About Wyrd Smythe
The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts.
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
evaluate(2B || !2B)
Hamlet’s famous question, “To be or not to be?” is just one example of a question with a yes/no answer. It’s different from a question such as, “What’s your favorite color?” or, “How was your day?” What it boils down to is that the young Prince’s question requires only one bit to answer, and that bit is either yea or nay.
Computers can be very good at answering yes/no questions. We can write a computer program to compare two numbers and tell us — yea or nay — if the first one is bigger than the second one. Computers are also very good at calculations (they’re just big calculators, after all). For example, we can write a computer program that divides one number by another.
But there are questions computers can’t answer, and calculations they can’t make.
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11 Comments | tags: Alan Turing, algorithm, calculation, Cantor's Diagonal, discrete mathematics, Halting Problem, Turing, Turing Halting Problem | posted in Computers, Sideband
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
In the recent post Inevitable Math I explored the idea that mathematics was both universal and inevitable. The argument is that the foundations of mathematics are so woven into the fabric of reality (if not actually being the fabric of reality) that any intelligence must discover them.
Which is not to say they would think about or express their mathematics in ways immediately recognizable to us. There could be fundamental differences, not just in their notation, but in how they conceive of numbers.
To explore that a little, here are a couple of twists on numbers:
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8 Comments | tags: alien math, Frederik Pohl, Heechee, math origins, math theory, more math, prime numbers, real numbers, surreal number | posted in Math, Opinion, Sideband
Oh, no! Not math again!
Among those who try to imagine alien first contact, many believe that mathematics will be the basis of initial communication. This is based on the perceived universality and inevitability of mathematics. They see math as so fundamental any intelligence must not only discover it but must discover the same things we’ve discovered.
There is even a belief that math is more real than the physical universe, that it may be the actual basis of reality. The other end of that spectrum is a belief that mathematics is an invented game of symbol manipulation with no deep meaning.
So today: the idea that math is universal and inevitable.
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44 Comments | tags: alien math, cardinal numbers, cardinality, counting, counting numbers, first contact, Leopold Kronecker, math origins, math theory, mathematics, natural numbers, numbers, Philosophy of Math, rational numbers, real numbers, Theory of Mathematics | posted in Math, Opinion
The seventh post I published here, Yin and Yang, introduced my fascination with the Yin-Yang idea of duality, that life is filled with pairs of opposites (left-right, day-night, black-white). Since then, I’ve written a number of posts about some of those pairs.
In that first post I mentioned that life was also filled with threes (and some of the other numbers, but especially threes). As we look around, we see an awful lot of things that do come in triplets. Today I thought I’d finally get around to tripping on life’s triples.
Ready? Then: One… Two… Three… Let’s go!
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10 Comments | tags: rule of three, three, three-legged, three-pole, triangle, tricycle, trilogy, trinary, triple, tripod, Yin and Yang | posted in Life
Put on your arithmetic caps, dear readers. Also your math mittens, geometry galoshes and cosine coats. Today we’re venturing after numeric prey that lurks down among the lines and angles.
There’s no danger, at least not to life or limb, but I can’t promise some ideas won’t take root in your brain. There’s a very real danger of learning something when you venture into dark territory such as this. Even the strongest sometimes succumb, so hang on to your hats (and galoshes and mittens and coats and brains).
Today we’re going after vectors and scalars (and some other game)!
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16 Comments | tags: 2D, 3D, azimuth, coordinates, declination, dimensions, direction, elevation, location, scalars, speed, Technology, vectors, velocity | posted in Math
Logos con carne 