daniel-levin

>> Though the proof has not undergone a rigorous peer review, experts expressed no concern over whether it would survive a critical look.

Such is people's confidence in Terence Tao - not unfounded by any means - but the result has not been peer reviewed yet. Tim Gowers has said that they'll be conservative in their review process [0] so any errors will probably be picked up quickly.

[0] https://gowers.wordpress.com/2015/09/10/discrete-analysis-an...

Many of the comments in this thread follow a similar pattern. They are all essentially derivatives of Goodhart's law. [0]

>> Once a metric becomes a target, it ceases to be a good measure.

It's quite useful to have a name - a label - for this sort of behaviour. In this case, the means by which VW optimised for this metric was crafty computer software! A metric is only as good as the cost of the unintended consequences that come with imposing it on people, in particular large corporations.

I am not surprised that this is done by many corporations as mentioned elsewhere in the comments (ATI/Nvidia etc). This is because regulations and benchmarks that can be gamed, such as engine efficiency, will be gamed because the incentives of corporations work out that way:

(I hope this isn't perceived as an anti-corporate rant because it's not. Just a way of framing facts).

For regulations imposed on large corporations in general (think EPA admissions standards):

1) Regulations are mandated by a government to effect some purpose (stop destroying Earth)

2) Executives - the people running the corporations - are bound by legal responsibility - their fiduciary duty [1] - to create value for their shareholders (selling lots of cars, and profitably).

3) Regulations can obstruct the activities of a corporation by making them do things they don't want to (making efficient cars is hard and costly and affects the bottom line - its cheaper to manufacture a car with less platinum [2] in it)

4) Companies are incentivized to minimize the time and money spent on adhering to regulations

5) Once a regulation is standardised and codified, it becomes possible to follow the letter of it, while ignoring the spirit of it. All a corporation has to do is meet the metrics in the specification to abide by the regulation - in other words - game the system.

Given these incentives, we have seen that corporations prefer to abide by regulations in the maximally efficient way: gaming them. Thus reducing a well-meaning government initiative to gamesmanship.

Kudos to the EPA for calling VW out on this. This kind of incident reinforces (in me at least) the idea that environmental legislation is an extraordinarily difficult thing to get right.

[0] https://en.wikipedia.org/wiki/Goodhart%27s_law

[1] https://www.law.cornell.edu/wex/fiduciary_duty

[2] Catalytic convertors

Greenspun's Tenth Law [0] is a humorous aphorism that applies here.

>> Any sufficiently complicated C or Fortran program contains an ad-hoc, informally-specified, bug-ridden, slow implementation of half of Common Lisp.

[0] http://c2.com/cgi/wiki?GreenspunsTenthRuleOfProgramming

Are you the same Jim Hefferon who wrote the free (as in freedom and beer) linear algebra text [0]? If so, I'd first like to thank you (your book is great) and then agree that it is possible to publish a .pdf online.

That said, patio11 is talking about writing books in highly specialised academic areas. Linear algebra is standard fare for an undergraduate curriculum - taught at thousands of universities - using innumerable textbooks. So it is not something highly specialised. It is conceivable that your book was largely inspired by other linear algebra books, if indirectly. For instance, you might have had strong opinions about why a particular approach does not work [1], and chose not to follow it. The search space has been reduced by authors who have come before. An academic writing a book in a more specialised area would probably not have the luxury of a writing precedent and would have to figure out a lot themselves. This translates to more time spent on a book for which they would otherwise receive no reward.

Of course, it is possible that this premise is false and that it is easier for a researcher to write a book on their own research specialty.

I would imagine that your research appeals to 'a very, very niche audience'. Would you consider spending a lot of time and effort on a book (.pdf) in your research area - for no material reward? To be read by a very small audience? Orders of magnitude smaller than undergraduates looking for a good linear algebra text?

[0] http://joshua.smcvt.edu/linearalgebra/ [1] I certainly do - I dislike Anton and Rorres

Shameless plug: here is my GPL'd MATLAB implementation of Chebyshev approximation [1]

[1] https://github.com/daniel-levin/numerical-methods-3/blob/mas...

You can use both at the same time for extremely nice results. Compute some truncated Chebyshev polynomial approximation (i.e. the first few terms) and then use Pade approximation [1]. The cool part about this is that you can prescribe your maximum allowed error (between exact solution and approximation) ahead of time, and compute the order of the Pade approximation that under all circumstances guarantees that your error will be bounded!

[1] http://siber.cankaya.edu.tr/NumericalComputations/Fall2004/c...

This could also be because students are already familiar with doing numerical computations in MATLAB from courses they'd done before. It is conceivable that students that take a machine learning course have already done some numerical analysis or scientific programming, likely using MATLAB.

>> “Obesity has traditionally been seen as the result of an imbalance between the amount of food we eat and how much we exercise, but this view ignores the contribution of genetics to each individual’s metabolism,” says senior author Manolis Kellis, a professor of computer science and a member of MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL) and of the Broad Institute.

The article is pretty clear in stating that this new research is novel because it might depose the firmly held belief that diet and exercise is the sole cause/determinant of one's obesity.

>> Rated for -30°C to +50°C [1]

-22F ~ -30C

[1] http://www.getohm.com/

Hi Hunter

How much safety testing have you done on your battery? Specifically, if an Ohm battery is involved in a collision, how will it fare? I know you are not content with shipping anything you aren't comfortable with your own family members driving with [1]. But, how do you know this? What makes you so sure? I don't mean to come across as interrogative - I am just curious.

[1] http://www.getohm.com/

edit: grammar

It seems as though Google (Alphabet) is splitting its business divisions into:

1) Google - a company comprised of reliably profitable products that run at massive scale (search, video, mobile, mail etc), and they know that Sundar Pichai can manage this

2) Everything else - these are high risk ventures with possibly enormous pay-offs. This is a breeding ground for positive black swans which Google are keen to expose themselves too.

To borrow Nassim Taleb's nomenclature, Google is splitting into mediocristan (1) (bounded variance - existing products [like YouTube] are predictably profitable) and extremistan (2) (Calico - if a major breakthrough in combating aging related diseases is made it will be both unpredictable and hugely materially beneficial)

>> We will rigorously handle capital allocation and work to make sure each business is executing well.

This sounds like the business restructuring will allow Sergey and Larry to apply just as much capital as they see fit to the extremistani business divisions. In other words they would like to control their exposure to possible consequential rare events in a simple fashion: by controlling a very simple set of parameters - i.e. how much cash each business division gets.

On the contrary, the first line of the abstract reads "Machine learning offers a fantastically powerful toolkit for building complex systems quickly."

No, this is absolutely not the first (correct) proof that infinitely many prime numbers come in pairs! That is the twin prime conjecture, and at the time of writing this comment, steadily remains a conjecture. I wonder why Nature, a publication held in high regard, would publish an article with such a title. This is not to say that the result is anything less than incredible.

Terence Tao delivered a very good lecture on this result here [0]

[0] https://www.youtube.com/watch?v=pp06oGD4m00

Another advantage: Uber is robust to changes in country-specific conditions such as legislation and disruption by ordinary taxi drivers. If Uber is made illegal in one country, it can still exist a business in other countries.

This is very close to the model of private active security in wealthier suburbs of Johannesburg [1], [2], [3]. Crime in suburbs got so bad that residents are prepared to pay for active patrolling. There are 24 hour patrols by armed guards, many of whom are ex-military. It is quite fucked up to think that we are paying armed men to drive around my suburb all day and night to stop other armed men from coming into my house. These companies also do investigations and are permitted to (citizens') arrest people under certain circumstances. They ostensibly supplement the police, but effectively supplant them. It must be mentioned that these services work tremendously well and crime has been driven to near zero in many areas.

[1] http://www.capgroup.org.za/ [2] http://www.csstactical.co.za/ [3] http://www.24-7security.co.za/

Back in the day, HN's reaction to Dropbox was also extremely negative [1]

[1] https://news.ycombinator.com/item?id=8863

Well, no, it's not empirical until we design some experiments to test the theory, make predictions, test them, come up with potentially observable data that would falsify our hypotheses, publish our results and let them be peer reviewed, reproduced elsewhere etc... The jump from anecdotes to empiricism is a large one that is not to be undertaken lightly.

From an io9 article on the same research:

>> [Hu] and Dickerson constructed a flight arena consisting of a small acrylic cage covered with mesh to contain the mosquitoes but permit entry of water drops. The researchers used a water jet to simulate rain stream velocity while observing six mosquitoes flying into the stream. Amazingly, all the mosquitoes lived.

The researchers used simulated rain drops on six mosquitoes. There are more than six species of mosquitoes. They controlled for wind effects (which are part and parcel of rain). So they excluded horizontally travelling raindrops. My immediate reaction to the conclusion that mosquitoes can fly in rain was "Really? Not always". Here is a methodologically lacking and wholly unscientific anecdote: I have lived in Johannesburg my entire life, where mosquitoes are quite prevalent during the summer months. When it is raining heavily (it is usually quite windy as well), the local species of mosquito that feeds of humans do not present a problem as the number of airborne mosquitoes tends to zero.

Better coverage of the same research can be found here [0], with no statements such as "300 Gs is a crazy amount of pressure"

[0] http://io9.com/5916251/why-can-mosquitoes-fly-in-the-rain

Telegram is really cool. I have long thought about what additions and modifications I could make to my mobile texting program. Now I have to convince all my friends to move from Whatsapp.

OK, what the hell is going on here?

One of the reasons that these sort of paradoxes can exist is because real numbers can get arbitrarily small. In principle, you could build a horn that very closely matches Gabriel's horn, but it would necessarily be an approximation of the mathematical object because you do not have available particles of arbitrary size with which to build. This last notion hints at an important property of the real numbers: they can be divided into pieces smaller than any size you can specify. They are useful abstractions upon which to build extremely successful models of reality [1], because at those scales, real numbers work very well. However, at extremely small scales, the correspondence between real numbers and reality breaks down. What does it mean to model a horn made of atoms with numbers that are arbitrarily small fractions of the width of an atom? This is not a 'real numbers / axiom of choice bad' rant, but rather I'd like to point out that real numbers exist in our minds, and using our physical intuition about to reason about them at very small scales is bound to lead to paradoxes.

[1] Electromagnetism, classical mechanics, etc

The YouTube channel [1] where this video comes from is a treasure trove for the intellectually curious, and it's one of my favourite things on the internet. The guy behind it, Ben Krasnow, is an engineer at Google. From explaining and demonstrating (reverse) spherification to encoding information in fucking fire and picking it up with his oscilloscope, this channel will interest and delight most folks who enjoy HN for hours.

[1] https://www.youtube.com/channel/UCivA7_KLKWo43tFcCkFvydw

Can you substantiate your comment?

>> Instead, the company is now using its Test Center certification program as a revenue source (the tests cost $20) and says that it has other plans to monetize.

>> “This was so strange that we sat on this observation for several years”

>> "We tried for five years to model the production of the positrons"

Why would a scientist withhold data for 6 years? How typical is it for scientists to not reveal data until they can explain it using current models? I would think that Dwyer would have rushed to publicize such fascinating results.

Well possibly the point here is the double pronged attack on the fact that Mac OS stopped at X (ten) and there is a common expression 'turn it up to eleven' [1]

[1] http://en.wikipedia.org/wiki/Up_to_eleven

This needs considerably more content. I find that 'graphical' linear algebra becomes a powerful tool when it is used to develop visual intuition for concepts such as determinants (areas/volumes in space and what it means for this quantity to be zero), solutions to linear systems (intersecting lines/planes/hyperplanes), subspaces (lines embedded in planes/hyperplanes and planes/hyperplanes embedded in planes), why a transform from R^2 -> R is not invertible (collapsing a plane into a line) what an eigenvector looks like and how it relates to other matrix properties such as invertibility (with illustrative examples such as a scaling matrix and a rotation matrix)

Having said that, I like the lego analogy for direct sums and why they don't commute. It explains concepts a lot more abstract than the basics of linear algebra. I was not expecting that from the title

In 2 dimensions, the absolute value of a determinant of a matrix is just the area of the parallelogram subtended by the row vectors of the matrix. If this area is zero, it means that the vectors are co-linear. And of course the intersection of co-linear vectors is an infinite set (in R^n anyways). The same idea holds in higher dimensions, with the 3d case being similarly possible to visualise (as a volume). Since the unique solution of a linear system is the point at which a bunch of lines/planes/hyperplanes meet, a zero determinant implies a zero area which means that at least two vectors are coincident and hence there are infinitely many solutions.

[1] https://www.math.ucdavis.edu/~daddel/linear_algebra_appl/App...

I just recently discovered an awesome visual intuition for what a determinant is, and why one cannot solve a linear system with a zero determinant. I'd love to contribute to this!