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Showing posts from December, 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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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
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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
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