Category Archives: Science
Well, it’s Pi Day once again (although this date becomes more and more inaccurate as the century proceeds). So, once again, I’ll opine that Tau Day is cooler. (see: Happy Tau Day!)
Last year, for extra-special Pi Day, I wrote a post that pretty much says all I have to say about Pi. (see: Here Today; Pi Tomorrow) That post was actually published the day before. I used the actual day to kick off last Spring’s series on Special Relativity.
What remains to be said? Not much, really, but I’ve never let that stop me before, so why start now?
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14 Comments | tags: irrational numbers, normal number, pi, pi day, tau, tau day, transcendental numbers | posted in Math
Credit where credit is due, both the major ideas in this post come from Fareed Zakaria on his CNN Sunday program, GPS. If you follow TV news at all, you know Sunday mornings have such long-running standards as Meet the Press (on NBC since 1947!) and Face the Nation (on CBS since 1954). (Or was it Meet the Nation and Face the Press?)
Zakaria is one of the good ones: very intelligent, highly educated, calm and measured. He’s well worth listening to. (I’ve realized one attraction to TV news is the chance to — at least sometimes — hear educated, intelligent talk. It’s a nice respite from most TV entertainment.)
Two things on Zakaria’s last episode really rang a bell with me.
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23 Comments | tags: AI, computer code, digital computer, DNA, electrons, Face the Nation, Fareed Zarkaria, fire, genetic code, genetics, internet, interweb, language, mechanical physics, Meet the Press, printing press, quantum physics, robotics | posted in Science, The Interweb, TV
It took almost exactly 100 years. In 1905, über-geek hero Albert Einstein presented four papers of major significance to the world. One of those was about Special Relativity. It took Einstein ten more years to figure out the General theory of Relativity. He presented that work in November of 1915.
One of the predictions of General Relativity is that gravity warps space, creating gravity waves (which move at the speed of light). And while many other predictions of GR have been tested and confirmed (to very high precision), we’ve never quite managed to detect gravity waves.
Until September 14th of 2015!
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10 Comments | tags: Albert Einstein, black hole, General Relativity, gravity, gravity wave, LIGO, Special Relativity, Theory of Relativity | posted in Physics
I seem to be doing a lot of reblogging lately (a lot for me, anyway). But I’m on kind of a math kick right now, and this ties in nicely with all that.
4 gravitons
You’ve probably seen it somewhere on your facebook feed, likely shared by a particularly wide-eyed friend: pi found hidden in the hydrogen atom!
From the headlines, this sounds like some sort of kabbalistic nonsense, like finding the golden ratio in random pictures.
Read the actual articles, and the story is a bit more reasonable. The last two I linked above seem to be decent takes on it, they’re just saddled with ridiculous headlines. As usual, I blame the editors. This time, they’ve obscured an interesting point about the link between physics and mathematics.
So what does “pi found hidden in the hydrogen atom” actually mean?
It doesn’t mean that there’s some deep importance to the number pi in nature, beyond its relevance in mathematics in general. The reason that pi is showing up here isn’t especially deep.
It isn’t trivial either, though. I’ve seen a few people…
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2 Comments | tags: math theory, mathematics, pi, quantum physics | posted in Math
When I was a high school kid, my dad and I sometimes played a game where one of us would make up a secret code, write a message in that code, and the other would try to decipher the message. We generally used simple substitution ciphers, so it was an exercise in letter frequency analysis and word guessing.
There’s a cute secret code I found in a book back then that really stuck with me because of the neat way it looks. It also stuck with me because it’s so simple that once you learn it, you really can’t forget it.
So, for some Saturday fun, I thought I’d share it with you.
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6 Comments | tags: Alan Turing, Alienese, cipher, code, decipher, decoder ring, Freemasons Cipher, Futurama, one-time pad, Pigpen Cipher, secret codes, substitution cipher | posted in Basics, Math
Long-time readers of this blog know I very rarely re-blog. Occasionally something strikes my fancy so hard, I have to (if nothing else) mention it and post a link to it here.
Derek Lowe, a chemist who also writes In the Pipeline, a great chemistry blog, recently posted something striking:
…a new analysis of clinical trials for pain medication shows that the placebo effect in [the area of pain relief] has been getting stronger. The same also seems to be true for antipsychotics and antidepressants, but this effect seems to be mainly (or only) visible in large-scale US trials…
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1 Comment | tags: belief, chemistry, Derek Lowe, drug trials, In The Pipeline, medical trials, pain relief, placebo, power of will, USA | posted in From My Collection, Science
Is that you, HAL?
Last time, in Calculated Math, I described how information — data — can have special characteristics that allow it to be interpreted as code, as instructions in some special language known to some “engine” that executes — runs — the code.
In some cases, the code language has characteristics that make it Turing Complete (TC). One cornerstone of computer science is the Church-Turing thesis, which says that all TC languages are equivalent. What one can do, so can all the others.
That is where we pick up this time…
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2 Comments | tags: Alan Turing, algorithm, Church-Turing thesis, code, data, flowchart, lambda calculus, state diagram, stored program computer, Turing Machine, Universal Turing Machine, Von Neumann architecture | posted in Math
The previous post, Halt! (or not), described the Turing Halting Problem, a fundamental limit on what computers can do, on what can be calculated by a program. Kurt Gödel showed that a very similar limit exists for any (sufficiently powerful) mathematical system.
This raises some obvious questions: What is calculation, exactly? What do we mean when we talk about a program or algorithm? (And how does all of this connect with the world of mathematics?)
Today we’re going to start exploring that.
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13 Comments | tags: Alan Turing, algorithm, binary digits, calculation, Church-Turing thesis, code, computer program, data, information theory, lambda calculus, mathematical expression, Turing Machine, Universal Turing Machine | posted in Math, Opinion
But my brain is full!
You may have noticed that, in a number of recent posts, the topic has been math. The good-bad news is that there’s more to come (sorry, but I love this stuff). The good-good news is that I’m done with math foundations. For now.
To wrap up the discussion of math’s universality and inevitability — and also of its fascination and beauty — today I just have some YouTube videos you can watch this Sunday afternoon. (Assuming you’re a geek like me.)
So get a coffee and get comfortable!
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6 Comments | tags: algebraic numbers, math and sex, math ontology, mathematics, numbers, Philosophy of Math, Theory of Mathematics, transcendental numbers | posted in Math, Opinion
Take a moment to gaze at Euler’s Identity:
It has been called “exquisite” and likened to a “Shakespearean sonnet.” It has earned the titles “the most famous” and “the most beautiful” formula in all of mathematics, and, in a mere seven symbols, symbolizes much of its foundation.
Today we’re going to graze on it!
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19 Comments | tags: complex numbers, Euler's Formula, Euler's Identity, exponential function, Leonhard Euler, trigonometry, Yin and Yang | posted in Math, Opinion, Philosophy
Logos con carne 