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Showing posts from April, 2018

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

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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
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Bose and Einstein, nanosized

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Around two weeks ago I heard about a very interesting article called " Bose-Einstein Condensation in a Plasmonic Lattice ." I must admit, the first time I heard about it, I knew what all those words meant separately, but together it was some mumbo jumbo that made no sense to me. What exactly is condensing? Don't these condensates exist only at extremely low temperatures? And what do plasmons have to do with this? Reading the abstract didn't help at all. Going through the whole article, I understood maybe half of it. But apparently they had done something great, and it was going to be published in Nature Physics! By chance, I happened to be in contact with one of the authors and he explained everything to me in a way that I finally got what they were doing. And it really was something great. First of all, what is a Bose-Einstein condensate? About a century ago, Indian scientist Satyendra Nath Bose sent an article to Albert Einstein, humbly asking for his op
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In search of lost rationality, part 1.

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Probably the biggest reason why I chose physics, was the belief that it is completely dictated by rational arguments. If you can show that from A comes B because of C, then everyone will accept it as being true. Given of course that you didn't mess up the calculations and the premise is realistic. However, a few years of work in this field has proven that belief to be false. You can prove your point rigorously with widely accepted mathematical tools and leave no wiggling room. And still there will be people who do not agree with your reasoning. It wouldn't be a problem if these doubters were some internet trolls who obviously have no idea what they're saying, since you can just ignore them. Unfortunately, they can also be esteemed scientists in the field. Senior researchers, award winning scientists, professors, even so called living legends. Sure, it's fine to make mistakes, and everyone does make them. I have been locked in several heated discussions
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Messing around in the lab

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What did the MythBusters ultimately teach us? "Remember kids, the only difference between screwing around and science is writing it down." A picture is worth more than a thousand words, so I guess I was doing science after all, and lots of it! Got that "evil genius" -thing going on. I have been thinking of making a video series called: "Will it ablate?" in which I will put all kinds of things in front of an extremely powerful laser. I also have plans for some other videos as well, so stay tuned. I made a youtube channel for the blog, and here are the fruits of the first filming day at the lab, hope you like it! If you have some suggestion on what I should film next, throw me a comment!
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