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Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

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In a report posted online today, Peter Scholze of the University of Bonn and Jakob Stix of Goethe University Frankfurt describe what Stix calls a “serious, unfixable gap” within a mammoth series of papers by Shinichi Mochizuki, a mathematician at Kyoto University who is renowned for his brilliance. Posted online in 2012, Mochizuki’s papers supposedly prove the abc conjecture, one of the most far-reaching problems in number theory.

Despite multiple conferences dedicated to explicating Mochizuki’s proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 pages, are written in an impenetrable style, and refer back to a further 500 pages or so of previous work by Mochizuki, creating what one mathematician, Brian Conrad of Stanford University, has called “a sense of infinite regress.”

Between 12 and 18 mathematicians who have studied the proof in depth believe it is correct, wrote Ivan Fesenko of the University of Nottingham in an email. But only mathematicians in “Mochizuki’s orbit” have vouched for the proof’s correctness, Conrad commented in a blog discussion last December. “There is nobody else out there who has been willing to say even off the record that they are confident the proof is complete.”

Nevertheless, wrote Frank Calegari of the University of Chicago in a December blog post, “mathematicians are very loath to claim that there is a problem with Mochizuki’s argument because they can’t point to any definitive error.”

That has now changed. In their report, Scholze and Stix argue that a line of reasoning near the end of the proof of “Corollary 3.12” in Mochizuki’s third of four papers is fundamentally flawed. The corollary is central to Mochizuki’s proposed abc proof.

“I think the abc conjecture is still open,” Scholze said. “Anybody has a chance of proving it.”

Scholze and Stix’s conclusions are based not only on their own study of the papers but also on a weeklong visit they paid to Mochizuki and his colleague

Yuichiro Hoshi

in March at Kyoto University to discuss the proof. That visit helped enormously, Scholze said, in distilling his and Stix’s objections down to their essence. The pair “came to the conclusion that there is no proof,” they wrote in their report.

But the meeting led to an oddly unsatisfying conclusion: Mochizuki couldn’t convince Scholze and Stix that his argument was sound, but they couldn’t convince him that it was unsound. Mochizuki has now posted Scholze’s and Stix’s report on his website, along with several reports of his own in rebuttal. (Mochizuki and Hoshi did not respond to requests for comments for this article.)

In his rebuttal, Mochizuki attributes Scholze and Stix’s criticism to “certain fundamental misunderstandings” about his work. Their “negative position,” he wrote, “does not imply the existence of any flaws whatsoever” in his theory.

Just as Mochizuki’s high reputation made mathematicians view his work as a serious attempt on the abc conjecture, Scholze and Stix’s stature guarantees that mathematicians will pay attention to what they have to say. Though only 30, Scholze has risen quickly to the top of his field. He was awarded the Fields Medal, mathematics’ highest honor, in August. Stix, meanwhile, is an expert in Mochizuki’s particular area of research, a field known as anabelian geometry.

“Peter and Jakob are extremely careful and thoughtful mathematicians,” Conrad said. “Any concerns that they have … definitely merit being cleared up.”

The Sticking Point

The abc conjecture, which Conrad has called “one of the outstanding conjectures in number theory,” starts with one of the simplest equations imaginable: a + b = c. The three numbers a, b and c are supposed to be positive integers, and they are not allowed to share any common prime factors — so, for example, we could consider the equation 8 + 9 = 17, or 5 + 16 = 21, but not 6 + 9 = 15, since 6, 9 and 15 are all divisible by 3.

Given such an equation, we can look at all the primes that divide any of the three numbers — so, for instance, for the equation 5 + 16 = 21, our primes are 5, 2, 3 and 7. Multiplying these together produces 210, a much larger number than any of the numbers in the original equation. By contrast, for the equation 5 + 27 = 32, whose primes are 5, 3 and 2, the prime product is 30 — a smaller number than the 32 in the original equation. The product comes out so small because 27 and 32 have only small prime factors (3 and 2, respectively) that get repeated many times to make them.

If you start playing around with other abc triples, you’ll find that this second scenario is extremely rare. For example, among the 3,044 different triples you can make in which a and b are between 1 and 100, there are only seven in which the product of primes is smaller than c. The abc conjecture, which was first formulated in the 1980s, codifies the intuition that this kind of triple hardly ever happens.

More specifically, coming back to the 5 + 27 = 32 example, 32 is larger than 30, but only by a little. It’s smaller than 302, or 301.5, or even 301.02, which is about 32.11. The abc conjecture says that if you pick any exponent bigger than 1, then there are only finitely many abc triples in which c is larger than the product of the prime factors raised to your chosen exponent.

“The abc conjecture is a very elementary statement about multiplication and addition,” said Minhyong Kim of the University of Oxford. It’s the kind of statement, he said, where “you feel like you’re revealing some kind of very fundamental structure about number systems in general that you hadn’t seen before.”

And the simplicity of the a + b = c equation means that a wide range of other problems fall under the conjecture’s sway. For instance, Fermat’s Last Theorem is about equations of the form xn + yn = zn, and Catalan’s Conjecture, which says that 8 and 9 are the only two consecutive perfect powers (since 8 = 23 and 9 = 32), is about the equation xm + 1 = yn. The abc conjecture (in certain forms) would offer new proofs of these two theorems and solve a host of related open problems.

The conjecture “always seems to lie on the boundary of what is known and what is unknown,”

Dorian Goldfeld

of Columbia University

has written

.

The wealth of consequences that would spring from a proof of the abc conjecture had convinced number theorists that proving the conjecture was likely to be very hard. So when word spread in 2012 that Mochizuki had presented a proof, many number theorists dived enthusiastically into his work — only to be stymied by the unfamiliar language and unusual presentation. Definitions went on for pages, followed by theorems whose statements were similarly long, but whose proofs only said, essentially, “this follows immediately from the definitions.”

“Each time I hear of an analysis of Mochizuki’s papers by an expert (off the record) the report is disturbingly familiar: vast fields of trivialities followed by an enormous cliff of unjustified conclusions,” Calegari wrote in his December blog post.

Scholze was one of the paper’s early readers. Known for his ability to absorb mathematics quickly and deeply, he got further than many number theorists, completing what he called a “rough reading” of the four main papers shortly after they came out. Scholze was bemused by the long theorems with their short proofs, which struck him as valid but insubstantial. In the two middle papers, he later wrote, “very little seems to happen.”

Then Scholze got to Corollary 3.12 in the third paper. Mathematicians usually use the word “corollary” to denote a theorem that is a secondary consequence of a previous, more important theorem. But in the case of Mochizuki’s Corollary 3.12, mathematicians agree that it is at the core of the proof of abc. Without it, “there is no proof at all,” Calegari wrote. “It is a critical step.”

This corollary is the only theorem in the two middle papers whose proof is longer than a few lines — it fills nine pages. As Scholze read through them, he reached a point where he couldn’t follow the logic at all.

Scholze, who was only 24 at the time, believed the proof was flawed. But he mostly stayed out of discussions about the papers, except when asked directly for his thoughts. After all, he thought, perhaps other mathematicians would find significant ideas in the paper that he had missed. Or, perhaps, they would eventually come to the same conclusion as he had. One way or the other, he thought, the mathematics community would surely be able to sort things out.

Escher’s Staircase

Meanwhile, other mathematicians were grappling with the densely written papers. Many had high hopes for a meeting dedicated to Mochizuki’s work in late 2015 at the University of Oxford. But as several of Mochizuki’s close associates tried to describe the key ideas of the proof, a “cloud of fog” seemed to descend over the listeners, Conrad wrote in a report shortly after the meeting. “Those who understand the work need to be more successful at communicating to arithmetic geometers what makes it tick,” he wrote.

Within days of Conrad’s post, he received unsolicited emails from three different mathematicians (one of them Scholze), all with the same story: They had been able to read and understand the papers until they hit a particular part. “For each of these people, the proof that had stumped them was for 3.12,” Conrad later wrote.

Kim heard similar concerns about Corollary 3.12 from another mathematician, Teruhisa Koshikawa, currently at Kyoto University. And Stix, too, got perplexed in the same spot. Gradually, various number theorists became aware that this corollary was a sticking point, but it wasn’t clear whether the argument had a hole or Mochizuki simply needed to explain his reasoning better.

Then in late 2017 a rumor spread, to the consternation of many number theorists, that Mochizuki’s papers had been accepted for publication. Mochizuki himself was the editor-in-chief of the journal in question, Publications of the Research Institute for Mathematical Sciences, an arrangement that Calegari called “poor optics” (though editors generally recuse themselves in such situations). But much more concerning to many number theorists was the fact that the papers were still, as far as they were concerned, unreadable.

“No expert who claims to understand the arguments has succeeded in explaining them to any of the (very many) experts who remain mystified,”

Matthew Emerton

of the University of Chicago

wrote

.

Calegari wrote a blog post decrying the situation as “a complete disaster,” to a chorus of amens from prominent number theorists. “We do now have the ridiculous situation where ABC is a theorem in Kyoto but a conjecture everywhere else,” Calegari wrote.

PRIMS soon responded to press inquiries with a statement that the papers had not, in fact, been accepted. Before they had done so, however, Scholze resolved to state publicly what he had been saying privately to number theorists for some time. The whole discussion surrounding the proof had gotten “too sociological,” he decided. “Everybody was talking just about how this feels like it isn’t a proof, but nobody was actually saying, ‘Actually there is this point where nobody understands the proof.’”

So in the comments section below Calegari’s blog post, Scholze wrote that he was “entirely unable to follow the logic after Figure 3.8 in the proof of Corollary 3.12.” He added that mathematicians “who do claim to understand the proof are unwilling to acknowledge that more must be said there.”

Shigefumi Mori, Mochizuki’s colleague at Kyoto University and a winner of the Fields Medal, wrote to Scholze offering to facilitate a meeting between him and Mochizuki. Scholze in turn reached out to Stix, and in March the pair traveled to Kyoto to discuss the sticky proof with Mochizuki and Hoshi.

Mochizuki’s approach to the abc conjecture translates the problem into a question about elliptic curves, a special type of cubic equation in two variables, x and y. The translation, which was well known before Mochizuki’s work, is simple — you associate each abc equation with the elliptic curve whose graph crosses the x-axis at a, b and the origin — but it allows mathematicians to exploit the rich structure of elliptic curves, which connect number theory to geometry, calculus and other subjects. (This same translation is at the heart of Andrew Wiles’ 1994 proof of Fermat’s Last Theorem.)

The

abc

conjecture then boils down to proving a certain inequality between two quantities associated with the elliptic curve. Mochizuki’s work translates this inequality into yet another form, which, Stix said, can be thought of as comparing the volumes of two sets. Corollary 3.12 is where Mochizuki presents his proof of this new inequality, which, if true, would prove the

abc

conjecture.

The proof, as Scholze and Stix describe it, involves viewing the volumes of the two sets as living inside two different copies of the real numbers, which are then represented as part of a circle of six different copies of the real numbers, together with mappings that explain how each copy relates to its neighbors along the circle. To keep track of how the volumes of sets relate to one another, it’s necessary to understand how volume measurements in one copy relate to measurements in the other copies, Stix said.

“If you have an inequality of two things but the measuring stick is sort of shrunk by a factor which you don’t control, then you lose control over what the inequality actually means,” Stix said.

It is at this crucial spot in the argument that things go wrong, Scholze and Stix believe. In Mochizuki’s mappings, the measuring sticks are locally compatible with one another. But when you go around the circle, Stix said, you end up with a measuring stick that looks different from if you had gone around the other way. The situation, he said, is akin to Escher’s famous winding staircase, which climbs and climbs only to somehow end up below where it started.

This incompatibility in the volume measurements means that the resulting inequality is between the wrong quantities, Scholze and Stix assert. And if you adjust things so the volume measurements are globally compatible, then the inequality becomes meaningless, they say.

Scholze and Stix have “identified a way that the argument can’t possibly work,” said Kiran Kedlaya, a mathematician at the University of California, San Diego, who has studied Mochizuki’s papers in depth. “So if the argument is to be correct, it has to do something different, and something a lot more subtle” than what Scholze and Stix describe.

Something more subtle is exactly what the proof does, Mochizuki contends. Scholze and Stix err, he wrote, in making arbitrary identifications between mathematical objects that should be regarded as distinct. When he told colleagues the nature of Scholze and Stix’s objections, he wrote, his descriptions “were met with a remarkably unanimous response of utter astonishment and even disbelief (at times accompanied by bouts of laughter!) that such manifestly erroneous misunderstandings could have occurred.”

Mathematicians will now have to absorb Scholze and Stix’s argument and Mochizuki’s response. But Scholze hopes that, in contrast with the situation for Mochizuki’s original series of papers, this should not be a protracted process, since the gist of his and Stix’s objection is not highly technical. Other number theorists “would have totally been able to follow the discussions that we had had this week with Mochizuki,” he said.

Mochizuki sees things very differently. In his view, Scholze and Stix’s criticism stems from a “lack of sufficient time to reflect deeply on the mathematics under discussion,” perhaps coupled with “a deep sense of discomfort, or unfamiliarity, with new ways of thinking about familiar mathematical objects.”

Mathematicians who are already skeptical of Mochizuki’s abc proof may well consider Scholze and Stix’s report the end of the story, said Kim. Others will want to study the new reports for themselves, an activity that Kim himself has commenced. “I don’t think I can completely avoid the need to check more carefully for myself before making up my mind,” he wrote in an email.

In the past couple of years, many number theorists have given up on trying to understand Mochizuki’s papers. But if Mochizuki or his followers can provide a thorough and coherent explanation for why Scholze and Stix’s picture is too simplistic (assuming that it is), “this might go a long way towards relieving some of the fatigue and maybe giving people more willingness to look into this thing again,” Kedlaya said.

In the meantime, Scholze said, “I think this should not be considered a proof until Mochizuki does some very substantial revisions and explains this key step much better.” Personally, he said, “I didn’t really see a key idea that would get us closer to the proof of the abc conjecture.”

Regardless of the eventual outcome of this discussion, the pinpointing of such a specific part of Mochizuki’s argument should lead to greater clarity, Kim said. “What Jakob and Peter have done is an important service to the community,” he said. “Whatever happens, I’m pretty confident that the reports will be progress of a definite sort.”

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The Syrian Civil War: Air Power Can Win! If you want it. (Part I)

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    A few years back, I wrote a piece about the Syrian Civil War titled "The West v ISIS: Air strikes just means endless war minus victory". That now seems, in hindsight, not only trite but embarrassingly off the mark.  Some could say that I failed utterly as an analyst because look what the Russians did in Syria with a few planes and some Spetsnaz forward observers. They literally wiped the rebel forces arrayed against Assad (termed by Western media as ISIS) off the map. And they did it with so few aircraft, many of them aging, considered second/third generation planes compared to NATO's overpriced "fifth generation" stealth fleet, that it makes you wonder if it was NATO's or the Western powers intention to ever defeat ISIS at all?

   And here we come to what I'll call "the darkness".

   The darkness you will never see on any news channel or media outlet in any country under the umbrella of the post WWII globalist order. And by that I mean every English speaking country's news channels, including mainland Europe's, Israel's, South Korea's and Japan's. Whatever language is spoken, this post WWII order has held but is now descending into is this darkness I speak of?

  The darkness is first and foremost that the media and the entire political establishment is lying to you. That's certainly dark but the darkness I am positing rocks the foundations of my beliefs in the post WWII Western order I grew up in as a citizen of the British Isles and  benefited from as a European world traveler.

   And the question I ask myself is now, as I see darkness, is "are we the bad guys now?"





  For anyone who reads this obscure blog, this may not be new information. But let's indulge in a game. Let's talk about the Syrian Civil War now. Now that it is almost over, let's uncover from the rubble and the darkness some truth that war makes the first casualty of. The average person in Western OECD countries is busy making a living and feeding their family. It's difficult to be too much concerned with what your tax money is paying for. For instance, a Tomahawk missile costs 1.2 million dollars. And 300 million worth were launched against Syria because of some bullshit gas story pushed by the media in April. Gas is indiscriminate and horrible but it also has some especially evil connotation in the minds of the public who have never been near a war zone.

  Gas in war drives foreign civilian populations insane. It's a trigger word. And the media knows this. If your child in a war zone dies by air burst artillery (a common occurrence in Aleppo or Damascus or Gaza) that means such munitions pepper your child with ball bearings travelling at Mach 3. Fucking horrible and unthinkable. You'd think. But let an enemy open a barrel (allegedly) that spreads some weaponized chlorine/sarin for at best a square block and now you've got an international casus belli on your hands. But any soldier will tell you artillery is far worse and more terrifying then some dissipating cloud you have a small but possible fighting chance at running from. What's worse is the media pushing the public into outrage using gaseous fear and demanding intervention in a desert war thousands of miles away from the average taxpayer doing his best to feed his family.



   The famous Churchill quote "Nothing in life is so exhilarating as to be shot at to no result." is probably true. How about gassing people? He would know. How about bombing people and killing them via kinetic blast energy? Is that more evil then gas? In 2001, as we all know, 19 Saudis flew two planes and took down three buildings in New York, wrecked a wing of the Pentagon with another plane and nose dived a fourth into a field because of the heroism of the passengers. Officially. That was quite a feat in a country with a military larger than the next ten country's militarys combined. Try anything like that today near Damascus and your plane isn't even going to make it over land from the Mediterranean. We're talking about a city with the 4th most sophisticated anti aircraft defense network on the planet. That's why the Israelis launch their AGMs at Syria from F-16s from their airspace or Jordanian airspace. The Syrians could take a shot at them but they don't exactly need another next door neighbor flinging more shit over the garden fence at them right now. 

   The point being?

   Syrian airspace became impregnable and that was the beginning of the turning of the tide in favor of Assad. Russian intervention we'll talk about in Part II but for now let's stick to how we got to where we are today. 

   


The Russians like their naval base at Tartus. And why wouldn't they? Geopolitics is a chessboard, why give up a square?


      How did we get to a place where bombing wins a war.

    I mean this figuratively of course, bombing wins wars but only as a component of a combined ground strategy and other factors. The Syrian Civil War is unique in the sense that never have so few aircraft done so much to change a major war. There's a Churchill Battle of Britain quote in there but I'm not using it because it's just too obvious.

     To begin talking about Syria, we're going to have to go all the way back to 2010. Remember that thing called the "Arab Spring"? Western media touted it on your TV screen. Maybe you do, maybe you don't but let's do a quick primer.

     It's possible it was a genius destabilizing operation run by Western intelligence agencies but there was an organic nature to it too. Since all Western media is a propaganda operation {and not just the news), I mean all of it. From the Kardashians to the Walking Dead and all the commercials in between, it's all a kind of mind control telling you what to aspire to, what to fear, what is good or bad in life and in our case, who the bad guys are. It's all controlled opposition aimed at priming the public. The Arab Spring story went something like this. Some Tunisian bazaar merchant set himself on fire due to some injustice. A local authority figure made him buy a permit to continue selling whatever bullshit  a street vendor in Tunisia would sell to tourists. Who knows why? But some local official took away his livelihood and he lost his mind. That I can understand. Any man can. But setting yourself on fire to make a point is a drastic maneuver and does tend toward making the man with the match a martyr for a cause. And that's exactly what happened. 

    For many reasons, this act of self-immolation led to a wave of popular uprisings that destabilized every country in North Africa but especially Egypt. That was the biggest domino to fall but surely an unintended target. Israel and the US liked Mubarak but not his people, the Egyptians. Sinai is a hard, calcine forbidden desert but it is a point of contention. The Americans were paying Mubarak a billion a year to keep his population under control and not cause trouble for the Israelis. The most important thing for them was his zealous efforts to police the border with Gaza and make sure other Arab nations or shady arms dealers could not funnel weapons into Gaza, especially not shoulder mounted AA weapons that could challenge Israeli air superiority every time they bombed a hospital they claimed had a bottle rocket in the basement.

   Nobody expected the Arab Spring to get out of the control. Sure the CIA, Mossad, MI5 and whatever the French call their intelligence agencies took advantage. Maybe they poured fuel on the fire. The point being, the Arab Spring spiraled out of control. It wasn't exactly engineered but it wasn't organic either. Egypt got destabilized simply by the fact that every house in North Africa and the Middle East by 2010 had a satellite dish on their roof. And the population were not swallowing the local line of bullshit their media propaganda were pumping out. They could see the world outside and realize they were getting fucked over big time. So there were riots. Tanks on the streets did nothing, not even bullets could quell the uprising in Cairo.


The Arab Spring.


  Mubarak, the man on the Western payroll had nowhere to run and had to stand trial. Suddenly he got sick. Seriously, this shit reads like a bad novel. The revolutionaries put him on trial and first fined him 33 million dollars and locked him up in a jail cell where he suddenly had a heart attack (who wouldn't)? It's possible that a bunch a hard hitting Bedouin motherfuckers went medieval on his ass, but either way, Egyptian prison didn't agree with him.

   Interestingly, the Israeli's offered him asylum (he was, after all, on their payroll via the US anyway) but the Egyptian courts put him on trial again anyway and grabbed another 22 million from his bank accounts before things started going to absolute shit on the streets of Cairo again. This was almost certainly funded by foreign money (the usual suspects), but even so, it turned out that just because the Muslim Brotherhood might be good at praising Allah and fooling some of the people all of the time didn't mean they were any good at running a bus line to the Pyramids never mind running a whole fucking country. Egypt went to shit and Mubarak got free, ran for the hills and is still alive somewhere living far better than you or me.

  But lets slow this story down a bit.

  The Arab Spring was getting out of hand. With Mubarak gone and the Muslim Brotherhood taking control of Egypt that made Israel's strategic position precarious. Every AIPAC activist was funneling millions to every Congressman and Senator. Something had to be done to stop this threat to Israel's southern border and the Gazan infiltration point.

   And so Western nations arrived at the usual answer when tact is difficult and bombs are cheap.

   "Let's blow the shit out of everything in North Africa."

   And so Libya became the target in the cross hairs of Western avarice.

   The second richest country in Africa, run by a dictator and strongman, Gaddafi. (go ahead and tell me a Middle East country that isn't run by a strongman) and for that matter, go ahead and tell me any country not run by a person with a motivation that Nietzsche called the "will-to-power.". Democracy these days is just something to make you feel good; like you have some say in the ways of the world as you deposit your voting slip. Meanwhile, we're all run by strongmen or these days, strong women. Who cares who fronts the organization, man or woman, what matters is the power behind the person in the suit they push in front of the TV cameras.

   But I've digressed.

   Libya.

  Here's who attacked. For no reason other than to destroy an oil rich success story on the Mediterranean. This is your tax money at work.



Your taxes at work.



   What did Libya do to deserve this international coalition of death via air power?

   Now we must enter more darkness and things they'll never tell you on TV.

   Libya, committed the crime of going against the international system. They hoarded gold and exported oil. Sure, Gaddafi got rich and let's face the man was no saint. But every Libyan newlywed got a house. Gaddafi used Libya's oil wealth to pipe aquifers and turn the desert into farmland. Libya had the highest literacy rate in Africa and free education; free education to the point that any gifted Libyan could get their university fees paid even in foreign universities like Oxford or Harvard. Think about that while you're paying off your student loan for the next 20 years.




    Gaddafi was even floating the idea of an African investment bank, and a gold backed currency, that meant oil sales for gold instead of paper and that's the kind of talk that gets you killed real quick.


    


    
      What is Libya today?

     A nightmarescape worse then South Chicago with open air slave markets and rival rebel factions roaming the streets in pick-up trucks brandishing heavy machine guns and battling rival gangs for local control from Tripoli to Benghazi. Meanwhile the population hide in their houses. Thanks Obama. Thanks Hillary Clinton. Thanks Sarkozy. International criminality dressed as a leader in a suit and painted for you by a bought and paid for media industrial complex so as to have a "nice person" to put in front of the TV cameras and read bullshit off the teleprompter.

   That's the absolute state of modern "democracy".

    Far, far from the ideals of the ancient Athenians.

   The Syrian Civil War started out as an opportunistic attempt by Western powers to get rid of Assad. Since Libya went down so easily, foreign think-tanks and NGOs got high on the idea that if you pump enough bullshit into a satellite dish and funnel enough arms to a hired local militia, (ISIS, AL Nusra, Al-Qaida) whatever; and then feed your home population a series of gruesome beheading vids just to make sure they know who the bad guys are; you can take over a whole country for less cash than the daily profits of Google or Apple.

   With total media control, you've got an enemy your domestic population hates while at the same time a private army you can use to run roughshod all over the Middle East. Also, you've got a bunch of crazies who'll eviscerate and mow down hundreds in Paris, stab their way across London, mow down hundreds with trucks in France and Germany and generally keep the public focused on who the bad guys are before they wheel out the piano guy who sings "Imagine" at the candlelit vigil while the citizenry holds flowers and gets misty eyed while doing absolutely fucking nothing about their own government causing all this mayhem in the first place.

   Anyway, the Syrian Civil War started out as a foreign funded protest movement in Deraa. And by foreign funded I mean container loads of weapons shipped from the newly failed state of Libya. That's the fun thing about chaos and failed states.. Anyone can do anything and not only avoid scrutiny but straight up commit every crime imaginable and have no authority bat an eyelid. Because there is no authority.

That's what chaos is. 

And chaos was coming to Syria...


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99 – Things I Never Knew About Las Vegas Until I Ran a High-Roller Suite

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99 points, 67 comments

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Caves all the way down

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Do psychedelics give access to a universal, mystical experience of reality, or is that just a culture-bound illusion?

By Jules Evans

Read at Aeon

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  The Syrian Civil War 2018: Chaos is a Ladder    Is anybody...

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  The Syrian Civil War 2018: Chaos is a Ladder










    Is anybody else interested in a way to end the Syrian Civil War and make the threat of WWIII go away for a few more years? 

    Surely, I'm not alone here unless I'm some kind of sociopath.

   Let's call me an optimist said nobody ever but I've became one these hopeful idealists over the last few months because I think I've figured out a way to end a potential world war. And it doesn't involve a radical solution. 

   How about we just let Assad win the Syrian Civil War? 

   You want peace? You want ISIS dead? You want an end to the refugee crisis that has displaced 14 million people and killed 600,000 in cold blood?

  If so, Assad is your man. He has already practically won his war. His forces have gained most of Syria back. It's a kind of peace treaty they'll never advertise on TV because it's called victory. Victory NBC, CBS, SKY and all of the other corporate media cannot say because fuck you.

   Yes, there are a few outstanding pockets of "Sunni groups", "Kurdish opportunists", Turkish encroachments, Israeli consolidation of the contested Golan etc and still more "moderate rebel" Islamic front groups funded and receiving money and weapons from the US/UK/France/Saudi Arabia but, in spite of all of this foreign aid, with Russian and Iranian intervention, the mild mannered eye doctor Bashar al-Assad has won the war anyway.

   In 20 years the historians will write about it honestly.

    Here's a man, Bashar al Assad, an eye doctor,  who never really wanted the top job in Syria but got it anyway because his older brother Bassel, groomed for the job by his father offed himself in a car crash because rich kids and a supercharged Mercedes rarely mix. The Assad father Hafez, the Middle East strongman on par with Gaddafi and Saddam who 'eliminated' enough people via whatever means necessary to secure his lineage chartered a career path for his sons. Bashar may not have been the first choice but fate is fickle, sometimes cruel and often lays waste the best laid plans of mice and dictators. And so here the lispy eye doctor sits, the face of evil on Western media and Trump is telling you weakly on Twitter without much  conviction that this is the bad man, Assad is "animal" dictator that must be destroyed. 

    Why exactly?

    Because using gas kills children unfairer than indiscriminate artillery strikes?

    We all know now that those gas attacks never happened.

    Then as now, so what?

    Apparently all you've got to do to survive a gas attack in Syria these days is be male. If you're a woman or a child you're fucked. If you're a child you're getting badly administered CPR, a water hosing and you're going on the Internet. Social media it seems, has transformed 21st century warfare into battle via dead baby. It's not new but it's instant and wars by emotional manipulation of your populace means that that very conflict is suspect.

    The gas argument fallacy has been deconstructed all over the Internet. So I won't even bother here. The moral case for these strikes is a mainstream media construction. US and UK media claim it's punishment for gas. The gas used was chlorine. We have no independent verification but lets take the TV talking heads at their word. Chlorine is bad. It was used on the Somme in 1917. Yet a trip to your local hardware store will yield you a gallon of bleach and ammonia for twenty bucks that can release a lot of gaseous chlorine. (PS never attempt or do this.) However the question must be asked, with the surveillance state in full effect, are we all now potential mobile chemical weapons facilities on our drive to Home Depot?



    There's an argument circling the Earth that even if Assad didn't 'barrel bomb' the chlorine bomb he still deserves the standoff missile attack because of who he's allies with. Russia, somehow, has been ginned up by US media as the "enemy" because Hillary Clinton didn't win the election. "The Russians did it" buys into a fear a lot of older post war baby boomers have (older people who actually vote) and see this narrative as plausible because the Cold War was their youth and death via nuclear fire was a very real thing. The legacy media are selling them an idea of Syria being the bad guys because chemical weapons cross a red line. Never mind the fact that the leader of the county there (Assad) is destroying ISIS along with Russia and winning the war against (ISIS/Al-Qaida) but this is bad now because gas?

   Yes, it's all very confusing.

   Gas in war drives civilian populations insane. It's a trigger word. If your child in a war zone dies by air burst artillery (a common occurrence in Aleppo or Damascus) that means such munitions pepper your child with ball bearings travelling at Mach 3. Fucking horrible and unthinkable. You'd think. But let the enemy open a barrel that spreads some weaponized Clorox and now you've got an international casus belli on your hands. Civilian populations in the US/Europe hate gas irrationally because they've never been under fire via bullets or kinetic blast energy (correction: Las Vegas shooter, Paris Bataclan attack, Manchester Ariane Grande bomber etc etc) but the usual response is to wheel out a piano, have a street musician sing "Imagine", have a candlelit vigil for the dead, post it on Facebook and go home and forget the chaos. Even after you add up the actuary tables on war deaths in Syria you soon realize that chlorine or sarin gas is about the most ineffective way to kill people in a war since Zeppelins.


Assad's 'barrel bombs' are evil because Raytheon did not manufacture them. GBU-28 is the sanctioned baby killer.


    But enough of this. Lets get to the geopolitics.

    SYRIA / DAMASCUS

    Damascus is critical. Saudi Arabia has Mecca and Medina and the Israelis have control of the Dome of the Rock (technically) and these are the three most sacred places in Islam. But I'm with T.E.Lawrence here in my belief that Damascus is the capital of what's left of the Arab world. If unification of the aggrieved Arab peoples could ever be achieved, it'd happen in Damascus. It'll never occur now in our post modern world and the Assad family were no help, running a police state against dissenters and all citizens. And yet Damascus, a true multicultural city consisting of Sunnis, Alawites (Assad's ruling tribe), Kurds (the largest minority), Christians but also Armenians, Circassians, Shia and a small Greek Orthodox community is the diverse city the Euros crave.  If Assad (the strongman) falls like Gaddafi did in Libya, those who have not fled understand that the Islamic sharia horde at the gates waiting will not be sympathetic to them. The nightly news will become a steady stream of gore porn. If it's ever even shown. Nobody on TV shows the open air slave markets happening right now in Libya after what NATO did by deposing Gadaffi.

   This is why the Syrian Army fights like patriots. Not for Assad. Not even for Syria. But because the alternative is an enemy willing to go medieval on them and their families. No man in a trench dies for his country, he dies for the guy next to him. Ghouta is the last suburb in Damascus the Syrian forces have not taken. Why? Because urban combat is a shit show with at least a 3 to 1 kill ratio in favor of those holed up in fortified buildings. Why assault if you don't need to? It's far easier for the Syrian Army to surround the pocket and wait. Yes there is fighting but time is the true enemy of the besieged going all the way back to Caesar at Alesia. Why force the issue with gas now and turn the world against you when entropy is your friend and calories make an army?

   Sometimes in war all you need to do is wait for victory.



Siege is the oldest act of war. Risk in battle is for young men and fools. Great generals know the ultimate weapon.
Patience.
     TRUMP / USA

    Easily the most interesting President since... since nothing you or I can remember. A reality star and a knife fighter in the NYC real estate market. Also, an insufferable narcissist, a natural showman and a gifted salesman. He campaigned on a populist agenda, wrecked the Republican party line by charisma alone and promised some simple, straight up honest values that most traditional Americans felt in their gut made sense. Chief among them was the dismantling of surplus US military bases, no foreign wars, a policy of America first, a return of American manufacturing, a southern wall to stop the influx of cheap labor into the US that undermines the US working class, repeal of NAFTA to stop Mexican sweatshops dumping $5 sneakers and jeans into US stores for a 5000% mark up and a renegotiation with China on trade deals that have flooded the US with cheap sweatshop Walmart plastic that made China rich in return for subsidizing the American working poor. For profit.

   Globalism in a nutshell right?

  The Trump campaign promised a return to tradition for a lost Americana and his voters hit the like button. Of course, none of it happened. Trump is a political neophyte with no knowledge of the the world outside the cut throat Manhattan real estate market and his narcissism led him down a very dark path. He learned on day one that the US Presidency is not a power position like a CEO. It's a PR job for a guy in a suit and it's been turmoil for him since day one. The 'deep state' is a term being bandied about a lot these days but as with everything, there's an element of truth to it. Trump has no clue of geopolitics, nuance, international relations, political science and the judicious use of American power. His ghost written "Art of the Deal" book is about as useful to him now as a compass on a desert island surrounded by cannibals. Who cares where true north is? He and the people around him have fired just about everyone who engineered him into the Oval Office and now John Bolton, arch neocon, is his national security adviser. Trump is in above his head now and if he doesn't want to get JFK'd, he's going with the neocon agenda.

    And to stop the constant bad press, the Mueller investigations, to prove he's not a Russian agent, to appease the hostile press and to mitigate whatever dirt they've found after the raid on his lawyer's offices that could ruin him and the Trump brand; he's obviously had to sell out his base and make a deal.

    And so the Tomahawks flowed on some Syrian airbases.

    To be fair, the attacks was pure theater. Even less damaging than the last one. It's biggest effect was to light up the Syrian AA grid which around Damascus is the fifth largest AA defense in the world. Though a lot of it is mobile, the intel on those static radars is useful to the Israelis who are already complaining that the attack was a fraction of what was needed.

   

Possibly the worst optics for a US President since the Zapruder tape.



     ISRAEL / NETANYAHU

    Let's face it, Israel wants Assad gone. Assad is the last surviving member of a now defunct political movement known as the Ba'ath Party. Nationalism these days has become a dirty world everywhere and pan Arab unity has been crushed from North Africa to Mesopotamia. 

      The strategic analysis of Syria for Israel is clear. They feel under threat and much of it is their own fault and a result of their own hubris. Iran is their real enemy. When they get their nuke, theater parity will have been achieved with Israel's 200+ nukes. The Iranians will never use it of course because for one, they'd be glassed back to the Stone Age, but it's very existence is the balance in the region the Israelis cannot accept. An Iranian nuclear weapon would be Iran's Fleet in being ;not for use but for theater denial.

    But we've jumped ahead here, let's step back a bit.

    Post 9/11, Iraq was Israel's bogeyman. Saddam Hussein was paying $20k to the family of every Palestinian suicide bomber. Hussein fired Scud missile at Tel-Aviv during Gulf War I. So the Israeli K Street lobbying wing in Washington and their US media operation went into overdrive post 9/11 and linked Iraq to the Trade Center attacks and pushed the WMD narrative on the news networks 24/7. And with the Bush cartel in the White House, it was easy pickings to sell a war in the desert.





    
     The irony of this is that though Saddam was dug from a hole and hung in a basement on the Internet what was the geopolitical gain? The law of unintended consequences did a number on these neocons that basically handed over, after 5 years of US public war fatigue and hundreds of US soldiers dying in IED attacks, the diplomats/Obama Administration ended up handing over Basra and Baghdad to Shia leaders in the name of peace and withdrawal of US forces. All of these leaders Iranian agents and financed by Tehran. The Israelis, in their zeal to rid the world of Saddam and using the US military to do it for them, inadvertently handed over half of Iraq to Iran. And the result now is a supply route from Tehran, across Syria to Hezbollah in Lebanon.

   In military terms, this is called encirclement via the northern flank.

   With Assad's victory in Syria, the supply route is assured. And this is no small thing. In 2006 the IDF got their nose bloodied trying an incursion into Lebanon but Iranian supplied Hezbollah held back that attack with entrenched heavy infantry and the latest shoulder mounted anti tank and anti air weaponry. That was 12 years ago. Think for a minute what Hezbollah might have today? Do they have a two stage missile like the Iranian Shahab I/II that can easily hit Tel Aviv but why bother with soft targets? What about if they launched everything they've got at the Israeli nuclear plant at Dimona? A bunch of fanatics in Southern Lebanon could theoretically, via a lucky but successful shot, turn southern Israel into Mad Max: Fury Road.

   Of course, we're talking WWIII by this stage but remember WWI started, ostensibly, because an Archduke's driver took a wrong turn down a side street.

   For the Israelis, the fear is real and they will do anything to perpetuate the war in Syria until Assad dies. For them, chaos in Syria is a ladder not only to break hostile encirclement but also to permanently annex the Golan Heights and secure the drilling rights via Genie Energy for the oil that has been discovered there.

   Ever notice too how ISIS, the hardcore fucks that behead people on camera, throw gays off buildings in front of crowds, chop children's hands off for stealing an apple from a market, and drive around in new Toyota trucks supplied through a myriad of shell companies and international shadiness. Who pays for all this? Where does the money trail lead to where it all came from?

   Ever wonder why ISIS has never once tried an attack on Israel which is next door to Syria and the sworn enemy of all Muslim fundamentalists? Ever wonder why Israel gives medical care to these people? ISIS, more often than not, seems to create chaos and destabilize countries and regimes hostile to Israel, Mossad and CIA interests. 

   To conclude, for Netanyahu and the hard right in Israel, Israeli goals are simplen not secret and published in Haaretz and the Jerusalem Post Op Eds weekly.

  • Assad must fall to prevent northern encirclement of Israel via Lebanon.
  • North Korea must fall so they don't sell a nuke to Iran or give them one for chaos' sake
  • Iran must be degraded, sanctioned and locked out of the international financial system (SWIFT) before they make their own nuke by themselves
   For Israel, total chaos in the Middle East is good.

   Stable, prosperous and cohesive countries are bad.

   And Syria is but a single rung. Because chaos is a ladder. 


Latest live map here.




    RUSSIA / PUTIN

   Russia has multiple geopolitical aims in the preservation of Assad and the cohesion of Syria. But let's keep it simple. Russia wants their Mediterranean naval base at Tartus and in 2015 signed a 50 year lease on the air base at Khmeimim outside Latakia giving them permanent air strike ability in the region. Russia under Putin is a product of Soviet era realpolitik and along with China wishes to contest NATO's idea of a unipolar world order.

   Syria is the nexus point at which Russia can contest NATO at the least possible cost.

   In Russia's estimation, NATO broke its gentleman's agreement with Russia in the 1990s not to encroach into Eastern Europe in exchange for German unification and "peace". But then, from the mid 1990s onward NATO, sensing weakness and knowing Russian leader Boris Yeltsin was drunk most of the time and barely survived a coup, encroached into Eastern Europe, and allowed Poland, Hungary, the Czech Republic, Latvia, Lithuania all to join NATO thus kicking the Russians while they were down. 







   Putin, a product of KGB era 70s/80s Soviet dominance (he would call it pride) never forgot this. For him, and Russian elites generally, Ukraine opening talks to join NATO was the final straw. Nothing in the Russian soul could allow this. The vast and endless grasslands that held back Napoleon and Hitler from European aggression have always been Russia's buffer zone. NATO in Ukraine on their doorstep was the final straw. And so Putin took Crimea because it could be taken, buffered zoned Donetsk and moved tanks to the border. And won. And NATO could do nothing because who wants WWIII over a Black Sea port and Sevastopol, a second rate holiday seaside town?

  Syria presented Putin with a chance to drive a knife into NATO and twist it into the heart of Western attempts to consolidate the mess they made in the Middle East after Iraq. He had bases in Syria, Tartus especially, and the Syrian leadership has been a consistent buyer of Soviet/Russian military hardware for decades. So he decided to allocate some aircraft and special forces and destroy ISIS, something the US, UK and France had been claiming to be trying to do since 2012.

   The Russians did the job in a matter of months with 30ish aircraft, most of them 3rd and 4th generation Cold War era machines. That's all it took to send the idiot beheaders in Toyota trucks back to the desert. It makes you wonder what the Obama Administration and Israelis were doing with all that high tech drone weaponry from 2012 to 2016 v ISIS while achieving nothing except the occasional wedding party massacre.

   And finally, there's the financial aspect.

   It always comes back to the money right?

   If Syria were to fall under the control of Sunni/ISIS mercenaries on the Saudi payroll with CIA backing, they could be persuaded via financial incentives to swap their Toyota trucks for swimming pools and harems; then, during the relative 'peace' a rival natural gas pipeline could be built from Qatar's South Pars gas claim (Iran contests this claim) in the Persian Gulf, through Iraq and Syria into the Mediterranean. This would destroy Russian owned Gazprom's monopoly on the European natural gas market and wreck Russia's economy worse than lower oil prices and sanctions already did since 2015.

   The longer the Syrian Civil War continues, the safer Russian energy exports shall remain.

   Because chaos is a ladder.


   IRAN v SAUDI ARABIA

   Iran's goal right now is to stay off the front pages of Western newspapers, supply its allies in the region, improve its air defenses around its critical infrastructure (with Russian equipment), play nice with the Europeans and maintain the nuclear deal they made with the Obama Administration that has driven the Israelis insane. The nuclear deal did not touch the Iranian missile program and every neocon in the Trump Administration is scouring the fine print looking for a way to tear up that nuclear and put military strikes back on the drawing board. This may happen in May when the deal comes up for review.

   But it won't be easy.

  Since the lifting of sanctions, the Iranians and Europeans have made oil and energy deals that are near impossible to tear up without international arbitration through the WTO.

   Iran is also involved in a bitter proxy war with Saudi Arabia in Yemen and it's driving the Saudi royals insane. Iran is supplying the Houthi rebels there with Russian ATGMs that are wrecking the Saudi military's tanks and APCs. In return the Saudis are starving Yemen to death. No pictures of starving kids on the nightly news of course. No grainy videos of women getting beheaded every weekend in stadiums in Riyadh for the crime of adultery. I'll spare you the LiveLeak videos. Suffice to say, war is hell and people die every time you fill up your gas tank and you might think you give a fuck but you can't because you're late for work.

   Welcome to the oil business.

   The purge of the Saudi royals went almost unnoticed in Western media last November. Those disappeared princes included major shareholders in 20th Century Fox, Citibank, Apple, Twitter and Lyft. The new Crown Prince bin Salman is on a roll of power consolidation and he's got the backing of the US and Israel and $350 billion in new war toys. He hates Assad, is on board with supplying the "moderate rebels" with arms and is playing bending ball with the West better than Beckham. And yet he still can't decisively win in Yemen because money can buy you fancy tanks but never zeal. That's a price only soldiers know. And his captive population do not make for a good fighting force.

   Iran meanwhile, despite its sanction induced economic woes has one of the highest educated populations per-capita-income in the world. For the Saudi royals, infinite wealth can buy you only so much and therefore their new leader has done the unthinkable. He has aligned himself with the Jews. This is something his population would never accept and only constant police state brutality will maintain order and contain this sentiment. 

   If the Houthi rebels can start landing missiles at Saudi Aramco which they recently did then we're looking at darkness beyond the scope of this article. Not least because of the disruption to oil tankers Yemenis could be called on to attack if Iran where to come under attack. In fact it is Iran's unconventional forces from Lebanon, to Syria and Iraq that allow the Ayatollah both plausible deniability and instant strike capability.

  Of course, Iran is playing a dangerous game here. But so is everybody else.

  Chaos is not a ladder in the Middle East.

  Chaos is the snake.
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If You Say Something Is “Likely,” How Likely Do People Think It Is?

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People use imprecise words to describe the chance of events all the time — “It’s likely to rain,” or “There’s a real possibility they’ll launch before us,” or “It’s doubtful the nurses will strike.” Not only are such probabilistic terms subjective, but they also can have widely different interpretations. One person’s “pretty likely” is another’s “far from certain.” Our research shows just how broad these gaps in understanding can be and the types of problems that can flow from these differences in interpretation.

In a famous example (at least, it’s famous if you’re into this kind of thing), in March 1951, the CIA’s Office of National Estimates published a document suggesting that a Soviet attack on Yugoslavia within the year was a “serious possibility.” Sherman Kent, a professor of history at Yale who was called to Washington, D.C. to co-run the Office of National Estimates, was puzzled about what, exactly, “serious possibility” meant. He interpreted it as meaning that the chance of attack was around 65%. But when he asked members of the Board of National Estimates what they thought, he heard figures from 20% to 80%. Such a wide range was clearly a problem, as the policy implications of those extremes were markedly different. Kent recognized that the solution was to use numbers, noting ruefully, “We did not use numbers…and it appeared that we were misusing the words.”

Not much has changed since then. Today people in the worlds of business, investing, and politics continue to use vague words to describe possible outcomes. Why? Phil Tetlock, a professor of psychology at the University of Pennsylvania, who has studied forecasting in depth, suggests that “vague verbiage gives you political safety.”

When you use a word to describe the likelihood of a probabilistic outcome, you have a lot of wiggle room to make yourself look good after the fact. If a predicted event happens, one might declare: “I told you it would probably happen.” If it doesn’t happen, the fallback might be: “I only said it would probably happen.” Such ambiguous words not only allow the speaker to avoid being pinned down but also allow the receiver to interpret the message in a way that is consistent with their preconceived notions. Obviously, the result is poor communication.

To try to address this type of muddled communications, Kent mapped the relationship between words and probabilities. In the best-known version, he showed sentences that included probabilistic words or phrases to about two dozen military officers from the North Atlantic Treaty Organization and asked them to translate the words into numbers. These individuals were used to reading intelligence reports. The officers reached a consensus for some words, but their interpretations were all over the place for others. Other researchers have since had similar results.

We created a fresh survey with a couple of goals in mind. One was to increase the size of the sample, including individuals outside of the intelligence and scientific communities. Another was to see whether we could detect any differences by age or gender or between those who learned English as a primary or secondary language.

Here are the three main lessons from our analysis.

Lesson 1: Use probabilities instead of words to avoid misinterpretation.

Our survey asked members of the general public to attach probabilities to 23 common words or phrases appearing in random order. The exhibit below summarizes the results from 1,700 respondents.

W180614_MAUBOUSSIN_HOWPEOPLE

The wide variation of likelihood people attach to certain words immediately jumps out. While some are construed quite narrowly, others are broadly interpreted. Most — but not all — people think “always” means “100% of the time,” for example, but the probability range that most attribute to an event with a “real possibility” of happening spans about 20% to 80%. In general, we found that the word “possible” and its variations have wide ranges and invite confusion.

We also found that men and women see some probabilistic words differently. As the table below shows, women tend to place higher probabilities on ambiguous words and phrases such as “maybe,” “possibly,” and “might happen.” Here again, we see that “possible” and its variations particularly invite misinterpretation. This result is consistent with analysis by the data science team at Quora, a site where users ask and answer questions. That team found that women use uncertain words and phrases more often than men do, even when they are just as confident.

W180614_MAUBOUSSIN_MENAND2

We did not see meaningful differences in interpretation across age groups or between native and nonnative English speakers, with one exception: the phrase “slam dunk.” On average, the native English speakers interpreted the phrase as indicating a 93% probability, whereas the nonnative speakers put the figure at 81%. This result offers a warning to avoid culturally biased phrases in general and sports metaphors in particular when you’re trying to be clear.

For matters of importance where mutual understanding is vital, avoid nonnumerical words or phrases and turn directly to probabilities.

Lesson 2: Use structured approaches to set probabilities.

As discussed, one reason people use ambiguous words instead of precise probabilities is to reduce the risk of being wrong. But people also hedge with words because they are not familiar with structured ways to set probabilities.

A large literature shows that we tend to be overconfident in our judgments. For example, in another survey we asked respondents to answer 50 true or false questions (for example, “The earth’s distance from the sun is constant throughout the year”) and to estimate their confidence. More than 11,000 people participated. The results show that the average confidence in answering correctly was 70%, while the average number of questions answered correctly was just 60%. Our respondents were overconfident by 10 percentage points, a finding that is common in psychology research.

Studies of probabilistic forecasts in the intelligence community stand in contrast. More-experienced analysts are generally well calibrated, which means that over a large number of predictions, their subjective guesses about probabilities and the objective outcomes (what actually occurs) align well. Indeed, when calibration is off, it is often the result of underconfidence.

How do you set probabilities intelligently?

When the odds are ambiguous, unlike in a simple gambling situation (where there’s a 50% chance of heads or tails), you are dealing with what decision theorists call subjective probabilities. These do not purport to be the correct probability, but do reflect an individual’s personal beliefs about the outcome. You should update your subjective probability estimates each time you get relevant information.

One way to pin down your subjective probability is to compare your estimate with a concrete bet. Let’s say that a competitor is expected to launch a new offering next quarter that threatens to disrupt your most profitable product. You are trying to assess the probability that the introduction doesn’t happen. The way to frame your bet might be: “If the product fails to launch, I receive $1 million, but if it does launch, I get nothing.”

Now imagine a jar full of 25 green marbles and 75 blue marbles. You close your eyes and select a marble. If it’s green, you receive $1 million, and if it’s blue, you get nothing. You know you have a one in four chance (25%) to get a green marble and win the money.

Now, which would you prefer to bet on: the launch failure or the draw from the jar?

If you’d go for the jar, that indicates that you think the chance of winning that bet (25%) is greater than the chance of winning the product-failure bet. Therefore, you must believe the likelihood of your competitor’s product launch failing is less than 25%.

In this way, using an objective benchmark helps pinpoint your subjective probability. (To test other levels of probability, just mentally adjust the ratio of green and blue marbles in the jar. With 10 green marbles and 90 blue ones, would you still draw from the jar rather than take the product-failure bet? You must think there’s less than a 10% chance the product won’t launch.)

Lesson 3: Seek feedback to improve your forecasting.

Whether you’re using vague terms or precise numbers to describe probabilities, what you’re really doing is forecasting. If you assert there’s “a real possibility” your competitor’s product will launch, you’re predicting the future. In business and many other fields, being a good forecaster is important and requires practice. But simply making a lot of forecasts isn’t enough: You need feedback. Assigning probabilities provides this by allowing you to keep score of your performance.

Opinion writers and public intellectuals often talk about the future, but typically they don’t express their convictions precisely enough to allow for accurate performance tracking. For example, an analyst might speculate, “Facebook will likely remain the dominant social network for years to come.” It’s difficult to measure the accuracy of this forecast because it is subjective and the probabilistic phrase suggests a wide range of likelihoods. A statement like “There is a 95% probability that Facebook will have more than 2.5 billion monthly users one year from now” is precise and quantifiable. What’s more, the accuracy of the analyst’s forecast can be directly measured, providing feedback on performance.

The best forecasters make lots of precise forecasts and keep track of their performance with a metric such as a Brier score. This type of performance tracking requires predicting a categorical outcome (Facebook will have more than 2.5 billion monthly users) over a specified time period (one year from now) with a specific probability (95%). It’s a tough discipline to master, but necessary for improvement. And the better your forecasts, the better your decisions. A few online resources make the task easier. The Good Judgment Open (founded by Tetlock and other decision scientists) and Metaculus provide questions to practice forecasting. Prediction markets, including PredictIt, allow you to put real money behind your forecasts.

The next time you find yourself stating that a deal or other business outcome is “unlikely” or, alternatively, is “virtually certain,” stop yourself and ask: What percentage chance, in what time period, would I put on this outcome? Frame your prediction that way, and it’ll be clear to both yourself and others where you truly stand.

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