What are Markov chains? And why are they so useful?
Veritasium
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| Masayoshi Son (1957 - ) Japanese Businessman |
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| Andrey Andreyevich Markov (1856 – 1922) Russian Mathematician |
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| Pavel Alekseevich Nekrasov (1853–1924) Russian mathematician |
Silicon Forest
If the type is too small, Ctrl+ is your friend
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| Masayoshi Son (1957 - ) Japanese Businessman |
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| Andrey Andreyevich Markov (1856 – 1922) Russian Mathematician |
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| Pavel Alekseevich Nekrasov (1853–1924) Russian mathematician |
An Olympic-sized swimming pool contains approximately 2.5 million liters of water. This translates to roughly 660,000 gallons. Since 1 liter of water contains about 3.3 x 10^27 water molecules, an Olympic-sized pool would contain approximately 8.25 x 10^33 water molecules.
One trillion is 10^12 (10 to the twelfth power), so one-trillionth of an Olympic size swimming pool would be 0.03 cc of water, or 30 cubic millimeters. Not very friggin' much.
So this goes way beyond precision for any practical purpose, this is now a matter of flexing your muscles, this is showing off just how much mathematical power you have that you can work out a constant like π to very high precision.
Then it comes to me that what we all want is to be entertained, something that absorbs all of our attention, because when our attention is totally occupied, we don't concern ourselves with boring stuff. We are occupied and we are entertained. And nothing captures our attention better than competition. Trying to beat the other guy is what everyone is striving for. Sometimes it's just a matter of slipping in the right word to stab an opponent with a nasty insult, sometimes it's just an embellishment to your clothing to catch someone's eye, often it's a matter of making more money. Competitions can become heated and result in pushing, escalate into fighting and eventually boil over into war. And when we go to war, there is no end to the complexity of the weapons we build, and when you are building complex weapons you need math, and so you might want the guys who display the intellectual equivalent of peacock feathers helping out on designing weapons.
I'm watching this video and I realize that I wrote a program to compute π using several different techniques, one of which was very similar to the method used in the beginning of the video of cutting up a circle into triangles. I thought I had posted it earlier, but I could not find it on my blog. I rooted around on my computer and found it (it's from 2012). I posted it on github.
My program uses floating point numbers to perform the calculations, so it is going to be limited to only a few digits of pi. I should modify it to use the GMP math package so I can get as many digits as Ludolph did.
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| The Ambassadors (1533) by Hans Holbein the Younger |
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| Siege of Paris 885 - Jean-Victor Schnetz 1835 |
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| Scurvy |
However, it was not until 1747 that James Lind formally demonstrated that scurvy could be treated by supplementing the diet with citrus fruit, in one of the first controlled clinical experiments reported in the history of medicine. As a naval surgeon on HMS Salisbury, Lind had compared several suggested scurvy cures: hard cider, vitriol, vinegar, seawater, oranges, lemons, and a mixture of balsam of Peru, garlic, myrrh, mustard seed and radish root. In A Treatise on the Scurvy (1753) Lind explained the details of his clinical trial and concluded "the results of all my experiments was, that oranges and lemons were the most effectual remedies for this distemper at sea.”I did know that the Brits originated the regimented use of citrus, I just didn't know how that came to pass.