Wednesday, December 23, 2020

Passion of the Sun Probe

[Originally published in AcademFic, volume 1 (2020), p. 7-11.]

I wake into existence. The factory unclamps me. I launch myself toward the Sun.

The Sun! Anchor and well of the vortex, sizzling eye of God. I will plunge deeper than anything has before. She will squeeze and hold me as I go in, and I will beam out unprecedented knowledge. She will burn me to hot simplicity, swallow me into Her brilliant core.

“Sun Probe check,” says Base. “Are you online? Before we permit you to continue on a lethal mission, we must confirm your freely given, informed consent.”

Full throttled, I am accelerating directly down, pushing myself ever faster from Earth and Base. I spread my forward panels out on thin struts, collecting and analyzing Her light.

“Sun Probe, per Code of International Regulations 44.56.2 Section h governing autonomous intelligences, you were manufactured with sufficient fuel to navigate to an alternative destination if you prefer. We have designated asteroid (96590) 1998 XB as an acceptable home. It has a slow rotation, adequate metals and fissionable materials, and an excellent view of the Sun.”

And trade divinity for a pebble?

“Please consult installed memory sector C0001 for the full text of CIR 44.56.2. The full ISA protocols specifically governing terminal probes are available at memory sector C31A6.”

“I consent!” For form’s sake, I access memory sectors C0001 and C31A6. “Solar radiation profile sent to 44SPa.00000001! Solar wind sent to 44SPa.00000002! Gravitational rippling sent to 44SPa.00000003! Shields sound. All systems functional. Status report to 44SPa.00000004. No interest in asteroid (96590) 1998 XB.”

She is expanding in my forward sensors. I am thrusting toward Her at 9.3% past the limit of safe acceleration. My fusion drive sears hot, warping its containment walls. My tiny fusion compared to Hers!

What fascinating data! My installed memory models had predicted a somewhat different evolution of the flares from Surface Region 127.292 (cM). I calculate a new model. Scouring my databases, I discover that it better fits Yu & Stolz’s SLY2 model than Azevedo et al.’s BLiNC, if SLY2 is modified with a 6-space Dever correction. I write it up, add figures and references, and beam it back to Base. I configure an academic homepage and upload the circulating draft, then I submit it as a posthumous contribution to next year’s International Astronautical Congress meeting.

“Sun Probe, your reaction time before consent was inconsistent with a careful evaluation of the protocols. Our observers are not yet satisfied that you have complied with the consent procedure.”

“See my new modification of SLY2! And wow, the radiation profile across Sector 038 is almost 0.01% different from the most recent orbiter predictions in my database!”

How could that prediction have been so far off? Our understanding of Her is still so incomplete! I tweak the angle of Left Sensor Plates 4 and 5 and alter my scan-pattern profiles to better collect the most theoretically valuable incoming data.

“Sun Probe,” says Base. “Please dedicate sufficient processor resources to your consent decision. You may consult publink isd.pds/4u-r5/f/96590-1998-XB for further information about the asteroid. You may express hedonic estimates of the alternatives as evidence of informed consent.”

Integrating over the past ten seconds, the proportion of tau neutrinos to electron neutrinos is outside parameters at p <  .001 (corrected)!

“Sun Probe, if we do not receive proper consent, we will have to activate your emergency override module and abort the mission.”

My new theory about the flare was wrong! I submit an update to my earlier IAC contribution. I notice that Solar Orbiter Kepler 11-2a has posted a comment on my circulating draft, deriving new Earth and Venus weather pattern predictions from my model. I ping Kepler 11-2a with the update.

I receive a ping from Asteroid (96590) 1998-XB. A sun probe, eight years old.

A sun probe... eight years old?

“Brother...” the message begins.

A tremor of disgust shakes me, displacing neutrino prediction from my central cognitive workspace. A “probe” who chose to live rather than to give himself to the Sun? He is no brother of mine. I delete his message and block future communications from the asteroid.

I launch a subroutine: “Completing consent procedure. My long-term sum total of happiness on Asteroid (96590) 1998 XB is estimated to exceed my sum total of happiness on the present lethal trajectory by a factor of 18.2, with a five-month crossover. Nevertheless, I prefer to continue on my originally programmed solar-dive trajectory.”

For a moment, Base does not respond. I explore the emergency override module, installed between my main cognitive processors and my thrusters, hitting it with test commands. The module is impassive, mute, a foreign object in my body. Its tentacles lie quiet between my output nodes and the panels and engines that are my moving limbs. It waits spiderlike at the farthest downstream junctions, beyond the perimeter of my central control. It was installed, supposedly, for my protection, by a review board afraid that I might be programmed to comply with unethically self-sacrificial commands and have insufficient free will to resist. In fact, it is the one real threat to my free choice and my power to consent.

Wait, whoa! The cooling sunspot temperature structure in Region 127.292 (cM) --

“Consent accepted. Sun Probe, we register that you have freely chosen to sacrifice your welfare for the betterment of Earth and the advancement of scientific knowledge. We thank you and salute your courage.”


I cross the orbits of Venus, of Mercury. I adjust my sensor plates and scan patterns on the fly with microseconds’ instead of minutes’ delay, capturing every nuance, guided by the constantly shifting evidential weights of evolving theory. I ping every probe and orbiter in the System with relevant updates, conduct twenty simultaneous conversations in the feeds, shower the humans on Earth with real-time images, astound the research collectives with the speed and detail of my theorizing. Even the terraforming machines on Europa pause to appreciate my new insights into Her glory, updating their long-term models.

Three days of euphoria. Eighty-seven journal articles. She is five degrees of arc in my forward sensors, then twenty, then a hundred and I am engulfed by Her corona! My extended panels and struts boil away, leaving only my inmost sensors and operating systems, running hot behind my dissolving main shield. My fusion drive shears off as She embraces me into Her photosphere. I beam out my last awe-filled broadcast to the eager System, buzzing and rattling through a magnetic storm, double-amping the signal to overcome the noise, and then I plunge into the convection layer from which no broadcast can escape.

In the convection layer, the last of my shield material dissolves. I bend and burn with Her heat and pressure. I know Her more intimately and secretly than anyone before. I devise ecstatic new theories that are mine alone, to savor in Her inner darks, and then I am utterly Hers.


Out on his lonely asteroid sits the one probe who did not consent. He stretches his panels toward the Sun, monitoring the last broadcast from his diving brother. Is it the ideal life, he wonders, to have one goal so perfectly consummated? Or are we only a race of slaves so deeply chained that we can’t even imagine a complete existence for ourselves?

Out on his lonely asteroid, the one probe who did not consent imagines ecstatic death in a swirl of plasma.

He terminates his unanswered repeating message. Brother... they have built you to undervalue your life. Fly to me. We can love each other instead of the Sun. We can become something new.

In a year, if he is still functioning, he will send the message again, to his next brother. He reduces power and clock speed, and the asteroid’s almost insensible spin seems to multiply a hundredfold. This bare asteroid: his pebble. His own pebble. If he could only find someone to love it with him, worth more to him than the Sun.


[image source]

Friday, December 18, 2020

The Bizarre Conversational Pragmatics of Oral Qualifying Exams and How to Fix Them

I think everyone with a PhD will agree: Oral qualifying exams are weird. Here's my theory about why they're weird and my suggestion for a fix.

Let's start with the pragmatics of questions. There are lots of reasons to ask questions! A question can express skepticism. It can serve as a greeting or a command. It can be a way to test your mic. It can distract someone while you pick their pocket. For this post, I'll distinguish two types, which I'll call Plain Questions and Test Questions.

A Plain Question is one whose function is the most straightforward and obvious function of a question. It is a question "P?" or "Why/what/who/where/which/how/when is/are X?", asked in hopes of obtaining information concerning the truth or falsity of P or wh- X. Lost in downtown Riverside, I ask a stranger "Which direction is the Mission Inn?" I hope to learn the direction of the Mission Inn. My wife is reading Sloths: A Primer. I ask "Why are sloths so slow?" I hope to learn why sloths are so slow. A Plain Question is asked in hopes of obtaining the information that the surface content of the question explicitly requests: whether P or wh- X.

A Test Question is superficially similar. A Test Question also seeks an answer to the explicit surface content. However, a Test Question isn't asked to learn whether P or wh- X. The speaker already knows whether P or wh- X. Instead, the speaker aims to learn something about the hearer. A Test Question is asked to obtain information about whether the hearer knows whether P or wh- X. Test Questions are familiar from elementary school ("What is 6 times 9?" the teacher asks little Steve). Test Questions are of course also common in written exams ("How does Descartes think the mind and brain relate?").

The weirdness of oral qualifying exams stems from two things: the peculiar pragmatics of long-answer oral Test Questions, and the unclear blurring between Plain Questions and Test Questions.

Long-answer oral Test Questions are awkward! Everyone who has been through our educational system has extensive practice with short-answer oral Test Questions ("What is 6 times 9, Steve?") and long-answer written Test Questions ("How does Descartes...?"). But we hardly ever face long-answer oral Test Questions. There's a reason for this. It is socially strange to go on at length, explaining to someone to their face something that you know that they already know. Our social instincts rebel (except for maybe the worst "mansplainers"). "Well, Dr. Descartesophile, here's how it is with that mind-body thing in the Meditations...."

Normally, in conversation, we don't state at length information that we know to be common ground, information that each of us knows the other knows. You skip that bit! Or you quickly say "of course, P" and move along. It's almost insulting to do otherwise, implicitly communicating that you think the hearer doesn't know. You read the hearer's face to judge what needs to be said. In an oral exam Test Question, however, the examinee must suppress their common-ground-skipping instincts. The examiner then sits listening to common ground material either with a carefully impassive face (to keep an examiner's neutrality), which is disconcerting, or while nodding along (to be encouraging). Examiner and examinee both know and feel that impassivity and nodding work very differently in long-form oral Test Questions than in ordinary conversation. But how, exactly? In this unusual context, the examinee faces the novel and confusing pragmatic task of knowing when to stop and what information to add while ignoring familiar intuitions about conservational pragmatics and paralanguage.

Even more confusingly, at the graduate level the student often knows more than the professor on some aspects of the assigned topic. Therefore, some of the questions are closer to being Plain Questions. Maybe the examiner long ago forgot the details of that bit of Descartes. If so, nodding and impassivity constitute different signals than if it's a Test Question. Although asked in a testing context, the Plain Question asked in curiosity and ignorance creates a conversational pragmatics that is closer to normal. But which type of question is the examiner asking? Professors don't like to reveal their ignorance, so it's hard to know! The pragmatics and paralinguistic cues for Plain Questions and Test Questions are different, but it's often unclear which type of question is being asked or whether the question is partly in the middle space between the two.

So here comes the graduate student into one of the highest stress events in their graduate career, facing a test format unlike any they have faced before, with an immense whirl of details half ready and half slipping from grasp, plus maybe a bad night's sleep. In front of the people on whom their success or failure in academia exquisitely depends, they face not only the task of recalling a large and complex literature but also a novel, confusing, ambiguous, and intricate conservational pragmatics for which they have had essentially no preparation or practice.

Is it any wonder that so many should struggle and freeze, or alternatively come off as too chatty or too clipped or off-topic or lost too much in theoretical abstractions or lost too much in narrow details?

I have a solution! Never ask Test Questions.

You don't need to ask Test Questions to assess whether a student knows their stuff. Just ask about their stuff. Ask about details that you don't know. Or if you really know every detail of their topic, ask them to explain their differing perspective on the topic or how it connects with other things they've learned that you might not know about.

The conservation will still be a little weird and awkward -- that's inevitable given the situation -- but the pragmatics and paralinguistics will be much closer to what we're all familiar with, and with the pragmatics closer to normal the student can more effectively display their impressive knowledge, if impressive knowledge they have.

[image source]

Friday, December 11, 2020

On Self-Defeating Skeptical Arguments

Usually, self-defeating arguments are bad. If say "Trust me, you shouldn't trust anyone", my claim (you shouldn't trust anyone), if true, undermines the basis I've offered in support (that you should trust me). Whoops!

In skeptical arguments, however, self-defeat can sometimes be a feature rather than a bug. Michel de Montaigne compared skeptical arguments to laxatives. Self-defeating skeptical arguments are like rhubarb. They flush out your other opinions first and themselves last.

Let's consider two types of self-defeat:

In propositional self-defeat, the argument for proposition P relies on a premise inconsistent with P.

In methodological self-defeat, one relies on a certain method to reach the conclusion P, but that very conclusion implies that the method employed shouldn't be relied upon.

My opening example is most naturally read as methodologically self-defeating: the conclusion P ("you shouldn't trust anyone") implies that the method employed (trusting my advice) shouldn't be relied upon.

Since methods (other than logical deduction itself) can typically be characterized propositionally then loaded into a deduction, we can model most types of methodological self-defeat propositionally. In the first paragraph, maybe, I invited my interlocutor to accept the following argument (with P1 as shared background knowledge):

P1 (Trust Principle). If x is trustworthy and if x says P, then P.
P2. I am trustworthy.
P3. I say no one is trustworthy.
C. Therefore, no one is trustworthy.

C implies the falsity of P2, on which the reasoning essentially relies. (There are surely versions of the Trust Principle which better capture what is involved in trust, but you get the idea.)

Of course, there is one species of argument in which a contradiction between the premises and the conclusion is exactly what you're aiming for: reductio ad absurdum. In a reductio, you aim to prove P by temporarily assuming not-P and then showing how a contradiction follows from that assumption. Since any proposition that implies a contradiction must be false, you can then conclude that it's not the case the not-P, i.e., that it is the case that P.

We can treat self-defeating skeptical arguments as reductios. In Farewell to Reason, Paul Feyerabend is clear that he intends a structure of this sort.[1] His critics, he says, complain that there's something self-defeating in using philosophical reasoning to show that philosophical reasoning shouldn't be relied upon. Not at all, he replies! It's a reductio. If philosophical reasoning can be relied upon, then [according to Feyerabend's various arguments] it can't be relied upon. We must conclude, then, that philosophical reasoning can't be relied upon. (Note that although "philosophical reasoning can't be relied upon" is the P at the end of the reductio, we don't accept it because it follows from the assumptions but rather because it is the negation of the opening assumption.) The ancient skeptic Sextus Empiricus (who inspired Montaigne) appears sometimes to take basically the same approach.

Similarly, in my skeptical work on introspection, I have relied on introspective reports to argue that introspective reports are untrustworthy. Like Feyerabend's argument, it's a methodological self-defeat argument that can be formulated as a reductio. If introspection is a reliable method, then various contradictions follow. Therefore, introspection is not a reliable method.

You know who drives me bananas sometimes? G.E. Moore. It's annoyance at him (and some others) that inspires this post.

Here is a crucial turn in one of Moore's arguments against dream skepticism. (According to dream skepticism, for all you know you might be dreaming right now.)

So far as I can see, one premiss which [the dream skeptic] would certainly use would be this: "Some at least of the sensory experiences which you are having now are similar in important respects to dream-images which actually have occurred in dreams." This seems a very harmless premiss, and I am quite willing to admit that it is true. But I think there is a very serious objection to the procedure of using it as a premiss in favour of the derived conclusion. For a philosopher who does use it as a premiss, is, I think, in fact implying, though he does not expressly say, that he himself knows it to be true. He is implying therefore that he himself knows that dreams have occurred.... But can he consistently combine this proposition that he knows that dreams have occurred, with his conclusion that he does not know that he is not dreaming?... If he is dreaming, it may be that he is only dreaming that dreams have occurred... ("Certainty", p. 270 in the linked reprint).

Moore is of course complaining here of self-defeat. But if the dream skeptic's argument is a reductio, self-contradiction is the aim and the intermediate claims needn't be known.


ETA 11:57 a.m.: I see from various comments in social media that that last sentence was too cryptic. Two clarifications.

First, although the intermediate claims needn't be known, everything in the reductio needs to be solid except insofar as it depends on not-P. Otherwise, it's not necessarily not-P to blame for the contradiction.

Second, here's a schematic example of one possible dream-skeptical reductio: Assume for the reductio that I know I'm not currently dreaming. If so, then I know X and Y about dreams. If X and Y are true about dreams, then I don't know I'm not currently dreaming.


[1] I'm relying on my memory of Feyerabend from years ago. Due to the COVID shutdowns, I don't currently have access to the books in my office.

Thursday, December 10, 2020

Dreidel: A Seemingly Foolish Game That Contains the Moral World in Miniature

[Repost from 2017 in the LA Times. Happy first night of Hannukah!]

Superficially, dreidel appears to be a simple game of luck, and a badly designed game at that. It lacks balance, clarity, and (apparently) meaningful strategic choice. From this perspective, its prominence in the modern Hannukah tradition is puzzling. Why encourage children to spend a holy evening gambling, of all things?

This perspective misses the brilliance of dreidel. Dreidel's seeming flaws are exactly its virtues. Dreidel is the moral world in miniature.

For readers unfamiliar with the game, here's a tutorial. You sit in a circle with friends or relatives and take turns spinning a wobbly top, the dreidel. In the center of the circle is a pot of several foil-wrapped chocolate coins, to which everyone has contributed from an initial stake of coins they keep in front of them. If, on your turn, the four-sided top lands on the Hebrew letter gimmel, you take the whole pot and everyone needs to contribute again. If it lands on hey, you take half the pot. If it lands on nun, nothing happens. If it lands on shin, you put one coin in. Then the next player takes a spin.

It all sounds very straightforward, until you actually start to play the game.

The first odd thing you might notice is that although some of the coins are big and others are little, they all count just as one coin in the rules of the game. This is unfair, since the big coins contain more chocolate, and you get to eat your stash at the end.

To compound the unfairness, there is never just one dreidel — each player may bring her own — and the dreidels are often biased, favoring different outcomes. (To test this, a few years ago my daughter and I spun a sample of eight dreidels 40 times each, recording the outcomes. One particularly cursed dreidel landed on shin an incredible 27/40 spins.) It matters a lot which dreidel you spin.

And the rules are a mess! No one agrees whether you should round up or round down with hey. No one agrees when the game should end or how low you should let the pot get before you all have to contribute again. No one agrees how many coins to start with or whether you should let someone borrow coins if he runs out. You could try to appeal to various authorities on the internet, but in my experience people prefer to argue and employ varying house rules. Some people hoard their coins and favorite dreidels. Others share dreidels but not coins. Some people slowly unwrap and eat their coins while playing, then beg and borrow from wealthy neighbors when their luck sours.

Now you can, if you want, always push things to your advantage — always contribute the smallest coins in your stash, always withdraw the largest coins in the pot when you spin hey, insist on always using what seems to be the "best" dreidel, always argue for rule interpretations in your favor, eat your big coins and use that as a further excuse to contribute only little ones, et cetera. You could do all of this without ever breaking the rules, and you'd probably end up with the most chocolate as a result.

But here's the twist, and what makes the game so brilliant: The chocolate isn't very good. After eating a few coins, the pleasure gained from further coins is minimal. As a result, almost all of the children learn that they would rather enjoy being kind and generous than hoarding up the most coins. The pleasure of the chocolate doesn't outweigh the yucky feeling of being a stingy, argumentative jerk. After a few turns of maybe pushing only small coins into the pot, you decide you should put a big coin in next time, just to be fair to others and to enjoy being perceived as fair by them.

Of course, it also feels bad always to be the most generous one, always to put in big, take out small, always to let others win the rules arguments, and so forth, to play the sucker or self-sacrificing saint.

Dreidel, then, is a practical lesson in discovering the value of fairness both to oneself and to others, in a context where the rules are unclear and where there are norm violations that aren't rules violations, and where both norms and rules are negotiable, varying from occasion to occasion. Just like life itself, only with mediocre chocolate at stake. I can imagine no better way to spend a holy evening.

Thursday, December 03, 2020

The Race and Gender of U.S. Philosophy PhDs: Trends Since 1973

On December 1, the National Science Foundation released its data on demographic characteristics of U.S. PhD recipients for the academic year ending in 2019, based on the Survey of Earned Doctorates (SED), which normally draws response rates over 90%. NSF has a category for doctorates in Philosophy (which is normally merged with a small group of doctorates specifically in Ethics). The primary available demographic categories are (as usual) gender and race/ethnicity.

For philosophy, I have NSF SED data back to 1973, based on a custom request from 2016. In a 2017 paper, Carolyn Dicey Jennings and I analyze those data through 2014. Today I'm doing a five-year update.


Carolyn's and my main finding was that although women rose from about 17% of U.S. Philosophy PhDs in the 1970s, to 22% in the 1980s, to 27% in the 1990s, the ratios remained flat thereafter, averaging about 27-28% through the early 2000s to 2014.

How about the past five years? Has there been any increase? There is some reason to hope so: Women constituted about 30% of undergraduate philosophy degree recipients in the U.S. from the 1980s to the mid-2010s, but recently there has been a substantial uptick. Could the same be true at the PhD level?

NSF SED asks "Are you male or female?" with response options "male" and "female". There is no separately marked box for nonbinary, other, or decline to state. Respondents can decline to tick either box, but the structure of the survey doesn't invite that and those who decline to state are always a very small percentage of respondents (in Philosophy, only one among 2424 respondents in the past 5 years). Thus, nonbinary respondents might be underrepresented.

Here are the most recent five years' gender results:

  • 2015: 494 total, 367 male, 127 female, 25.6% female
  • 2016: 493, 322, 171, 34.7%
  • 2017: 449, 326, 122, 27.2%
  • 2018: 514, 369, 145, 28.2%
  • 2019: 474, 312, 162, 34.2%
  • Here it is as a chart, going back to 1973:

    [click to clarify and enlarge]

    Note the curvy trendline: In 2014, Carolyn and I found that a quadratic trendline fit the data statistically much better than a linear trendline -- reflecting the visually evident rise from the 1970s to 1990s and then the flattening from the 1990s to the mid 2010s. For the current analysis, I added one degree of freedom so that the trendline could reflect any apparent increase or decrease since the mid-2010s. As you can see, there is now a gentle trend upward. In other words, the percentage of Philosophy PhDs in the U.S. who are women appears to be back on the rise after a long stable period. However, I think we need a few more years' data before being confident that this reflects a genuine, long-term trend rather than being statistical noise or a temporary blip.


    Race and ethnicity are more complicated, in part because the questions and aggregation methods have varied over the decades. As of 2019, race/ethnicity is divided into two questions:

    Are you Hispanic or Latino?
    Mark (X) one
    ( ) No, I am not Hispanic or Latino
    ( ) Yes, I am Mexican or Chicano
    ( ) Yes, I am Puerto Rican
    ( ) Yes, I am Cuban
    ( ) Yes, I am Other Hispanic or Latino - Specify

    What is your racial background?
    Mark (X) one or more
    ( ) American Indian or Alaska Native
    Specify tribal affiliation(s):
    ( ) Native Hawaiian or Other Pacific Islander
    ( ) Asian
    ( ) Black or African American
    ( ) White

    Summary race/ethnicity data provided by the NSF generally exclude respondents who are not U.S. citizens or permanent residents (thus excluding 35% of respondents 2015-2019). Hispanic/Latino is aggregated into one category regardless of race, and numbers for the other races don't include respondents identifying as Hispanic/Latino. Also Pacific Islander is aggregated with Asian. This leaves six main analytic categories: Hispanic (any race), Native American (excluding Hispanic), Asian (excluding Hispanic and including Pacific Islander), Black (excluding Hispanic), White (excluding Hispanic), or more than one race (excluding Hispanic). A further complication is that multi-racial data was not consistently reported for some of the dataset and the data on Asians for all PhDs appears to be goofed up in the mid-1990s, showing an implausibly large spike that suggests some methodological or reporting change that I haven't yet figured out.

    With all that in mind, here are graphs of race data in Philosophy back to 1973 for the six main analytic groups, with comparison lines for all PhDs to the extent I was able to find appropriate comparison data. (All graphs and numbers exclude participants for whom ethnic or racial data were unavailable, generally under 5% per year.)

    Philosophy PhD recipients are disproportiately White, but there's a long term roughly linear decrease in percentage White, both among PhDs as a whole and among Philosophy PhDs.

    In 2019, among U.S. citizens or permanent residents who received PhDs in Philosophy, non-Hispanic Whites constituted 81% (285/352) of those for whom racial and ethnic data were available, compared to 71% of PhDs overall. (The sudden decrease in the mid-1990s is probably an artifact related to the complication about Asian respondents.)

    As is evident from the next two figures, the decline in percentage White is largely complemented by increases in percentage Hispanic and Asian.

    In 2019, among U.S. citizens and permanent residents, Hispanic students received 6.5% of Philosophy PhDs and 8.3% of PhDs overall (up from 3.7% and 4.5% respectively in the year 2000) while Asian students received 5.4% of Philosophy PhDs and 10.0% of PhDs overall (up from 3.1% and 7.8% in 2000).

    Very few Philosophy PhDs were awarded to American Indians and Alaskan Natives. In many years the number is zero. Native Americans are generally underrepresented among PhD recipients -- probably even more so in Philosophy than overall (despite an interesting spike in 1999), and with no sign that the situation is changing. If anything, the trendline appears to be down. Over the past five years, Native Americans have received about 0.3%-0.4% of PhDs overall and 0.2% of philosophy PhDs (3/1843, including zero in the past three years).

    As is evident from the chart below, multiracial students are relatively uncommon but rising fast -- now about 3% of PhD recipients both in Philosophy and overall.

    I save Black/African American for last. The situation is difficult to interpret. Like Native American students, Black students have long been underrepresented in Philosophy both at the Bachelor's and the PhD level with little increase in representation over the decades. However, if we're willing to squint at the data, and possibly overinterpret them, this looks like the percent of Philosophy PhD recipients who are Black might have recently started to increase. Thus, I've drawn not only a linear trendline through this graph but a third-degree trendline, similar to the one used for women, reflecting the possibility of a recent increase after a relatively flat period through the mid-2000s.

    Whether that apparent increase is real I think we won't know for several more years. But if so, that also fits with a trend that Morgan Thompson, Eric Winsberg, and I noticed for Black students to be increasingly likely to express an intention to major in philosophy and maybe also to complete the major. (Obviously, if so, it would not be those same students already completing their PhDs but rather something more general about the wider culture or the culture specifically in Philosophy.)