What material is this sculpture made of?

Viktoria by Deborah Butterfield. Source: My own photo! Sorry about cutting off the legs – see below for better examples on how exquisitely these sculptures are balanced.

Short answer: Bronze!

Last weekend, I visited the Cantor Arts Center at Stanford for the first time since I’d been chased off for climbing on the OY/YO statue. During my visit, I walked by the sculpture of the horse above. Although it was certainly made by an artist with an excellent eye for equine form, I definitely didn’t give the piece much thought. My friend then pointed out the sculpture was actually wrought from bronze!

Deborah Kass: OY/YO | Cantor Arts Center Exhibitions
OY/YO by Deborah Kass. Not pictured: a person sitting inside the O. Perhaps EH/HE is coming next?

We’ve all seen examples of wood painted to look like bronze and laminate painted to look like wood, but I’d never seen bronze look so much like wood. Perhaps those experienced in working with bronze will not be so impressed – but even if I can envision how the casting was done, the patination is truly beyond me. I wasn’t able to find more information specifically on patination to make bronze look like wood – but if anyone knows – I’d love to learn!

Lost wax bronze casting. Briefly: A) A model is provided by the artist. B) Molds are made of plaster/silicone C) Molten wax is poured into the mold D) Excess wax is poured away leaving a thin wax layer E) Wax copy removed from mold F) Copy is “chased” to remove imperfection G) Copy is “sprued” together to allow casting material to flow/ air to be introduced H) Copy is surrounded by ceramic shell mold of sand-like stucco I) Copy is fired in the kiln to harden the shell and wax is lost J) Bronze is cast into the negative space left by the wax K) Shell is hammered away and sprues removed L) Metal “chasing” to remove imperfections. Source: [2]

Moreover, on second look, the form is quite impressive – there’s just enough abstraction that the viewer has to engage their imagination- yet not so much that the artist’s undeniably deep knowledge of horses doesn’t shine through. Looking more into Deborah Butterfield (b. 1949), her work has focused on driftwood horses for the better part of 40 years. She even cites being born on the same day as the 75th anniversary of the Kentucky Derby as influencing her choice of subject matter.

I seek that fleeting moment of… perfection [in my sculptures]. It’s like life, you might have a fabulous day, but you still have to get up the next morning and do it again.

Deborah Butterfield

For comparison, another prominent sculptor of driftwood horses was Heather Jansch (1948-2021). She was a British sculptor that initially focused on abstract art. She settled into driftwood horses later – with her website also stating she “collaborated over several years with skilled mould-makers at a fine art foundry, at last finding a seminal new method of casting highly complex forms in bronze. The resulting casts brought a new permanence and gravitas to the work.” Not particularly informative. In any case, Jansch’s works are also very impressive – if much less abstract than Butterfield’s.

File:The Eden Horse by Heather Jansch 2002.jpg
Eden Horse by Heather Jansch. Source: [4]

Three other artists came up a few times when looking up driftwood horses: Rita Dee Hudson, James Doran Webb, and Matt Torrens. Mr. Torrens has a cute (if uninformative) video of one of these sculptures coming together.

As a bonus fact, there was also a historical horse named “Driftwood” that sired numerous rodeo and ranch horses and is in the American Quarter Horse Association Hall of Fame. As a bonus from the Cantor Arts Center, I leave you to decipher this text from a truly bizarre exhibit by Ian Cheng at the intersection of art, AI, cognitive science.

“Have you ever gotten high from reading?”


  1. https://museum.stanford.edu/exhibitions/deborah-kass-oyyo
  2. https://www.thesculpturepark.com/lost-wax-bronze-casting/
  3. http://www.artnet.com/artists/deborah-butterfield/
  4. https://commons.wikimedia.org/wiki/File:The_Eden_Horse_by_Heather_Jansch_2002.jpg
  5. https://www.ritadee.net/
  6. http://www.driftwoodhorse.com/#portfolio.html
  7. https://museum.stanford.edu/exhibitions/ian-cheng-emissary-sunsets-self

How can a trial say you are both more and less likely to die after an intervention?

Short answer: Composite endpoints

Medium answer: Many clinical trials report composite outcomes such as: “stroke, acute coronary syndrome (acute myocardial infarction and hospitalization for unstable angina), acute decompensated heart failure, coronary revascularization, atrial fibrillation, or death from cardiovascular causes.” [1] In this particular trial evaluating blood pressure control regimens in 9,624 Chinese adults, the primary composite outcome favored more aggressive control (hazard ratio [HR] 0.74, 95% CI 0.60-0.92, p = 0.007). However, all-cause mortality was actually increased in the intense treatment group, although not significantly so (HR 1.11, 95% CI 0.78-1.56). While not a particularly striking example (I just clicked on a random recent paper in NEJM), one can imagine this being very confusing to patients. To paraphrase a hypothetical scenario from a review on composite outcomes in the BMJ:

“Mr. Chen, here is a drug that will reduce your combined risk of getting a heart attack that will not kill you, stroke, specific arrythmias, or of dying from heart disease.”

“Doctor, I am not sure I quite understood you, but please give me this drug.”

“But I should also mention that the drug will increase your risk of dying.”

“Didn’t you just tell me that the drug would decrease my risk of dying? I am confused.”

Adapted from Cordoba et al. [2]

Full Answer: The American Heart Association meeting took place from 11/16/21-11/18/21 and there has been a rush of medical podcasts based on the content from this meeting. Full disclosure: as an aspiring ophthalmologist, my working knowledge of body medicine is to “keep the heart full of blood, keep the lung full of air.” Nonetheless, while skimming some of the papers from the AHA meeting, I was once again reminded of the preponderance of composite outcomes in clinical trials.

In particular, I was thinking about a paper I presented at rounds a few weeks ago, EMPEROR-Preserved, (Empagliflozin in Heart Failure with a Preserved Ejection Fraction), published in NEJM in August 2021. Empagliflozin (Jardiance) an SGLT-2 inhibitor, has already been shown in the EMPEROR-reduced trial to have benefit in all HFrEF patients regardless of type 2 diabetes (T2DM) status. This double-blind trial compared empagliflozin 10mg vs. placebo (in addition to usual therapy) in approximately 6000 patients with HFpEF (EF >= 40, NYHA II-IV) assessing for a primary outcome of cardiovascular death or hospitalization for HF. About 50% of patients in both groups had T2DM at baseline. Primary outcome in 13.8% in empagliflozin group vs 17.1% in placebo group (HR 0.79, NNT = 31). This benefit was seen in patients with and without diabetes (Table 2). The benefit was driven by decreased hospitalizations (8.6% vs 11.8%, HR 0.71), but no benefit was seen for cardiovascular death (7.3% vs 8.2%, HR 0.91 [CI 95% 0.76-10.9]). Adverse effects of UTI and genital infections are more common in the empagliflozin group. For this group of patients in which there have been so few effective treatments, SGLT-2 inhibitors are certainly a game-changer. However, I couldn’t help but think that the trial would have been even more convincing if it had been powered to detect benefit in either cardiovascular or all-cause mortality alone.

The question of composite outcomes has plagued the field for a long time. For example, the recent ASCNED trial showed that aspirin was not shown to significantly decrease the risk of developing dementia in diabetics. This work reminded me of some of the original work on aspirin for primary prevention of CV events in diabetics (Ogawa et al. JAMA 2008). Cordoba et al. singled out this study for particularly egregious abuse of composite outcomes:

Because components can be combined in so many ways, it is easy to find significant results. In one of the trials we included (Ogawa et al.), the composite consisted of eight cardiovascular end points, but there were also secondary composites that consisted of “combinations of primary end points as well as death from any cause.” These combinations were not specified, but nine end points can be combined, as two or more components, in 502 possible ways (29−1(empty sample)−9(samples with only one component)). The result for the composite was not statistically significant, but the abstract noted that the hazard ratio was 0.10 for a combined end point of fatal coronary events and fatal cerebrovascular events (P=0.0037)—that is, a cherry picked result. One would expect 25 of 502 possible combinations to be significant purely by chance.

Unsurprisingly, more modern evidence has suggested aspirin may be of much more limited benefit than described in this study for primary prevention (note: this is not true for secondary prevention – don’t stop taking aspirin without asking your doctor!) The US Preventive Services Task Force no longer routinely recommends aspirin in patients younger than 50 or older than 60. Similarly, AHA guidelines say to not be given routinely to adults over 70 or at increased risk of bleeding (diabetes or not).

As another recent example highlighted by Dr. Mandrola in This Week in Cardiology, the AVATAR trial asked whether surgical aortic valve replacement is indicated for asymptomatic patients with severe aortic stenosis by ultrasound criteria. 157 patients were randomized in this trial to early surgery vs conservative treatment with a median follow-up of 35 months. The primary outcome was a composite of all-cause mortality, acute MI, stroke, and hospitalization for heart failure. The primary composite outcome favored early surgery (HR 0.46, 95% CI 0.23-0.90, p = 0.02). However, cardiovascular death did not differ between the two groups (HR 1.02, CI 0.40-2.58), while all-cause mortality strongly favored early surgery (HR 0.56, CI 0.24-1.27, 16 vs. 9 patients.). Turns out, 3 patients in the conservative management group died of COVID-19 – if two of these patients had been in the early surgery arm, the trial would not have been significant.

Some final thoughts on composite outcomes:

  1. Studies need to be better powered. Clinical trials are experiments on human beings! If we are going to do that, we must strive to get a clear answer on a meaningful clinical question.
  2. Studies should assess composite endpoints with fewer components (corollary of running better powered studies). Dr. Gregg Stone (EXCEL trial lead discussed below) even acknowledges the importance of doing so in a panel last year.
  3. If composite endpoints are necessary, studies should seek to ensure components of composite outcomes are both objective, clinically relevant, and of equal importance. This means avoiding lumping death together with outcomes like silent MIs, TIA, or doubling of baseline creatinine. It also means carefully considering if all-cause mortality, cardiovascular mortality, or cardiovascular mortality in patients proven to be COVID-19 positive is the more appropriate outcome depending on the clinical context.
  4. We need to do a better job of communicating outcomes of trials to patients. This goes beyond simply explaining what composite outcomes mean – we should also consider making explicit the value judgments baked into things like:
    • unequal impact of components of composite outcomes on patients’ quality of lives
    • non-inferiority margins (What percent difference do we consider non-inferior?)
    • number needed to treat (What our threshold for an NNT small enough that we would recommend an intervention?)

For those interested in further reading – I’d recommend persuing the controversy around the EXCEL trial (Stone et al. NEJM 2016) and the recent meta-analysis of the evidence regarding PCI vs CABG (Sabatine et al. Lancet, 2021). This debate between surgeons and interventionalists highlights the challenge of interpreting trials in which the results of the primary composite outcome and all-cause mortality conflict. I may eventually write a separate post about this whole saga – but I feel like it is already well-contextualized/discussed in great detail in the linked articles.

If anybody is out there reading, I’d love to hear your thoughts on this. As an early-career trainee, I obviously haven’t been involved in actually designing these kinds of trials – and I’m always striving to learn how to more critically evaluate evidence.


  1. Zhang W, Zhang S, Deng Y, et al. Trial of Intensive Blood-Pressure Control in Older Patients with Hypertension. N Engl J Med. 2021;385(14):1268-1279. doi:10.1056/NEJMoa2111437
  2. Cordoba G, Schwartz L, Woloshin S, Bae H, Gøtzsche PC. Definition, reporting, and interpretation of composite outcomes in clinical trials: systematic review. BMJ. 2010;341:c3920. Published 2010 Aug 18. doi:10.1136/bmj.c3920
  3. https://www.youtube.com/watch?v=k8CG0QrEEcg
  4. Anker SD, Butler J, Filippatos G, et al. Empagliflozin in Heart Failure with a Preserved Ejection Fraction. N Engl J Med. 2021;385(16):1451-1461. doi:10.1056/NEJMoa2107038
  5. Packer M, Anker SD, Butler J, et al. Cardiovascular and Renal Outcomes with Empagliflozin in Heart Failure. N Engl J Med. 2020;383(15):1413-1424. doi:10.1056/NEJMoa2022190
  6. https://www.acc.org/latest-in-cardiology/clinical-trials/2018/08/25/02/16/ascend-aspirin
  7. Ogawa H, Nakayama M, Morimoto T, et al. Low-dose aspirin for primary prevention of atherosclerotic events in patients with type 2 diabetes: a randomized controlled trial [published correction appears in JAMA. 2009 May 13;301(18):1882] [published correction appears in JAMA. 2012 Nov 14;308(18):1861]. JAMA. 2008;300(18):2134-2141. doi:10.1001/jama.2008.623
  8. https://www.medscape.com/viewarticle/963288
  9. https://www.youtube.com/watch?v=tQPrXwlUFC4
  10. Banovic et al. Aortic Valve ReplAcemenT versus Conservative Treatment in Asymptomatic SeveRe Aortic Stenosis: The AVATAR Trial. Preprint in Circulation. https://www.ahajournals.org/doi/10.1161/CIRCULATIONAHA.121.057639
  11. https://www.tctmd.com/news/former-excel-investigator-alleges-trial-manipulation-prompting-vehement-denials
  12. Stone GW, Sabik JF, Serruys PW, et al. Everolimus-Eluting Stents or Bypass Surgery for Left Main Coronary Artery Disease [published correction appears in N Engl J Med. 2019 Oct 31;381(18):1789]. N Engl J Med. 2016;375(23):2223-2235. doi:10.1056/NEJMoa1610227
  13. https://www.tctmd.com/news/no-mortality-difference-between-pci-and-cabg-left-main-pci-meta-analysis
  14. Sabatine MS, Bergmark BA, Murphy SA, et al. Percutaneous coronary intervention with drug-eluting stents versus coronary artery bypass grafting in left main coronary artery disease: an individual patient data meta-analysis [published online ahead of print, 2021 Nov 12]. Lancet. 2021;S0140-6736(21)02334-5. doi:10.1016/S0140-6736(21)02334-5

How many chess grandmasters have the same first and last name?

The short answer is 6 (3 pairs).

Alireza Firouzja just became the youngest player to reach 2800 ELO at 18 years and 5 months, surpassing Magnus Carlsen’s record of 18 years and 11 months. He did so by grinding out a tricky endgame at the European Team Chess Championships over GM Shakhriyar Mamedyarov. Alireza is truly a prodigy, and he certainly has the potential to become the world champion. He recently qualified for the Candidates Tournament 2022 (a tournament in which players compete for a spot to challenge the reigning world champion), giving him an opportunity to become the youngest world champion ever (a record currently held by Garry Kasparov at 22 years of age).

Alireza’s impressive 8/9 performance at the European Team Championship came on the heels of another 8/11 performance at the FIDE Grand Swiss. A 33.8 rating gain in less than a month at this level of chess is simply incredible. Source: 2700chess.com

Two of Alireza Firouzja’s teammates on the French team had somewhat similar names, Maxime Lagarde and Maxime Vachier-Lagrave (although Alireza was born in Iran, he changed federation due to Iranian rules barring their athletes from competing with Israelis). By some free association, this reminded me of the saga of Tigran Petrosian. Last fall, a friend sent an article about an Armenian grandmaster, Tigran Petrosian, who had been permanently banned from chess.com after cheating in the Pro Chess League. I naturally expressed surprise that a former world champion (and one that must be very elderly at that) would stoop to such lows. Moreover, Tigran Petrosian apparently sent unsavory messages to the GM that had reported him (Wesley So, Filipino-American super-GM and #7 on the live rankings).

“You are a biggest looser I ever seen in my life! You was doing PIPI in your pampers when I was beating players much more stronger then you!”

Tigran L Petrosian to Wesley So

To my surprise, it turns out there were actually two chess grandmasters named Tigran Petrosian! There was the world champion Tigran V. Petrosian (1929-1984), and Tigran L. Petrosian who was named after the world champion (1984-). The two were not related at all. Tigran V. was an 8-time Candidate, and became the first Armenian world champion in 1963 by defeating Boris Spassky. Tigran L. is a strong grandmaster (peak rating 2671, currently 2573) but is certainly not a super-GM.

In any case, this had me wondering how many chess grandmasters had the same name. I sorted through a Wikipedia list containing all 1948 chess grandmasters to try to identify other examples. The most common repeated last names were Guseinov (4), Hansen (5), Ivanov (5), and Petrosian (4). The only other grandmasters with identical first and last names that I identified were:

  1. Alexander Ivanov (b. 1956) and Alexander A. Ivanov (b. 1965). This was almost certainly just a concidence.
  2. Alexander Zaitsev (b. 1935) and Alexander Zaitsev (b. 1985). I was not able to find details on whether the younger Zaitsev was named after the other.
    1. Not a chess player, but Alexander Zaitsev (figure skater) and his partner Irina Rodnina are two-time Olympic gold medalists. See their short program at Innsbruck, Austria in 1976 below.


  1. https://www.chess.com/news/view/alireza-firouzja-youngest-chess-player-ever-to-break-2800
  2. https://en.chessbase.com/post/alireza-firouzja-to-play-for-france
  3. https://www.chess.com/news/view/saint-louis-arch-bishops-2020-pro-chess-champions
  4. https://en.wikipedia.org/wiki/List_of_chess_grandmasters
  5. https://en.wikipedia.org/wiki/Tigran_Petrosian
  6. https://en.wikipedia.org/wiki/Tigran_L._Petrosian

Phantom time hypothesis … for the glory of Russia?

I was chatting with a friend about the phantom time hypothesis last weekend, and he mentioned that this theory was popular in Russia. Apparently, the hypothesis helped maintain a sense of imperial glory among those disillusioned with Communism and the Russia of Yeltsin/Putin. Only half-remembering the conspiracy, I rewatched the Half as Interesting video on the topic.

In brief, Heribert Illig proposed in 1991 that Holy Roman Emperor Otto III, Pope Sylvester II, and Byzantine Emperor Constantine VII conspired to fabricate a few hundred years of history. This would both help legitimate Otto’s claim to the HRE and place themselves at the special year, 1000AD. Under this hypothesis, the entire history of the Carolingian period from 614-911 was fabricated out of whole cloth.

Timeline detailing the phantom time hypothesis from Hans-Ulrich Niemitz’s article “Did the Early Middle Ages Really Exist.” Source: [3]

The “evidence” for this claim is that:

  1. There is scarce archeological evidence that can be reliably dated to 614-911 due to perceived inaccuracies in the radiometric and dendrochronological methods in the 1990s.
  2. Presence of Romanesque architecture in 10th century Western Europe, which naturally suggests the Roman era couldn’t have been that long ago…
    • By this same logic, the architecture of the great Dome at MIT clearly indicates the unreality of at least a millenia
  3. Something about the relationship between the Julian calendar, Gregorian calendar, and astronomical solar year.
    • Without digging into this claim too much, it is not supported by astronomical events recorded by ancient sources (e.g. solar eclipses reported by Pliny the Elder in 59 AD, Photius in 418 AD, and all observations of the Tang dynasty).
File:Great Dome, MIT - IMG 8390.JPG
Great Dome at MIT. Source: https://commons.wikimedia.org/wiki/File:Great_Dome,MIT-_IMG_8390.JPG

However, there was nothing that suggests this history could glorify Russia, nor did it seem like Heribert Illig or his colleagues would have anything to gain from doing so. It turns out there was a separate, much more involved conspiracy theory promoted by Anatoly Fomenko called “New chronology.” It proposed that the events of Ancient Rome, Ancient Egypt, and the Roman Empire actually occurred more than 1000 years later than believed. Instead, history prior to 1600 CE had been falsified by powerful interests to obscure a true history of the world centered on “the Russian horde.” Unsurprisingly, this chronology is popular in Russia. Fomenko has sold over 1 million books, and the conspiracy has “the sympathy of up to 30% of the Russian public.”

New chronology (Fomenko) - Wikipedia
“Statistical correlation” of different historical dynasties by Fomenko – a method used to develop New chronology. Source: [5]

Of course, the phantom time hypothesis and New chronology are not the only dodgy chronologies in town. For the interested there is also:

  1. Glasgow chronology
  2. Ages in Chaos and all of Immanuel Veilovsky’s work
  3. New Chronology by David Rohl (a separate conspiracy from Fomenko’s)
  4. Short chronology
  5. Middle chronology


  1. https://en.wikipedia.org/wiki/Phantom_time_hypothesis
  2. https://modulestaging.wordpress.com/2016/12/18/are-we-living-in-the-18th-century-an-exploration-of-the-phantom-time-hypothesis-revised/
  3. https://www.medievalists.net/2020/04/why-phantom-time-hypothesis-wrong/
  4. http://museum.mit.edu/150/70
  5. https://en.wikipedia.org/wiki/New_chronology_(Fomenko)
  6. https://en.wikipedia.org/wiki/Category:Alternative_chronologies

Palmstruh and Paper Money in Sweden

History is a fragment of biology – the human moment in the pageant of species. It is also a child of geography – the operation of land and sea and air, and of their forms and products, upon human desire and destiny.

Will and Ariel Durant in The Age of Louis XIV

It’s been a little while since I’ve read Money by Jacob Goldstein, but I remember a fascinating vignette about goldsmiths in Britain being the first to create proto-paper money in Europe. Goldstein also discusses this in a Planet Money podcast that “China had actually used [paper money] hundreds of years earlier, but it’s a new thing in Western Europe.” He then goes on to discuss a charming ruffian, John Law, that used paper money to ruinous effect in France. I highly recommend giving the story a listen!

I guess Western Europe is not a super well-defined entity, but I was interested to come across this passage in the Durants’ The History of Civilization when reading about the zenith of Swedish power in the latter half of the 17th century:

To supplement the coinage of silver and gold, Charles [X Gustavus] commissioned Johann Palmstruh to establish a national bank and issue paper money (1656) – the first such currency in Europe.

Charles X Gustavus succeeded Christina, the daughter of Gustavus Adolphus in 1654. When Charles ascended to the throne, the Swedish monarchy was in a precarious financial state. Charles solved this problem by “reducing” (e.g. seizing) the holdings of the nobility. To further expand the economy, Charles also ordered chartered the first national bank, the Stockholms Banco (1657), and the first paper banknotes issued by a central bank (1661). These were managed by Johan Palmstruch (sometimes Palmstruh), a Latvian-born Dutch entrepreneur.

Initially, these paper banknotes were certificates of deposit for copper. Abundant domestic copper supply from the Falun mines lead to Gustav Adolphus ordering the minting of dalers, large copper coins. The value of these coins plummeted after competition from copper producers from East Asia, forcing the Swedish government to issue heavier copper coins to maintain the parity between dalers and silver coins. This quickly became impractical, with a 3kg sheet of copper being equivalent to two silver dalers. When the Banco opened, depositors eagerly exchanged these sheets of copper for certificates. In 1661, Palmstruch decoupled the value of deposited copper from the value of certificates issued, creating the first “modern” banknote.

Swedish riksdaler - Wikipedia
A sheet of copper weighing almost 20 kilograms worth 10 pieces of silver.

This experiment ultimately failed within 3 years. Predictably, the increased money supply initially stimulated the economy, but the overzealous issuing of paper money lead to inflation, a run on the bank, bankruptcy, and abandonment of the experiment by 1664.

Palmstruch was charged with irresponsible book-keeping and was sentenced in 1668 to a loss of title, loss of banking privileges, and a choice of eternal exile or death. This was later commuted to a life sentence, although Palmstruch died in prison by 1670.

As a side note, the Durants are an ample source of GRE vocabulary. Can you define?

  1. Celerity
  2. Seignorial
  3. Propitious


  1. Durant, Ariel and Durant, Will. The Story of Civilization 8: The Age of Louis XIV. Page 365-367.
  2. Goldstein, Jacob. Money. Atlantic Books, 2020.
  3. https://www.npr.org/transcripts/909876702
  4. https://www.citeco.fr/10000-years-history-economics/great-discoveries/creation-of-the-first-central-bank
  5. https://www.citeco.fr/en/first-european-banknote
  6. https://en.wikipedia.org/wiki/Johan_Palmstruch


  1. Celerity – Swiftness of movement. “Charles marched his army westward with Napoleonic celerity…”
  2. Seignorial – Relating to or befitting a nobleman. “By this reduction of seignorial holdings the state regained three thousands homesteads, and solvency.”
  3. Propitious – Favorable, indicating a good chance of success. “He [John III] had a propitious origin as the son of the castellan (military governor) at Cracow…”

Coordinate and cumulative adjectives

I was editing a hypothetical situation in which a patient had an abdomen that was “appropriately mildly tender.” I was pretty sure there should be a comma between appropriately and mildly. This is in the context of describing an abdominal exam on a patient after surgery. In this situation, it is both appropriate to have tenderness and the tenderness should be mild.

From my understanding, if two adverbs both describe the same adjective, one may either use a conjunction (appropriately and mildly tender) or elide the conjunction with a comma (appropriately, mildly tender). I asked this on English stack exchange (under a pseudonym) and got some surprisingly hilarious responses.

I can just about imagine a context where being appropriately mildly tender might make sense in relation to a fillet steak, but not someone’s abdomen! Perhaps you mean His abdomen is mildly tender, as one might expect in the circumstances. Note that this use of appropriately means as is fitting / as is right and proper, which isn’t quite the same as as is to be expected


My ultimate conclusion was that “appropriately” was modifying “mildly” and not tender. Therefore, not adding a comma was reasonable. In my mind though, I kept processing the phrase as “appropriate mild tenderness” which didn’t seem like it required a comma. This got me thinking about adjectives and commas. Although I’m sure I learned this in elementary school at some point, I definitely needed a refresher… Apparently, adjectives can be categorized in 1 of 9 categories (the so-called “royal order of adjectives”).

  1. Determiner – articles, possessives, number, demonstratives
  2. Opinion
  3. Size
  4. Shape
  5. Age
  6. Color
  7. Origin
  8. Material
  9. Qualifier (Purpose)

Multiple adjectives within the same category are “coordinate” and adjectives in different classes are “cumulative.” Coordinate adjectives require commas between them, cumulative adjectives do not. Moreover, cumulative adjectives must be presented in the order listed above (Khan Academy gives the mnemonic DOSA-SCOMP). For example, “that metal key large ring” doesn’t sound right (correct – “that large metal key ring”).

The Chicago Manual of Style nicely lays this out.

“A coordinate adjective is one that appears in a sequence with one or more related adjectives to modify the same noun. Coordinate adjectives should be separated by commas or by and {skilled, experienced chess player} {nurturing and loving parent}. If one adjective modifies the noun and another adjective modifies the idea expressed by the combination of the first adjective and the noun, the adjectives are not considered coordinate and should not be separated by a comma. For example, a lethargic soccer player describes a soccer player who is lethargic. Likewise, phrases such as white brick house and wrinkled canvas jacket are unpunctuated because the adjectives are not coordinate: they have no logical connection in sense (a white house could be made of many different materials; so could a wrinkled jacket). The most useful test is this: if and would fit between the two adjectives, a comma is necessary.”

Chicago Manual of Style 17. Section 5.9.1

Of course, this begs the question, where the heck does the royal order of adjectives come from? Some low-quality internet sleuthing led to David Schmidt’s comment on a Daily Writing Tips article.

The “Royal Order of Adjectives” was compiled and organized by an American college teacher, Dr. Charles Darling, Professor of English, Capital Community College. I believe it was titled as it is just for a pun.

Of course, the ordering of adjectives certainly predates the compilation of Prof. Darling’s Guide to Grammar. I wasn’t able to find confirmation that the royal order was titled for a pun either.

Finally, I stumbled across a preprint article from Leung et al. at Cambridge and ETH Zurich on Investigating Cross-Linguistic Adjective Ordering Tendencies. They nicely summarized the most popular explanatory account of this ordering phenomenon – namely that there are natural hierarchical tendencies based on semantic categories. Interestingly, this tendency is not unique to English and is present across many languages with English-like adjectives.

However, much of the previous work focused on the intuitive judgment of native speakers. This paper examined corpus data across 24 languages with English-like adjectives and was able to predict the order of adjectives, even when the training dataset was in one language and the testing dataset in another. This suggests a universal, cross-linguistic, hierarchical tendency in adjective ordering.


  1. https://english.stackexchange.com/questions/578736/comma-in-appropriately-mildly-tender
  2. https://www.khanacademy.org/humanities/grammar/parts-of-speech-the-modifier/adjective-order-and-commas-with-adjectives/v/commas-and-adjectives
  3. Chicago Manual of Style 17. Section 5.9.1
  4. http://guidetogrammar.org/grammar/adjectives.htm
  5. https://aclanthology.org/2020.emnlp-main.329.pdf

Why is the Earth made of iron-56 and not nickel-62?

Since elementary school, we’ve learned that iron is the most abundant element on earth (32.1% by mass). The standard explanation was that iron (iron-56 specifically) was the “most stable nucleus.” However, I recently learned that Nickel-62 is actually the most tightly bound nucleus!

Although the nuclei of atoms consist only of neutrons and protons, simply summing the masses of these particles always yields a value less than the true mass. The missing mass is accounted for by the nuclear binding energy, a consequence of the strong nuclear force that attracts nucleons. Since energy is released as nucleons bind more tightly (by fusion for lighter elements and fission for heavier elements), one might expect Nickel-62 to be more common than iron-56. However, this is not the case, as evidenced by the data about the abundance of chemical elements in the Solar System below.

Binding energy per nucleon. Iron-56 is actually in 3rd place! Figure from http://hyperphysics.phy-astr.gsu.edu/ which was adapted from a paper by M.P. Fewell
Abundance of chemical elements in the Solar system. Note the logarithmic scale and the peak at iron. Figure from https://en.wikipedia.org/wiki/Iron_peak

This conundrum can be partially resolved by noting that both iron-58 and nickel-62 do not have mass numbers divisible by 4. This means they cannot be produced by the alpha process. The alpha process is the process by which stars convert helium into heavier elements, essentially by adding alpha particles (He2+) to existing nuclides. Moreover, it seems that conditions in the stellar interior begin to favor photodisintegration over the alpha process around iron, ultimately leading to more iron-56 than nickel-62.


  1. http://hyperphysics.phy-astr.gsu.edu/hbase/NucEne/nucbin.html#c1
  2. https://en.wikipedia.org/wiki/Iron_peak
  3. http://hyperphysics.phy-astr.gsu.edu/hbase/NucEne/nucbin2.html#c1
  4. https://en.wikipedia.org/wiki/Iron-56
  5. https://en.wikipedia.org/wiki/Nickel-62

Spiral of Tillaux

Spiral of Tillaux | Optometry, Optician, Spiral
Spiral of Tillaux. Measurements are given in millimeters. From aao.org.

Paul Jules Tillaux was a French surgeon that is the namesake of the spiral of Tillaux, an imaginary curve through the insertions of the eye’s rectus muscles.

There are six extraocular muscles that control the movement of the eye (the legendary 7th extraocular muscle, the levator palpebrae, controls eyelid elevation). These are:

  1. Medial rectus
  2. Lateral rectus
  3. Superior rectus
  4. Inferior rectus
  5. Superior oblique
  6. Inferior oblique

The 4 rectus muscles originate in the back of orbit at the annulus of Zinn and insert anteriorly on the globe near the limbus. Starting from the superior rectus and going to the lateral rectus, inferior rectus, and medial rectus, the muscle insertions lie progressively closer to the limbus (border between the cornea and sclera). This forms the aforementioned spiral of Tillaux.

As seen in the image above, for the average adult, the medial rectus inserts 5.5mm from the limbus, the inferior rectus 6.5mm, the lateral rectus 6.9mm, and the superior rectus 7.7mm. For the time-crunched resident reviewing for OKAPs, Dr. Pouw and Dr. Young on Eyes for Ears remind us that these values may be more easily remembered as 5.5, 6.6, 7.7, and 7.0.

The spiral of Tillaux has some importance when performing ophthalmic surgery. As the superior rectus insertion is quite posterior, a scleral pass that is too deep may perforate the retina (it doesn’t help that the sclera is the thinnest [a mere 0.3mm] directly posterior to the rectus muscle insertions). In cases when there is a remote history of strabismus surgery but the amount of advancement or recession is unknown, measurements of muscle insertions from the limbus may allow the surgeon to estimate the extent of previous surgeries.

Muscles of the right orbit from Gray’s Anatomy.

Other Eponyms

Like many other surgeons of yesteryear, Dr. Tillaux is honored with eponyms across a variety of fields. He is best known to orthopedic surgeons for the Tillaux-Chaput fracture, an unusual fracture of the anterolateral tibial epiphysis. This Salter-Harris III fracture is most commonly seen in adolescents after forced lateral rotation of the foot.

The Tillaux maneuver is a physical exam technique to demonstrate adherence of a breast tumor to the pectoralis major.

There is also a Tillaux apparatus that maintains femoral diaphysis fractures in constant, steady adduction; Tillaux’s sign, an indication of a mesenteric tumor; and a Tillaux painful crepitus sign tenosynovitis of the adductor and short extensor of the thumb.


  1. https://eyesforears.net/episodes/2019/12/26/episode-34-strabismus-fundamentals-part-i
  2. American Academy of Ophthalmology,. (2021). 2021-2022 Basic and Clinical Science Course, Section 02: Fundamentals and Principles of Ophthalmology. Page 18-20.
  3. https://www.orthobullets.com/pediatrics/4028/tillaux-fractures
  4. https://litfl.com/paul-jules-tillaux-eponym/
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