Profile cover photo
Profile photo
Ashish Hota
About
Ashish's posts

Post has shared content
For decades, desalination was seen as a pipe dream: so costly in terms of energy that it could never be useful. Reverse-osmosis was hailed as a possible change, but the problem of "biofouling" -- basically, bacterial growth in the filters requiring constant chemical cleaning -- made it impractical. But a few years ago, this problem started to get cracked, and now Israel is doing something previously unthinkable: running a net surplus of water.

To give you some context for this: In 1948, Israel was more than half parched, nearly-uninhabitable desert. The steady northward spread of the desert had been greatly accelerated by Ottoman deforestation, and the whole ecosystem verged on collapse. David Ben Gurion, the first president, made it his crusade to make the country green: "There will be bears in the Negev (desert)!," he would famously say. This meant everything from aggressive water conservation across the country, to research in water technologies, to a steady program of reclaiming the desert, with schoolchildren routinely going out in large groups to plant trees.

Today, I can barely recognize the country of my childhood; as you go south of Jerusalem, miles and miles which I remember as barren deserts are now lush forests and farms.

But this was almost lost in the past decade, as powerful droughts -- the same droughts which triggered the Arab Spring -- have ravaged the Middle East. The Kinneret (also known as the Sea of Galilee) saw its water level drop terrifyingly, year after year, close to the threshold where osmotic pressure would fill it with salt and destroy it as a freshwater lake. The Dead Sea was shrinking into a giant mud puddle, and we talked about it meeting the same fate as the Aral Sea, now just a memory.

The rise of modern desalination has changed this calculus completely. Because it doesn't rely on boiling or similar processes, it's energy-cheap. It's maintainable, and while it requires capital outlays in the way that building any large plant does, it doesn't require astronomical or unusual ones. This makes it a technology ready for use across the world.

There is one further potential benefit to this: Peace. Water is a crucial resource in the Middle East (and elsewhere!), far more scarce than oil. It's needed not just for humans, but most of all for crop irrigation, as droughts destroying farmland have been one of the biggest problems facing the region. The potential for desalination to change this creates a tremendous opportunity for cooperation -- and there are nascent signs that this is, indeed, happening.

At an even higher level, relieving the political pressures created by lack of water, and thus lack of working farms, could have far more profound effects on the region as a whole. Even before the recent droughts, things like the steady desertification of Egypt's once-lush Nile Valley (a long-term consequence of the Aswan Dam and the stopping of the regular flooding of the Nile) were pushing people by the million into overcrowded cities unable to support them. Having farming work again doesn't just mean food, it also means work, and it means a systematic reduction in desperation.

Desalination looks to be one of the most important technologies of the 21st century: it's hard to overstate how much it could reshape our world.

Via +paul beard 

Post has shared content
A simple-to-state problem has been resolved, and there's surprisingly little about this in the news.

The question was this: is it possible to partition the set of all natural numbers into two parts, such that neither part contains a Pythagorean triple?

(A Pythagorean triple is a triple of numbers (a, b, c) such that a² + b² = c². Thus for instance, we cannot put {3, 4, 5} all in the same part, because 3² + 4² = 5².)

The answer, as the researchers (Marijn J. H. Heule, Oliver Kullmann, Victor W. Marek) have found out, is that it is not possible. In fact, you cannot even partition the numbers 1 to 7825 into two parts such that neither contains a Pythagorean triple, while you can partition the numbers 1 to 7824 that way.

The only article written about it, AFAICT, is here: http://www.i-programmer.info/news/112-theory/9718-a-mathematical-proof-takes-200-terabytes-to-state.html (linked from http://cacm.acm.org/news/202462-a-mathematical-proof-takes-200-terabytes-to-state/fulltext).
The main website for the paper is here: https://www.cs.utexas.edu/~marijn/ptn/

The problem is also known as the "partition regularity" of the equation a² + b² = c².

This is a timeline of the problem as I've pieced together from following the citations:

https://en.wikipedia.org/wiki/Ramsey_theory

- Schur's theorem for the r=2 case: this is something a 10-year-old can do. This is about the "partition regularity" of the equation x + y = z, i.e. it asks whether you can split into two sum-free parts. For instance, you can split the numbers {1, ..., 8} into two (weakly) sum-free parts as {1, 2, 4, 8} and {3, 5, 6, 7}, but you can check that you can't split {1, ..., 9} into two such sets. (If you allow x = y then you can't even get to 4, you can only split {1, 2, 3}… but thanks to the irrationality of √2 we don't have to worry about that in the Pythagorean case.) (The general Schur's theorem is for any r, there is a largest n such that you can partition {1, ..., n} into r sum-free parts: https://en.wikibooks.org/wiki/Combinatorics/Schur%27s_Theorem .)

- Van der Warden's theorem for the r=2, k=3 case: this is about the partition regularity of the equation x + y = 2z; i.e. there's a largest n for which you can partition {1, ..., n} into 2 AP-free parts. https://en.wikipedia.org/wiki/Van_der_Waerden%27s_theorem

- Rado's theorem: generalizes both of these and a lot more; is about partition regularity of systems of linear equations.
https://en.wikipedia.org/wiki/Rado%27s_theorem_(Ramsey_theory)

- In 1980, Paul Erdos and Ron Graham (Old and New Problems and Results in Combinatorial Number Theory) proposed the problem. (Somewhere in http://www.math.ucsd.edu/~ronspubs/80_11_number_theory.pdf and I don't know the page number.)

- It is listed as an open problem in 2007 (page 14) "Open Problems in Additive Combinatorics" by Croot and Lev (proposed by Graham): http://people.math.gatech.edu/~ecroot/E2S-01-11.pdf noted as the simplest non-linear equation for which we can ask about partition regularity (and we don't know the answer)

- Ron Graham in 2008 (Old and New Problems and Results in Ramsey Theory) gives it as a problem worth $250 (Problem 7, page 6) to determine whether the equation is partition regular, and says "There is actually very little data (in either direction) to know which way to
guess." http://www.math.ucsd.edu/~ronspubs/08_06_old_and_new.pdf

- In 2008, Cooper and Poirel gave a partition for n = 1344: https://arxiv.org/abs/0809.3478 / http://people.math.sc.edu/cooper/pth.pdf

- In 2012, a thesis by William Kay used an algorithm by Moser and Tardos, to get a bipartition for n = 1514.

- A 2013 paper by Joshua Cooper, Michael Filaseta, Joshua Harrington, Daniel White: http://people.math.sc.edu/cooper/CPTWCPI.pdf

- A May 2015 thesis by Kellen Myers, a student of Doron Zeilberger, gave a partition of {1, ..., 6500}. The thesis also has interesting historical background on Issai Schur.
(https://rucore.libraries.rutgers.edu/rutgers-lib/47479/PDF/1/)

- In 2015 (the arXiv preprint is tagged 9 May 2015), Joshua Cooper and Ralph Overstreet had an entire paper which "addressed" this question. They showed that a natural obstruction did not exist, so the answer may still be yes. They also found a partition for {1, ..., 7664}, thus giving a lower bound. https://arxiv.org/abs/1505.02222

- Finally, this paper. You can read about it in the paper itself: http://www.cs.uky.edu/~marek/papers.dir/15.dir/Pythagorean.pdf and the site: https://www.cs.utexas.edu/~marijn/ptn/
(See also https://mathoverflow.net/questions/1051/splitting-pythagorean-triples)

They used a SAT solver and clever encoding and enough computational power to settle this.

It's easy to prove that {1, ..., 7864} can be partitioned: just give a partition (takes only 1 bit for each integer!), and it's trivial to check that the partition is ok.

But proving that {1, ..., 7865} cannot be partitioned is to prove that none of the 2^7864 partitions can work. How is this possible? Apparently modern SAT solvers can also generate a proof of unsatisfiability. This proof is the thing that takes 200 TB to encode, though it can be compressed into a "mere" 68 GB.

Now a future question might be: is there a human-understandable proof that the answer is no? (May not be for 7865, just for any finite n.)

Post has shared content

Post has shared content
There are many, many very deep things here. These people are, at best, well-meaning idiots, or at worst, leeches thriving on the blood and fear of innocent, trusting people.

Mostly everyone starts off as a 'medical virgin'. The body just works, and the mind is occupied with life. Then, either because of some pain or some syncope event or some well-meaning person's suggestion, one gets a diagnostic test done. The test shows a catastrophe seemingly approaching in slow motion -- a tumor deduced from a CT, a high regurgitation fraction calculated from an echo, a mass in the liver from an ultrasound, anything. This article's super-forward-looking blood tests and genetic data from 23andme and the like are at another level entirely.

The first response is alarm and reaching for support, driven by an implicit trust of the first "anchoring" test. One very quickly starts thinking of choices, consequences and costs, and the vast fraudulent medical ecosystem is more than happy to oblige. One's instincts to be a responsible person are milked to the extreme. Many follow-up diagnostic tests emerge, seemingly independent, but still very much "anchored" by the first test, and once a pattern is set it is simply confirmed in the tea leaves (with appropriate boilerplate caveats, of course). At this point, one still trusts the medical ecosystem, one considers it an ally in fighting off a threat. Hospital doctors who speak nicely, nurses who are kind, procedures which are easy -- all this contributes to that fatal illusion.

Soon, life-changing events like surgeries and major drug regimens are proposed and accepted. It is not uncommon for a major surgery to be planned based on 3-4 diagnostic test reports conducted in labs of questionable expertise. Of course, at that point one is thinking of the surgery, not the credibility of the labs -- one has been persuaded to 'think past the sale. As far as one is concerned, "the report came and said X", that's all. "Who was the doctor who signed off on the report? Is he trustworthy? Who is the lab run by? How are they running it?" -- none of these questions even arise.

It is only past this point that it likely dawns that hospitals are horrible, horrible places where unexpected horrible things happen all the time. Surgeries go wrong, hospital infections prove to be drug-resistant, nurses and attendants make errors -- the list is infinite. Suddenly, the seemingly supportive medical ecosystem vanishes behind old cliches: "Old age" "Ultimately it is not in our hands" "This is fate" "Mistakes happen, we are only human" or even "Look, this is what we can do. If you want to, stay. Otherwise get out"

Those who lose their virginity through a genuine medical emergency route (e.g. a major accident) usually follow a different trajectory. The suddenness and impact of the original event might mask the horrors of the medical ecosystem -- one tends to think, "Well what more could these people do anyway?", and that gives a measure of peace and one is content. If one digs further though, one is bound to discover unsettling things.

Ultimately, the concept of 'expertise' is very poorly understood. In medical matters, it is meaningful only in a very rare fraction where it is ably supported by a good ecosystem, no corrupting factors, copious amounts of trust, etc. In most cases, it is not.

Post has attachment
Instead we have billions of apps. :)

Post has attachment
Scott Adams has a nice set of articles about Donald Trump's campaign. For instance,

http://blog.dilbert.com/post/127079241801/political-reporters-cover-a-business-candidate

Very insightful.

Post has shared content
BOMBAAT CHINDI SUPER-O-SUPER-U!!!!!! With an even better Part 2 !!! https://www.youtube.com/watch?v=xjy7eB_L9m4&feature=youtu.be (feat. classic Pyar ge agbuttaite in Raga * (+Somashekaracharya Gunasagara Bhaskaracharya please help))

Post has attachment
Constitution of India on GitBub. :)

https://github.com/anoopdixith/TheConstitutionOfIndia

Post has attachment

Post has attachment
Waterloo folks: I give you a regular January morning at WL. 
PhotoPhotoPhoto
1/30/15
3 Photos - View album
Wait while more posts are being loaded