Removing: PGP Key and Content Licensing

I have removed two pages from my website—my PGP key and my content license.

PGP Key

I removed my public PGP key because I no longer intend to use it for signing messages. My same key remains on Keybase and other public key servers, but I no longer sign outgoing mail, nor do I intend to use my key regularly in any way.

I don’t feel that my key has been compromised. However, it does me little good to keep using it, and most encryption in actual use in my daily life doesn’t involve PGP. In the wake of a mostly minor vulnerability called E-Fail earlier this month—which didn’t impact me—I found myself persuaded of the ultimate futility of keeping up with PGP by an op-ed on Ars Technica from a couple of years ago.

Content Licensing

I removed my CC BY-NC 4.0 license notice page from my site. This post hereby serves as notice that from this date forward, I no longer license my existing or new content (writing, photos, videos, or audio) under a CC license, and so all that content falls back to the default copyright of the relevant jurisdiction.

Any works that have already been used under the CC license have been done so irrevocably, and so I have no ability to revoke those licenses. They may be licensed until their rights lapse under the copyright laws of those jurisdictions.

If anyone wants to use some of mine, they are certainly welcome. The removal of the license only implies one practical change—you must ask permission. That’s all.

Math, She Rote

My friends often have different educational backgrounds than mine. Some of them are younger, but even if they aren’t, they’re often from urban areas that had moved to more modern educational curricula before my school system had. The way I learned basic arithmetic remained unchanged from how it was taught from the early 1980s by the time I learned it in the late 1980s and early 1990s because that’s when our books dated from.

I learned during an interesting period in mathematical education history. It represented a kind of educational interbellum—a bit after the “New Math” of the 1960s and 1970s but before the “math wars,” instigated by the 1989 Curriculum and Evaluation Standards for School Mathematics. The latter 1989 publication has been called “reform mathematics,” which emphasizes processes and concepts over correctness and manual thinking. In other words, the educators promoting reform mathematics began to believe that the path students took toward the answer mattered more than whether they got the answer right. Many states’ standards and federally funded textbooks followed reform mathematics in the 1990s and beyond.

Reform mathematics emphasized constructivist teaching methods. Under this approach, instead of prescribing to students the best way how to solve a problem, teachers pose a problem and allow the student to surmount it by building on their own knowledge, experiences, perspective, and agency. The teacher provides tools and guidance to help the student along the way. Constructivist approaches involve experiments, discussions, trips, films, and hands-on experiences.

One example of a constructivist-influenced math curriculum, used in elementary school to teach basic arithmetic, was known as Investigations in Numbers, Data, and Space. It came with a heavy emphasis on learning devices called manipulatives, which are tactile objects which the student can physically see, touch, and move, to solve problems. These are items like cubes, spinners, tapes, rulers, weights, and so on.

As another example, someone I know recently described a system they learned in elementary school called TouchMath for adding one-digit numbers, which makes the experience more visual or tactile (analogous to manipulatives). They explained that for each computation, they counted the “TouchPoints” in the operands to arrive at the result.

I had never heard of TouchMath. In fact, I never solved problems using manipulatives, nor any analogue of them. I had little experience with this form of math education. We were given explicit instructions on traditional ways to solve problems (carrying, long division, and so on). Accompanying drawings or diagrams rarely became more elaborate than number lines, grids, or arrangements of abstract groupings of shapes which could be counted. They served only as tools to allow students to internalize the lesson, not to draw their own independent methods or conclusions.

I contrasted my friend’s experience with TouchMath to my experience. To add or subtract one-digit numbers, we merely counted. We were given worksheets full of these to do, and since counting for each problem would have been tedious and impractical, memorization for each combination of numbers would become inevitable. Given the expectations and time constraints, I’m certain rote memorization was the goal.

In a couple of years, we were multiplying and dividing, and we were adding and subtracting two- or three-digit numbers using carrying—processing the numbers digit-wise. At the same time, we were asked to commit the multiplication tables to memory. These expectations came in third grade, and it would be nearly impossible to make it out of fourth grade without committing the multiplication table and all single-digit addition and subtraction to memory (the age of ten for me).


Our teachers did not bother to force us to memorize any two-digit arithmetic operations. But I have some recollection a lot of years ago of my grandma telling me she had most two-digit additions and subtractions still memorized. It was just an offhand remark—maybe something she said as I was reaching for a calculator for something she had already figured out. Maybe we were playing Scrabble.

For context, she would have gone to school in rural Georgia in the 1940s and 1950s, and she graduated high school. (In that time and place, it was commonplace for many who intended to do manual, trade, or agricultural work not to continue through secondary school.)

I remember feeling incredulous at the time about the number of possible two-digit arithmetic operations that would imply memorizing. Of course, many would be trivial (anything plus or minus ten or one, or anything minus itself); others would be commonplace enough to easily memorize, while still others would be rare enough to ignore. But that still leaves several thousand figures to remember.

The more I thought about it, the more I saw that, in her world, it would make better sense to memorize literally thousands of things rather than work them out over and over. She had no way of knowing that affordable, handheld calculators would exist in a few decades after she graduated from school, after all. Each time she memorized a two-digit addition or subtraction, she saved herself from working out the problem from scratch over and over again for the rest of her life. This saved her effort and time every time she

  • balanced her checkbook,
  • filled out a deposit slip at the bank,
  • calculated the tax or tip on something,
  • tallied up the score for her card game,
  • totaled up a balance sheet for her business,
  • made change for a customer, or
  • checked that the change she was being given was correct,

to say nothing of all the hundred little things I can’t think of. She married young and has run small businesses for supplemental income all her life, so managing the purse strings fell squarely into her traditional gender role. Numbers were part of her daily life.

So for the first half of her life, none of this could be automated. There were no portable machines to do the job, and even the non-portable ones were expensive, loud, slow, and needed to be double-checked by hand.

I don’t believe she remembered these all at once for a test, the way I learned the multiplication tables in third grade. It seems likely she memorized them over time. It’s possible that expectations in her school forced a lot of memorization that I didn’t experience when I went many decades later, but maybe she was just extra studious.


I recall, as I went through school, having to rely more on a calculator as I approached advanced subjects. Before calculators became available to students, appendices of lookup tables contained pre-calculated values for many logarithms, trigonometric functions, radicals, and so on. Students relied on these to solve many problems. Anything else—even if it were just the square root of a number—came from a pen-and-paper calculation. (Many of my early math books did not acknowledge calculators yet, but this changed by the 1990s.)

Charles Babbage reported that he was inspired to attempt to mechanize computation when he observed the fallibility of making tables of logarithms by hand. He began in the 1820s. After a hundred and fifty years, arithmetic computation would become handheld and affordable, fomenting new tension around what rote memorization plays in both learning and in daily life.

Today, we’re still trying to resolve that tension. Memorization may feel like it has a diminished role in a post-reform education environment, but it’s by no means dead. Current U.S. Common Core State Standards include expectations that students “[b]y end of Grade 2, know from memory all sums of two one-digit numbers,” and, “[b]y the end of Grade 3, know from memory all products of two one-digit numbers.” That sounds exactly like the pre-reform expectations I had to meet.

All this means is that there has been neither a steady march away from rote memorization nor a retreat back to it. Research is still unclear about what facts are best memorized, when, or how, and so there’s no obvious curriculum that fits all students at all ages. For example, the Common Core Standards cite contributing research from a paper which reports on findings from California, concluding that students are counting more than memorizing when pushed to memorize arithmetic facts earlier. The paper reasons this is probably due to deficiencies in the particulars of the curriculum at the time of the research (2008).


I’m not an expert, and I don’t have easy answers, but my instinct is that rote memorization will always play an inextricable role in math education.

Having learned about the different directions in which the traditional and reform movements of math education have tugged the standards over the years, I tend to lean more traditional, but I attribute this to two things. One is that I was educated with what I remember to be a more traditional-math background, and though I didn’t like it, it seems serviceable to me in retrospect.

The other reason is that, for me, memorization has always come easily. I don’t really know why this is. It’s just some automatic way I experience the world. Having this point of view, though, I can easily see how beneficial it is to have answers to a set of frequent problems ready at hand. It’s efficient, and its benefits never cease giving over time. The earlier you remember something, the more it helps you, and the better you internalize it. Even for those who can’t remember things as easily, the returns on doing so are just as useful.

I do completely agree with the underlying rationale of the constructivist approach. Its underpinnings are based on Piaget’s model of cognitive development, which is incredibly insightful. It seems useful to learn early to accommodate the discomfort of adapting your internal mental model to new information by taking an active role in learning new ideas in order to surmount new problems.

I don’t necessarily believe that a constructivist learning approach is intrinsically at odds with rote memorization—that is to say, that memorization necessarily requires passive acquisition. In fact, the experience of active experimentation and active role may help form stronger memories. It’s more likely they compete in curricula for time. It takes longer to mathematically derive a formula for area or volume by independent invention, for example, than to have it given to you.

In fact, constructivist learning works better when the student has a broader reservoir of knowledge in the first place from which to draw to begin with when trying to find novel solutions to problems. In other words, rote memorization aids constructivist learning, which then in turn aids remembering new information.

My feeling is that math will always require a traditional approach at its very heart to set in place a broad foundation of facts, at least at first, before other learning approaches can have success. Though the idea of critical periods in language acquisition has detractors and heavy criticism, there is a kernel of truth to the idea that younger minds undergo a period of innate and intense linguistic fecundity. Maybe as time goes by, we can learn more about math acquisition and find out which kinds of math learning children are more receptive to at which ages. Until then, I feel like we’re figuring out the best way to teach ourselves a second language.

I am grateful to Rachel Kelly for her feedback on a draft of this post.

Privacy Policy Updates: Data Storage

I updated WordPress today to version 4.9.6. I noticed this version comes with support for implementing privacy policies throughout the site. I seem to have been ahead of the curve in implementing my own, but when the GDPR in the EU comes into effect this month, it will clarify and simplify data privacy for much of Europe. This implies enforcement will become a more direct matter as well. Any web service accessible to Europe and which does business in Europe now has updated their privacy policies to ensure it complies with the GDPR—which is why everyone has gotten a raft of privacy policy updates.

Most of these privacy policy updates pertain to what rights customers or users have to their own data. Often, they grant new rights or clarify existing rights. This week’s new version of WordPress is yet another GDPR accommodation.

Today, I have to announce my own GDPR update. Yes, I’m just a tiny website no one reads, and I provide no actual services. But having already committed to a privacy policy, which I promised to keep up to date (and announce those changes), I’m here to make another update.

One nice thing that came with the the WordPress update is a raft of suggestions on a good privacy policy (and in what ways WordPress and its plugins may cause privacy concerns). I found that I had covered most of them, but one thing I needed to revisit was a piece of functionality in Wordfence.

I use Wordfence for security: It monitors malware probes and uses some static blacklists of known bad actors. It also, by default, sends cookies to browsers in order to track which users are recurring ones or which users are automated clients. The tracking consisted only of an anonymous, unique token which distinguished visitors from one another. Unfortunately, this functionality had no opt-out and did not respect Do Not Track.

Although my tracking was only for security purposes—not for advertising—and although did not store any personal information, nor did I share with anyone else, I realized I would have to disable it.

I had made explicit mention of this tracking in my previous revision of my privacy policy:

I run an extra plugin for security which tracks visits in the database for the website, but these are, again, stored locally, and no one has access to these.

This is unfortunately more vague than it should have been, since it doesn’t mention cookies. It also provides no provision for consent. It merely states the consequences of visiting my site.

The GDPR makes it clear that that all tracking techniques (and specifically cookies) require prior consent. Again, I’m not a company, and I don’t provide any service. I’m not even hosted in the EU’s jurisdiction. My goal, though, is to exist as harmoniously with my visitors as possible, whomever they may be, and have the lightest possible touch.

So I’ve disabled Wordfence’s cookie tracking. I’ve added a couple of points to my privacy policy which clarify more precisely which data is logged and under which circumstances cookies may be sent to the browser.

This interferes my analytics, unfortunately—it’s no longer possible to be sure which visitors are humans anymore. I think it’s worth it, regardless.

I also made a couple of other changes based on WordPress’s suggestions. I moved a few bullet points around to put some points closer together which feel more logically grouped. I also added a point which specifies which URL my site uses (meaning the policy would be void if viewed in an archived format, within a frame, or copied elsewhere).

Privacy Policy Update: No Mining

I got a weird spam e-mail overnight asking if I wanted to embed someone’s cryptocurrency miner into my website. They purport to be opt-in only, but all the other examples I’ve read about online up to now have been surreptitious, hijacking the browser for its own ends without asking. The end user only notices when their computer fans switch on or their computer gets too hot.

Such mining scripts have been strongly contentious in other websites. They exert excessive and unilateral control over the browser’s system. I certainly had such things in mind when I promised never to embed ads and the like in my website, but I had never spelled out that I had no intention of hijacking the browser for my own ends (ad or not).

This morning, I added a new point to my privacy policy.

  • This website does not load software in the user agent (your browser) which serves any purpose beyond displaying the website and its assets—meaning it does not use your browser to mine cryptocurrency, for example.

Most of my privacy policy describes what the website does without mentioning the browser. This point adds a clear expectation for browsers which visit.

I generalized the point a bit to include things which aren’t just cryptocurrency miners. It might be tempting to grab a few of my users’ cycles for SETI@home or the like, for example, but if a user wants to contribute to a project like that, they can do so themselves. I’ll have to rely on persuasive words to bring people around to a cause like that.

The Apology Contract

A binding contract has three elements: offer, consideration, and acceptance—all of which must exist among mutually assenting parties. These elements, in some form or another, have existed since time immemorial. A contract of sale, for example, contains an offer (the good for sale at a price), the consideration (the money exchanged for the good), and the acceptance (the actual mutual agreement to exchange the good for the price).

Many of our social interactions implicitly follow a similar structure because they rely upon offering, considering, and accepting one another’s social cues in more-or-less formulaic ways. Some of these interactions are rigidly ritualistic—”thank you,” “you’re welcome”—and some are not (flirting, for example).

I have read several articles on the best way to apologize, with which I agree, and which address the person giving the apology with humility and sincere intent, acknowledging the harm done, and reducing further harm. (One such popular example was written by John Scalzi. Another good example aimed at children comes from a parenting blog.)

However, I have lately come to worry that the act of the apology often still imposes a contract-like, ritualistic exchange. On receiving an apology, I have in the past found myself at odds with every instinct in my body to assuage the apologizer who, having recognized their fault and promising in good faith to do better, awaits something like an absolution from me before moving on.

The formula for how we’re taught to apologize, as children, goes:

— I’m sorry.

— It’s okay.

I’ve tried withholding that second part of the exchange as I’ve gotten older. Sometimes I don’t feel okay. Sometimes it’s not okay. Maybe I need space or time to get there. Maybe I just want to move on without needing to perseverate on the feelings of the person who wronged me.

This is especially difficult for an in-person conversation. Without the expected words, “it’s okay,” or, “it’s fine,” in my mouth, what am I to say? I don’t necessarily want to prolong the moment, either. I often have an interest in moving past the moment, but I don’t have some alternative wording that isn’t focused on the feelings of the apologizer.

When I don’t automatically say, “it’s okay,” a loaded pause often seems to follow. The apologizer feels they have done everything right, and I haven’t followed through on my end of the apology. They wait for me to give them some way to get past the moment, and when I don’t offer that back, they also don’t know how to continue.

The ritual of the apology feels a lot like a social contract because we’re conditioned to treat it as such from a young age, to offer some comfort to someone who has apologized and meet them part way. However, this is no contract. The formula, like so many social rituals, instead imposes an expected response on the recipient. There’s not necessarily mutual assent.

What I have read about the best way to offer an apology sometimes, but doesn’t always, offers a final step I believe is extremely important—once given, expect nothing back. Any forgiveness, grace, or acceptance on the part of the recipient is a gift, not an exchange. Beyond that, though, you need not expect any response whatsoever, not even acknowledgement. The apology, for the one giving it, is both the understanding of harm and the promise to reject furthering it. It is not a request.

What’s more, I can’t recall seeing anyone write for the person receiving the apology. I address you now: You owe nothing. Take comfort, if you can, that someone has seen how they have harmed you. Find peace, if you can, in the closure they offer. Exchange what you like, and repair the relationship if you want it. But your duty to them ended when the apologizer wronged you in the first place.

Announcing My Content Licensing

Note: Please see this post explaining the revocation of my licensing.

A couple of recent popular posts I’ve made have motivated me to license my content here on my site. This doesn’t directly affect readers. It just means that I want to disclose what others are allowed to do with what I write without asking me first.

If anybody wants to re-license anything here (for some reason), I’m open to discussing it, but I may ask for compensation. The easiest way to contact me is just by sending email to to any address at my domain (which all lands in my inbox).

It’s Done

Finally got through the extended edition of Lord of the Rings. Made a GIF to celebrate. It pretty well encapsulates work this last few days.

its-done-640

Puzzling

Screen Shot 2013-12-31 at 13.39.54I’ve been playing a lot of the older Legend of Zelda games lately, since OpenEmu arrived on the scene and changed things. Link to the Past was my favorite.

The entire in-game world was just a single massive interconnected puzzle that took months of playtime to unravel as a kid. Every single thing you saw, got, heard, or did had some significance in understanding and unraveling the next piece in the puzzle. For a kid with wicked, above-average recall, it played to my strengths. That was probably the reason it appealed to me so much, and at the same time, fucked me up so much.

I went into life later already in the habit of working out and memorizing every single thing that passed in front of me as if it were some puzzle that held a part of the key of figuring out the entire world. That definitely didn’t serve me well.

My interest in the Legend of Zelda series waned around the time I hit puberty (and video games began figuring out 3D).