[We interrupt the previously scheduled rant for another rant.]
At some point, if you are so lucky, you will be old. You may already be old. Somebody you love may already be old. Old people, being people, require medical care, and are often treated – because this is basically what primary care in our society consists of – with medications.
Thing is, old bodies handle medicine differently than young ones.
( Take the liver... [3,340 Words] )
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But nonetheless there has been sightseeing.
I already mentioned Rynek Underground.
There is probably more to see than we saw at Wawel Hill, but we did the State Rooms and the Royal Private Apartments of the Royal Palace, and the cathedral. Must remark that dwelling in marble halls, or at least spending several hours walking/standing on floors of that substance, does my lower back thing no favours.
Today we went to Kazimierz, which on reflection, was not, being Saturday, the ideal day to do so - had intended going earlier in the week but ran out of time/energy.
There have also been visits to a number of churches, which after a while tend to run together - lotsa baroque.
Hulu has episodes from 3 seasons of A Crime to Remember, which is an Investigation Discovery show. In my ongoing love/hate relationship with true crime media, ID stands out for their high production values and for about as unexploitative an attitude as you can have. (I wonder, perhaps unworthily, if part of what makes ACtR seem thoughtful rather than vulture-like is that the executive producer and a bunch of the writers & directors are women.) I have also been very fond of Homicide Hunter, partly because the show does not try to sugarcoat Lt. Joe Kenda at all. He's very good at his job, and he is a ruthless avenging angel, but he is not a nice man. I kind of adore him. (I'm pretty sure he'd hate me, but that's okay.)
But ACtR. All the episodes are period pieces. (I joked to my therapist that they must have come up with the idea because they wanted everyone to be able to smoke on camera.) I'm not super fond of the gimmick, in which every episode has a narrator who is a minor fictional character in the real crime being portrayed, but most of the time it works okay. (It works extremely well--give credit where it's due--in "The 28th Floor" (2.4).) The actors--"character" actors all--are excellent, and most of the time they even get the accents matched up to the region. (There are exceptions.) And the producers have interview clips with true crime writers who have written about the cases; with people who investigated the cases (when those people are still alive); with Mary Ellen O'Toole and other experts in various fields; with friends and family of murderers and victims alike. They frequently featured Michelle MacNamara before her death in April 2016--pretty obviously because she was very good at conveying information clearly but without sounding scripted. And, again, because they seem to look for women. They also have gotten Catherine Pelonero more than once. (I actually haven't been able to bring myself to watch the episode about Kitty Genovese, but Pelonero does a great job in the other episodes I have watched her in.)
My true, serious beef with ACtR is its insistent trope of the loss of American innocence. Almost every case is framed as something that destroyed a piece of American innocence, and this is infuriating to me for several reasons:
1. America has never been innocent.
2. The idea of the Golden Age, the before time just out of reach in which everything was perfect, is a very, very old fallacy. (The Romans were all over it.) I think it is pernicious, because it validates reactionary attempts to return to "the good old days," which are "good" (in 20th century America) only if you are white, middle-class or above, and it helps if you're male. ACtR does deal with racism, sexism, and classism, but it doesn't seem to recognize the contradictory position it puts itself in thereby.
3. Casting these crimes as destroyers of American innocence erases crimes that went before. I can give one very specific example: "Baby Come Home" (2.8) about the 1953 kidnapping and murder of Bobby Greenlease, who was murdered before his kidnappers ever tried to extort ransom from his parents. Now I am not at all denying that what happened to Bobby Greenlease is vile and horrible and an expression of the worst part of human nature, but claiming that Carl Austin Hall and Bonnie Heady somehow invented kidnapping children for ransom--or even just the worst and most cruel of bad faith negotiations after the child was already dead--erases what happened to, for one example, Charles Lindbergh, Jr. Or, for another example, Charley Ross. If there was any innocence to be lost in this particular genre of crime, it was lost in 1874, 79 years before Bobby Greenlease's death.
So, yeah. That's the one thing that I really think they get wrong. Otherwise, they do a lovely job, and they have taught me about murders I'd never heard of but I think should not be forgotten: the terrible deaths of Judge Curtis Chillingworth and his wife Marjorie in West Palm Beach in 1955; Charles Whitman's sniper assault on the students, faculty, and staff of the University of Texas in 1966 (which I knew about, but knew kind of wrongly); the bizarre murder of Betty Williams in Odessa, Texas, in 1961; the murder of Veronica Gedeon in New York in 1937, and how the case was largely solved by the editors of the true crime magazines she was a cover model for; the murder of Roseann Quinn in New York in 1973, which was the inspiration for Looking for Mr. Goodbar, and I deeply appreciate the way ACtR questions the LfMG myth and suggests that Theresa Dunn is a cruel travesty of the real Roseann Quinn and the reality of her death. If you are interested in criminology or American history (because nothing tells you more about a culture than its cause celebre murders), I commend this series to your attention.
The latest version of Obamacare repeal seems dead or on life support, with Arizona Sen. John McCain declaring on Friday that he will not support the Graham-Cassidy legislation. Maine’s Susan Collins, Alaska’s Lisa Murkowski and Kentucky’s Rand Paul are also leaning against voting for the bill, which would put the Republicans two votes shy of passage, so it’s not clear whether Graham-Cassidy will even be taken up for a vote next week.
But I don’t think the Obamacare wars are over — or even close to over. We tend to think there are only two possible futures for the Affordable Care Act: It remains in place or Republicans in Congress repeal it. But there are really four paths:
- Repeal and replace succeeds. Republicans in Congress find a way to repeal or partially repeal Obamacare. Sen. Orrin Hatch of Utah has already floated the idea of adopting a reconciliation bill for 2018 that includes tax reform and an Obamacare repeal. This would allow Republicans to attempt to accomplish both major GOP goals using a single bill that would require only 50 votes to pass. It would be hard to pull off, but the fac that Hatch is floating the idea suggests that Republicans may not give up trying to pass an Obamacare repeal with 50 votes, even if they can’t use the 2017 reconciliation process, which expires after Sept 30.
- Executive branch undermines Obamacare. President Trump’s administration could do a number of things — such as cutting the advertising budget for the Obamacare marketplaces (which has already happened) or refusing to pay insurers for cost-sharing subsidies (which Trump has not yet done) — that don’t outright repeal the law, but that severely weaken its effect and over four years might add up to a partial repeal.
- Bipartisanship. A bipartisan congressional effort to fix the law — along the lines of the bill Republican Sen. Lamar Alexander of Tennessee and Democratic Sen. Patty Murray of Washington were working on until GOP leaders decided this week to focus on Graham-Cassidy — could still gain traction.
- Trump implements Obamacare. In this scenario, the Trump administration and Republican governors decide to give up on repeal and instead implement Obamacare. This would mean Trump’s team would need to encourage insurers to remain in the program and some of the 19 states that have not yet expanded Medicaid under Obamacare, nearly all of which are led by Republicans, would likely opt to do so.
Congressional Republicans and the Trump administration, in trying to pass an Obamacare repeal for much of the year, have essentially been vacillating between these four approaches. The White House has taken steps, like paying out the cost-sharing subsidies owed to insurers under the law, that move in the direction of approach No 4. But cutting the Obamacare ad funding is more like No. 2, a kind of Obamacare sabotage. And the Trump administration didn’t formally oppose Alexander’s bipartisan approach until this week, when it seemed like Graham-Cassidy could pass.
It’s hard to say which path Republicans will take, even next week. And this is not because party leaders are stupid or confused about their goals, but because each of these paths is fraught for Republicans.
Repeal and replace succeeds: It’s not an accident that Republicans keep coming up a handful of votes short. The party’s ideology keeps pushing it toward approaches that would cut Medicaid and leave millions more people uninsured. But those ideas are unpopular with the public, and the Obamacare provision that ensures people with pre-existing conditions can get affordable coverage has become a kind of political red line that can’t be crossed,
So Republicans keep trying to advance bills that cut Obamacare’s regulations, rules and costs without leaving more people uninsured or pricing out people with pre-existing conditions. These bills annoy more moderate GOP members (Collins) and also more conservative members (the House Freedom Caucus and Paul) by trying to split the difference between divergent views of health care. The goals (keep the good parts of Obamacare while repealing Obamacare) also fall apart under scrutiny from policy analysts like the Congressional Budget Office, creating some incentive for rushed, opaque processes that annoy more institutionalist Republicans (McCain, Murkowski).
Obviously, this option goes away if Democrats win control of the House or Senate in 2018 or if Republicans no longer occupy the Oval Office.
Executive branch undermines Obamacare: Millions of Americans are already buying insurance through Obamacare exchanges or living in states that have expanded Medicaid. Cutting off the advertising budget for Obamacare is most likely to affect potential beneficiaries of the law, that is, people who have not yet signed up. So I would argue Trump is on safer political ground there.
But any steps that take health care away from people who already have it are more politically complicated. Arkansas, West Virginia and Kentucky all expanded Medicaid under Democratic governors but now have GOP chief executives. All those states could withdraw themselves from the Medicaid expansion. None of them have, because those governors know such a move would be politically perilous.
If Trump’s team used the executive branch to take steps that would gut protections for people already getting coverage through Obamacare, they would face similar political challenges.
Bipartisanship: Even if Senate Republicans drop their Obamacare repeal effort and never come back to it again, I’m skeptical that a bipartisan Obamacare “fix” can pass Congress. Republican members of the House and Senate have spent almost a decade attacking this law. They have told party activists it is terrible. Key groups within the party, like Americans for Prosperity, are deeply committed to ending Obamacare. Would House Speaker Paul Ryan want to bring some kind of “Obamacare stabilization” legislation to the floor and watch it pass even as the majority of Republican House members vote against it? I doubt it.
Trump implements Obamacare: To me, this is the easiest path — or at least the one with the fewest land mines. Team Trump would ratchet down the Obamacare wars, stop criticizing the law and take some steps to implement the ACA, but in a conservative way. (This might include measures like having the 19 states that have not currently expanded Medicaid opt in to the expanded program, but require recipients to have jobs or be in college or a training program, plus pay some small premiums.) Some of Trump’s remarks about Obamacare (he seems open to signing a bill that doesn’t really repeal the law as long as he can claim he fixed it) suggest that the president would not be opposed to such a path. And if he can flip-flop on DACA even though it involves one of his signature issues (tough immigration policies), surely he can flip on health care. Trump could then say that he fixed American health care.
But Trump’s Health and Human Services Department is run by Tom Price, who has been a consistent and fervent opponent of Obamacare. I doubt Price would favor such an approach. In fact, I think Trump’s HHS staff would slow-walk a pro-Obamacare strategy (think of how Trump’s national security staff seems to be trying to stop him from withdrawing the U.S. from the Iran nuclear deal) if the president called for one.
The news of this week suggests that Republicans won’t pass an Obamacare repeal by Sept. 30, although that could change if Collins, Murkowski or Paul suddenly switch positions. But Republicans, I would argue, only have hard choices on Obamacare. And that’s why the last seven months in Washington have felt like Groundhog Day.
Sen. John McCain announced on Friday that he would vote no on the Graham-Cassidy bill, a renewed GOP effort to repeal the Affordable Care Act. FiveThirtyEight’s Politics podcast team weighs in on whether Republicans can still muster a repeal with only a week before their options narrow significantly.
The FiveThirtyEight Politics podcast publishes Monday evenings, with occasional special episodes throughout the week. Help new listeners discover the show by leaving us a rating and review on iTunes. Have a comment, question or suggestion for “good polling vs. bad polling”? Get in touch by email, on Twitter or in the comments.
The Bengals entered this year as playoff contenders with a retooled offense that was considered one of the fastest units in the NFL. But two games into the season, they’ve kicked three field goals. And that’s it, that’s all the points the team has scored. Cincinnati’s inability to score a touchdown in its first two games (both losses) has led to the quick dismissal of offensive coordinator Ken Zampese in his 15th season with the team.
It may not sound like that big a deal to be held without a touchdown for the first two games of the season, but going back to 1970, this has only happened 15 times prior to 2017. Another eight teams registered only a return touchdown, failing to score with their offense.
The 23 teams that got left at the starting gate should not give Bengals fans much confidence in this year’s unit. These offenses would go on to average 17 points per game for the remainder of the season. If you include the two clunkers each team had in Weeks 1 and 2, the group finished the season with a paltry 15.6 points per game. When compared to their previous season’s scoring output, teams — not counting the 1976 Tampa Bay Buccaneers, who were an expansion team and so did not have a previous season — declined by an average of three points.
|AVERAGE POINTS PER GAME|
|YEAR||TEAM||FULL YEAR||GAMES 1-2||REST OF YEAR||PRIOR YEAR||DIFF|
All is not lost here for the Bengals. Eight of those teams that didn’t score an offensive touchdown in their first two games actually went on to score more on average in their remaining games than they did in the previous year. But all of these gains were modest, in many cases less than a point. The biggest rebounders were the 1990 Pittsburgh Steelers, who averaged 16.6 points in 1989, failed to score an offensive TD in Weeks 1 and 2, and then averaged 19.3 points for the rest of the year. The news is less rosy when you look at three most recent examples: The 2016 L.A. Rams, the 2006 Oakland Raiders and the 2006 Tampa Bay Bucs. The inauspicious starts for these three were a dark omen for what was to come. The trio combined to go 10-38.
The hope of modest gains isn’t much for Bengals fans to cling to. This team was expecting its offense, which ranked 24th in the NFL last year, to get much better — not to plateau or fall off a cliff. Since history tells us to expect that teams in the Bengals’ position will score an average of three fewer points per game than they did in the previous season, and Cincinnati scored 20.3 points per game last year, we’d expect the team to post about 17 points per game in 2017. In the 16-game era,1 teams that average between 16 and 18 points per game are 871-1,635-6 for a .348 winning percentage that translates to between five and six projected wins this year for the Bengals.
Of course, the Bengals could have just run into hot defenses in their first two games, against the Baltimore Ravens and Houston Texans. But even the great 1985 Bears gave up 22 offensive touchdowns that season, or 1.4 per game. Getting shut out from paydirt in two straight games is epic futility no matter who you’re facing. Cincinnati might pin Week 2’s offensive fiasco on the fact that is was playing a Thursday night game on short rest, but that likely had no effect given that in games through Week 2 since 2014, teams have actually averaged more points per game on Thursdays (23.3) than in the season as a whole (22.6).
Some expressed worries that the Bengals’ attack would suffer after the team let 35-year-old Pro Bowl tackle Andrew Whitworth leave for the Rams in free agency, but the Bengals attempted to compensate for the loss by picking up even more skill players in the draft. Owner Mike Brown and head coach Marvin Lewis selected world-class sprinter John Ross to be a game-changing deep threat with the ninth overall pick. And in the second round, the club added 226-pound running back Joe Mixon, who ran a 4.5 40-yard-dash at his Pro Day.
And those players were added to a mix that already included three-time Pro Bowl quarterback Andy Dalton, perennial Pro Bowl wideout A.J. Green and one of the league’s most efficient scorers in tight end Tyler Eifert, who since 2000 has the third most touchdowns per catch (minimum 20 touchdowns) among tight ends. The team has 11 offensive players who are home-grown first- or second-round draft picks.
All of which makes the offense’s ineptitude even more perplexing. Which explains why the team took drastic measures: This is the first time in the Bengals’ 50-year history, all of which has been spent under the guidance of the Brown family, that an offensive coordinator has been fired during the season.
But the bigger issue may be Dalton, who currently ranks last in the NFL in QBR with a rating of just 10. The league average QBR through Week 2 is 49; last year, Dalton’s was 52.3. There have even been rumblings about benching Dalton, including from a former NFL Executive of the Year.
Either way, Cincy has no excuses this week — at least, that is, no excuses for not scoring a touchdown. The Bengals are in Green Bay facing a Packer defense that ranks 25th in yards allowed per play through Week 2 after finishing 28th in 2016.
But perhaps the Bengals can look to one of their NFC counterparts for offensive inspiration. The Bengals were the 24th team to go through their first two games without scoring an offensive TD, but the 25th team, this year’s San Francisco 49ers, joined the club just a few days later. After a fortnight of grim, incompetent offense, Brian Hoyer and the Niners exploded for five touchdowns and 39 points in Thursday night’s loss to the Rams.
Then again, when it’s only Week 3 and you are already trying to emulate the feats of the Niners, something has gone terribly wrong.
Every new presidency brings its own language to America, a set of names, acronyms and slang that work their way into the zeitgeist. The Bush era had 9/11, WMDs, freedom fries and misunderestimated, while Obama’s tenure included the 1 percent, Occupy Wall Street, drone strikes and Obamacare. Though President Trump is only eight months into his term, we have already seen some words and phrases making a bid to help define his time in office.
We’ve analyzed every comment posted to Reddit from October 2007 to December 2016 to track how people use language on the site. Search billions of Reddit comments »
At FiveThirtyEight, we have a tool that tracks the popularity of terms used on Reddit, the massive internet message board that is the fourth-most-visited site in the U.S. and the gathering place of some of Trump’s more rabid followers. We’ve now updated that tool with data through the end of July, which means you can use it to search through Reddit comments posted during the first six months of Trump’s presidency. Here we share some of the more intriguing trends we’ve found — changes in how often words, expressions and the names of popular figures crop up — and we encourage you to check out the tool yourself. Tweet @fivethirtyeight if you find something interesting.
MUSLIM BAN vs. TRAVEL BAN vs. IMMIGRATION BAN vs. EXECUTIVE ORDER
BANNON vs. PENCE vs. KUSHNER vs. PRIEBUS
COLLUSION vs. VOTER FRAUD
AMERICA FIRST vs. MAGA vs. BUILD THE WALL
NATIONALIST vs. POPULIST vs. GLOBALIST
COVFEFE vs. BIGLY
AHCA vs. BCRA vs. SKINNY REPEAL vs. TRUMPCARE
ALT RIGHT vs. ALT-RIGHT vs. ANTIFA vs. ANTI-FA
SCARAMUCCI vs. MOOCH vs. SPICER vs. SPICEY
Hop over to the interactive and see what you can find.
You’re reading Significant Digits, a daily digest of the numbers tucked inside the news.
Aaron Hernandez, a former NFL tight end who killed himself in prison while serving a life sentence for murder, suffered a severe form of chronic traumatic encephalopathy, or C.T.E., researchers say. He died at 27 — and having not played football for several years — but nonetheless had stage 3 C.T.E (there are four stages). [ESPN]
Looks like tickets for last night’s Los Angeles Rams-San Francisco 49ers game weren’t exactly highly sought-after commodities: Resale sites had them going for as cheap as $14, or a little less expensive than two pretzels at Levi’s Stadium. Rams won, 41-39. [SF Gate]
Check out Besides the Points, my new sports newsletter.
Percentage of actors cast in British films produced in 1913 who were women, according to a British Film Institute study. That figure in 2017: 30 percent. [The Guardian]
The full consequences of the Flint water crisis are still coming to light: Fertility rates dropped 12 percent while women in the city were exposed to increased lead in their drinking water, according to a new study. Fetal death rates rose by 58 percent. [Detroit Free Press]
Facebook agreed to give Congress more than 3,000 advertisements linked to a Russian group that spent at least $100,000 on divisive ads during the 2016 election. [The New York Times]
Amount owed by North Korea in parking tickets to the city of New York, dating all the way back to the 1990s. Of course, unpaid parking tickets are just one of several downsides of hosting the United Nations, especially when the general assembly is in session. Others include: abysmal traffic, dinner reservations becoming impossible, motorcades being less cool than normal and midtown hotel lobby bathrooms no longer being a reliable emergency option for the week. [NBC News]
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If you see a significant digit in the wild, send it to @WaltHickey.
Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-size and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,2 and you may get a shoutout in next week’s column. If you need a hint, or if you have a favorite puzzle collecting dust in your attic, find me on Twitter.
This week, we’ve got two puzzles from the forthcoming puzzle book “The Original Area Mazes,” by Alex Bellos, Naoki Inaba and Ryoichi Murakami. The goal of these puzzles, which are also known by the Japanese term “menseki meiro,” is to figure out what the “?” equals. The only math you’ll need to know is that length times width equals area. Keep in mind that the diagrams aren’t necessarily to scale — this is about logic, not measuring.
Solution to last week’s Riddler Express
Congratulations to Kristian Hougaard of Copenhagen, Denmark, winner of last week’s Express puzzle!
Twenty ghostbusters are on their annual camping retreat. Two of them, Abe and Betty, have discovered that another pair, Candace and Dan, are in fact ghosts posing as ghostbusters. Abe and Betty hatch a plan: When all 20 campers are sitting in a circle around the campfire, Abe will fire his proton pack at Candace, and Betty will simultaneously fire her proton pack at Dan, annihilating the ghosts. However, if two proton streams cross, it means the end of all life on Earth. If the ghostbusters are arranged randomly around the fire, what are the chances that Abe and Betty will cross the streams?
The chances are 1/3.
There are 20 ghostbusters, but we only really care about four of them — Abe, Betty, Candace and Dan. The position of the other 16 won’t affect the possible crossing of the streams, so let’s ignore them. (Sorry, you 16 irrelevant ghostbusters.)
Fix Abe’s spot at the campfire — say he’s on the north side. There are then three places his co-ghostbuster Betty can sit — east, west or south. The ghosts, Candace and Dan, will sit in the other two seats. There are 3*2*1 or six possibilities for the seating in the east, west and south seats. In exactly two of these arrangements — the two where Candace occupies the southern seat, forcing Abe to fire across the circle — the ghostbusters will cross their proton streams. Each of these six arrangements is equally likely, so the chances of stream-crossing disaster are 2/6 = 1/3.
Solution to last week’s Riddler Classic
Congratulations to Carl Ober of New Britain, Connecticut, winner of last week’s Classic puzzle!
Last week, you faced four sticky questions:
- If you break a stick in two places at random, forming three pieces, what is the probability of being able to form a triangle with the pieces?
- If you select three sticks, each of random length (between 0 and 1), what is the probability of being able to form a triangle with them?
- If you break a stick in two places at random, what is the probability of being able to form an acute triangle — where each angle is less than 90 degrees — with the pieces?
- If you select three sticks, each of random length (between 0 and 1), what is the probability of being able to form an acute triangle with the sticks?
The probabilities are, respectively, 1/4, 1/2, \(\ln(8)-2\) and \(1-\pi/4\).
To solve these geometry problems, let’s draw some pictures! We’ll take the questions one by one.
For No. 1: Call the lengths of the three pieces \(x\), \(y\) and \(z\). They form a triangle if the sum of any two sides are larger than the third side (\(x+y>z\), \(y+z>x\) and \(x+z>y\)). This is called the triangle inequality!
Now to our stick, which we’ll assume is one unit long. Call the points where we broke it \(a\) and \(b\), both chosen at random. That gives us pieces of length \(a\), \(b\) minus \(a\) and 1 minus \(b\). Substituting those lengths in for \(x\), \(y\) and \(z\) above simplifies those triangle equalities:
- \(x+y>z \Rightarrow a+(b-a)>1-b \Rightarrow b>1-b \Rightarrow 2b>1 \Rightarrow b>1/2\)
- \(y+z>x \Rightarrow (b-a)+(1-b)>a \Rightarrow 1-a>a \Rightarrow a<1/2\)
- \(x+z>y \Rightarrow a+(1-b)>b-a \Rightarrow 2a+1 > 2b \Rightarrow b-a<1/2\)
So, armed with the lengths of those three pieces, we can visualize the answer to the problem. As long as our randomly selected points on the stick (\(a\) and \(b\)) satisfy those inequalities we just made, we know we can make a triangle. We can plot values of \((a,b)\) as coordinates in a plane, as Laurent Lessard did:
The shaded areas are where the inequalities are satisfied. (There are two triangles because one corresponds to when \(a>b\) and the other when \(b>a\).) Those areas take up ¼ of the total square, which gives us our answer: 25 percent.
For No. 2: What if, instead of pieces from one stick, we pick up three sticks of random length somewhere between zero and one? This is a little trickier. When we plotted the first problem, it could be collapsed to two dimensions, because we were only really worried about two sticks — the length of our third piece was automatically determined by the length of our first two pieces. But this problem is in three dimensions, so the solution needs to be plotted not in a one-by-one square but rather in a one-by-one-by-one cube.
To help solve the problem, consider what wouldn’t solve it: a violation of our triangle inequalities. Suppose, for example, that \(x>y+z\), which makes it impossible to build a triangle. In that formulation, those points are contained in a pyramid bounded by the planes \(y=0\), \(z=0\), \(x=1\) and \(x=y+z\). There are three such pyramids in this cube, one for each of the ways the triangle inequality can be violated.
Each of those pyramids has a volume of ⅙. (A pyramid has a volume equal to the area of its base times its height, all divided by three. Our pyramid in question has height 1 and a triangular base with area ½.). Therefore, there is a ½ chance we can’t make a triangle, and a ½ chance we can. And so we have the answer to the second problem.
No. 3: Getting tougher still (as though that were possible)! Now it’s time for calculus. Guy D. Moore explains this one for us:
The problem asks us to ensure that three pieces form an acute triangle. Consider three pieces with lengths \(x>y>z\).
First, think about a right triangle. The formula for that, as our middle school teachers drilled into our heads, is \(x^2=y^2+z^2\). (Otherwise known as the Pythagorean Theorem.) To have an acute triangle, all angles must be less than 90 degrees, so we tweak that formula: \(x^2<y^2+z^2\).
From this we get that y<x and \((1-x)^2<y^2+(x-y)^2\), which is the same as
Since we’re dealing with pieces of the same stick and not three separate sticks, we can return to plotting in two dimensions, not three. And our mirrored-triangle plot is useful again since our answer lies within those two original triangles. This time, though, we need to draw two new three-pointed shapes within those two triangles. The area of those shapes will be our answer — the probability of an acute triangle.
So to calculate our new shapes, we need to cut pieces out of our original triangles. The area of one of those pieces is expressed in an integral (which is the calculus part of the solution). That integral is:
There are six shapes, each with the same area, cut out of our one-by-one square, leaving:
In that equation, “ln” is the natural log, which equals an implied probability of acute triangle-formation of about 7.9 percent. (Who knew that natural logs are a great way to solve stick problems?) Guy also provided this illustration of the curvy areas we calculated:
No. 4: We’re back to three dimensions again for the final question. This solution furthers the solution from problem No. 2, the way that solution No. 3 furthers solution No. 1. Laurent explained his solution this way:
We’ll solve this problem the same way we solved No. 2, but we’ll replace the triangle inequalities with the acute triangle inequalities. As in No. 2, we end up with a three-dimensional volume rather than a two-dimensional area. For simplicity again, we’ll assume that \(c\) is the largest length, which accounts for one-third of all possibilities.
Laurent provided a lovely illustration of this volume:
Our answer will ultimately be three times the area of this shape (this shape only accounts for stick c being longest, and two identical shapes will be generated for stick b being longest and stick a being longest).
Our solution lies in the filled-in parts of that shape. While this looks complicated, the curved surface inside that area has the equation \(c^2 = a^2 + b^2\), which is, conveniently, the equation of a right circular cone! So we can calculate the volume of the region of interest by subtraction. It’s ⅓ of the volume of the cube minus ¼ of the volume of the cone. (One-third because we’re considering only one out of three scenarios, the one where c is longest. And ¼ because the cone’s base is ¼ of a circle.) The total probability is three times this volume, because we must account for the remaining identical pieces. The final answer is \(3(1/3 − 1/4 ( \pi/3 ) ) = 1 − \pi/4\) or about 0.2146. So the probability of forming an acute triangle with three randomly chosen lengths is about 21.5 percent.
Want to submit a riddle?
Email me at firstname.lastname@example.org.
Planning a trip to Ukiah on Sunday with Donald.
- I want to check the drip irrigation and see if the coyotes chewed it up again.
- Carrie needs help finding a fault in the fence at the Iris Barn.
- We plan to spend a bunch of time painting the plywood for the Shelter. I want it done soon!!!
Called the Ranch insurance agent and reminded her that I need a breakdown of the insurance cost.
Now I need to write an e-mail to the Union office about a couple of things.
- The planning department gave me an extension to my permit for the shelter at the Red Barn. It is hard to believe that it has been a whole year since we began trying to get that thing together.
- Johnny came and helped me get the last 6 sheets of roofing onto the shelter.
- I purchased more paint primer (now there is 10 gallons) and 5 gallons of the tan top coat.
- I fixed a lot of problems on the Howell Creek drip irrigation. Sadly a whole lot of plants had died of lack of water. It looks like Mr Coyote got in and chewed up the drip lines so he could get a drink. Even with the dead plants there were plenty of plants that survived, thank goodness. Most of the damage was on the lower end, the upper end was relatively unscathed.
- I pulled the tarp back over the top of one of the storage tents. The knots holding it had been tied by my helper and were clearly sub-standard. Shouldn't be a problem now. The tarp is to help reduce sun damage to the tent itself.
- Dave the Deer Hunter came by as we were finishing up the roofing and we agreed to have dinner together up at his camp. It was very pleasant, if sad, since Dave's dad died recently.
Which, given the weather - today was persistent drizzle rather than yesterday's chucking it relentlessly down - was a good idea. Salt mine, to be precise.
However, has been a long day - only just in from a Mahler concert - so any more detailed reports on touristic activities may follow at some later season.
Here we have our two contestants for this week’s match, the first in SFF Equines history (but not, perhaps, the last): on this side the tall, white, shining, magical, beautiful king of stallions who deigns to carry the great Wizard; and over on that side, the short, brown, fuzzy, unromantic, pretty definitely not-a-stallion who is not asked whether he wants to carry the Fellowship’s baggage (but as far as Sam can determine, he’s willing).
A serious mismatch, you say?
That, I reply, remains to be seen.
Before we get down to the one-on-one, let’s clarify that a pony is. Just about everybody gets the concept of horse, more or less: four legs, hooves, mane and tail, long neck, long head, eats grass, one end kicks, the other bites, you sit in the middle or you hitch it up to a cart and drive it. The size varies, and sometimes can be very big, especially if it’s a Fantasy Stallion(tm), but it’s always big enough for the standard (male)(Western)(very probably white unless he exists in a different universe where a Khal can be named Drogo, not to be confused with Frodo’s very respectable Hobbit father) human to ride.
So what’s a pony? It is not, contrary to all too popular belief, a baby horse. A baby horse is called a foal or a colt, though a colt is actually, technically, a male baby horse. A female baby horse is a filly.
A pony can be quite small and still be a fully grown animal. In fact the main distinction between horse and pony is height. A pony comes in at or below the standard measure of 14.2 hands at the withers, which at four inches per hand equals 58 inches. A horse comes in above that height.
But! because horse lore can never be that simple, there are horses below 14.2 and ponies (not excessively but still) above it. That’s where you get into physical characteristics. Both horses and ponies are the same subspecies of equid, but pony breeds tend more toward shorter, thicker, and furrier, with extra helpings of mane and tail, and extra coat, especially in winter. They may also have smaller heads than the average horse, and adorable little bitty ears, though that is not a given.
Horses would generally be more lightly built, leggier, with less hair—but you still get Icelandic horses, Mongolian horses, and Fjord horses, all of whom are short, thickset, and furry. So it varies. And some breeds of horse run a gamut from pony-sized to well up in the horse range, including the Arabian; whereas you can get Connemara ponies over 15 hands, and the upper end of the Welsh pony continuum, the Welsh Cob, which gets up over 15 hands as well.
So it all depends.
What it comes down to really is the fact that the horse (or pony) can vary widely in size, and when you get way down to the Mini, that’s called a horse, though it’s much smaller than the pony (top range being 36 inches). The lay person may just want to ask a horse person whether this equine is considered a pony or a horse, and take it from there.
Fortunately for that lay person’s sanity, there really is no ambiguity about the difference between Shadowfax and good old Bill. Shadowfax in my mind’s eye presents as a particularly lovely English Thoroughbred. In the films he was played by an Andalusian (the gorgeous often-white or technically grey horse of Spain with the long, long hair—but not quite like pony hair, it’s finer and flowier). He’s tall and clean-limbed and proud, says Tolkien of the horses of Rohan in general, and he’s long-lived and has machinelike stamina and understands the speech of Men. And, Tolkien adds, he tolerates no training or handling until his One True Person arrives, that being Gandalf, but once he’s consented to let the Wizard train him, he makes certain sure the person (or Hobbit) allowed on his back will never be lost or thrown unless he actually throws himself off.
That’s a lot of horse, and a lot of self-determination. Against that we have Bill, who is small enough to be ridden comfortably by a person between three and four feet tall, so he’s probably between twelve and thirteen hands. He’s a rescue with a past, having been starved and abused by the wicked Bill Ferny, and is sold as a pack horse. He has no say in the matter, and offers no objection. When the Fellowship reaches the back door of Moria, he has to be turned loose (to Sam’s great grief) and left to survive as he can, if he can escape the Watcher in the Water.
Which we know he does, because we’re told he turns up back in Bree, and Barliman puts him to work. Eventually he finds his Sam again, and that’s Bill’s happy ending. Better yet, he gets his revenge on Bill Ferny at the Brandywine Bridge during the Scouring of the Shire, and he’s Sam’s mount when Frodo and company ride to the Grey Havens.
Shadowfax meanwhile carries Gandalf nobly through the end of the War of the Ring, and then takes him to the Havens, but it’s not clear whether he’s loaded on the grey ship for the journey to Valinor. Bill gets to go home with Sam. Shadowfax may or may not get his happy ending. Like Elrond and Arwen, he may have been parted from his loved one forever.
So that’s the first possible win: Bill gets to keep his person. Shadowfax might not. If he is left behind, he gets to go back to being King of the Mearas, which involves running free and making more Mearas, but in terms of emotional life, he’s suffered a terrible loss.
(Then again, if he does make it to Valinor, I’m sure the horses there will welcome a good outcross.) (Ooo, fanfic prompt.)
Even if Bill does get the better end of the keeping-one’s-person deal, Shadowfax has all the advantages in size, speed, and even endurance, doesn’t he? Size and speed are definite wins for Shadowfax, but for sheer blunt sticktoitiveness, there’s a lot to be said for a pony. He won’t be spectacular, he won’t be fast, but he can go on and on and on, and when it comes to living off the land, he’s the clear winner.
Shadowfax appears to live on air and wizardry, but when he’s on his own, he most probably has to eat like a normal horse. That means lots of fiber and some protein and minerals—extra protein for those extra stallion muscles—and that means plenty of good grass or other forage, and grain if he has human help. Because of his size, even if he’s an easy keeper, he’ll need quite a few pounds of fodder a day in order to keep weight and condition, plus he’ll need water to keep it all moving down that one-way street called the equine digestive system.
Bill has the same basic needs, but his smaller body means he can survive on a much smaller amount of feed and water. Pony metabolism tends to be much more efficient than horse metabolism, to the point that in feeding ponies, modern horsekeepers have to be very careful not to overfeed and founder their charges. That includes not just hay and concentrates but pasturage. A pony on rich grass blows up horribly fast. He’ll do much better on smaller quantities of poorer forage.
Shadowfax may need magical help to survive the terrain between Rivendell and Moria in winter cold and hard weather without starving to death, but Bill can live off the country and arrive back at Bree both alive and able to recover from the weight loss he’s suffered from living wild in winter. Tough terrain breeds tough equines, and smaller size allows the animal to make better use of the resources available. An extreme example of this would be the Shetland Isles, whose ponies (and dogs) are famously small, sturdy, and furry.
Pound for pound, too, a pony can be stronger than a horse. Shetlands can carry a grown man with ease, though his feet may drag on the ground. Horses will lose weight-bearing capability as they get larger; a very large horse is challenged enough to carry his own weight around without also carrying a heavy rider. A really big horse is not what you want to carry your very heavy rider, especially if he’s in armor. You want a cob, a stocky, sturdily built animal in the mid rage between pony and horse—14.2 to 15.2 hands. The Welsh Cob is a great example, as is the Lipizzaner. Forlong the Fat, in my head, is riding a largeish Welsh Cob, and the Cob is rocking it.
Shadowfax is quite happy to carry Gandalf, who according to the Eagle is “light as a feather,” and who is not wearing armor or carrying a lot of extra baggage. When that baggage includes a young Hobbit, he’s still not too challenged, since Pippin probably weighs a lot less by that time than he did when he left Hobbiton, and he’s likewise not wearing armor or carrying a heavy pack.
Now Bill at somewhat shy of thirteen hands may not be carrying an armed human or Wizard to battle, but if he’s serving as a packhorse for nine foot travelers, he’s probably got a significant load on his initially bony back. And he’s managing it quite well and even gaining weight as he goes on, just from being able to graze along the way. Not to mention they stop to sleep, and while they’re sleeping, Bill is hoovering up the available forage and immediately converting it to body mass and energy.
All right, so Bill is holding his own here, but what about a literal cage match? Shadowfax has a major size advantage, right? And can pound Bill to a pulp. Right? Especially since Shadowfax is a stallion, ergo testosterone, ergo more muscle mass, ergo stronger.
Well. Maybe. Also aggression, so he’ll have no compunction about ripping Bill’s throat out.
Except Bill has one thing, or maybe one and a half, that helps him manage better than you might think. He’s small, and he’s agile. While Shadowfax is still getting all that real estate up into the air for the rear and strike, Bill has skipped underneath, whipped around, and planted two good, if small, back hooves right where the future foals of the Mearas reside. Then he scampers out of there before the whole screaming mass comes toppling down.
Or if he decides to spare the potential offspring, there’s still the duck-and-bolt, and the hamstring-rip, and the hard kick to the hind cannon that does the big guy in permanently. Bill is quite a good kicker, as his namesake Bill Ferny can testify.
You see, Bill is smart. So is Shadowfax, and horses can be very smart indeed. But ponies have their very own level of ‘tude, and a degree of cunning that has been the bane of many a pony-keeping person of any age, who has to deal with the opening of gates, the jumping of fences (some ponies, notably Connemaras, can jump the moon and throw in Venus for a lark), the breaking down of walls (see above re: pony strength), the thwarting of ropes and ties, the scraping off of riders, and many another would-be restraint on life and freedom.
While Shadowfax is waging noble war, Bill is winning by any means necessary. If that means kneecapping the opposition, that’s fine with Bill. The big guy may have all the strength and speed, but Bill is down low, he can get out of the way fast, and he keeps his eye on the low-hanging targets.
In the end, your noble white steed will win the beauty contest and the race to Gondor, but the little grubby guy with the forelock in his eyes is quite likely to come out of the cage with the prize. He’s got smarts and determination, and overall toughness that even the King of the Mearas will struggle to match.
Judith Tarr is a lifelong horse person. She supports her habit by writing works of fantasy and science fiction as well as historical novels, many of which have been published as ebooks by Book View Cafe. Her most recent short novel, Dragons in the Earth, features a herd of magical horses, and her space opera, Forgotten Suns, features both terrestrial horses and an alien horselike species (and space whales!). She lives near Tucson, Arizona with a herd of Lipizzans, a clowder of cats, and a blue-eyed spirit dog.
It is late in the workday and I am really annoying Carl Engle-Laird, assistant editor for Tor.com Publishing and the acquiring editor for Alter S. Reiss’ novella Sunset Mantle. He explains the plot of the story to me, this congenial monolith standing before a shrieking, bone-wielding ape, but it is not enough.
“Okay, Carl…but what is the book about?”
Two days later I have read Reiss’s story—the prose is speedy, engaging, and ideal for 45-minute commutes on the subway—but I still don’t have an answer to my own question. Sunset Mantle, as far as I can tell, is about a man who thinks he is done fighting but who ends up becoming the figurative rock that allows an enormous independent community to withstand the tide of culturalization. Richard Anderson’s cover is very apt in this regard, a scene from the book exaggerated in scale so that the essence of that scene is given the emotional weight it deserves. So really I do have an answer to the question of just what Mantle is about. I’m just not satisfied with that answer.
(P.S.—Here’s the full Richard Anderson cover because it’s just TOO. PRETTY. to be contained within a mere crop.)
A man who finds himself holding the line against impossible odds, even begrudgingly, is a very common dramatic framework. Conveying that kind of drama in the setting of an epic fantasy can be a lot of fun, as it allows a writer to enlarge the drama to an extent that we rarely get to experience in the real world. In Tolkien’s Lord of the Rings saga, all Frodo has to do is drop a ring in a hole, but that hole is actually a VOLCANO and that volcano is secreted deep within THE DARKEST KINGDOM ON EARTH and SAM CAN BE REALLY ANNOYING SOMETIMES. We know that Frodo is the least physically powerful combatant in the saga, but that he carries the same desire for resistance that we as readers see in ourselves. So it’s thrilling to see Frodo’s struggle inspire others to help him continue his efforts. This is an inspiring genre of fiction to read; and popular, as evidenced by the fact that there’s so very much of it available.
Sunset Mantle shares this progression, but despite it carrying the trappings of a medieval-esque epic fantasy, its story about resistance is a small one. The main character, Cete, finds himself central to the story simply because he’s the most experienced and competent warrior in the Reach Antach, the distant city into which he has wandered. To be sure, Sunset Mantle chronicles an event that is important to establishing the future of this city, but the outcome of this event surely isn’t the end of the story. The gears continue to turn in the world at large and although the events of Mantle may start a ripple in the pond of this fantasy world, it is left to the reader to imagine what those ripples may be. To continue the Lord of the Rings comparison, it’s like starting Tolkien’s saga with the story of the pragmatic general who trained the soldiers of Helm’s Deep just before it was swarmed with orcs.
Those familiar with video game RPGs like Final Fantasy or Dragon Quest would call this kind of small story a “sidequest.” In these epic fantasy video games, these are optional quests that have implications towards your main quest, but aren’t large enough to justify occupying your entire gaming experience. These games communicate repeatedly that the focus of you the player will be the problems menacing the entire world, not just one person, or one town.
Readers of epic fantasy demand a scope of a similar world-shattering size, if only to justify the time they will invest in poring through several 900+ page novels. Grand adventures are emotionally satisfying, as well, and the deeper a reader can get pulled into them, the more the reader will feel as if they are the one undertaking the quest. The length of epic fantasy novels is a factor in achieving this depth, as a longer story allows for greater detail and variation to be depicted.
My head has been filling up with works of fantasy this year. I finally checked out Max Gladstone’s Craft Sequence series, which is epic, and fantasy, but somehow neither. I’ve read Jason Denzel’s forthcoming debut novel Mystic, and skimmed the two new Mistborn novels, but mostly I’ve been entirely submerged within The Wheel of Time Companion. The companion volume to Robert Jordan’s epic is dense with information, so much so that it’s been difficult for me to find things that are truly unknown. But they’re definitely in there. And it’s a rewarding experience to stumble across them. As if Robert Jordan is answering a question that only he and I ever thought to ask.
To me, the most rewarding bits within Jordan’s Companion are the “small stories.” The Sunset Mantles that he never managed to fit within the worldwide scope of The Wheel of Time, like Mazrim Taim’s harassment of The Two Rivers, the tragedy behind Serafelle Sedai’s decision to become an Aes Sedai, or the “training” that Cadsuane foisted upon an Amyrlin. These have little, if any, real effects on the main storyline of The Wheel of Time but they give a surprising amount of momentum to the series as a whole. These are stories, small stories, that play out quietly in their entirety while I’m off paying attention to other characters. Missing these small stories in an epic makes that fantasy world feel more like our own. After all, how many stories do we miss in our own lives?
There is plenty of room in epic fantasy for the small stories, it seems. Not only that, but I’d go so far as to say that the “small stories” are what define the epic scope of fantasy. These are the “bricks” in the firmament of these worlds, the guarantee that there is something the reader can explore just over the horizon, the promise that there are real people affected by their world’s perch on the edge of doom.
So maybe, when I asked Carl what Sunset Mantle was about, he was stymied as to why someone whose head has been bubbling under the surface of epic fantasy all this year would be unaware of the obvious truth of “small stories.” This truth was obvious to editor Robert Silverberg when he assembled Legends. And to John Joseph Adams when he assembled Epic. And Shawn Speakman when he crafted Unfettered. The impact of small stories in epic fantasy certainly doesn’t escape George R. R. Martin, who has fashioned several epics, several anthologies, and ascended to the status of cultural icon on the strength of his “small stories.”
See, now I just feel foolish. Better informed, and foolish. Thanks, Carl and accompanying horse calendar.
This article was originally published in September 2015.
Chris Lough is the production manager of Tor.com and was actually thrilled to discover the major exports of all the countries in Randland. What? Economies are interesting.
Yesterday, the Extended Edition of The Hobbit: The Battle of the Five Armies played in theaters as a prelude to its release on DVD/Blu-ray. And so with battle cries, the clash of weapons, and then a somber dirge, we have seen the trilogy-that-wasn’t-really-a-trilogy conclude. To be honest, I found it to be a curious admixture of satisfying and unfulfilling; the former because as a film saga, there is both excitement and sufficient closure, and the latter because it would have felt more complete, more “extended,” if Peter Jackson had deigned to drop in a few more looked-for elements from the books. But hey, war goats!
Spoilers follow for The Hobbit films.
Peter Jackson’s Hobbit films get a lot of flak for being overwrought, overlong, or “like butter scraped over too much bread.” Many of the criticisms are valid enough (I have some of my own), some are a matter of taste, and some, I feel, are simply misguided. My view, as a fan of Tolkien first and Jackson second, is that the naysayers are judging the films for what they’re not. They are not a cinematic translation of J.R.R. Tolkien’s singular novel but an adaptation in the truest sense of the word. Specifically, they are an adaptation of events in Middle-earth 60 years prior to the Bilbo’s famous eleventy-first birthday party, and that includes those from the The Hobbit and those implied from the Appendices of The Lord of the Rings.
To adapt something is to change, alter, or modify it to make it suitable for new conditions, which is where the problems occur for fans of a richly detailed story. No, not merely a story, a whole legendarium (Tolkien himself called it such) that lots of people care a hell of a lot about. The expectation seems to have been that Jackson should have kept to the books closely, should have told the story just as Tolkien did. But ultimately, that’s just not realistic and it would have made for a disjointed prequel.
It’s not like Jackson didn’t know what’s in the books; in addition to knowing them well, he was surrounded by Tolkien scholars, Elvish linguists, and other literary experts. Rather, he’s an uber-successful director, producer, and screenwriter who has to wrangle massive movie budgets and we’re not. He loves Tolkien’s work but had taken on the self-imposed, if herculean task of maneuvering a beloved tale through the Hollywood machine. Have you ever watched a comic book, novel, or even play adapted to film and thought, “That’s exactly how I would have done it”? If you have, then that’s amazing! If not, well, in this age of Hollywood remakes, reboots, and adaptations, why expect these films to be any different?
I want a faithful adaptation as much as anyone. But I am not a Tolkien purist about it because I think that Peter Jackson adding Tom Bombadil to The Fellowship of the Ring would have been as absurd as, oh, say, adding a scene in The Hobbit where Thorin & Co. enter the Lonely Mountain right after sending Bilbo in—you know, to go in quietly and do what they had specifically employed him to do. “That, Master Burglar, is why you are here,” Thorin says to him. So yes, that scene was too much. Do I love seeing what various chambers in Erebor might look like? The forges, the billows, the vats, the cavernous abyss of a great mine shaft? The fantasy nut in me says hell yes! But the Tolkien reader in me says no, not for a gratuitous and overlong action sequence, and not at the cost of undermining Bilbo’s quiet resolve.
Certainly not at the cost of losing this wonderful moment from the book:
It was at this point that Bilbo stopped. Going on from there was the bravest thing he ever did. The tremendous things that happened afterwards were as nothing compared to it. He fought the real battle in the tunnel alone, before he ever saw the vast danger that lay in wait.
Of course, it’s hard for any film to portray a character’s internal thoughts, which is all that moment is, but I think most of us would agree that Martin Freeman would have done an excellent job visually depicting Bilbo’s trepidation. Peter Jackson opted not to try this, and we can and must live with that. The book is not demeaned, but the movie is the lesser for it.
Likewise, Peter Jackson opted to keep Bombadil out of The Fellowship of the Ring, which it must be remembered had been his first foray into Middle-earth. And which, honestly, we’re still lucky even happened. And I agree with nixing Tom not because I wouldn’t like to see him or his oft-referenced yellow boots on the big screen—because that would be both fun and surreal—but because I don’t think anyone but die-hard book fans would have had the patience for him, his lovely but passive wife Goldberry, or his flamboyant, “Ring a dong dillo” self. Simply look at the numerous complaints of “too many endings” levied against The Return of the King. Jackson’s Fellowship would have faltered with the excess of Tom Bombadil (and even the barrow-wights, which I’d dearly love to have seen) and then millions of people would never have come to know or appreciate the greater works of Professor Tolkien. And the Tolkien Estate’s book revenue wouldn’t have increased by 1,000% (in the UK) as they did despite its utter contempt for Jackson’s meddling.
I reread all the books after seeing the films and I enjoying every unabridged word. Likewise, I’m happy to watch Peter Jackson’s six adaptations as a hybrid member of the audience, fully accepting that no one demographic can be fully satisfied. Among the many, you’ve got:
- Hardcore Tolkien fans who gripe at every change from the books (but still go see the films).
- New fans who loved the films and have now discovered the books.
- Action-adventure moviegoers who just want to be entertained but probably won’t ever read the books but “OMG look how badass that elf is with all the arrows and the shield-skating acrobatics and crumbling-tower-climbing and monster-bat-riding!”
- Kids, especially young girls who, according to the director himself, might be glad to have a relatively strong female character to root for (in Tauriel and Galadriel), where otherwise The Hobbit would have had none.
The point is that untold numbers of people have enjoyed all three Hobbit films, sometimes because of—and sometimes despite—their Jackson-expanded elements. Now that the Extended Edition of The Battle of the Five Armies is upon us, I’d like to consider the bigger picture.
I found The Battle of the Five Armies to be extremely fun. And a fine conclusion. And by that I mean that it’s a fitting capstone to the prequels for Jackson’s Rings trilogy. I never had qualms about The Hobbit being split into three films on principle. From the coming of Thorin to Bilbo’s home (July of the year 2941) to the return of Bilbo to Bag End (June of 2942), about 11 months pass. That story is told with three films. Meanwhile, from Frodo’s departure with the One Ring from Bag End (September 23, 3018) to all four hobbits returning to the Shire after Sauron’s defeat (November of 3019), about 14 months elapse. Again, three films. The span of diegetic time is comparable. Granted, there are more moving parts and political conflicts during the War of the Ring, but just as in the Rings trilogy, there is plenty happening behind the scenes during the quest for Erebor that Tolkien addressed long after writing it. The White Council moving against Sauron in Dol Guldur is one prime example.
It’s been said that “the filmmakers have wrung all they could out of the source material,” but I find that to be a lazy stab because it’s simply untrue. Indeed, that’s the irony. While three Hobbit films meant there should be room for some fleshing out of otherwise sparse details—the very thing people are complaining about, that he made a short book longer than they felt it needed to be—Jackson still didn’t actually cover everything. What he did do was garnish the films with more action and adventure. The Extended Five Armies is rife with monstrous combatants and innovative new war machines—trolls clad with gruesome-if-amusing armaments, dwarven ballistae that can and do shatter a hail of elven arrows, and bolt-firing war carts to name a few. It’s a true spectacle. Where Tolkien nerds might roll their eyes and wish for the story to get on with things, there is an audience for this and it does please.
And here’s an interesting development from the Extended Five Armies that really struck me: Before the orcs arrive, the Elves and dwarves do actually begin their battle at Dáin Ironfoot’s command. There is a clear loss of life on both sides, even though it’s brief. It’s heartbreaking to watch, a tragic consequence of the tension built up to that moment. You would think Azog, spying this elf-dwarf conflict from his command tower, would just let things play out! Regardless, the orcs arrive and with seemingly no hesitation—I love the unspoken certainty of this—the Elves and dwarves cease their fight with one another and engage the common foe. As if they had no heart to fight one another anyway. But both have an ancient hatred for orcs!
Battles and monsters are certainly Jackson’s forte, and the films cater to the movie-going crowd more than to the book-reading crowd. For those of us in the middle of that Venn diagram, it’s enough. At least in the new scenes, we are treated to seeing more of Thorin’s company engaged in the battle—including the unexpected removal of the axe blade in Bifur’s head! There is plenty of dwarf humor in the fray, but against the gravity of what’s going on, I found that to be quite welcome. Oh yeah, and Balin riding the war cart and peppering wargs with ballista bolts? Yes to that. This is part of a larger segment showing that the ride to Ravenhill to challenge Azog was considerably more difficult than we first assumed from the film’s initial release.
Some of the Extended moments weren’t quite enough to satisfy and they didn’t tie in well with previous ones. For example, we get only a few extra seconds of Beorn’s arrival at the battle and his ursine, orc-mashing fury, but nothing more. And though Gandalf has a few additional words for Thorin while the dwarf fumes at Erebor’s makeshift gate, I kept waiting for him to somehow mention Thrain, who he discovered in Dol Guldur in Desolation. If not in this scene, then in another. “Tell Thorin that I loved him,” Thrain had said to Gandalf. “Will you do that? Will you tell my son that I loved him?” Gandalf never does. It’s a small thing, but it would have made for better continuity to include.
I can abide almost any extension or stretching of characters and themes and battles, so long as they’re not completely antithetical to Tolkien’s ideals, but only if the existing story, including the appendices-based backstory, is exhausted first. There is much we never get to experience from the books. The animals at Beorn’s house; the Eagles and their eyries (and why they help at all); the drunk Wood-elves and Thranduil’s interrogation of the dwarves; the thrush and its world-saving delivery of vital information; the aftermath of the battle—all of these have been kept out. In the behind-the-scenes features of the DVDs, you can even see that some of these were filmed (such as all the captive dwarves being brought before the Wood-elf King, not merely Thorin), but never made even the Extended cut. Sadly.
But these are movies; they need to take into account a movie-goer’s patience (and bladder). Think of all that was removed from The Lord of the Rings, which has a full run-time of just over 11 hours. Given that, are you in the “What, no ‘Scouring of the Shire’?” camp or the “Nah, it’s fine as is” camp?
Still, in The Battle of the Five Armies, every second of screen time given to the character of Alfrid was one less that could have been better used developing the White Council’s purpose. Explaining who they are exactly, how their Rings of Power relate to one another, that sort of thing. We get only teasings of the world these immortal Elves and wizards come from: we glimpse Narya, Gandalf’s ring, and of course Galadriel’s. There is so much story in the rings that never comes out. Whereas Alfrid is an unnecessary, cartoonish weasel. In any case, it seems the Master of Lake-town’s fate in the book has become Alfrid’s fate in the film and the dragon-sickness gets to him. In the Extended cut, Alfrid does get his comeuppance. While I’d prefer he simply vanish to starve in the Waste with his stolen gold—but how do you show that in a film? (you can’t)—for some it may be satisfying to see Alfrid meet his mouthy end.
The White Council’s ousting of Sauron from Dol Guldur still feels the most truncated, even in the Extended Edition, if only because we know there’s plenty of lore behind it. It has a direct bearing on other events, which Gandalf touches on briefly later and it explains why he stirred Thorin to his quest and nosed around Dol Guldur in the first place.
Per Appendix B of The Lord of the Rings:
Among many cares he was troubled in mind by the perilous state of the North; because he knew then already that Sauron was plotting war, and intended, as soon as he felt strong enough, to attack Rivendell. But to resist any attempt from the East to regain the lands of Angmar and the northern passes in the mountains there were now only the Dwarves of the Iron Hills. And beyond them lay the desolation of the Dragon. The Dragon Sauron might use with terrible effect. How could the end of Smaug be achieved?
I enjoyed seeing the ringwraiths in their more spectral form, even if their inclusion via the High Fells of Rhudaur were an addition. This is a prime example of where I don’t mind Peter Jackson’s tinkering; it was never made clear by Tolkien where the Nazgûl would have been during this timeframe. No harm, no foul, why not see them again? That said, more spellcasting and less wizard-fu in the Dol Guldur skuffle would have been preferred, but it’s still gratifying to see Galadriel finally invoke some epic, Silmarillion-flavored might. She will one day return there, after all, when the Shadow is defeated.
Also from Appendix B:
Three times Lórien had been assailed from Dol Guldur, but besides the valour of the elven people of that land, the power that dwelt there was too great for any to overcome, unless Sauron had come there himself. Though grievous harm was done to the fair woods on the borders, the assaults were driven back; and when the Shadow passed, Celeborn came forth and led the host of Lórien over Anduin in many boats. They took Dol Guldur, and Galadriel threw down its walls and laid bare its pits, and the forest was cleansed.
But I do wish her bearing was brighter and less dark-queen creepy, which is clearly meant to gel with her Fellowship manifestation. In Five Armies, she is not being tempted by great power, she’s using her own. I think the visual connection was too much handholding. Likewise, I wish her voice was not once again layered and pitch-dropped—Jackson’s sound crew, having proved themselves throughout all six films, could have done way better than use that cheap trick.
Still, in the Extended cut, we now get to see her utterly obliterate Gandalf’s orc jailor—who seconds before was ready to cut the wizard’s ring from his finger after beating on him. Indeed, the orc was strangely informed: he knew of the Ring of Fire and demanded to know “Where are the others?” That is when Galadriel arrives and makes short work of the orc.
Saruman himself is underused throughout the trilogy, though it was a joy to see the much-aged (and now late) Christopher Lee return to the role. He is the head of the White Council, and though he kicks serious Nazgûl ass in Five Armies, he seemed more horrified than intrigued at the sight of the Enemy, who he was charged to oppose from the start. I was hoping for deeper insight into his own corruption and eventual betrayal. In the canon, he was already desiring the One Ring for himself at this time and had discovered only two years prior that Sauron’s servants were searching the Anduin near Gladden Fields. Which is why he’d finally agreed to move against the Dark Lord, to keep him from finding the One first.
“Leave Sauron to me,” seems to be the only hook we get. But anyone who’s read more about Saruman knows that he regarded Sauron as a rival, not merely an enemy, at this point in time.
As for Tauriel and Kili, this is all there is to it: In An Unexpected Journey and only in the Extended Edition, we see Kili eyeing an Elfmaid in Rivendell, so we know he’s prone to elven interests. Then in Desolation, he meets Tauriel and actually falls for her (as much as a dwarf can in so brief a time) and is subsequently saved by her efforts. Then in Five Armies, it all comes to a head and one dies trying to save the other.
I’ll say two things about this subplot then leave it alone, since much has already been said and because it’s a small matter compared to the rest of the story.
Tolkien’s Elves, while portrayed quite differently in the films than in the books (a topic for another time), are still presented as a tragic, if powerful race. To me, the tale of Kili and Tauriel is less about an Elf and dwarf romance as it is the adversity that lies between an immortal and a mortal. That is a theme that Tolkien cared much more about and he played with this idea several times, in Beren and Lúthien, in Aragorn and Arwen. Even Elrond and his brother Elros were given the choice of mortality or immortality; Elros chose the doom of a mortal Man (and surprise, chose a mortal wife), while Elrond chose immortality. The brothers were therefore parted by the passage of thousands of years.
There is also precedence for a rare fondness between Elves and dwarves despite their ancient and Silmarillion-documented feuds of the past. In the Rings trilogy, not only do Legolas and Gimli forge an everlasting friendship with far-reaching effects, but Gimli is powerfully smitten by the beauty of Galadriel and it changes him deeply. The dude won’t shut up about her sometimes, it’s awesome.
And it happened in a moment, at their first meeting. Like…Tauriel and Kili, though of course one is romantic and the other is not. Against all these, the cinematic contrivance of Tauriel and Kili’s brief but unexplored love is nothing to fret about. Yes, it’s annoying to see an Elf lose her head, teenager-style, in the midst of a great battle—and more so because she’s one of the few female characters—but she’s still the only Elf pushing to oppose the orcs because it’s the right thing to do. Even Legolas would not have without her urging, and daddy Thranduil merely covets gems. (Side note: In one podcast interview, Hobbit writer Philippa Boyens clarified that the white gems that Thranduil wanted to badly had been commissioned for his wife, before her death, and that is why he is so fixated on his claim. It’s all he’d have of her, since Legolas tells Tauriel that his mother’s body was never found. To immortals such as Elves, memory can be everything. Even Boyens wasn’t sure if Peter Jackson would add this detail into the Extended cut, and in the end, he did not.)
So you may feel the Elf-dwarf romance feels forced, and the alleged affection between Legolas and Tauriel is also hard to buy into—in part because the films have made Elves colder than their literary counterparts—but it’s also harmless. So a character with little personality in the book (Kili) is given feelings for a character nonexistent in said book (Tauriel). Big deal. It’s not like Jackson gave Bilbo a girlfriend. Thankfully.
Honestly, I’m just happy to see female Elves, period, especially in battle. In the massive ranks of armored and militant Elves—at Helm’s Deep or even in the Last Alliance prologue—are there any? I did manage to glimpse a few female warrior Elves among the masses in Five Armies, though. Good.
The fact is, the biggest portion of the trilogy are the adventures of the titular hobbit, and Martin Freeman’s Bilbo remains the highlight, diminished only in scenes where he’s upstaged by the actions of others. I was quite content with his role in Five Armies, since the “Thief in the Night” sequence was more or less faithful to the book and his involvement in the battle itself was extended only lightly. Bilbo’s parting words with Thorin as the dwarf lies mortally wounded were meaningful to me, if much too abridged—but then that’s generally my only complaint. The Extended cut, at least, does reveal the funeral for Thorin, Fili, and Kili, as well as the crowning of Dáin Ironfoot. Though it is brief, it brings more closure to the story.
If you watch the films and then read the corresponding events in the book, you’ll find that Tolkien’s storytelling method has a curious, tell-don’t-show chronology to it—something he did in The Lord of the Rings but perhaps not as arbitrarily as in The Hobbit. I’ve heard it complained that Fili and Kili’s deaths were “much better” in the book by naysayers of the film. To that I say, there was no scene at all in the book relating their deaths, merely a past perfect, after-the-fact summation of what happened. All we get is:
Of the twelve companions of Thorin, ten remained. Fili and Kili had fallen defending him with shield and body, for he was their mother’s elder brother.
So I for one am grateful for the things we do get to see brought to life on the big screen. The Rings trilogy was full of satisfying “off screen” moments from the books brought on screen, like the Ents’ assault on Isengard and Boromir defending the hobbits from orcs. Hell, to me Dáin Ironfoot’s portrayal in Five Armies was enjoyable even CGI’d as he was, and seeing an army of dwarves gratifies the D&D freak in me. Dáin, like Bolg, like Thranduil, like most of the dwarves, are given personalities Tolkien doesn’t take the time to do.
And that’s fine that he didn’t. It was a single book he wrote before launching the true enormity of Middle-earth. Tolkien was a revisionist, and even went back and made changes to The Hobbit once he started to write The Lord of the Rings. (In the first edition of The Hobbit, Gollum bets Bilbo his magic ring if the hobbit wins their riddle game—imagine that!) But Tolkien was content merely to bridge The Hobbit with Rings in other ways and not rewrite everything from the start.
2001’s The Fellowship of the Ring is a miraculous, groundbreaking film and each of Jackson’s installments since have, in spirit, style, and Tolkien lore, been like a carbon copy of the previous one, so that 2003’s The Return of the King was still excellent and felt close to Fellowship, but 2014’s The Battle of the Five Armies is certainly a far cry from it. Yes, it’s far more flash and action than rich storytelling and certainly bears even less resemblance to the source material, but it is at least consistent with its own vision of Middle-earth. And that’s what they all are: the vision of one man (Jackson) who stands at the vanguard of an army of talented artists and filmmakers. Because of that army, it’s still a hell of a lot of fun to experience. And Howard Shore’s score still somehow legitimitizes it, just like a John Williams score and a lightsaber sound effect can still, just for those choice moments, invoke nostalgia in even the crappiest Star Wars film.
The Hobbit trilogy is not perfect, of course not. There are numerous things to pick at. The stone giants sequence in An Unexpected Journey was needless showing off of CGI and presented a hazard to the characters only vaguely suggested in the book. The barrel-riding scene was turned into an action sequence that downplayed Bilbo’s day-saving role in their escape. But at least the stone giants and the barrels are in the book. Some of the added dialogue just doesn’t work. Fili telling his brother “I’ve got this!” at Ravenhill is gratingly anachronistic and not remotely Tolkien-esque. Though a pretty mild offense, I found Saruman referring to the Necromancer as a “human sorcerer” disappointing because the word “human” is never used by Tolkien to refer to Men in the books. Legolas and Tauriel reaching Gundabad and returning again in so short a time undermines the length of Bilbo’s entire journey. Jackson certainly played fast and loose with geography.
All the birds and beasts have been de-anthropomorphized. The Eagles did not speak, and neither does Roäc the raven nor the thrush. Beorn’s sheep, dogs, and pony friends don’t serve Thorin and Co. their meal as they do in the book. But these things wouldn’t exactly be in keeping with The Lord of the Rings, anyway—neither Tolkien’s nor Jackson’s.
When I first saw An Unexpected Journey, I loved it but I have learned to accept the things that didn’t play out more like in the book. Why, I fretted, didn’t they use the Great Goblin’s actual dialogue from the book? Sure, add some new lines but don’t replace what was there wholly. But I’ve learned to let it go. As J.R.R.’s own grandson has said, the films “kind of have to exist in their own right.”
Repeated viewings of all six films continue to impress me, and watching the making-of featurettes on the Extended Edition DVDs you can see some light shed on reasons for the changes even if they’re not what you’d have done. For me, I pine not for a perfectly faithful translation of the books but for the additions that could have been. The opportunities for greater context were there, right under Peter Jackson’s nose. We’ve met Radagast (who totally would have been given at least a cameo in Fellowship if Jackson has made the Hobbit films first), we’ve heard of the “two Blueses,” and we’ve seen the White Council in action. Why not use all that to show, even just a little, what Gandalf really is, why he’s constantly prodding everyone to oppose Sauron, and how he had the power to “rekindle hearts in a world that grows chill.”
Why not address the Nine, the Seven, and the Three? Especially the Seven, since the fate of Durin’s folk, their greed, and Sauron are all related? It was Sauron’s work that fanned the gold lust of the dwarves through the Seven Dwarf-rings. In the Extended Desolation, some time is spent showing how Thrain once had the last of the Seven but how it was cut from his hand by Azog. Why show the rings at all if we’re not going to learn something more of their power?
But alas, that would not have been done so easily, as a lot of that lore comes from The Silmarillion and the Tolkien Estate has not yielded that license. Not to mention the awesomeness of The Unfinished Tales, which reveals all kinds of good stuff about the Istari—and Saruman specifically.
The films are not the books and shouldn’t be judged as such. If they’re not what you hoped for, fair enough. You can’t please everyone, but don’t try and take them away from those they did please. As old John Ronald Reuel himself wrote in his Foreword to the Second Edition of The Lord of the Rings:
As a guide I had only my own feelings for what is appealing or moving, and for many the guide was inevitably often as fault. Some who have read the book, or at any rate have reviewed it, have found it boring, absurd, or contemptible; and I have no cause to complain, since I have similar opinions of their works, or of the kinds of writing that they evidently prefer.
Personally, I’m pleased with any franchise which shows, however briefly, Belladonna Took’s son as a small child, merrily play-battling with Gandalf the Grey, a symbolic and touching moment for all that would follow. Not only does it show that a mighty Maia spirit was fond of the simple Shire folk, it also shows why he would select one of them in particular to turn the tide.
Jeff LaSala can’t wait to read The Hobbit to his son, who is much too young to realize how nerdy his dad is. For now, they’ll just be pointy-eared denizens of Middle-earth together for Halloween.
Friday has been having trouble keeping up on the blogging lately…
- Living with Lots of Pets. I think #2 is my favorite.
- Retired Couple Proving Awesome Cosplay has no Age Limit
- The Art of Creative Book Dedications