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Showing posts from October, 2019

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 ...

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...