Category Archives: Science
Imagine the watershed for a river. Every drop of water that falls in that area, if it doesn’t evaporate or sink into the ground, eventually makes its way, through creeks, streams, and rivers, to the lake or ocean that is the shed’s final destination. The visual image is somewhat like the veins in a leaf. Or the branches of the leaf’s tree.
In all cases, there is a natural flow through channels sculpted over time by physical forces. Water always flows downhill, and it erodes what it flows past, so gravity, time, and the resistance of rock and dirt, sculpt the watershed.
The question is whether the water “computes.”
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16 Comments | tags: algorithm, computation, computationalism, computer code, computer model, computer program, consciousness, full-adder, Theory of Consciousness, theory of mind, Turing Machine | posted in Computers, Philosophy, Science
Previously, I wrote that I’m skeptical of interpretation as an analytic tool. In physical reality, generally speaking, I think there is a single correct interpretation (more of a true account than an interpretation). Every other interpretation is a fiction, usually made obvious by complexity and entropy.
I recently encountered an argument for interpretation that involved the truth table for the Boolean logical AND being seen — if one inverts the interpretation of all the values — as the truth table for the logical OR.
It turns out to be a tautology. A logical AND mirrors a logical OR.
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9 Comments | tags: algorithm, AND gate, boolean logic, computation, computationalism, consciousness, human consciousness, interpretation, logic gate, NAND gate, NOR gate, OR gate, Theory of Consciousness, theory of mind, truth table | posted in Computers, Math, Philosophy
My illusion of free will decided the month of May must be made for Mind (and maybe a dash of Mandelbrot). Lately, online discussions about consciousness have me pondering it again. I never posted on topics such as Chinese Rooms or Philosophical Zombies, largely because sensible arguments exist both ways, and I never decided exactly where I fell in the argument space.
It’s not that I’ve decided[1] on the topics so much as I’ve decided to write about them (and other topics). I’ve found that writing about a topic does a lot to clarify my mind about it. (Trying to teach a topic does that even more.)
I’ll start today with some personal observations and points of view.
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11 Comments | tags: brain mind problem, cargo cult, computationalism, consciousness, human brain, human consciousness, human mind, interpretation, mind, Theory of Consciousness, theory of mind | posted in Computers, Philosophy, Science
I’d planned a different first post for May Mind Month, but a recent online conversation with JamesOfSeattle gave me two reasons to jump the gun a bit.
Firstly, my reply was getting long (what a surprise), and I thought a post would give me more elbow room (raising, obviously, the possibility of dueling posts). Secondly, I found the topic unusual enough to deserve its own thread.
Be advised this jumps into the middle of a conversation that may only be of interest to James and me. (But feel free to join in; the water’s fine.)
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55 Comments | tags: neuron, semantic vectors, vector space, vectors | posted in Computers, Philosophy, Science
Last time we considered a cube-shaped room where we could indicate our opinion about Neapolitan ice cream with a single marker. That worked well because we were dealing with three flavors and the room has three dimensions: east-west, north-south, up-down.
Later I’ll explore other examples of a 3D “room” but while we’re talking ice cream, I want to give you an idea where this goes, I want to jump ahead for a moment and consider good old Baskin-Robbins, who famously featured “31 flavors!”
So now the question is, can we set a marker for all 31 flavors?
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7 Comments | tags: 3D space, configuration space, ice cream, multiple dimensions, Neapolitan ice cream, parameter space, phase space, vector space | posted in Basics, Science
Have you ever had (or at least seen) Neapolitan ice cream? It’s the kind with chocolate, vanilla, and strawberry, usually as separate layers in one package. As a kid, I didn’t care for the strawberry. I loved the chocolate and was fine with the vanilla (wouldn’t usually choose it, but don’t disdain it).
That’s just my take on it: one flavor liked, one not liked, and one that’s just okay. Someone else might have the same pattern with different flavors. Or love them all equally or want just the strawberry. Some might not like ice cream at all — any combination is possible.
What if we wanted to describe our feeling about Neapolitan as a whole?
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18 Comments | tags: 3D space, configuration space, ice cream, multiple dimensions, Neapolitan ice cream, parameter space, phase space, vector space | posted in Basics, Science
This is a Sideband to the previous post, The 4th Dimension. It’s for those who want to know more about the rotation discussed in that post, specifically with regard to axes involved with rotation versus axes about which rotation occurs.
The latter, rotation about (or around) an axis, is what we usually mean when we refer to a rotation axis. A key characteristic of such an axis is that coordinate values on that axis don’t change during rotation. Rotating about (or on or around) the Y axis means that the Y coordinate values never change.
In contrast, an axis involved with rotation changes its associated coordinate values according to the angle of rotation. The difference is starkly apparent when we look at rotation matrices.
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5 Comments | tags: 2D, 3D, 4D, column vector, matrix math, matrix transform, rotation, rotation matrix, unit vector, vectors | posted in Math, Sideband
Here on the 4th day of the 4th month, I feel I really should be writing about the 4th dimension. I did say that I would during March Mathness, and I tried to set the math foundation here and here.
But two problems: Firstly, I’m kinda burned out. Those three posts were a bit of work, diagrams & models & math (oh, my!), and then trying to explain them clearly. Secondly, obviously no one finds this interesting except me, so not much motivation for the effort involved. Which was expected (kinda the story of my life). I also said these posts were as much recording my notes as attempts to share.
But it is 4/4 (and no Twins game today), so I thought I’d try winging it anyway.
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20 Comments | tags: 2D, 3D, 3D space, 4D, coordinates, cube, dimensions, square, tesseract | posted in Science
An old saying has it that “March comes in like a lion and goes out like a lamb.” That was certainly the case for us this year. February and early March were full-on old-fashioned winter, yet when baseball season started (in the USA) this past Thursday, the snow was mostly gone, and temps were in the 50s. (That’s the thing about winter: spring is pretty sweet.)
The end of March means the official end of the Mathness, but it’s not exactly the end of the math. The whole point of the rotation study was trying to understand 4D rotation, and I haven’t explored that, yet. I plan to, and soon.
But today, as an exit March, I want to talk about math phobia.
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9 Comments | tags: March, math anxiety, math phobia, mathematics, numeracy | posted in Math
I was gonna give us all the day off today, honestly, I was! My Minnesota Twins start their second game in about an hour, and I really planned to just kick back, watch the game, have a couple of beers, and enjoy the day. And since tomorrow’s March wrap-up post is done and queued, more of the same tomorrow.
But this is too relevant to the posts just posted, and it’s about Special Relativity, which is a March thing to me (because Einstein), so it kinda has to go here. Now or never, so to speak. And it’ll be brief, I think. Just one more reason I’m so taken with matrix math recently; it’s providing all kinds of answers for me.
Last night I realized how to use matrix transforms on spacetime diagrams!
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Leave a comment | tags: Albert Einstein, faster than light, light speed, matrix math, matrix transform, simultaneity, spacetime, Special Relativity, speed of light | posted in Math, Physics
Logos con carne 