument no one cares about but me has been made. Rhyme is an equivalence relation. You can all go home.

he's like a stress ball to me.

This idea for an SCP article came to me in a dream, so it’s not necessarily good, but I have to get it out there. My subconscious was clearly influenced by memories of mathematical SCPs (like SCP-033 and SCP-1313) and semiotic SCPs (like SCP-4703, though I hadn’t actually read that one before, and another one I can’t for the life of me find right now but I’ll add it if I do).

Keep reading

In Defense of Tolkien’s Mountains

At tor.com, Alex Acks asserts that the mountain ranges of northwestern Middle-earth are geologically implausible. But I think a fair reconstruction of Middle-earth tectonic history can be made. This is a long post, so I’m putting it behind a read-more:

Keep reading

the world's end memes (1/?)

the craziest part is how it ends with the prototype local hero theme

Suggested Alternatives to the One China Policy

Currently, the policy of the United States on the Taiwan question is that the US recognizes that polities on both sides of the Taiwan Strait hold that there is only one China and that Taiwan is part of China. In the current tense international climate, it may be useful to considers alternatives to that policy.

Two Chinas Policy: The United States recognizes the independence of Taiwan as a sovereign state, separate from the People's Republic of China.

Three Chinas Policy: The US recognizes Taiwan, Hong Kong, and the mainland as independent states.

Four Chinas Policy: The US recognizes Taiwan, Hong Kong, Macau, and the mainland as independent states.

One China Policy (Retro 1978): The US switches its diplomatic recognition back from the PRC to the ROC.

One China Policy (Retro 1911): The US recognizes the Qing Dynasty as the legitimate government of China and finds some schmuck to play Emperor-in-Exile.

Many Chinas Policy: The US recognizes the sovereign independence of every Chinese province.

Too Many Chinas Policy: Hong Kong makes a perfectly fine city-state, so why not let everyone do that? The US recognizes every Chinese municipality as its own independent state.

1436506450 Chinas Policy: The US recognizes the sovereign independence of every Chinese person.

2^1436506450 Chinas Policy: The US recognizes the sovereign independence of every subset of of the set of all Chinese persons.

2^1436506450-1 Chinas Policy: Same as above, but not including the empty set, because that doesn't even make sense because it's already claimed by Germany.

Infinite Chinas Policy (Countable): The US recognizes that (1) The PRC is a China and (2) for every China c, the successor S(c) is also a China, and (3) for every China c, c != S(c).

Infinite Chinas Policy (Uncountable): The US recognizes that the set C of all Chinas is an ordered field, and that every non-empty subset of C with an upper bound in C has a least upper bound in C.

No Chinas Policy: The United States embraces mereological nihilism and recognizes only atoms and the void.

@paradife-loft​ recently posted something jokingly commenting about how the fact that Hobbits call the Baranduin the “Brandywine” implies that the words for “brandy” and “wine” in Westron are in fact, “brandy” and “wine.”

I used to wonder about that myself and a while ago I looked it up. The truth is, maybe unfortunately, something different, but really interesting and it involves not one but two layers of puns:

 Brandywine is actually a very loose translation of the pun. The Hobbits first named the river Branda-nîn, which means border water, because it is, in fact, a border marker, and it sounds like the Sindarin name, Baranduin. But then later they started calling it the Bralda-hîn, which means “heady ale.”

So from there we have Tolkien “translate” it to Brandywine, to preserve the pun being based on a very Hobbit-like alcoholic drink and the sound similarity to the Baranduin, even if it did miss one of the linguistic layers.

But here’s the best part - the Hobbits named the river the Bralda-hîn because it was the color of ale. And the original Sindarin name, Baranduin? It means golden-brown river. So basically the Hobbits took a Sindarin name whose meaning they probably didn’t know, gave it a similar sounding name in Westron, and then made a pun off that Westron to give the river’s name a meaning similar to its original Sindarin one in the first place.

furry cornetto trilogy? furry cornetto trilogy.

shaun’s a ram, ed’s a cow, nicholas is a dog, danny’s a cat, gary’s a lion, king of the jungle ofc, and andy’s a bear 

I got the Thrilling Adventures of Lovelace and Babbage for free from Thriftbooks (after much fussing about getting the book rewards points spent for the best value) and it's like YES, SOMEONE WHO LIKES FOOTNOTING THEIR COMICS AS MUCH AS ME.

Also it's an amazing set of 4 panels

What would Michelle look like if she was an opinicus instead of a Grecian sphinx?

I normally only take reader questions from patreon or the comments of the website because it's easier for me to keep track of them there, but this one was cute and I wanted to answer it! So it's today's reader question!

Favorite book round up

(Gordon ramsay chewing out a restaurant owner over his old expired ingredients) And where the fuck does this door lead? If I see a- (there is a hallway miles long, with ashen black walls and no end in sight)¹

1. oh for fucks sake

What issues would a Jewish Werewolf face? I mean with a lunar calendar and so many of the holidays near the full moon, they would have to get pretty inventive, just think about sleeping in the succah, or since Yom Kippor is about 4 days from the full moon, it should make things interesting as in most stories weres start to lose control near the full moon.

HMMM! (and thank you for sending me these anons!)

I suspect it depends on what tradition we’re drawing from. Werewolves as a whole are mostly a European thing, although people changing into or communing with animals is pretty much a worldwide myth. 

Some things to think about: If you’re not fully conscious (or not conscious in the same way) when you’re a wolf, are you accountable for any destruction you cause? Does transformation count as work? (Also, if you can’t stop yourself from doing work, you probably aren’t breaking Shabbat..) Can you attend synagogue as a wolf?

 And we do have recorded cases of nice werewolves! In Latvia in 1692, an eighty-year-old man named Thiess confessed to being a werewolf who, with other werewolves, regularly went to Hell three times a year to fight Satan to ensure a good harvest. This would be a great tradition for Sukkot, Shavuot, and Tu B’Shevat, and I propose we all adopt the custom immediately!

Some doodles to mark 5 years of The Owl House, because I may be at work but I've gotta commemorate it somehow

"A Lying Witch and a Warden" premiered 5 years ago, on January 10, 2020. The episode was scripted by Dana Terrace (Tiny Nose):

directed by Stephen Sandoval (Mr. Sandoval):

with story by Dana Terrace, Rachel Vine (Viney), John Bailey Owen (Jerbo), and Zach Marcus (Barcus), and teleplay by Dana Terrace and Rachel Vine:

and storyboarded by Bosook Coburn (Bo), Catherine Harman-Mitchell (Cat), Stephen Sandoval, and Dana Terrace:

Yes, if you hadn't caught on yet, they all have self-inserts in the show.

Thanks for creating this universe!

Based on context clues I've put a green dot where I kinda think Tom's house might be. They come out of the forest, which can be seen from Tom's west window, and they saw the downs to the east of his house. And then there's this bit:

By his advice they decided to make nearly due North from his house, over the western and lower slopes of the Downs: they might hope in that way to strike the East Road in a day's journey, and avoid the Barrows.

The yellow arrow is the journey they're hoping to make today :]