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Tag Archives: algorithm

*One solution to the puzzle.*

I’ve written a lot lately about the physical versus the virtual. I’ve also written about algorithms and the role they play. In this post, I revisit both by exploring what is, for me, an old friend: **The Eight Queens Puzzle**. The goal is to place eight chess queens on a chessboard such that none can take another in a single move.

The puzzle is simple enough, yet just challenging enough, that it’s a good problem for first-year student programmers to solve. That’s where I met it, and it’s been a kind of *“Hello, World!”* algorithm for me ever since.

I thought it might be a fun way to explore a simple virtual reality.

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6 Comments | tags: abstract system, algorithm, chess, chess queen, chessboard, computationalism, eight queens puzzle, information system, physical system, virtual reality | posted in Computers

*Math version 1.0*

This image here of the **Mandelbrot fractal** might look like one of the uglier renderings you’ve seen, but it’s a thing of beauty to me. That’s because some code I wrote created it. Which, in itself, isn’t a deal (let alone a big one), but how that code works kind of is (at least for me).

The short version: the code implements special *virtual* math for calculating the Mandelbrot. That the image looks anything at all like it should shows the code works.

Yet according to that image, something wasn’t quite right.

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7 Comments | tags: algorithm, Mandelbrot, Mandelbrot fractal, virtual reality | posted in Computers

In the last post I explored how algorithms are defined and what I think is — or is not — an **algorithm**. The dividing line for me has mainly to do with the requirement for an ordered list of instructions and an execution engine. Physical mechanisms, from what I can see, don’t have those.

For me, the behavior of machines is only *metaphorically* algorithmic. Living things are biological machines, so this applies to them, too. I would not be inclined to view my kidneys, liver, or heart, as embodied algorithms (their behavior can be *described* by algorithms, though).

Of course, this also applies to the brain and, therefore, the mind.

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43 Comments | tags: algorithm, brain, brain mind problem, computationalism, consciousness, human brain, human consciousness, human mind, mind, Theory of Consciousness, theory of mind | posted in Computers

There’s a discussion that’s long lurked in a dusty corner of my thinking about computationalism. It involves the definition and role of algorithms. The definition isn’t particularly tricky, but the question of what fits that definition can be. Their role in our modern life is undeniably huge — algorithms control vast swaths of human experience.

Yet some might say even the ancient lowly thermostat implements an algorithm. In a real sense, any recipe is an algorithm, and any process has some algorithm that describes that process.

But the ultimate question involves algorithms and the human mind.

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8 Comments | tags: algorithm, computation, computationalism, digital | posted in Computers

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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8 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

Back at the start of March Mathness I promised the math would be “fun” (really!), but anyone would be forgiven for thinking the previous two posts about Special Relativity weren’t all that much “fun.” (I really enjoy stuff like that, so it’s fun for *me*, but there’s no question it’s not everyone’s cup of tea.)

Trying to reach for something a bit lighter and potentially more appealing as the promised “fun,” I present, for your dining and dancing pleasure, a trio of number games that anyone can play and which might just tug at the corners of your enjoyment.

We can start with **277777788888899** (and why it’s special).

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2 Comments | tags: 277777788888899, algorithm, calculation, Collatz conjecture, computation, Mandelbrot, mathematics, multiplicative persistence, Numberphile | 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, algorithm, Antonin Scalia, cable news, CNN, computer code, DNA, electrons, Face the Nation, Fareed Zarkaria, fire, genetic code, genetics, internet, interweb, language, mechanical physics, Meet the Press, printing press, quantum physics, robotics, TV | posted in Science

No, sorry, I don’t mean the Bletchey Bombe machine that cracked the Enigma cipher. I mean his *theoretical* machine; the one I’ve been referring to repeatedly the past few weeks. (It wasn’t mentioned at the time, but it’s the secret star of the *Halt! (or not)* post.)

The Turing Machine (TM) is one of our fundamental definitions of calculation. The Church-Turing thesis says that *all* algorithms have a TM that implements them. On this view, any two *actual* programs implementing the same algorithm do the same thing.

Essentially, a Turing Machine *is* an algorithm!

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8 Comments | tags: Alan Turing, algorithm, Church-Turing thesis, flowchart, state diagram, Turing Halting Problem, Turing Machine, Universal Turing Machine | posted in Computers

The ultimate goal is a consideration of how to create a working model of the human mind using a computer. Since no one knows how to do that yet (or if it’s even possible to do), there’s a lot of guesswork involved, and our best result can only be a very rough estimate. Perhaps all we can really do is figure out some minimal requirements.

Given the difficulty we’ll start with some simpler software models. In particular, we’ll look at (perhaps seeming oddity of) using a computer to *model* a computer (possibly even itself).

The goal today is to understand what a software model is and does.

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4 Comments | tags: algorithm, American checkers, checkers, complexity, computer model, computer program, English draughts, Kolmogorov complexity, software, software model, state space | posted in Computers

We started with the idea of *code* — *data* consisting of instructions in a special language. Code can express an *algorithm*, a process consisting of instruction steps. That implies an *engine* that understands the code language and *executes* the steps in the code.

Last time we started with Turing Machines, the abstract computers that describe algorithms, and ended with the concrete idea of modern digital computers using stored-programs and built on the Von Neumann architecture.

Today we look into that architecture a bit…

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17 Comments | tags: address bus, algorithm, assembly language, bits, code, computer language, computer program, CPU, data, data bus, RAM, source code, stored program computer, Von Neumann architecture | posted in Computers