NN Taleb
Antifragile



***clothes***
p. 52--"Take this easy-to-use heuristic...to detect the independence and robustness of someone's reputation. With few exceptions, those who dress outrageously are robust or even antifragile in reputation; those clean-shaven types who dress in suits and ties ar fragile to information about them."

Leave it to the hipsters to "aestheticize" this heuristic. Hence we need to develop another heuristic just for them: who is professionally accoplished and who just has a trust fund?





***scale+McLuhan***
p. 88-"biology plays a role in a municipal environment, not in a larger system. An administration is shielded from having to feel the sting [89] of shame (with flushing in his face), a biological reaction to overspending and other failures such as killing people in Vietnam. Eye contact with one's peers changes one's behavior. But for a desk-grounded office leech, a number is just a number. ... On the small, local scale, his body and biological response would direct him to avoid causing harm to others. On a large scale, others are abstract items; given the lack of social contact with the people concerned, the civil servant's brain leads rather than his emotions—with numbers, spreadsheets, statistics, more spreadsheets, and theories."

My note says: "has McLuhan grasped this?" i.e. This is an even greater challenge than Mumford's critique to the Global Village coinage. There are no villages without face-to-face contact.

Of course Taleb's go-to is Stalin, but don't forget that Ron Reagan has made precisely this analysis of his pops.












p. 163--"There is a tradition with French and other European literary writers to look for a sinecure, say, the [164] anxiety-free profession of civil servant, with few intellectual demands and high job security, the kind of low-risk job that ceases to exist when you leave the office, then spend their spare time writing, free to write whatever they want, under their own standards. There is a shockingly small number of academics among French authors. American writers, on the other hand, tend to become members of the media or academics, which makes them prisoners of a system and corrupts their writing, and, in the case of research academics, makes them live under continuous anxiety, pressures, and indeed, severe bastardization of the soul. Every line you write under someone else's standards, like prostitution, kills a corresponding segment deep inside. On the other hand, sinecure-cum-writing is a quite soothing model, next best to having financial independence."

It's funny how easily Mr. Negative Empiricism himself can slip into enormous generalizations and inferences without bothering to offer up the kind of hard evidence he demands from others. Til then I'm going to play skeptic about the details here even though I am sympathetic to his general point. Are we sure that it is not the American AUDIENCE who are more hynotized by academic credentials than are Europeans? And how can we be sure it was academia that "corrupted" these leech-writers, who otherwise would have developed normally? NNT is the first to pipe up about how little academia succeeds in educating. If so, how could it succeed any better at "corrupting?"

(Flannery O'Connor: <i>“Everywhere I go I'm asked if I think the university stifles writers. My opinion is that they don't stifle enough of them. There's many a best-seller that could have been prevented by a good teacher.”</i>)

Incidentally, I was on my way down the sinecure path with my airport job. I really wanted to make it work. Unfortunately I found it too unpleasant to be situated at the butt end of a long hierarchical chain of Accountability. Ironically that is the most job-secure location along the entire chain! And it was part-time with benefits! It was perfect! But the job did not actually cease to exist after leaving the office. The accountability-pressure and the brain-frying were too intense. I can't say I regret leaving, and I don't think I would go back if I could, but it the ideal of it is very seductive for all the reasons NNT outlines here.






p. 278--[heading <b>SMALL MAY BE UGLY, IT IS CERTAINLY LESS FRAGILE</b>]
"A squeeze occurs when people have no choice but to do something, and do it right away, regardless of costs.

...

[279]Squeezes are exacerbated by size. When one is large, one becomes vulnerable to some errors, particularly horrendous squeezes. The squeezes become nonlinearly costlier as size increases.

...consider the reasons one should not own an elephant as a pet... Should there be a water shortage...you would have to pay a higher and higher price for each additional gallon of water. That's fragility, right there, a negative convexity effect coming from getting too big. ...

"In spite of what is studied in business schools concerning "economies of scale," size hurts you at times of stress; it is not a good idea to be large during difficult times. Some economists have been wondering why mergers of corporations do not appear to play out. The combined unit is now much larger, hence more powerful, and according to the theories of economies of scale, it should be more "efficient." But the numbers show, at best, no gain from such increase in size—that was already true in 1978, when Richard Roll voiced the "hubris hypothesis," finding it irrational for companies to engage in mergers given their poor historical record. Recent data, more than three decades later, still confirm both the poor record of mergers and the same hubris as managers seem to ignore the bad economic aspect of the transaction."





p. 280--"On January 21, 2008, the Parisian bank Societé Générale rushed to sell in the market close to seventy billion dollars' worth of stocks, a very large amount for any single "fire sale." Markets were not very active (called "thin"), as it was Martin Luther King day in the United States, and markets worldwide dropped precipitously, close to 10 percent, costing the company close to six billion dollars in losses just from their fire sale. The entire point of the squeeze is that they couldn't wait, and they had no option but to turn a sale into a fire sale. For they had, over the weekend, uncovered a fraud. Jerome Kerviel, a rogue back office employee, was playing with humungous sums in the market and hiding these exposures from the main computer system. ...

"... A fire sale of $70 billion dollars worth of stocks leads to a loss of $6 billion. But a fire sale a tenth of the size, $7 billion would result in no loss at all, as markets would absorb the quantities without panic, maybe without even noticing. So this tells us that if, instead of having one very large bank, with Monsieur Kerviel as a rogue trader, we had ten smaller banks, each with a proportional Monsieur Micro-Kerviel, and each conducted his rogue trading independently and at random times, the total losses for the ten banks would be close to nothing."

p. 281--"Clearly, the postmortem analyses were mistaken, attributing the [282] problem to <i>bad</i> controls by the <i>bad</i> capitalistic system, and lack of vigilance on the part of the bank. It was not. Nor was it "greed," as we commonly assume. The problem is primarily size, and the fragility that comes with size."

...








"In project management, Bent Flyvberg has shown firm evidence that an increase in the size of projects maps to poor outcomes and higher and higher costs of delays as a proportion of the total budget. But there is a nuance: it is the size per segment of the project that matters, not the entire project—some projects can be divided into pieces, not others. Bridge and tunnel projects involve monolithic planning, as these cannot be broken up into small portions; their percentage costs overruns increase markedly with size. Same with dams. For roads, built by small segments, there is no serious size effect, as the project managers incur only small errors and can adapt to them. Small segments go one small error at the time, with no serious roles for squeezes."

[footnote on this page]<font size=1>"A nuance: the notions of "large" and "small" are relative to a given ecology or business structure. Small for an airplane maker is different from "small" when it comes to a bakery. As with the European Union's subsidiarity principle, "small" here means the smallest possible unit for a given function or task that can operate with a certain level of efficiency.</font>


p. 283--"Imagine how people exit a movie theater. Someone shouts "fire," and you have a dozen persons squashed to death. So we have a fragility of theater to size, stemming from the fact that every additional person exiting brings more and more trauma... A thousand people exiting (or trying to exit) in one minute is not the same as the same number exiting in half an hour. ...

"It so happens that contemporary economic optimized life causes us to build larger and larger theaters, but with the exact same door. They no longer make this mistake too often while building cinemas, theaters, and stadiums, but we tend to make the mistake in other domains, such as, for instance, natural resources and food supplies. Just consider that the price of wheat more than tripled in the years 2004-2007 in response to a small increase in demand, around 1 percent."






***Mumford's "same high level"***
p. 322--"with so many technologically driven and modernistic items—skis, cars, computers, computer programs—it seems that we notice differences between versions rather than commonalities. We even rapidly tire of what we have, continuously searching for versions 2.0 and similar iterations. ... These impulses to buy new things that will eventually lose their novelty, particularly when compared to newer things, are called <i>treadmill effects</i>. ...they arise from the same generator of biases as the one about the salience of variations mentioned in the section before: we notice differences and become dissatisfied with some items and some classes of goods. This treadmill effect has been investigated by Danny Kanhneman and his peers when they studied the psychology of what they call hedonic states. People acquire a new item, feel <i>more satisfied</i> after an [323] initial boost, then rapidly revert to their baseline of well-being. ...

"But it looks as though we don't incur the same treadmilling techno-dissatisfaction with classical art, older furniture—whatever we do not put in the category of the technological. You may have an oil painting and a flat-screen television set inhabiting the same room of your house. ... I am quite certain that you are not eager to upgrade the oil painting but that soon your flat-screen TV set will be donated to the local chapter of some kidney foundation.

...

"...Whenever I sit on an airplane next to some businessman reading the usual trash businessmen read on an e-reader, said businessperson will not resist disparaging my use of the book by comparing the two items. Supposedly, an e-reader is more "efficient." It delivers the essence of the book, which said businessman assumes is information, but in a more convenient way, as he can carry a library on his device and "optimize" his time between golf outings. I have never heard anyone address the large differences between e-readers and physical books, like smell, texture, dimension (books are in three dimensions), color, ability to change pages, physicality of an object compared to a computer screen, and hidden properties causing unexplained [324] differences in enjoyment. The focus of the discussion will be commonalities (how close to a book this wonderful device is). Yet when he compared his version of an e-reader to another e-reader, he will invariably focus on minute differences. Just as when Lebanese run into Syrians, they focus on the tiny variations in their respective Levantine dialects, but when Lebanese run into Italians, they focus on similarities.

[324]"There may be a heuristic that helps put such items in categories. First, the electronic on-off switch. ... For these items, I focus on variations, with attendant neomania. But consider the difference between the artisinal—the other category—and the industrial. What is artisinal has the love of the maker infused in it, and tends to satisfy—we don't have this nagging impression of incompleteness we encounter with electronics.

"It also so happens that whatever is technological happens to be fragile. Articles made by an artisan cause fewer treadmill effects. And they tend to have some antifragility—recall how my artisinal shoes take months before becoming comfortable. Items with an on-off switch tend to have no such redeeming antifragility."












































***music business classes***
p. 302--"I have used all my life a wonderfully simple heuristic: charlatans are recognizable in that they will give you positive advice, and only positive advice, exploting our gullibility and sucker-proneness for recipes that hit you in a flash as just obvious, then evaporate later as you forget them. ... Yet in practice its the negative that's used by the pros, those selected by evolution: chess grandmasters usually win by not losing; people become rich by not going bust (particularly when others do); religions are mostly about interdicts; the learning of life is about what to [303] avoid. You reduce most of your personal risks of accident thanks to a small number of measures."



















***awards+30-year-rules***
p. 329--"The problem in deciding whether a scientific result or a new innovation is a "breakthrough," that is, the opposite of noise, is that one needs to see all aspects of the idea—and there is always some opacity that time, and only time, can dissipate. ...

"Likewise, seemingly uninteresting results that go unnoticed, can, years later, turn out to be breakthroughs.

"So time can act as a cleanser of noise by confining to its dustbins all these overhyped works. Some organizations even turn such scientific [330] production into a cheap spectator sport, with ranking of the "ten hottest papers" in, say, rectal oncology or some such sub-sub-specialty.

"If we replace scientific results with scientists, we often get the same neomaniac hype. There is a disease to grant a prize for a promising scientist "under forty," a disease that is infecting economics, mathematics, finance, etc. Mathematics is a bit special because the value of its results can be immediately seen—so I skip the criticism. Of the fields I am familiar with, such as literature, finance, and economics, I can pretty much ascertain that the prizes given to those under forty are the best reverse indicator of value... The worst effect of these prizes is penalizing those who don't get them and debasing the field by turning it into an athletic competition.

"Should we have a prize, it should be for "over a hundred": it took close to one hundred and forty years to validate the contribution of one Jules Regnault, who discovered optionality and mapped it mathematically—along with what we dubbed the philosopher's stone. His work stayed obscure all this time."

These prizes have their counterparts in the music world, and there too they are strong "reverse indicators of value" (at least to everyone outside the immediate social orbit of the committee and the recipients). A certain amount of focus on the under-forties arises from a good-faith response to a good-faith criticism: lifetime achievement awards are obscene when the achiever really could have used that money to stay afloat during their starving-artist years. This, together with the realization that many small grants to individual artists would do more good than a few massive grants to superstars and large organizations, has (re)shaped the landscape somewhat. I suspect there are good intentions behind this; yet NNT's observations here supply the necessary "damned if you do" caveats. Radical postmodernists get the most attention for rejecting the cleansing effect of time, for junking the Thirty Year Rule that historians formerly observed, etc., and yet functionally the bourgeois mainstream has also rejected these things, much more quietly but with equal thoroughness and equally strident rationalizations. In one respect it it obvious that people need the money more when they are younger. The problem, though, is that it is not so easy to see the future. To attempt to do so is a <i>fragilista</i> maneuver through and through.

In claiming this, I am certainly weary of embracing Taleb's peculiar brand of Darwinism. He is not the least bit convincing when he claims to be content with merely passing on his genes and riding into the sunset. Clearly he also wants to read, argue, eat, drink,... I'm not in favor of a Hunger Games approach to artisthood. The point, rather, that Taleb's books reveal, and which is in my experience simply not yet acknowledged in artists' circles, is that the fragilizing effects of awards are <i>even worse</i> than the trappings of a pure survival competition. They compound "cumulative advantage," lead to "Matthew effects," and claim to see the future. I'm sure we will continue to have them even so. We all might as well apply just in case. But please don't believe anything anyone involved in this says about the recipients, and please don't believe that competitions and awards are about supporting the next generation's finest practitioners. The list of Pulitzer winners speaks for itself here.

Synchronically, lifetime achievement awards are indefensible; diachronically they are the only defensible kind of award in fields that are, for our purposes here, the opposite of math, where the value of results is very rarely immediately seen, indeed where this value is all but guaranteed to change, and where that mere fact in and of itself does not need to be elevated to a risk by our having previously bet against it. Of course we can collectively decide to redefine value as strictly limited to that which can be immediately seen. It may seem like this has already happened; but watch those hipsters carefully, especially when they don't know they are being watched, and you will find all the evidence you'll ever need that this presentism is no more a part of who they really are than their mismatched tube socks.







=-=-=
PINKZ
=-=-=

"Man-made complex systems tend to develop cascades and runaway chains of reactions that decrease, even eliminate, predictability and cause outsized events. So the modern world may be increasing in technological knowledge, but, paradoxically, it is making things a lot more unpredictable. Now for reasons that have to do with the increase of the artificial, the move away from ancestral and natural models, and the loss in robustness owing to complications in the design of everything, the role of Black Swans in increasing. [sic!] Further, we are victims to a new disease, called in this book <i>neomania</i>, that makes us build Black Swan-vulnerable systems—"progress." (7)





***bigsmall***
p. 17--"for those who think that academia is "quieter" and an emotionally relaxing transition after the volatile and risk-taking business life, a surprise: when in action, new problems and scares emerge every day to displace and eliminate the previous day's headaches, resentments, and conflicts. A nail displaces a nail, with astonishing variety. But academics (particularly in social science) seem to distrust each other; they live in petty obsessions, envy, and icy-cold hatreds, with small snubs developing into grudges, fossilized over time in the loneliness of the transaction with a computer screen and the immuntability of their environment. Not to mention a level of envy I have almost never seen in business. . . .[ellipsis in original]My experience is that money and transactions purify relations; ideas and abstract matters like "recognition" and "credit" warp them..."

Many fair points. One quibble: NNT elsewhere emphasizes quite forcefully that something like "recognition" is nothing less than a biological necessity for human beings. My father the career academic once pointed out to me (not in these words) that much academic bickering is a result of fighting over crumbs. Musicians also fight over crumbs, and so this passage describes us very well also. Indeed, it describes many practical, business-oriented pros who didn't attend or didn't finish college. I have seen this many times, and it gives me reason to doubt that the academics are such a special case. Sure, "money" can "purify" these "relations," but in Extremistan this is beside the point. And to be sure, mere "transactions" don't seem to have any such effect. The recently-discussed phenomenon of elite artists scrapping over local recognition could be another counterexample here. Nonmaterial, supratransactional considerations (tribe, nation, honor, status) can cause secure elites to behave like cornered animals.

NNT emphasizes the bio-determinist angle in such matters, e.g. the finding that celebrities seem to live longer. I'm inclined to believe this, but I see no realistic path to achieving it for myself, nor, I hasten to add, do I want to be railroaded into chasing "recognition" as a matter of sheer survival value, even though I'm willing to believe that it does has some. The reason I don't want to do this is that I can't see any ethical way to do it. (Feel free to share if you think you've found one! I'm skeptical already!) Someone somewhere had hard evidence of artists being the most unhappy/unfulfilled vis-a-vis career choices. I see only two ways around this. The obvious one of not having any more artists (or academics) doesn't work for me. At that point, I think that what we're left with is the necessity for those of us who insist, against the rational-actor model, on living in Extremistan to mind-trick ourselves into acceptance of non-recognition, not just superficial acceptance but the kind of deep acceptance that can actually change our body chemistry. Obviously this is extemely challenging and entails cultivating some sort of mindfulness practice alongside whatever other cultivated practices we are already preoccupied with. This is something I think about a lot but have trouble seeing myself actually committing to. Further, it is not so easy to compartmentalize an attitude toward the outside world from our attitude to our own life's work: Kenny Werner wrote that musicians must stop caring how we sound, and his records also sound like he doesn't care how he sounds. Faced with that outcome, I would rather die of non-recognition.

[possibly see Silverstein in Pleck and Sawyer (1) in Ymail, 6 Jan 2015]
[possibly see Lonely Crowd, pp. 273-275 (pinks)]






















p. 43--"It is said that the best horses lose when they compete with slower ones, and win against better rivals. Undercompensation from the absence of a stressor, inverse hormesis, absence of challenge, degrades the best of the best. ...

"...it is a well-known trick that if you need something urgently done, give the task to the busiest (or the second busiest) person in the office. ...

"... Some [publishers] try sending authors to "speech school"—the first time it was suggested to me I walked out, resolved to change publishers on the spot. I find it better to whisper, not shout. Better to be slightly inaudible, less clear. When I was a pit trader...I learned that the noise produced by the person is inverse to the pecking order: as with mafia dons, the most powerful traders were the least audible. One should have enough self-control to make the audience work hard to listen, which causes them to switch into intellectual overdrive. This paradox of attention has been a little bit investi[44]gated: there is empirical evidence of the effect of "disfluency." Mental effort moves us into higher gear, activating more vigorous and more analytical brain machinery. ...

"The same or a similar mechanism of overcompensation makes us concentrate better in the presence of a modicum of background random noise, as if the act of countering such noise helps us hone our mental focus."




p. 50--"a simple rule of thumb (a heuristic): to estimate the quality of the research, take the caliber of the highest detractor, or the caliber of the lowest detractor whom the author answers in print—whichever is lower."





p. 72--"Every plane crash brings us closer to safety, improves the system, and makes the next flight safer... these systems learn because they are antifragile and set up to exploit small errors; the same cannot be said of economic crashes, since the economic system is not antifragile in the way it is presently built. Why? There are hundreds of thousands of plane flights every year, and a crash in one plane does not involve others, so errors remain confined and highly epistemic—whereas globalized economic systems operate as one: errors spread and compound."

p. 73--"If every plane crash makes the next one less likely, every bank crash makes the next one more likely. We need to eliminate the second type of error—the one that produces contagion—in our construction of an ideal socioeconomic system."









p. 75--"While sacrifice as a modus is obvious in the case of ant colonies, I am certain that individual businessmen are not overly interested in hara-kiri for the greater good of the economy; they are therefore necessarily concerned in seeking antifragility or at least some level of robustness for themselves. That's not necessarily compatible with the interest of the collective—that is, the economy. So there is a problem in which the property of the sum (the aggregate) varies from that of each one of the parts—in fact, it wants to harm the parts.

"It is painful to think about ruthlessness as an engine of improvement. Now what is the solution? There is none, alas, that can please everyone—but there are ways to mitigate the harm to the very weak.

"The problem is graver than you think. [No, it's graver than YOU think!!] People go to business school to learn how to do well while ensuring their survival—but what the economy, as a collective, wants them to do is to <i>not</i> survive, rather to take a lot, a lot of imprudent risks themselves and be blinded by the odds. Their respective industries improve from failure to failure. Natural and naturelike systems want some overconfidence on the part of individual economic agents, i.e., the overestimation of their chances of success and underestimation of the risks of failure in their businesses, provided their failure does not impact others. In other words, they want local, but not global, overconfidence."

So, he realizes the problem, or at least the existence of a problem. But really, how do you "[build] a system in which nobody's fall can drag others down" and still have an "economy"? Can these things even be reconciled?!







p. 97[footnote]--"Note that people invoke an expression, "Balkanization," about the mess created by fragmented states, as if fragmentation was a bad thing, and as if there was an alternative in the Balkans—but nobody uses "Helvetization" to describe its successes.













p. 108--"My definition of modernity is humans' large-scale domination of the environment, the systematic smoothing of the world's jaggedness, and the stifling of volatility and stressors.

"Modernity corresponds to the systematic extraction of humans from their randomness-laden ecology—physical and social, even epistemological. Modernity is not just the postmedieval, postagrarian, and postfeudal historical period as defined in sociology textbooks. It is rather the spirit of an age marked by rationalization (naive rationalism), the idea that society is understandable, hence must be designed, by human. With it was born statistical theory, hence the beastly bell curve. So was linear science. So was the notion of "efficiency"—or optimization."

All such attempts to define such widely-deployed terms are slanted by self-interest. (Yes, mine are too.) But the "extraction from randomness" angle seems worth taking seriously. Effectively it builds on older, cruder, rationalistic analyses of technological modernity by grounding them in NNT's empirical bent. Put another way, freedom from necessity and freedom from randomness are not entirely the same thing. Taken as goals, they will lead society in somewhat different directions. 





--"you need a name for the color [109] blue when you build a narrative, but not in action—the thinker lacking a word for "blue" is handicapped; not the doer. (I've had a hard time conveying to intellectuals the <i>intellectual</i> superiority of practice.)







***bigsmall/marketing***
p. 402--"with the exception of, say, drug dealers, small companies and artisans tend to sell us healthy products...larger ones are likely to be in the business of producing wholesale iatrogenics, taking our money, and then, to add insult to injury, hijacking the state thanks to their army of lobbyists. Further, anything that requires marketing appears to carry such side effects. You certainly need an advertising apparatus to convince people that Coke brings them "happiness"—and it works.

"There are, or course, exceptions: corporations with the soul of artisans, some with even the soul of artists. Rohan Silva once remarked that Steve Jobs wanted the inside of the Apple products to look aesthetically appealing, although they are designed to remain unseen by the customer. This is something only a true artisan would do—carpenters with personal pride feel fake when treating the inside of cabinets differently from the outside. Again, this is a form of redundancy, one with an aesthetic and ethical payoff. But Steve Jobs was one of the rare exceptions in the Highly Talked About Completely Misunderstood Said to Be Efficient Corporate Global Economy."

Not much of an exception really if it's true that he wouldn't let his kids use ipads! Iatrogenics+marketing! But the point about artisans holds regardless.

Moreover, to Kenji's contention, not in these words, that Scrabble "requires marketing," to believe this contention you have to disbelieve NNT's contention here that "anything that requires marketing appears to carry such side effects." You have to believe that he has identified, at most, correlation, but nothing like causality.









p. 458 [from the bibliography]--"<b><i>Private Correspondence with Bar-Yam:</b></i> Yaneer Bar-Yam, generously in his comments:
"If we take a step back and more generally consider the issue of partitioned systems versus connected systems, partitioned systems are more stable, and connected systems are both more vulnerable and have more opportunities for collective action. Vulnerability (fragility) is connectivity without responsiveness. Responsiveness enables connectvity to lead to opportunity. If collective action can be employed to address threats, or to take advantage of opportunities, then the vulnerability can be mitigated and outweighed by the benefits. This is the basic relationship between the idea of sensitivity as we described it and your concept of antifragility." (With permission.)"

(Sorry cats, I'm a blogger. We don't ask permission. But thank you for your work.)

So, perhaps the currency issue is an excellent illustration of "connectivity without responsiveness." The next question, then, is whether "responsiveness" per se can exist at scale. Assuming perfect "connectivity," chart "responsiveness" against global population. Is the function linear?










p. 463 [from bibliography]--"<b><i>Anecdotal knowledge and power of evidence:</i></b> A reader, Karl Schluze, wrote: "An old teacher and colleague told me (between his sips of bourbon) 'If you cut off the head of a dog and it barks, you don't have to repeat the experiment.'" Easy to get examples: no lawyer would invoke an "N=1" argument in defense of a person, saying "he only killed once"; nobody considers a plane crash as "anecdotal."

"I would go further and map disconfirmation as exactly where N=1 is sufficient.

"Sometimes researchers call a result "anecdotal" as a knee-jerk reaction when the result is exactly the reverse. Steven Pinker called John Gray's pointing out the two world wars as counterevidence to his story of great moderation "anecdotal." My experience is that social science people rarely know what they are talking about when they talk about "evidence.""

Incidentally, Jane Jacobs also reports being told by academics that her examples of downscaled economic success stories were "anecdotal."