Scott's posts

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My bicycle odometer when I got home from work today, and after a trip around the block. This is in km and was set to 0 in Dec 2013. I keep thinking that if I hadn't just been going back and forth to work, I could have really gone somewhere.

11/4/16

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There is a leap second coming next week, don't be caught unaware!

Perhaps some day we'll be able to control the Earth's rotation so that it keeps time accurately. Until then we have to adjust our clocks.

Perhaps some day we'll be able to control the Earth's rotation so that it keeps time accurately. Until then we have to adjust our clocks.

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Math/stats question:

If X_i are iid r.v.s that are exponentially distributed with E[X] = mu, and I define Y = sum{i=1..N}{X_i}

then Y has a Gamma (or Erlang) distribution with parameters N, and mu (or mu^{-1} depending how you like to write your Gamma distribution).

Now what happens if N is a random variable with a Poisson distribution with mean, say lambda? Is there a named distribution for that?

I can generate random variables with this distribution in MATLAB (the accumarray function rocks!), and they match extremely well to my data, and I can even make up some plausible physics for why this is the correct distribution. It would be much more convenient, though, if I had a nice way to fit for the two parameters (mu and lambda). Given the huge number of variations on exponential distributions that have been studied, it seems like there is a chance for this to exist.

If X_i are iid r.v.s that are exponentially distributed with E[X] = mu, and I define Y = sum{i=1..N}{X_i}

then Y has a Gamma (or Erlang) distribution with parameters N, and mu (or mu^{-1} depending how you like to write your Gamma distribution).

Now what happens if N is a random variable with a Poisson distribution with mean, say lambda? Is there a named distribution for that?

I can generate random variables with this distribution in MATLAB (the accumarray function rocks!), and they match extremely well to my data, and I can even make up some plausible physics for why this is the correct distribution. It would be much more convenient, though, if I had a nice way to fit for the two parameters (mu and lambda). Given the huge number of variations on exponential distributions that have been studied, it seems like there is a chance for this to exist.

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Here is a very nicely written explanation of something one normally takes for granted: metals are shiny. The reason illustrates how weirdly electrons can behave.

And, like all good physics answers, more questions. Why are metal atoms willing to share their electrons? Why are some metals (like gold) colored instead of silver?

The reason for the yellow color of gold has to do with the fact that some of the electrons that are not free to wander the entire metal volume are able to absorb blue (and shorter) photons. The specific way that the energy levels of these valence electrons in gold differ from those in silver has to do with the increased number of protons increasing the "speed" of the electrons and (via special relativity) the effective mass of the electrons. So, I think you could say that the shininess of gold illustrates QM while the color illustrates SR.

And, like all good physics answers, more questions. Why are metal atoms willing to share their electrons? Why are some metals (like gold) colored instead of silver?

The reason for the yellow color of gold has to do with the fact that some of the electrons that are not free to wander the entire metal volume are able to absorb blue (and shorter) photons. The specific way that the energy levels of these valence electrons in gold differ from those in silver has to do with the increased number of protons increasing the "speed" of the electrons and (via special relativity) the effective mass of the electrons. So, I think you could say that the shininess of gold illustrates QM while the color illustrates SR.

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Found on the Minuteman Bikeway this morning, in Bedford, about 100 meters NW of the intersection with Wiggins. There was also a trail meandering through the woods and a field and crossing the bikepath several times. The trail had an occasionally visible hoof print and an occasionally visible canine track, but was mostly too beaten down and chaotic to interpret.

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Here is the result of another outing to see ice in the harbor. I failed to photo the food associated s with this one, bit suffice or to say that the sausage, onion, pepper pie at Santarpio's is worth a trip.

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We went out to Deer Island in the Boston Harbor this morning to see if the sunrise on the frozen sea would look interesting. It wasn't as frozen as I had hoped it would be, but it was very pretty and slushy.

Afterwards we stopped at Union Square Doughnut. I highly recommend the browned butter and hazelnut doughnut, surprisingly more so than the maple bacon doughnut, which was also quite good.

Afterwards we stopped at Union Square Doughnut. I highly recommend the browned butter and hazelnut doughnut, surprisingly more so than the maple bacon doughnut, which was also quite good.

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Frozen Harbor

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Finally a clear enough night to see comet Lovejoy! Binoculars required.

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Why will June 2015 be different from June in most years? It will be one second longer than usual.

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