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Is 0.999... = 1? (spoiler alert: no it is not)

You may have encountered the popular claim that \( 0.999... = 1 \), where the three dots signify that the decimal continues forever. This is a somewhat weird claim, since it would mean that mathematics is broken. There should be no way for two different numbers to have the same value. What makes it weirder is that this is quite popular claim. I've even seen mathematicians say that it's true! But is it though? One popular proof is to first denote \( S = 0.999...\) and then multiply by \(10\) to get \( 10S = 9.999...\) and subtract \( S \) from it, to get  \( 10S - S = 9.000...\) and finally dividing by \(9\) yields  \( S = 1.000... = 1 \) and we see that  \(0.999... = 1\)! However, there's a problem. This short derivation is not strictly speaking correct. It is veeeery close to being correct, and to see why let's look at finite decimals first. Let's say that \(S = 0.999\) (note that this is not the same as \(S = 0.999...\) ). Let's do the same trick as before, so

The year 2019 in optics and photonics

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Another year, another review. 2019 was quite a wild year for me, and whew, what a decade it has been! It's hard to imagine that at the beginning of the decade, I was still in high school. In chronological order, starting from 2010: I graduated from high school, served in the army, moved across the country, got my BSc, met five Nobel laureates, started a scicomm platform, got my MSc, moved abroad for work, moved back, got my PhD, got married, moved again across the country, and got a postdoc position. I don't think there will be another decade quite like this one for me! What was your year/decade like? Share in the comments! The winner of this years OSA photography contest, by Dr. Pascale Müller and Prof. Dr. Dan Curticapean: the cross section of a bean, imaged with a scanning electron microscope and digitally colored. Anyway, let's get to the sciencey stuff; here are the news that caught my eye from the past year: Nobel prize in physics This years Nobel prize

Do we live in a simulation? Probably not.

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A while back I came across the article: The Lowest-Bid Universe , where the idea of whether we live in a simulation is examined. The premise of the text is that if this really is the case, then we should lodge complaints of our own reality. Because, apparently, the reality we live in is not that well made. The article starts by superficially mentioning some of the wilder ideas in physics, and then moves on to a "more philosophically motivated" idea that the reality as we experience it is the product of an experiment or a simulation. The standard motivation behind this is to argue that even if only a few civilizations evolve so far that they can produce simulations of whole universes, they inevitably will do a large number of them. Therefore, if there are a large number of simulated realities, it is very likely that our reality is also simulated. Then the writer concludes that if this is truly the case, then our simulation is poorly built. Why would he say so? Becau

Blog is still alive!

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Dang it, I just realized that I haven't updated the blog in over half a year. Oops.  The blog is speaking to you. The last few months have been hectic as hell, and in the beginning of the year I was busy writing my PhD thesis. I got a severe case of "blargh, I never want to write anything again" because, well, I kind of overdid it. Not to brag (as if), but my thesis ended up containing enough material to cover three or four average theses in physics. Oops. Although it was really challenging to write something like that, it was totally worth it. I got my PhD right before the summer vacation; with the highest possible grade might I add (okay, now I am bragging). Also, at the end of the summer I moved across Finland and started a job as a postdoc at Tampere University, yay! Now I am working on things I'm familiar with (coherence of light) and stuff I'm not so familiar with (metamaterials). This research direction seems really interesting, and I wil

Forced correlations & In search of lost rationality, part 2.

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As promised, I'm back for some more lost rationality! And ranting. Yeah, mostly ranting. But before I go there, I'll lay out the research that this rant is related to. This one was about temporal coherence, where we look at correlations between different points in time instead of space. To measure those correlations, you need a device such as a  Michelson interferometer  where you split the incoming light to two, delay one of the copies, and then recombine them. This simple setup is sufficient only for some special cases, and measuring the correct correlations is way more complicated. There actually isn't a general method to do that, modern detectors are far too slow! Let's just say that if you need to measure the temporal coherence of a pulse train, then one way to do it is to isolate individual pulses and measure them with a  FROG  (yes, that is a real scientific instrument) and then study their correlations from the measured data. Anyhow, if you have a de

The year 2018 in optics and photonics

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It's that time of the year again, the time to look back on what was accomplished. I couldn't find the time or the energy to write this sooner, and I kind of left this to the last minute. But well, here it is now, the photonics news that really caught my eye this year: OSA Photo Contest winner Here is the photo that won this years annual OSA Photo Contest!  Shot by Tobias Tieß from Leibniz-IPHT, Germany, the photo features a glass cup filled with fluoresciing liquid and a UV-laser is coupled into the handle of the cup. Quite nice effect, I must say. The rest of the contestants can be found here . Nobel prize The Nobel prize in physics was awarded "for groundbreaking inventions in the field of laser physics," To Donna Strickland, Gerad Mourou and Arthur Ashkin. I made a whole post on this, which you can find here for more info. SI system redefinition The SI system underwent a major overhaul! Or to be more precise, it was decided that it will be o

Le Grand K announces retirement, at last

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Starting from 1889 and scheduled to become emeritus (emerita?) sometime in 2019, the International Prototype Kilogram (also known as Le Grand K) had a service of 130 years. Which is a remarkably long time for a standard of measurement based on a metallic cylinder. The change is rather massive (pun intended), because it affects every SI-system unit. However, the biggest change is not the kilogram, but the fact that some of the old SI units had a dependence on measured values. The new definition relates the base units to constants of nature, which will be redefined as being exact. The speed of light is a good example of setting some constant to be exact. We used to measure it's value, which leads to experimental error. But then in the 15th General Conference on Weights and Measures in 1975 it was decided to set it at exactly 299 792 458 meters per second . This also allowed us to define the meter in a very precise way, by establishing some temporal yardstick. Simil