Washington v. Trump

Today, the 9th Circuit denied President Trump’s appeal that would have reinstated his Executive Order on immigration. This opinion addressed only a preliminary question of whether the Executive Order will remain in effect while its constitutionality is fully argued in a lower court, but it reveals the trouble that the Government will have defending it.

One of the Government’s arguments was that “the President’s decisions about immigration policy, particularly when motivated by national security concerns, are
unreviewable, even if those actions potentially contravene constitutional rights and protections.”

The court rejected that argument.

There is no precedent to support this claimed unreviewability, which runs contrary to the fundamental structure of our constitutional democracy.

The Government also argued that “if the four corners of the Executive Order offer a facially legitimate and bona fide reason for it […] the court can’t look behind that.” In this argument, they were trying to prevent the court from considering statements, tweets, and interviews by President Trump and his advisors that could reveal that the Executive Order was, in part, religiously-motivated.

The court rejected that argument.

The States argue that the Executive Order violates the Establishment and Equal Protection Clauses because it was intended to disfavor Muslims. In support of this argument, the States have offered evidence of numerous statements by the President about his intent to implement a “Muslim ban” as well as evidence they claim suggests that the Executive Order was intended to be that ban, including sections 5(b) and 5(e) of the Order. It is well established that evidence of purpose beyond the face of the challenged law may be considered in evaluating Establishment and Equal Protection Clause claims.

The Government also tried to rely on “authoritative guidance” from White House counsel that the Executive Order does not affect legal permanent residents. The Government argued that the court should understand the Executive Order based on the most recent interpretation by the White House counsel. The court was concerned about the Government’s “shifting interpretation”, and rejected that argument.

Nor has the Government established that the White House counsel’s interpretation of the Executive Order is binding on all executive branch officials responsible for enforcing the Executive Order. The White House counsel is not the President, and he is not known to be in the chain of command for any of the Executive Departments. Moreover, in light of the Government’s shifting interpretations of the Executive Order, we cannot say that the current interpretation by White House counsel, even if authoritative and binding, will persist past the immediate stage of these proceedings. On this record, therefore, we cannot conclude that the Government has shown that it is “absolutely clear that the allegedly wrongful behavior could not reasonably be expected to recur.”

The most interesting part of my past week was listening, along with a hundred thousand other people, to this case’s oral argument. It was a display of the kind of work the judiciary does every day: checking whether the case should even be before the courts, probing the limits of the arguments presented by each side, and at the core, just trying to understand the case and arguments before them so they can correctly apply the law.

There is nothing better than an adversarial dispute to crystallize the meaning of a statute, the limits of Government power, or the extent of our rights. I’ve spent as much time reading appellate opinions as any other material over the past few years. It’s not because I miss first year philosophy or want to be a lawyer; it’s because they contain tough questions that reveal how the various parts of our society fit together. And, much of it is decent writing. They are written as much for us as they are for lawyers. Good journalism answers “so what”, but nothing can sub in for the opinion itself.

Here are some of the law people I’m following on Twitter who give context to significant cases and insight based on their personal experiences with the courts (and also, some entertainment).

And here are a couple of sites that present primary sources: oral argument audio, transcripts, briefs, opinions.

I haven’t found anything close to the same for Canada. But, you can search our Supreme Court’s judgements by date, topic, party, etc. here. (Try to find the one where a farmer harvested, saved, and planted Monsanto seed across 95% of his farm and then claimed he wasn’t using it.)

Washington, D.C.

January 16, Martin Luther King Jr. Day

With thousands of others who waited hours for free tickets, I got to see Gladys Knight and the Let Freedom Ring Choir perform at the Kennedy Center. You can watch the event here. It was a joy-filled celebration of a man, a movement, and imperfect, incomplete success.

In this temple, as in the hearts of the people, for whom he saved the union, the memory of Abraham Lincoln is enshrined forever.

After the concert, I walked to the Lincoln Memorial. I read the words above his head with a comma: “the people, for whom he saved the union, …” Without the comma, it reads, “in the hearts of the people for whom he saved the union”, connoting that he saved the union only for some people. He saved the union for all people, at least a more expansive concept of people than at the outset of the union.

20170116_204300

January 17, Visit to the Capitol and the Library of Congress

My visit to D.C. let me see the people and institutions that might check executive power. The ten-minute pro-forma session was an example of that. It was a reminder that people trust in the power of their institutions. The Senate would not have held many of its pro-forma sessions except that they prevent the President from making recess appointments.

Next was the Library of Congress.

6322480339_39454fdff0_o

I cannot live without books, but fewer will suffice…

Before I spent some time in the Reading Room, I visited Thomas Jefferson’s library. Jefferson offered to Congress his entire collection after the Library of Congress was largely destroyed in the 1814 burning of Washington. He numbered them, and arranged them by subject. It was filled with history, fiction, science, politics, religion, law, literary criticism, math… He had a Koran. Anticipating that Congress might think this collection too diverse, he wrote to them: “there is in fact no subject to which a member of Congress may not have occasion to refer.”

January 18, United States Supreme Court

20170118_042529.jpg

I chose to attend the oral argument of Lee v. Tam. It was a First Amendment case, it had a sympathetic plaintiff (Mr. Tam and the Slants), and the outcome will almost certainly determine the outcome for the “Redskins” trademark. A couple of people told me that I should arrive at 4am or even 3am to be guaranteed a spot in the audience. I arrived at 3:08 and was 8th in line, behind mostly line-holders who looked like they had been there overnight. By 4am, the line was past capacity.

At the front of the line, I was surrounded with people very familiar with the case: family of the attorney who would argue the case for Mr. Tam, an author of an NSFW amicus brief from the CATO institute,  somebody close to the legal team for Pro-Football, Inc…

The First Amendment protection of speech is an important check on the government. Expressive speech comes in many forms: journalism, literature, comedy, music. Today, much of this expression takes place in the commercial sphere. Sometimes, a speaker is emboldened to choose a particular message because they can trust in the protection of trademark law to secure exclusive use of that message as an indicator of their goods or services. The government has decided to withhold from a certain category of speech (speech that disparages) the special protections that trademark registration brings.

This case asks: is this kind of restriction a burden on speech, is that burden is viewpoint-based, and if so, is it nonetheless justified because of the purpose of the government’s trademark registration program?

The session started promptly at 10am with four minutes spent admitting attorneys from around the country to the Supreme Court Bar. Then, from Chief Justice Roberts: “Justice Sotomayor has our opinion this morning…” — I had already seen on SCOTUSBlog’s calendar that there would be an opinion announced today, so this wasn’t a complete surprise, but these don’t happen every session, and you never know what opinion will be presented — “…in case No. 14-1055, Lightfoot versus Cendant Mortgage Corporation.” I was unfamiliar with this case. She read her prepared opinion summary. Turns out that federal courts don’t have automatic jurisdiction over cases that happen to involve Fannie Mae. Who knew?

Chief Justice Roberts then introduced the first case, “We’ll hear argument first this morning in case No. 15-1293, Lee versus Tam.” You can listen to the argument here. Counsel for Mr. Tam and the Slants did not have a good day. Here are some excerpts:

A third of the audience departed after Lee v. Tam, so the room was much less full for the second case, Ziglar v. Abassi. This case relates to how hundreds of middle eastern men were detained and treated in the weeks and months after 9/11. The main question before the court was: can the men who were detained sue then Attorney General John Ashcroft (and others responsible for the detention and conditions) in his personal capacity?

Only six justices heard the case, the minimum allowed. Justices Kagan and Sotomayor had each recused themselves from the already shorthanded court. This case has been around so long that they each probably worked on it in some capacity before their appointments to the Supreme Court.

It was very well argued by Ms. Merropol (grandchild of Ethel and Julius Rosenberg). She took every opportunity to turn the argument back to points she wanted to emphasize or clarify. She was prepared for every question and handled hypotheticals with consistency. The oral argument audio is here.

This was also Mr. Gershengorn’s final argument as Acting Solicitor General for President Obama.

20170118_121827.jpg

January 19, Museum Day

NPR HQ! They were not hosting tours that day, but I still got to see their history exhibit and gift shop, and now I have a new mug.

The Smithsonian National Museum of African American History and Culture (that needs a shorter name) was out of passes, so I spent the afternoon in the Natural History Museum and then wandered the National Mall amongst the people who had already arrived for the inauguration the next day. The day-before-the-inauguration vibe was mostly one of spectacle and people watching people.

Pilots, you don’t need to carry your radio licence

radiolicence

That you must carry your radio operator’s certificate with you on board the aircraft is a widely spread myth in Canadian aviation. It’s not true! Here are some examples of that claim in the wild:

There are a number of documents that must be on board in order to fly […] I carry a Restricted Radio Operator Certificate, restricted to aviation. (Bits of Paper)

During flight operations in Canada, the following documents must be carried aboard the aircraft […] Pilot radiotelephone operator’s certificate… (Required documents)

So an operating certificate is always needed wherever a Canadian pilot is operating a
radio on a Canadian aircraft […] They have not been inspecting Canadian pilots recently to ensure
that pilots are carrying this licence, but can do so at any time. (The AOPA/COPA Guide to Cross Border Operations, Page 31)

The following must be carried by the pilot […] A Restricted Radiotelephone Operator’s Certificate is only required if you intend to transmit on an aviation-band radio. (Are you legal?)

Also on board must be […] the radio operator’s licence of the pilot […] (From the Ground Up, 27th Revised Edition 1996, p. 100)

What do the regulations actually say?

A person may operate radio apparatus in the aeronautical service, maritime service or amateur radio service only where the person holds an appropriate radio operator certificate as set out in column I of any of items 1 and 3 to 15 of Schedule II. (Radiocommunication Regulations, s 33)

The holder of a radio authorization shall, at the request of an inspector appointed pursuant to the Act, show the radio authorization or a copy thereof to the inspector within 48 hours after the request. (Radiocommunication Regulations, s 38)

You only need to produce the radio operator certificate (or even just a copy!) within 48 hours of a request by an Industry Canada inspector. You do not need to be able to produce the document while exercising the privileges. When Canada wants you to have the document with you, it knows how to say that:

[…] no person shall act as a flight crew member or exercise the privileges of a flight crew permit, licence or rating unless (a) the person holds the appropriate permit, licence or rating […]; and (d) the person can produce the permit, licence or rating, and the certificate, when exercising those privileges. (Canadian Aviation Regulations, s 401.03)

You must be able to produce your pilot licence and medical while exercising their privileges. You don’t need to do this for the radio operator certificate.

It’s a bird… it’s a plane… it… depends on your classifier’s threshold

Evaluation of an information retrieval system (a search engine, for example) generally focuses on two things:
1. How relevant are the retrieved results? (precision)
2. Did the system retrieve many of the truly relevant documents? (recall)

For those that aren’t familiar, I’ll explain what precision and recall are, and for those that are familiar, I’ll explain some of the confusion in the literature when comparing precision-recall curves.

Geese and airplanes

Suppose you have an image collection consisting of airplanes and geese.

Images of geese and airplanes
You want your system to retrieve all the airplane images and none of the geese images.
Given a set of images that your system retrieves from this collection, we can define four accuracy counts:
True positives: Airplane images that your system correctly retrieved
True negatives: Geese images that your system correctly did not retrieve
False positives: Geese images that your system incorrectly retrieved, believing them to be airplanes
False negatives: Airplane images that your system did incorrectly did not retrieve, believing them to be geese

Collection of geese and airplanes
In this example retrieval, there are three true positives and one false positive.

Using the terms I just defined, in this example retrieval, there are three true positives and one false positive. How many false negatives are there? How many true negatives are there?

There are two false negatives (the airplanes that the system failed to retrieve) and four true negatives (the geese that the system did not retrieve).

Precision and recall

Now, you’ll be able to understand more exactly what precision and recall are.

Precision is the percentage true positives in the retrieved results. That is:

where n is equal to the total number of images retrieved (tp + fp).

Recall is the percentage of the airplanes that the system retrieves. That is:

In our example above, with 3 true positives, 1 false positive, 4 true negatives, and 2 false negatives, precision = 0.75, and recall = 0.6.

75% of the retrieved results were airplanes, and 60% of the airplanes were retrieved.

Adjusting the threshold

What if we’re not happy with that performance? We could ask the system to return more examples. This would be done be relaxing our threshold of what we want our system to consider as an airplane. We could also ask our system to be more strict, and return fewer examples. In our example so far, the system retrieved four examples. That corresponds to a particular threshold (shown below by a blue line). The system retrieved the examples that appeared more airplane-like than that threshold.

This is a hypothetical ordering that our airplane retrieval system could give to the images in our collection. More airplane-like are at the top of the list. The blue line is the threshold that gave our example retrieval.

We can move that threshold up and down to get a different set of retrieved documents. At each position of the threshold, we would get a different precision and recall value. Specifically, if we retrieved only the top example, precision would be 100% and recall would be 20%. If we retrieved the top two examples, precision would still be 100%, and recall will have gone up to 40%. The following chart gives precision and recall for the above hypothetical ordering at all the possible thresholds.

Retrieval cutoff Precision Recall
Top 1 image 100% 20%
Top 2 images 100% 40%
Top 3 images 66% 40%
Top 4 images 75% 60%
Top 5 images 60% 60%
Top 6 images 66% 80%
Top 7 images 57% 80%
Top 8 images 50% 80%
Top 9 images 44% 80%
Top 10 images 50% 100%

Precision-recall curves

A good way to characterize the performance of a classifier is to look at how precision and recall change as you change the threshold. A good classifier will be good at ranking actual airplane images near the top of the list, and be able to retrieve a lot of airplane images before retrieving any geese: its precision will stay high as recall increases. A poor classifier will have to take a large hit in precision to get higher recall. Usually, a publication will present a precision-recall curve to show how this tradeoff looks for their classifier. This is a plot of precision p as a function of recall r.

The precision-recall curve for our example airplane classifier. It can achieve 40% recall without sacrificing any precision, but to get 100% recall, its precision drops to 50%.

Average precision

Rather than comparing curves, its sometimes useful to have a single number that characterizes the performance of a classifier. A common metric is the average precision. This can actually mean one of several things.

Average precision

Strictly, the average precision is precision averaged across all values of recall between 0 and 1:

That’s equal to taking the area under the curve. In practice, the integral is closely approximated by a sum over the precisions at every possible threshold value, multiplied by the change in recall:

where N is the total number of images in the collection, P(k) is the precision at a cutoff of k images, and delta r(k) is the change in recall that happened between cutoff k-1 and cutoff k.

In our example, this is (1 * 0.2) + (1 * 0.2) + (0.66 * 0) + (0.75 * 0.2) + (0.6 * 0) + (0.66 * 0.2) + (0.57 * 0) + (0.5 * 0) + (0.44 * 0) + (0.5 * 0.2) = 0.782.

Notice that the points at which the recall doesn’t change don’t contribute to this sum (in the graph, these points are on the vertical sections of the plot, where it’s dropping straight down). This makes sense, because since we’re computing the area under the curve, those sections of the curve aren’t adding any area.

Interpolated average precision

Some authors choose an alternate approximation that is called the interpolated average precision. Often, they still call it average precision. Instead of using P(k), the precision at a retrieval cutoff of k images, the interpolated average precision uses:

In other words, instead of using the precision that was actually observed at cutoff k, the interpolated average precision uses the maximum precision observed across all cutoffs with higher recall. The full equation for computing the interpolated average precision is:

Visually, here’s how the interpolated average precision compares to the approximated average precision (to show a more interesting plot, this one isn’t from the earlier example):

The approximated average precision closely hugs the actually observed curve. The interpolated average precision over estimates the precision at many points and produces a higher average precision value than the approximated average precision.

Further, there are variations on where to take the samples when computing the interpolated average precision. Some take samples at a fixed 11 points from 0 to 1: {0, 0.1, 0.2, …, 0.9, 1.0}. This is called the 11-point interpolated average precision. Others sample at every k where the recall changes.

Confusion

Some important publications use the interpolated average precision as their metric and still call it average precision. For example, the PASCAL Visual Objects Challenge has used this as their evaluation metric since 2007. I don’t think their justification is strong. They say, “the intention in interpolating the precision/recall curve in this way is to reduce the impact of the “wiggles” in the precision/recall curve”. Regardless, everyone compares against each other on this metric, so within the competition, this is not an issue. However, the rest of us need to be careful when comparing “average precision” values against other published results. Are we using the VOC’s interpolated average precision, while previous work had used the non-interpolated average precision? This would incorrectly show improvement of a new method when compared to the previous work.

Summary

Precision and recall are useful metrics for evaluating the performance of a classifier.

Precision and recall vary with the strictness of your classifier’s threshold.

There are several ways to summarize the precision-recall curve with a single number called average precision; be sure you’re using the same metric as the previous work that you’re comparing with.

92 things

A few months ago, I wrote about things I discarded. Now, I write about things I’ve kept. I moved to Mountain View for the summer, and I only have 92 things. In hindsight, that’s still 14 things too many (the red items), but I’m happy that I got that close to living with only what I’ve needed (for my own definition of “need”). These are the things I brought, the things I bought, and the things I borrowed.

Things I brought

Luggage etc.
1. Carry-on sized suitcase
2. Hiking backpack
3. Backpack

I packed the hiking backpack inside of my carry-on, so I just had a carry-on and a backpack and was able to avoid checking in any luggage. It turns out I only use the hiking backpack for day-to-day use. I think if I had not brought the unnecessary things below, I’d have been able to pack everything into the suitcase and the smaller hiking backpack.

Clothing
4. Hoodie
5-7. Jeans x 3
8. Pants
9. Shorts
10-12. t-shirts x 3
13. Long sleeve merino wool shirt
14-16. Merino wool t-shirts x 3
17-23. Underwear x 7
24-30. Sock x 7 pairs
31. New Balance shoes

I’ve used the hoodie as my pillow, so I guess it was useful to bring, although I could have made something else into a pillow otherwise. It’s way too hot to need a hoodie in Mountain View. If I’d been living in San Francisco like last summer, a hoodie would make more sense. I’ve only used one of my pairs of jeans. Although I’ve used all the t-shirts I brought, the Merino wool shirts have been pretty amazing and I’d have been able to get through the summer just with them. I wear them about 80% of the time. The great thing about them is that they evaporate sweat away so quickly that they don’t end up with even the slightest smell until about the fifth wear (so I’ve been told; I wash them after two or three wears).

Sports gear
32. Running tights
33. Swim shorts
34. Swim goggles
35. Ultimate jersey
36. Long sleeve base layer
37. Waterproof jacket
38. Shorts
39. Ultimate disc
40. Cleats

It’s too warm here to need bottoms for running. I was never really going to swim. Also, summer in Mountain View… why did I bring a waterproof jacket? My cleats had needed replacement for a few months, so I should have just bought a new pair when I arrived here.

Electronics
41. iPhone
42. iPhone charger
43. Laptop
44. Laptop charger
45. Camera
46. Camera battery charger
47. Camera USB cable
48. Mini-dvi to VGA converter
49. Headphones

I forgot that Google has projector converters for laptops in every conference room. The iPhone has been borderline unnecessary, since I’d be charged roaming data rates down here, but I have used it a few times. Its battery is usually empty, and I use Google voice on my computer to make and receive calls. That’s backfired a couple of times, though (sorry!)

Stationery
50-52. 3 pens
53. Notebook
54. Smaller notebook

Personal care
55. Razor
56. Contact lenses
57. Small first aid kit
58. Medicine
59. Travel towel

Documents etc.
60. A folder with Visa and other documents
61. Wallet (and cards)
62. Passport
63. Pilot licence

Again, I didn’t make the time to convert my Canadian pilot licence to a US pilot licence.

Other
64. House keys
65. Water bottle
66. Monopoly Deal

Things I’ve acquired

Luggage etc.
67. A Google branded Patagonia backpack

This was given to us on the first day. I’m giving this away; let me know if you want it.

Sports gear
68. A 2nd Ultimate disc
69. New cleats
70. New running shoes

Electronics
71. FitBit

On my first day, a person in my office called out to me as I walked by and tossed a small box my direction. Inside it was a FitBit. It’s been a fun way of tracking my activity and sleep patterns.

Personal care
72. A crappy bath towel
73. A bath towel
74. Q-Tips
75. Toothpaste
76. Floss
77. Shaving gel
78. Nail clippers
79. Contact lens solution
80. First aid/athletic tape
81. Neosporin
82. Non-stick pads
83. Gauze
84. Sunscreen
85. Aleve
86. Vitamin D

I learned that I should spend more than $3 on a bath towel. Four of these things (guess which ones) wouldn’t have been needed if I didn’t fail at riding a bike.

Documents etc.
87-88. 2 library cards

Other
89. A second water bottle

My recruiter gave me a free water bottle part-way through the summer. I like that it’s metal, so I’ll get rid of my plastic water bottle.

Things I’ve borrowed

90. Laptop
91. A Lovecraft compilation from the library
92. A bike

Things I miss

I do miss some things, though! I miss my panniers and I miss my Playstation. I miss real Dominion cards and Zendo. I miss being by the beach and I miss the mountains. Those last two don’t count though, since I’d never be able to bring them anyway.

What would be on your list of 92 things?

Stress fractures

I had a stress fracture. It think it is healed now. This is the story of how it came and went.

What are stress fractures?

When I would tell somebody I had a stress fracture, they would usually ask, “what’s a stress fracture”, or “what happened?”

A stress fracture is a fracture, but an incomplete one (the separation doesn’t go through the entire bone) and it’s caused by repeated impact stress over time and not a single, acute impact. Mine was in my leg (the medial tibia, at the junction of the middle and distal one thirds, to be exact). That’s the most common place for a stress fracture in adults.

What happened?

This is hard to answer, because of the gradual onset of the fracture. This spring, I was playing with UBC Men’s Ultimate B team and training casually for the Vancouver Sun Run, a 10k race. The schedule didn’t seem too intense. Ultimate practices were twice a week, two hours each. Weekend tournaments (infrequent) were two days long, where we would play up to five games in a day. I occasionally went to the gym and included plyometrics in my workouts. I had only one lingering injury… stiffness from a sprained right ankle (this could have reduced my ability absorb impacts as naturally).

What did it feel like?

I first noticed a general pain along my medial right tibia in March. It felt kind of nice to push on it like a massage. The pain gradually increased, but I got used to it. During a game or practice, the pain seemed to go away, but would come back afterwards, even during rest. Eventually, it hurt to step up onto things. The pain was localized to a single point about 1cm in diameter. I could poke at exactly the point on my tibia that hurt.

The Sun Run was when I finally realized/admitted that something was wrong. I ran with a strained left MCL, probably putting more stress onto my right leg than before. MCL strained, a stiff right ankle, and a burgeoning stress fracture in my right tibia: it was too much all at once.

After that run, I had all the symptoms of a tibial stress fracture: pin-point pain, I couldn’t jump on that leg, it hurt to walk for a few steps after standing up from a chair, it hurt to walk up or down stairs, and it hurt to stand on my right leg. But, I didn’t know this was a stress fracture yet.

Diagnosis

My first visit to the doctor was the week after the Sun Run. I waited a few days to confirm that it wasn’t getting any better on its own, then went to a sports doctor at UBC. From my description of the symptoms alone, he was pretty much ready to diagnose me with a stress fracture, but he couldn’t rule out a bone bruise. I was to do my regular activities as able, and if the pain didn’t go away, then he’d be more confident that it was a stress fracture (in which case, I shouldn’t have been doing my regular activities).

I played two more games of ultimate before returning to the clinic and saw a different doctor who ordered a bone scan to confirm the stress fracture. The bone scan was really cool. First, they injected me with technetium-99m-MDP. It’s a radioactive material that’s absorbed by bones undergoing more rapid turnover, like the healing site of a stress fracture. After a few hours of letting that go through my body, I returned for the scan. I lay down while the scanner imaged my leg. It was a slow scan — several minutes at a time for each of the views they wanted to get — and I could see the results of the scan as they filled in on the screen above me. It basically looked something like this:

Bone scan showing a stress fracture of the tibia
The bright white spot is where the radioactive material was being collected more heavily by the damaged and healing bone.

Treatment and progress

The bone scan confirmed my stress fracture. I’d probably had it since about mid-March, played ultimate and ran the Sun Run on it. But now, I had to give it rest. That is the only way a stress fracture will heal. No running, no ultimate. My instructions were to rest until I’d experienced ten consecutive days without pain from the normal activities of life. I was allowed to walk around as normal, and do non-impact activities like biking, but I avoided even jogging to catch up to a bus I was about to miss.

After about two days, it no longer hurt to bike. After five days, it didn’t hurt to walk or stand up anymore. After two weeks, it didn’t hurt to walk up or down stairs, and I’d started to forget occasionally that I was injured (not always a good thing). After three weeks of rest, I went to an ultimate clinic and was able to jog around lightly to participate in some of the drills. After the fourth week, I tried again to do some light drills, but this time, the fracture site hurt again for a few days… too much, too soon. I backed off and took another three weeks off from any jogging. I did a bike trip up the Sunshine Coast during this time, but biking had felt fine for weeks. After those three weeks (6th week after diagnosis), it really felt a lot better. I started practicing ultimate twice a week again, although at a lighter pace at the start. After week 8, I played in a weekend ultimate tournament. It’s now 15 weeks after the diagnosis, and it feels really good. I’ve sometimes tried to ramp up my activities too quickly, and that causes discomfort and sometimes pain at the old injury site. When that happens, I just take time off until it feels better (it’s needed a week at most) and then try again. It’s always been fine the second time.

Prevention

The main advice seems to be to give your bone time to adapt and rebuild in response to increased activity. If you add too much new stress at once, the bone will simply weaken. However, if you increase activity gradually, the bone will have time to heal, adapt, and strengthen in response.

An adequate intake of vitamin D and calcium is also important for maintaining bone density. Taking extra vitamin D supplements seem to decrease the likelihood of a stress fracture.

Actual doctors

If you want to hear what actual doctors have to say, here are some references that I found helpful and interesting:

What’s your story?

Was your recovery similar? Any advice that I missed?