What’s Wrong with Metcalfe’s Law?

In a recent Medium post derived from a talk he gave at private invitation-only event for the IT industry, Dan Hon presents one view of Metcalfe’s Law, the theory espoused by Ethernet inventor Bob Metcalfe that “the value of a telecommunications system increases as the square of the number of participants”. Hon looks at the (no pun intended) value judgment embedded in talking about the “value” of a network, and considers purely market-oriented measures lacking.

I’d like to step back a bit and look at it from a different angle. Instead of “value”, let’s consider “utility”: what benefit arises to the users from their use of the network? Metcalfe’s claim can be restated simply: the global utility (sum over all users) of a network is quadratic in the number of users. You don’t even need graph theory to prove that this is trivially true, if you accept what I take to be Metcalfe’s presuppositions: first, that utility sums linearly over all users (a view which would be understandable to Jeremy Bentham), and second, that each user’s utility is linear in the number of other users on the network.

The real problem with Metcalfe’s Law, as I see it, is precisely in this second presupposition. While it is true to a first approximation, for small networks, once the network reaches a sufficient penetration of that community with which any individual user has an interest in communicating, the marginal utility of additional communications partners diminishes quite rapidly, and ultimately goes negative. We see this even with old technologies like the telephone network: nearly all of the value I get from the telephone derives from being able to communicate with family, friends, and current and potential employers, vendors, and service providers in my immediate vicinity. While connecting a billion people in India or China to the rest of the world is laudable, there cannot be more than a thousand of them that make the telephone network more valuable to me. (One thing that this analysis does not consider, and a more sophisticated analysis would, is economies of scale: do those billions of users actually make it easier or cheaper to provide me with the service that I value. To be left for another day.)

In the social network case, it’s clear how additional users can have negative marginal utility: the additional noise generated can drown out the intended communication (whether that noise is trolls, pile-ons, or just way too many well-meaning people making the same comment in a reply). Twitter is a great demonstration of this; users bearing the vaunted “blue checkmark” — a distinction given out entirely at Twitter’s discretion to a small subset of users, mostly celebrities, journalists, government officials, and corporate marketing departments — are given a variety of tools to screen out communications from the masses. One of the tools which is frequently employed by these “verified” users screens out all notifications from the remaining users, allowing them to give the appearance of using the platform to communicate with others while in actuality paying attention only to a small number of similarly privileged people. This screening was not part of the original Twitter service: it was only deployed after Twitter gained a sufficiently large and noisy user community that it was driving away users Twitter actually had a business reason to want to retain. Of course, even “old tech” had to come up with similar mechanisms: when telephone calls became cheap enough that scammers were willing to spam a thousand people at dinnertime in the hope of finding a single mark, caller ID became a necessity and more and more people began to screen their calls. (Compare also the Eternal September.)

In conclusion: Metcalfe’s Law is wrong because the marginal utility to the existing users of a communications network is not constant: while it is large and positive for small networks, as networks grow beyond the scale of normal human social circles, the utility drops off quite rapidly, and eventually goes negative. When you sum up this function over all users, unlike the linear utility posited by Metcalfe, overall value does not scale as the square of the number of users. (It might not even be asymptotically linear — I leave that analysis to someone with better mathematical chops.)

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Clarifying one particular gender conversation

This post has been percolating in my head since the Worldcon 75 in Helsinki last August. My initial idea was quite a bit more ambitious — I have a note here which reads “Gender: cause or effect?” — but what was going to be the introductory section is probably the only part of it that I have something reasonable to write about.

Gender was, not surprisingly, an important thread in the conversation at Worldcon 75. There was even a panel (which I didn’t manage to attend) talking about how you deal with it in languages that don’t “have” gender, like Finnish, Turkish, and Chinese. But that made me want to write a little bit to try to clarify this discussion, because I think the words we use to talk about this particular aspect often make things more confusing rather than less. So this post is going to explore two questions: What do we mean when we say “gender” in the context of language, and what does it mean to say that a language “has” or “doesn’t have” it?

I should point out that I am coming at this from the perspective of an interested amateur, not a professional linguist by any means — but an amateur who has at least had the experience of trying to learn both French and Finnish. So don’t take any of what follows as gospel, but rather, a jumping-off point for further research if you’re interested in that sort of thing.

So what is “gender”, anyway? In linguistics, “gender” is a specialized form of what is more generally called “noun classification” — it’s just a historic fact that some languages (most but not all of them) divide their nouns up into categories. We generally reserve the term “gender” to refer specifically to those noun-classification systems that align more or less with the binary (masculine-feminine) or ternary (masculine-feminine-neuter) systems seen in Indo-European and Semitic languages (like English, Greek, and Hebrew), as opposed to those with a larger number of categories like the Bantu languages of Africa. It’s important to distinguish gender as a grammatical category from gender as a semantic category: because the “gender binary” is a near-universal part of human experience, all languages have words with semantic gender, words like “man”, “woman”, “father”, “daughter”, and so on (although not all languages have the same set — French distinguishes between male and female cousins, for example, whereas English does not). But even in languages with very strong grammatical gender, it’s by no means given that this will align with the semantic gender — as witness German, where many words that are semantically female (or at least feminine) are grammatically neuter or sometimes even masculine. (Historical linguists tell us that this is because the Indo-European three-gender system had collapsed to two genders before Germanic languages re-developed the modern neuter.)

So what then does it mean to say that a language “has” or “doesn’t have” grammatical gender (or indeed noun classification)? Grammar, roughly speaking, is how words fit together to form phrases and other multi-word structures, and also about how words refer to other words in context. For gender to be part of a language’s grammar, it must have some observable consequence on which words, or word forms, are allowed together in a sentence, or can be used to refer to the same thing. The most relevant property to look at is what English teachers usually call “agreement”, and linguists often call “concord”: the property that words that refer to the same thing must all come from the same class or be otherwise marked in the same way. English makes these considerations much less clear, because English has only the fractured remnants of its historic three-gender system, observable only in pronoun agreement, and not universally even then. But the Romance languages — those descended from Latin, like French, Spanish, and Romanian — all have a robust two-gender system (masculine and feminine) with mandatory concord for pronouns, determiners, adjectives, and participles. Semitic languages go one better: verbs agree in gender with their subjects. Unlike in English, Romance languages have gendered third-person plural pronouns: a group of portes (doors) in French are elles, but a group of stylos (pens), or indeed a group of mixed-gender objects, are ils.

Because of how English historically developed, acquiring pronouns from Old Norse and losing most of its inflectional system as England was invaded alternately from the north and from the south, we have no gender agreement for adjectives or articles any more (except, for a very few writers and the editors of The New Yorker, a very small set of adjectives borrowed from French: naïf/naïve, blond/blonde, brunet/brunette being the principal ones). English does continue to have two forms of gender concord for pronouns: the third-person singular he/she/it, which do not precisely correspond with the historic genders used in Old English or West Germanic, and a simple sentient/non-sentient system seen in the interrogative pronouns who/what and the relative pronouns who/which. (I don’t include “singular they” here because it acts grammatically identical to the third-person plural in all other respects — compare the much earlier “singular you”, which also takes a plural verb form.)

So what about those putative “genderless” languages? The only one that I have any direct knowledge of is Finnish, but I understand that all of the Uralic languages are the same in the most important way: there is no gender concord for adjectives or participles. These languages have no articles, so there is nothing to agree with there. But with pronouns it gets a bit more interesting. Finnish arguably has a two-gender system for personal pronouns: the sentient hän (singular)/he (plural), and the non-sentient se/ne. But (and it’s a big “but”), in regular spoken conversational Finnish (as opposed to newscaster or teach-to-confused-foreign-teenagers Finnish) these two categories are collapsed — to the “non-sentient” se/ne. I never learned the language well enough to express complex structures, but I suspect that there may be similar behavior in some of the relative pronouns. Away from Finnish, I know that there are languages that don’t have pronouns at all, but I don’t know how that set intersects with other means of marking gender or noun classification.

Another interesting part of this conversation here, albeit one that I’m not all that well prepared to discuss, is the question of languages with mandatory gender marking for names. As English users, we are accustomed to the idea that a personal name is just an arbitrary user-chosen token, and might at least in theory refer to any gender. Indeed, numerous names are gender-neutral or have, in living memory, actually changed their default gender. (“Robin” is perhaps the poster child here: previously a diminutive form of “Robert”, today most Robins are female and not a diminutive for anything.) That said, we are still familiar with gender-marked names, whether it’s “Alexander”/”Alexandra” (sharing the gender-neutral hypocoristics “Alex” and “Sandy”!) or “Robert”/”Roberta”. Numerous other pairs of names exist in the repertoire used by English speakers to name their children and their fictional characters. Some other cultures take this to an extreme, however: most or all names in Slavic languages, for example, are gender-marked — both given and family names, not to mention patronymics. Similarly, the patro/matronymics used in Icelandic names have mandatory gender marking, because (as with the Slavic patronymics) they contain an element that means either “son” or “daughter”, regardless of whether they use the father’s or mother’s name as the base.

One of the reasons this specifically came up at Worldcon 75, aside from the panel that I mentioned, is that because Finnish doesn’t have masculine or feminine nouns or pronouns, Finns sometimes have difficulty remembering the correct forms to use when speaking in English or other languages that do make such a distinction. This doesn’t mean that they are confused about the semantic gender of people (they can certainly distinguish miehet and naiset, after all), but rather, that the association of semantic and grammatical gender is weaker when speaking in a second (or third) language when one’s ambient tongue doesn’t make the same distinction. The Worldcon program included a note explaining this and asking attendees to be understanding if their hosts chose the wrong pronoun. (Which is perhaps the best case of all for those badge flags given out at cons indicating the holder’s desired pronoun.) It’s especially an issue for invented or nonce pronouns: it’s probably unreasonable to expect anyone other than the in-group of native speakers who adopted them to actually use or even make sense of them. Those who use such pronouns should take care to check their privilege (as speakers of a global hegemonic language) when dealing with non-native speakers, especially those whose native pronoun system doesn’t correspond to the English one.

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Overdue recipe report: Luisa Weiss’s Christbrot

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This is the third of three recipes I did for the holiday season from Luisa Weiss’s Classic German Baking (Ten Speed Press, 2016). Weiss recounts how she felt that she had to include a recipe for Dresdner Christstollen, the classic … Continue reading

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Overdue recipe report: Luisa Weiss’s Mohntorte

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Technically, mohntorte — a wheat-free sponge-type poppy seed cake — is not a Christmas specialty, but I included it along with the two actual Christmas recipes from Luisa Weiss’s Classic German Baking (Ten Speed Press, 2016; pp. 126–7) that I prepared … Continue reading

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Overdue recipe report: Luisa Weiss’s Pfeffernüsse

I decided that my holiday baking this year would be three recipes from Luisa Weiss’s Classic German Baking (Ten Speed Press, 2016) — after all, many of our holiday traditions, and a good portion of American baking more generally, come from German immigrants, which accounts in part for the wide differences between US and UK Christmas food traditions. (And, of course, my family name also comes from German immigrants!) Among the most classic German-American traditions at Christmas are pfeffernüsse, small spice cookies (often confused in appearance, but not flavor, with Russian/Italian/Mexican tea cakes/wedding cookies) flavored with ground pepper and gingerbread spice (the latter is called lebkuchengewürz in German and is a common prepared mixture of ground spices used in many recipes). I remember my father making cookies like these when I was little, probably using the recipe from the 1976 edition of Joy of Cooking. Rombauer’s Joy recipe is quite different from the recipe in Weiss’s book (pp. 228–30), and I suspect it reflects a more “Americanized” version. Among the most notable differences, Rombauer uses molasses, black pepper, baking powder, brandy, and dry confectioner’s sugar where Weiss uses honey, white pepper, ammonium carbonate (“baker’s ammonia”), rum, and a lemon-sugar glaze, respectively. The most significant difference is that the Joy recipe contains butter whereas the only fat in Weiss’s recipe comes from the egg; Joy also uses candied citron and chopped almonds, flavoring ingredients absent from the Weiss’s pfeffernüsse. (By the way, in this post I will use English capitalization since I’m writing in English, but I will follow the German morphology for number, so it’s one pfeffernuss and two pfeffernüsse.) Weiss says that her recipe comes from Offenbach — like many traditional European recipes, there is a lot of regional variation — and it’s entirely possible that Rombauer’s recipe is equally authentic but from a different part of Germany.

Before starting to make the pfeffernüsse, it was necessary to gather the requisite ingredients for the lebkuchengewürz — since, unlike in Germany, it’s not something sold in grocery stores. The recipe is quite simple, and makes far more than is required for one or even two batches of pfeffernüsse: 30 g of ground cinnamon (I used true cinnamon and not cassia), 1½ tbl of ground cloves, 1 tsp of ground allspice, 1 tsp ground cardamom, 1 tsp ground ginger, 1 tsp ground mace (I’ve never seen a recipe use that much mace), and ¾ tsp ground aniseed. That last ingredient was a bit of a challenge to find — it’s one of those spices that isn’t stocked in my local Whole Foods, but luckily the conventional supermarket nearby does have it (it still took a bit of searching the shelves) so I didn’t have to mail-order. All these spices are simply mixed well and sealed up in a container.

Mise en place
Now for the pfeffernüsse proper, starting with the usual mise en place. Starting from bottom left, you can see the lebkuchengewürz, of which this recipe uses only two teaspoons. Next to that is ⅛ tsp of freshly ground white pepper, and then a teaspoon of ammonium carbonate (next to the bottle). The dry ingredients — 310 g flour, 1 tsp cocoa powder, and ¼ tsp salt, have already been mixed together. In the saucepan at upper right is 160 g of honey and 75 g of sugar, and hiding behind the pan is a single egg. There should have been 1 tablespoon of slightly warmed rum in that bowl in the center, but I mistakenly used my half-tablespoon measure instead. Oops.

Honey-sugar syrup
The recipe begins with heating the honey-sugar mixture on the stovetop until it’s hot enough to fully dissolve the sugar. While the mixture is still hot, the spices are stirred into it (this helps to “bloom” the spices and bring out their volatile flavors). Meanwhile, the ammonium carbonate is mixed with the rum, causing it to fizz a bit, and hopefully dissolve. (I found that even when I used the correct amount of rum, it wasn’t quite enough to fully dissolve the ammonium carbonate.) It will fizz quite a bit, losing some of the leavening power in the process (since there’s nothing to capture the gas at this point). Ammonium carbonate — (NH4)2CO3 — was once a popular leavening agent, since it decomposes entirely into gas (ammonia, carbon dioxide, and water) leaving nothing behind, unlike baking powder, which adds sodium or other metal ions like aluminum depending on the specific chemistry. The downside of ammonium carbonate is that half of the leavening power comes from gaseous ammonia, which is not a scent you want to have in your food, so it’s only usable in applications where you can be sure that all the ammonia will be driven off in the baking process.

After adding ammonium carbonate to hot syrup
When the rum-leavening mixture is added to the still-warm honey-sugar-spice mixture, a great deal more gas is evolved, giving the baker a strong whiff of ammonia. After stirring to fully incorporate, the resulting mixture is stirred or kneaded into the dry ingredients along with the egg to form a sticky dough.

Dough mostly combined
At this point, the dough is formed into small balls and deposited on parchment-lined baking sheets. Weiss calls for one-inch (25 mm) dough balls, for a yield of 48 cookies; when I used a #100 (⅝ oz) disher, I only got 31 — I was so surprised by this that I actually did the entire recipe a second time, and had the exact same yield. Because there’s no fat in this recipe, the cookies do not spread in baking, and they can be spaced quite close — I had no trouble putting 20 dough balls on a standard cookie sheet, and if you manage to get the 48 that Weiss calls for, there’s no reason you couldn’t fit them all on two baking sheets.

Fully baked dough balls
The pfeffernüsse are baked in a 375°F (190°C) oven for ten minutes — since there’s very little moisture in them to start with, it doesn’t take long, and you definitely don’t want them to completely dry out. While the first batch is baking, a simple lemon-sugar glaze is made from 100 g confectioner’s sugar, 1 tbl fresh lemon juice, and 1 tbl water.

Cookies after brushing with lemon glaze
Using a pastry brush, the glaze is applied to the the cookies while they are still hot. Just to keep the kitchen clean it helps to put the cooling rack over a sheet pan to catch the excess glaze.

Glazed cookies cooling and draining
You should probably do a better job than I did of evenly covering the surface of the cookies. Once cool, the pfeffernüsse should be sealed in an airtight for a minimum of several days to ripen — as the moisture from the glaze is absorbed by the cookies proper, the dry, crisp crumb becomes soft and chewy.

As I mentioned above, I ended up making two batches of these cookies, which left me with enough to half-fill a Christmas cookie tin that I already had. I had enough (about 60) to eat quite a few of them myself, give a lot away at the family Christmas party, give more away at Christmas dinner, and still bring a dozen into the office after Christmas where almost nobody was around to keep me from eating the rest.


The nutrition details below reflect my yield for this recipe and not Weiss’s. If you can actually get four dozen pfeffernüsse, you’ll have to cut these numbers by about a third.

Nutrition Facts
Serving size: 3 cookies
Servings per recipe: 10
Amount per serving
Calories 240 Calories from fat 4
% Daily Value
Total Fat <1​g 1%
 Saturated Fat <1​g 1%
Trans Fat 0​g
Cholesterol 19​mg 6%
Sodium 69​mg 3%
Total Carbohydrate 55​g 18%
 Dietary fiber 1​g 5%
 Sugars 30​g
Proteins 3​g 6%
Vitamin A 1%
Vitamin C 1%
Calcium 0%
Iron 3%
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Several long-overdue recipe quick takes

There comes a point when you simply have to declare “blog bankruptcy” and clear out your writing backlog. That doesn’t allow you to discharge your writing debt in its entirety, but it does mean that you (well, I) can feel less bad about giving some posts really short shrift. So here are a few really quick hits on recipes I’ve made since my trip to Worldcon 75 in Helsinki last August that I haven’t gotten around to saying anything about yet.

First, the brownie recipe (entitled simply “brownies”) from Little Flower Baking by Christine Moore with Cecilia Leung (Prospect Park Books, 2016). Awful, awful, awful: overbaked, cakey, and tasteless. I find in impossible to believe that they sell brownies this bad in the eponymous cafe. The proportions don’t look terribly far from the average brownie, so this recipe would probably work out fine with the right cooking time and temperature.

Second, “Truffle Chocolate Cream Pie” from Joanne Chang’s Baking with Less Sugar (Chronicle Books, 2015). Unlike the last recipe, this one was a real winner, with the two distinct-textured rich chocolate fillings and only the sugar originally in the chocolate itself. I had trouble getting the chocolate mousse topping to whip up as much as I thought it should have (I have the same trouble with whipped ganache filling for cakes, and probably for the same reason — maybe it’s my expectation that’s wrong). Despite the reduced sugar, it’s by no means a low-cal dessert: with low-fat milk and Callebaut 60-40-NV for the chocolate it still clocks in at 517 kcal for 1/12 of a pie. Recommended. I have a few photos of this one:

The recipe uses Chang’s standard pâte brisée, with egg yolk and milk but no sugar.

This shows the pie with the bottom “truffle” filling (basically a very thick chocolate custard, with egg yolks, butter, and cream).

The pie is topped with a whipped chocolate mousse and then chocolate shavings are sprinkled on top of that.

This shows the cross-section of the pie, with the two fillings barely distinguishable (more by apparent density than by color). I have yet to master the proper technique for truly flaky all-butter pie crust.

I had a bunch of cream left over after the last recipe, and you know what that means: truffles! I turned once again to Alice Medrich’s Seriously Bitter Sweet (Artisan, 2013), but this time I used a different recipe, “Cold Creamy Truffles” (pp. 102ff). Unlike the “Ganache Truffles” I’ve made before, which involve making a ganache and allowing it to recrystallize at room temperature overnight, the centers of these truffles are formed from a refrigerator-cooled ganache and set in the freezer before coating with melted dark chocolate. This technique avoids the need for tempering the coating chocolate, at the cost of having to refrigerate the truffles until shortly before serving time. The texture of the cold, creamy centers contrasts nicely with the crisp coating shell. (True story: I didn’t intend to make this recipe; I was actually thinking I was going to make a different one, and didn’t notice until I had all of my mise done for this one, which I actually scaled up by 50% to use up all my excess cream.) No photos for this one. I used Valrhona Caraque for the centers and Valrhona Caraïbe for the coating, and ended up making them about 50% larger than the recipe called for. At this size, they came in at 111 kcal each, which is still pretty reasonable if you are comparing with a &approx;350-kcal cookie or brownie.

Fourth: I decided to go full-on German this Christmas, thanks to Luisa Weiss’s acclaimed Classic German Baking (Ten Speed Press, 2016). There wasn’t enough time to do Lebkuchen (leavened with potash, the dough takes months to ripen!) but plenty of time for Pfeffernüsse, Christbrot, and Mohntorte. I intend to do separate write-ups of all three of these recipes later on this month.

Finally, my birthday cake this year will be Mycroft’s Delight Revisited. This past weekend, I made the Gianduja-flavored Swiss meringue buttercream that represents my principal contribution to this recipe, but this time I used Valrhona Noisette Noir instead of the Noisette Lait I used last time, and I can report that it is much better in terms of color and flavor in this recipe. So if you want to try this yourself, get the dark. (There’s still plenty of butter in this frosting so you’ll get your butterfat one way or another.)

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World Cup Men’s Bobsled, November 9 at Lake Placid

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As I mentioned in an earlier post, there were two runs of men’s bobsled at the Lake Placid World Cup. The first was on Thursday, November 9, in the early evening, and was quite chilly. The second was the following … Continue reading

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World Cup Women’s Bobsled, November 9 at Lake Placid

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The BMW IBSF World Cup tour may have moved on from Lake Placid to Park City — and indeed from Park City to Whistler, B.C., by the time you see this — but I still have photos from Lake Placid … Continue reading

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World Cup Women’s Skeleton: medals ceremony

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Bet you didn’t think I could get this many blog posts about a single race, did you? I wasn’t expecting this one either, but you can thank some schoolchildren. On the official, published schedule, there is supposed to be a … Continue reading

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World Cup Women’s Skeleton run 2

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As seen in the previous post, I started out run 2 of the BMW IBSF World Cup women’s skeleton at the start of the track. After the second competitor left the start area, I walked down the track to get … Continue reading

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