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Around 4 years ago, I had just a couple years of experience yet I was a consultant for an international company in The Netherlands. At the time I was a contractor for an Italian company but my goal was to remain in The Netherlands no matter what. I was also fairly inexperienced in life, so my best bet was to stay there as long as possible in order to gain seniority at work and figure out how life works far from my parents and have an adult life (I'm Italian, did I mention it?).The combo little experience as a developer and strong will to survive in the project contributed to my high levels of stress.Not having a lot of trust from a part of the management, partly due to my high stress levels and my communication skills that needed to be improved, and a very weird application, did the rest.The application was a Firefox extension (of the overlay type) that was analysing every web page open in the browser to recognise suitable documents, extract metadata and store them in the right database (highly simplified). It was a case of high business value and low technical value. Despite my little experience I was really focused in improving the codebase, which was all hacky and spaghettish. The Firefox Extensions API, was to be fair quite nasty and buggy and very little documented. Not only that, but it looked like nobody did what we were doing and if I ever found a question on Stack Overflow covering my problems, it was always without answers. I was at the moment the only developer on the project.At a certain point it became a nightmare. One of the many weird features was to create a PDF out of a given web page. That was achieved by using a PDF printer driver via the Firefox Extensions API. It always worked without problems. At that moment, they were going to roll out the new Windows 7 machines with a specific version of Firefox. When testing the application on one of the new machines, I discover that the PDF print was causing the browser to crash. The application was the same, the driver was the same (same version), the OS should not make any difference, the browser is in another version. What is most likely to be the problem? I pointed out to the management that the problem was very likely to be that version of Firefox, which has been sent to the department responsible to the rollout and they simply answered that the browser has been tested and was working properly, so the problem was the application, and that the next rollout was in 6 months. My application has been flagged as blocker for the rollout of the new machines and part of the management started to gossip to the higher management that the quality of my application was going to the ground. Which simply wasn't true.I think I lost a lot of hair in that moment as the stress made me balding at a faster pace than due. It didn't help that one of the managers downloaded the codebase on his own laptop, added two lines of code which actually didn't produce any effect, and installed the extension on a completely different version of the browser - and of course it worked, because the problem was the browser, he didn't fix anything - and shown to the other managers that he could fix it while I couldn't, thing that caused a scandal in both directions (wtf why the developer is busy for weeks - and - wtf why the manager put his hands on the code). I also tried his fix - which of course didn't work. At a certain point someone else that wasn't me suggested - like I did months earlier - to test another version of Firefox, et voila: problem solved! Grrrrrrrrr. After that everything went back to normal and the managers were satisfied and my name hasn't been put anymore in discussion, and my relationship with the management improved significantly.Another low point on that project, and in that case the fault was 100% mine: I've been 2 weeks trying to solve programmatically an issue that was easily solvable with a line in a CSS file. I asked to the new junior dev they added in my support to try it out and after 10 minutes he fixed it. How could that happen? Well, I tried it as a first solution, and it didn't work. I blamed the crappy Firefox Extensions API since it gave me so many unexpected behaviours and weird bugs, and the truth was that there were 2 CSS files, and the right place for the fix was the one I didn't try. Why? Because the names of the CSS files were somehow semantically inverted, and I've been fool enough to jump immediately to the conclusion that it was the fault of the platform, instead to try what was more logical. (I changed the names immediately after)These two situations made me seriously question whether I was a good developer or not, but are two big lessons that helped me enormously to become a better professional.

Software bugs to know:F-16 autopilot flipped plane upside down whenever it crossed the equator.Air New Zealand crash in Antartica when computer data error detected but crew was not informed.Computer bug showed ghost train near Embarcadero station on San Francisco Muni.Software bug caused F14 to fly off the end of an aircraft carrier into the North Sea.F18 computer opened missile retention clamp, fired missile and re-closed clamp before missile had had enough time to move away from aircraft.San Francisco BART doors opened while train was at full speed; control system's inter-station delay time was too short for TransBay Tunnel.United Airlines 767 iced up because fuel-saving computer was over-efficient, causing engines to cool down too much on approach to Denver.Mariner 1 launch failed due to period instead of comma in FORTRAN program DO statement (famously know to - The most expensive hyphen).Computer error caused US naval vessel to open fire 180 degrees off target, in the direction of Mexican merchant ship.Gemini V splashed down 100 miles off target when program used 360 degrees for Earth's rotation in 1 day, i.e. ignoring its movement around the Sun.Vancouver Stock Exchange Index rose by 50% when 2 years of round-off errors in computer program were corrected.Viking spacecraft had misaligned antenna due to faulty code patch.F16 computer deadlocked, confusing left & right while plane was inverted.180 degree heading error caused Soviet test missile to aim for Hamburg instead of the Arctic.Autopilot error caused China Airlines 747 to stall near San Francisco.Robot killed Japanese auto worker attempting to repair another robot.AT&T software bug knocked out all long-distance phone service to Greece.Shuttle laser experiment failed because computer data was in nautical miles instead of feet.Woman killed daughter & tried suicide after computer incorrectly diagnosed incurable disease.Computer error caused nuclear reactor in Florida to overheat.KAL flight 007 strayed, shot down due to heading being mistyped into autopilot.The British destroyer H.M.S. Sheffield was sunk in the Falkland Islands war. According to one report, the ship's radar warning systems were programmed to identify the Exocet missile as "friendly" because the British arsenal includes the Exocet's homing device and allowed the missile to reach its target, namely the Sheffield.The Mars Climate Orbiter doesn't orbitThe Ping of Death. A lack of sanity checks and error handling in the IP fragmentation reassembly code makes it possible to crash a wide variety of operating systems by sending a malformed "ping" packet from anywhere on the internet. Most obviously affected are computers running Windows, which lock up and display the so-called "blue screen of death" when they receive these packets. But the attack also affects many Macintosh and Unix systems as well.Morris Worm - The first internet worm infects between 2,000 and 6,000 computers in less than a day by taking advantage of a buffer overflow.Mariner 18 lost due to missing NOT in program.Department store anti-theft microwave device reprogrammed heart pacemaker, killing its user.Autopilot error caused China Airlines 747 to stall near San Francisco.P.S: Thanks to Tommy Barnett. I almost forgot to share the source. Here it is guys http://www5.in.tum.de/persons/huckle/horrorn.pdf :-)

Non-linear dynamics are fascinating, if for no other reason than so many statistical models are linear, so testing for non-linearity often requires a more strong hypothetical foundation for understanding.I'll discuss these topics in rough order of my personal favorites.Oscillatory DynamicsOscillatory dynamics are the best. The most simple to understand is a pendulum, but you add a second pendulum to the end of the first and suddenly the non-linearities lead to some crazy complexities. Check it out:I love this because oscillations play an important role in neural communication, perception, etc. This is the focus of my neuroscience research and is even the name of my scientific blog (Oscillatory Thoughts).This is a figure from a paper of mine currently under review, for example, showing a model wherein neuronal oscillations coordinate communication between brain regions. This is nice because it allows for "cleaner" communication in a noisy environment (think about a radio):ResonanceClosely related to oscillatory effects, but can be nice to demonstrate certain emergence effects, in contrast to some of the chaotic effects of other non-linear systems.Check out this simple demonstration of resonance and emergence:Simulating 10^6 neurons sending signals to one another can also lead to interesting emergent "waves" of activity caused by the non-linearities of the interneuronal communication effects:Power LawsSocial networks are so hot right now. Social networks follow a power law (aka the six degrees of Kevin Bacon effect).Some people (influencers) know a lot of people, whereas most people know relatively few. This is the infamous "black swan" "long tail" effect.Without getting into too many details, power laws are "scale-free" in that they have no preferred length scale. This (roughly) means you can "zoom in" on any portion and retain the original complexity. By definition, this is a fundamental feature of fractals.I find fractals and power laws super interesting not only because of how prevalent they are in neuroscience, but also their real world consequences are fascinating. The classic example is the question of How Long Is the Coast of Britain?The famous Zipf's Law is a power law distribution concerning word frequency. Some words appear a lot in language, while many words are very infrequently used. Here's a plot of the English language Wikipedia's word frequency:Another power law that's received a lot of attention is Benford's Law, which states that the distribution of the first digit in a lot of data are not even, but power law distributed. For example, in base 10, the number one should, all things being equal, appear 10% of the time. But in many data sources one appears around 30% of the time. This fact is actually used to help detect fraud in, for example, tax returns (Following Benford's Law, or Looking Out for No. 1).One of my favorite answers on Quora, that by Michael Wolfe to Why are software development task estimations regularly off by a factor of 2-3?, embodies power laws in human perception very nicely.We tend to subjectively experience time as the log of objective, actual time. Meaning we're really really bad at estimating how long something took, or how much time has passed. Check out the results from this paper (Page on Duke):In the words of the authors, "subjective estimates of future time horizon change less than the corresponding change in objective time."Here's the same data, but log-transformed to highlight the power law effect:U-shaped curvesThese are ubiquitous in learning, economics, and pharmacology. The classic is the Kuznets curve:U-shaped (or inverted U-shaped curves, such as the one above) are also highly prevalent in pharmacology (U-shaped dose response in behavioral pharma... [Crit Rev Toxicol. 2008]). This is captured by the idea of Hormesis, "It is conjectured that low doses of toxins or other stressors might activate the repair mechanisms of the body. The repair process fixes not only the damage caused by the toxin, but also other low-level damage that might have accumulated before without triggering the repair mechanism.":Other non-linearitiesNon-linear relationships can be modelled using any number of non-linear equations.For example, I've got data that suggests that cognitive slowing increases not as a linear function of age, but rather it accelerates with age:Non-linear systems are, uhhh, awesome.