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Yeah, whatever that is:

Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.

“This is completely new and very much simpler than anything that has been done before,” said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work.

Also some good stuff at the HN discussion.

The idea is that physicists (starting with Feynman) have been using some incredibly complicated math to calculate the scattering pattern of particles after a collision. These initial calculations started out with Feynman drawing a picture of what the scatter pattern might look like then calculating its likelihood. Then draws another one and calculates that likelihood. Thousands of times. 500 pages of algebra, we’re told.

And now some physicists have figured out a standardized shape whose volume calculation replaces those 500 pages of algebra with a single step.

Using geometric objects to simplify very complicated calculations is an old and breathtaking trick. I first came across it studying the probability of events under constrained uniform distributions. I can trade in a triple integral for drawing a couple rectangles and a trapezoid? Deal.

Calculus is painful, drawing pictures is not. And yet they’re the same thing. Which is mind-blowing, and shows that math really can (should!) be simple.

Anyway, the fact that the amplituhedron works so well has all kinds of wacky implications for physics that I don’t really understand, and that even the real experts can only speculate about. My take-away is how neat it is that a visual metaphor can drastically reduce the apparent complexity of some physical phenomenon.

Social scientists everywhere sigh with envy.

Plucking geniuses from the slums of Mongolia:

How does a student from a country in which a third of the population is nomadic, living in round white felt tents called gers on the vast steppe, ace an M.I.T. course even though nothing like this is typically taught in Mongolian schools? The answer has to do with Battushig’s extraordinary abilities, of course, but also with the ambitions of his high-school principal. Enkhmunkh Zurgaanjin, the principal of the Sant School, was the first Mongolian to graduate from M.I.T., in 2009, and he has tried since then to bring science and technology labs to his students.

Note a few important preconditions:

1. Incredible ability
2. Internet connection
3. Mentor
4. MOOC

The first one is in abundance all over the world. This is the resource that lies untapped among billions of people. The second is the revolution, really. The third means that there needs to be a social infrastructure before genius can be unlocked. This takes time to build.

And the MOOC is the catalyst.

This is an excellent article on robots that help people. Check out these two quotes:

It is vital that a robot of this sort is not perceived as hostile, but as having its owner’s best interests at heart.

One way to do this is to give robots a defining human trait—the ability to make mistakes. Maha Salem, a researcher under Dr Dautenhahn, programmed a humanoid Asimo robot, made by Honda, to make occasional harmless mistakes such as pointing to one drawer while talking about another. When it comes to household robots, test subjects prefer those that err over infallible ones, Dr Salem says.

And this:

To interact smoothly with people, robots will also need “social intelligence”. It turns out, for example, that people are more trusting of robots that use metaphors rather than abstract language, says Bilge Mutlu, the head of the robotics laboratory at the University of Wisconsin-Madison. He has found that robots are more persuasive when they refer to the opinions of humans and limit pauses to about a third of a second to avoid appearing confused. Robots’ gazes must also be carefully programmed lest a stare make someone uncomfortable. Timing eye contact for “intimacy regulation” is tricky, Dr Mutlu says, in part because gazes are also used in dialogue to seize and yield the floor.

Two very different kinds of intelligence, from the perspective of a human.

A person who never makes mistakes about where things are might be considered smart in our society, one that does somewhat normal. On the other hand, a person with sloppy non-verbal communication is ruthlessly discriminated against and is probably constantly sparking unintended conflict, making a happy life impossible. Yet from a robot’s perspective the first is laughably trivial and the second unimaginably complex.

Which task do you think human intelligence evolved to perform? Maybe that’s why math class is so hard.

Nearly spit out my vermicelli today when I saw this chart:

What on earth is that about German house prices? Surely that’s an error. They cite Deutschebank, where I found this chart, which isn’t quite as dramatic, though the scales are different and perhaps even the variable being measured is different:

It does show a housing crash (of sorts) in 2005, though, which puts Germany completely at odds with English-speaking developed countries. Fascinating.

from a top comment on HN (funnily enough about a building right in the heart of the insurance world in London):

A developer hires an international ‘starchitect’ like Viñoly to design them an office block because the architects reputation for design helps them to get away with a larger building on the site and therefore get more net lettable area for their investment in land.

I don’t know anyone who works for Vinoly, I’ve no idea what it’s like to work for him, but I know other people who have worked in similar ‘gesture architecture’ practices and this is how it usually plays out:

The big boss will do a nice sketch of how he thinks a walkie talkie shaped skyscraper (or whatever shape is in fashion in the office) will fit on the site and then hand it off to a more junior member of staff to solve all the real problems. Meanwhile, he will have to go back to the international lecture/meet/greet circuit that pulls in the jobs and maintains their reputation for world class architecture.

The project team will then usually have a very tight deadline to produce the initial design, probably mostly drawn up by a team of recent architecture graduates who would be pretty low paid[1], and who will almost always end up working very long hours and weekends unpaid overtime to meet the deadline. Where the lead architectural practice is not based in the UK there will also be a local architect who will advise on local regulations, prepare the submissions for planning permission and generally deal with other regulatory authorities.

There will also be a large consultant team on a project of this scale. Probably consisting of two teams of civil engineers; one for superstructure and one for substructure. A geotechnical expert for the foundation design. A whole spread of HVAC engineers, probably separate mechanical, electrical, drainage and ventilation specialists. A facade engineer who specialises in problems specifically to do with the design of the glass cladding system. A fire engineer to design the fire escape strategy and help negotiate the fire fighting strategy with the local fire brigade. A vertical circulation engineer to design the lift and escalator strategy. A bomb blast engineer to model the effects of various bomb attack scenarios on the cladding and structure. A security consultant to advise on how defendable the building is and to design the cctv, active tramp deterrent systems 😦 etc. Finally a quantity surveyor will advise on how much this will all cost.

All of these people will have been consulted briefly, probably mostly by video conference, across a couple of time zones, before the planning permission submission[2]. All their requirements have to be juggled between the different disciplines by the architect. As an architect who has done services coordination on skyscrapers and international airports, I can tell you it’s not easy. One of the most frustrating things is that engineers from different disciplines don’t talk to each other, even if they are working for the same firm. On top of this, the time allowed to prepare the planning submission will be a few months at most, and a lot of the effort will be spent on optimising the design and more importantly the presentation strategy to get through the planning permission process.

Interesting discussion here on HN:

Guys, I am in Syria (specifically in Damascus). Seems war is rolling out. Most of the people are moving to border regions but I cant and I am a programmer worked as a remote dev for an Australian startup. But I am not sure how long I will be able to work living in Syria. I want move to Europe specially in Germany as the startup scene is booming in Berlin. 

Commenters are strongly discouraging the poster from going to Germany. Here is an excerpt:

As a war refugee my self, I urge you strongly to leave Syria now, for the love of god no matter the price, buy those tickets and get the hell out of there and far away as possible, Sweden, Canada, Australia. (Not Germany, France, Italy, USA, Turkey they all suck.)

Where would you go if you had to leave? It’s a question I’ve never considered but having (lightly) tangled with immigration authorities in a few different countries I can say the problem is a scary one.

One’s immediate instinct is to go for the biggest western country available. That’s where the economic upside is, after all, and one can nearly be guaranteed a community of distant friends/relatives that speak your native language. 

Of course, these communities drive native denizens nuts and strain various norms and institutions in the target country. The political backlash can be unpleasant to watch for liberally-minded folks. 

And how about that he works for an Australian startup? The economic magnet of a USA pulls somewhat less strongly in a world where a Syrian can boast of such a job. So pick a rich country with good telecoms infrastructure, lots of English and a political mood favoring a marginal increase in immigration. And hope that none of those things change.

With the option to use GPS to do our wayfinding for us, it might seem like we don’t have much need for mental maps anymore. But according to Veronique Bohbot, a neuroscientist affiliated with McGill University and the Douglas Institute who studies spatial memory and navigation, the process of generating mental maps also plays a role in activities that have nothing to do with getting to work. Becoming overly reliant on GPS and letting that skill atrophy, she and others suggest, might actually be bad for us. “It’s important for people to take responsibility for their health — including their cognitive health,” said Bohbot. “We can’t just take the back seat.”

more here.

What would you do with $5? Via Quora.

The best performing teams actually ignored the $5 and just went out and made money. And at least one Quora commenter takes exception to this ‘rule breaking’:

While it may be a clever story to tell at parties, I think the whole thing had a lot of ethical/ procedural holes. I may be being nitpicky and missing the entire picture, but here goes:

My main gripe is that the students were told to make the $5 grow, not just make the most money they can in 2 hours. Yes the real world has no rules, but then you can’t impose rules and then go around and say, wait, if you followed the rules you’ll be last.

1. The bicycle repair story is the only story that I feel truly won in the spirit of the test. I’m assuming they bought the pump for the $5 and proceeded to use that to make their profits. Fair enough.

2. The ‘winner’ felt like cheating because they probably spent more than the $5 to contact and make the deal with the company before they even had the deal. Whether they were remunerated for their costs of making the commercial and selling the time at a later date is assuming they were allowed to take credit, in which case the $5 is irrelevant.

3. The restaurant idea, while within the confines of the problem is an ethical grey to black area. This may also be a culture-specific notion though. In India, this is called selling things ‘in black’. You can’t hoard a resource and sell it to the highest bidder – oh wait a minute… you CAN, but it is generally frowned upon and not congratulated. 😉

Finally, while the post did incite some creative processes in my head, it still left a sour taste in my mouth by seeing the parameters of the problem and ethics bent and shaped to suit the most glitzy ‘story’.

I agree that this is rule breaking behavior. I sympathize with the students who showed up Monday morning having diligently invested their $5 yet found the winning team simply sold their presentation time to an advertiser. Probably took them 10 minutes. Rule broken? Contest won.

And here’s psyblog:

Those who turned out to be the best entrepreneurs often had a history of being rule breakers in their teenage years. They were more likely to have smoked marijuana, to have bunked off school and even to have assaulted others.

But these aren’t your run-of-the-mill deviants. These are high status rule breaker/benders.

But this illicit aspect was also coupled with a very stable family background. Successful entrepreneur’s were disproportionately likely to come from families that were:

• high-income,
• well-educated,
•  and stable.

So we’re not exactly talking about disadvantaged youths here.

But is it Ok to ‘break the rules’ to make money? How about to get good grades? Should means to these ends be evaluated differently? Deep stuff. I first heard from Robin Hanson that the entire purpose of school may be to promote rule-following behavior (here’s a version of this argument) and so keep order in society.

Breaking certain rules is of course punishable under criminal law, yet remember this quote attributed to Balzac: “Behind every great fortune there is a great crime”; interestingly, the real quote (translation) is probably even more appropriate: “The secret of great fortunes without apparent cause is a crime forgotten, for it was properly done”. 

One possible definition of creativity (or leadership for that matter) is the selective breaking of rules (implicit or otherwise) which nobody realized could be broken without consequence. Under this framework, creativity is a garbage collection process for out-of-date rules in our society. 

So we value rule-following behavior even while we reward creativity. Crucially, creativity is hard and fails most of the time. Either a rule isn’t broken and the discovery is useless/boring or a rule is broken that we collectively judge should not have been and the creator is punished.

There’s also a hint of unfairness about rule breaking and fairness is a strong social norm, particularly with children. Schools can’t really both teach rule following behavior and reward rule-breaking behavior. We don’t want to be unfair to our children.

To me, then, teaching creativity in school is paradoxical. We still benefit from creativity, of course, so we should find ways of promoting it, but putting creative training in school will neuter its (necessarily) subversive side and confuse kids about what creativity really is.

Here’s a claim I hadn’t heard before but seems to be fairly well established: lead poisoning increases rates of violent crime and when you take lead out of gasoline, violent crime drops. Here’s Yglesias:

Here is a great piece (pdf):

Why don’t we want our children to learn to do mathematics? Is it that we don’t trust them, that we think it’s too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon, why not about triangles? I think it’s simply that we as a culture don’t know what mathematics is. The impression we are given is of something very cold and highly technical, that no one could possibly understand— a self fulfilling prophesy if there ever was one.

I never took a math course in college, which is extremely uncommon for people in my line of work. I had to forget how math was taught to me (and how stupid it made me feel) before I had the confidence to take actuarial exams.

The trouble is that math, like painting or poetry, is hard creative work. That makes it very difficult to teach. Mathematics is a slow, contemplative process. It takes time to produce a work of art, and it takes a skilled teacher to recognize one.

I say I never took a math course, but I did take a statistics course for business majors. I don’t think of this as a math course because, though I feel like I learned some formulas and some concepts, I never really understood them. The best I can say is that the course got me familiar enough with some jargon that when I had to later learn it for real (quite recently, in fact), it took a bit less time. Somewhat valuable, but not math.

The curriculum is obsessed with jargon and nomenclature, seemingly for no other purpose than to provide teachers with something to test the students on. No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a “mixed number,” while 5/2 is an “improper fraction.” They’re equal for crying out loud. They are the same exact numbers, and have the same exact properties. Who uses such words outside of fourth grade?

You start learning math concepts for real when you feel, deep in your mind, the frustration of the problem you can’t solve without them. When I started working full-time on reinsurance problems that required some serious math I picked up much of what I needed on Wikipedia (etc). When I finally started taking the exams I had a framework in my mind for how to use these very abstract tools. Without that, I’d never have passed anything.

In place of discovery and exploration, we have rules and regulations. We never hear a student saying, “I wanted to see if it could make any sense to raise a number to a negative power, and I found that you get a really neat pattern if you choose it to mean the reciprocal.” Instead we have teachers and textbooks presenting the “negative exponent rule” as a fait d’accompli with no mention of the aesthetics behind this choice, or even that it is a choice.

Here the author and I part ways a bit. Math to me is more a tool than a pure art. My art is finding a way of expressing economic/social phenomena (eg. insurance) in mathematical models. I am constantly faced with situations like: this thing happened once before and these other circumstances were present. How are the variables related and how do I think about the risk of this thing happening again?

I get the beauty of math, of course. I get that it’s pretty cool that the normal distribution is a generalization of simple coin-flipping. But in my world any useful application of the normal distribution (or any other in its family) has nothing to do with truth, in the mathematical sense. Business math steals a hodgepodge of tricks from real math when the properties of those tricks are (for no reason anyone understands) convenient. The business mathematician needs to understand the difference between convenience and truth. Many who forget this lose lots and lots and lots of money.

So pure mathematical exploration for its own sake doesn’t turn me on. That’s why I’m not a math geek. I’m a business geek. Those are the problems that fascinate me.

So it falls on the teacher to find problems that students care enough about to get them to learn the material. Sometimes this is hard, particularly for more advanced topics. Here I feel like most math instruction would do well to illustrate the history and historical context of the concept or formula or idea. When was it first discovered? By whom? What motivated the investigation? What was considered the state of the art in other, related, areas of math? What refinements came later? Usually each of these questions is answered in a way that will help a student learn the math.

It takes longer to teach it this way, of course. But for god’s sake let math be slow without making kids feel stupid.