Reading the xkcd forum has turned me on to the awesomesauce that is Manufactoria.



The concept is simple at the start. Your job is to build a machine to test robots to ensure that their "program" (expressed as a string of red and blue dots) meets certain characteristics. For instance, the layout above tests to see if a robot's program ends with two blue dots. The conveyor belts pushes robots (that start in the circle at the top) into a neighboring square in the direction indicated, and the branches eat the first character in the string and push the robot in the indicated direction (or in the direction of the gray arrow if the string is empty). In this case, you can see that if the input string ends with two blue dots, the robot will be pushed to the acceptance square in the bottom, otherwise it will fall on the floor and be destroyed.

So it starts off as a fun model for deterministic finite automata, and that's cool enough. But over the course of the 31 levels, the ability to print dots at the end of the input string and a greater range of colors is added, and then you've got an entire range of formal grammar problems available for challenges. And once you've solved a problem, you can go back and tinker with it to make it smaller or faster as you wish. Or you can keep going through some pretty dense challenges that get hard to fit on the factory floor, much less read. That above example was maybe level 10 or 11 of the set, and let's call this level 29:



Still have two more challenges to figure out myself, but it's a great time if this is the sort of thing that you're into.
I've said it before, but if Wonderella and I agree that you are off the rails, then dude, you are seriously off the rails. However, people seem to eagerly argue that the KFC Double Down "sandwich" is the greatest abomination in fast food history.

Please.

Even if you handicapped them by putting a bun around it, it's a double chicken sandwich with cheese and bacon. That doesn't even survive the first round of the Fast Food Abomination playoffs. When I was living in California, Jack in the Box would routinely offer specials like double cheeseburgers with three slices of cheese, five strips of bacon, and ranch dressing. But this? Burger King has spent years with "buy one chicken sandwich, get one free" coupons, and you have to know that customers were routinely eating both of them in the same meal. Take a deep breath.

My only question is why people are going into a KFC and ordering processed products like this when their signature fried chicken is so outstanding and you can just SEE that it's made out of a whole chicken with breading and fried in oil and nothing mysterious except exactly what the specific herbs and spices are.

On a slightly broader and less silly note, Nate Silver at 538 does an interesting deconstruction of the issue (which is a great relief from that site's normal operation these days of relaying Obama's talking points without even pretending that it's about poll analysis or statistics any more), and I think he is onto a good point when he talks about the utility of understanding nutritional benefits and harm per calorie. I think that there are two tough parts about meal planning with an eye towards maintaining weight. The first is making sure that you're taking in the proper amount of calories considering what you burn off through your basil metabolism and exercise, and the second is making sure that you don't accidentally shoot your entire wad of sodium or polyunsaturated fats on a single small portion of it. And the data that we get doesn't always do the best job of driving that home. I don't think that Silver has the magic bullet right off the bat, but it's an interesting avenue for exploration.
I don't think I've ever been a fan of April Fool's Day. In fact, I suppose I'm antagonistic to it, as opposed to things like Groundhog Day that we seem to only do this year because we did it last year.

I mean, what's up with a holiday that celebrates unreliability? I see people who spend a day spreading a lie and wonder how that fills them compared with a day where you go out and tell the truth. I appreciate the creativity (when the hoaxes are creative), but direct the energy into something that will persist and grow! Okay, okay, I admit that without April Fool's Day we probably would never have had tauntaun sleeping bags, but I'm having trouble thinking of another boon.

This is just one more in a long line of indications that I am the personification of Lawful Good. I appreciate and adore individuality, but you need a strong structure in which to nurture creativity or else you are constantly under attack from people stronger or smarter than you. You deregulate the financial markets and greedy people will propagate a housing bubble that first drives up your property taxes and then leaves you on the hook to bail them out when the bubble bursts. The internet is high among the most awesome of human accomplishments, but we now have access to a larger supply of misinformation than ever before in history, allowing us to find data to justify our prejudices faster and more widely than ever before. Chaos within order should be like stars in the night sky; enough that we can appreciate their beauty but not so much light that we would be blinded to everything around us.

Perhaps on the first of October we might make a point of going around and being intentionally honest with one another. I like those days much better.
I've had my ups and downs with Barack Obama, but I am pleased at the decision to drop the 2020 moon landing project.

The United States is the only nation that has been to the surface of the moon, which we did over forty years ago now. As soon as it became clear that other nations were thinking about trying, George Bush decided to pledge to spend billions of dollars to ... get there first, despite the fact that we already had. We know better than anyone else that there's nothing there. There's no life, there are no moon diamonds, there is no ready sources of Helium-3. Maybe there is water, but you'd be pretty foolish to show up there thirsty with an empty cup instead of bringing your water from Earth. The only thing that's there is a metaphorical finish line, and we've already crossed it. (I wish the Chinese and Indian governments great luck in crossing it themselves, and hope that they don't have to spend as much in blood and treasure as we paid.)

More foolish yet is the notion that we were going to use some sort of moon base to stage our trip to Mars ten years down the road. This never made a lick of sense to me. I'd love to think that we could build something of value off-Earth, but I've never seen it. The ISS is in a constant state of FUBAR, and everything else in history has been constructed on Earth. If you somehow were to think that gravity is the enemy in aeronautical construction (and I can't imagine why you would in this case, which is making a craft that needs to survive Martian gravity), then why would you build it on the Moon when you have an infinite amount of zero-gravity real estate everywhere else in space?

Plus the dream that we're going to Mars in our lifetimes is something that we seriously have to wake up from. We're not talking about a three-day trip to the Moon. If you want a round trip to Mars, it's a year to get there, nearly a year to stay there while the orbits align, and then a year to come back. So you need to carry along three years of food and water for however large your crew is, and at least two years of protecting yourself from lethal solar radiation. So you need enough power to carry all that crew and food and water, plus enough tech to scrub oxygen that won't be replaced until you get home. Those are currently insurmountable problems. And God forbid you'd actually want to land on the Martian surface, because then you need your crew to repair your pod and somehow refuel it enough to allow it to relaunch and escape a real planet's gravity well and travel a year back to Earth. Can you imagine the Space Shuttle landing even on Earth on something other than a pre-fabricated runway and the crew single-handedly preparing it for the next launch while simultaneously worrying about their own survival in an inhospitable environment? No, you can't even imagine it; we've never seen anything like it before. Now take away the atmosphere and the moderate temperatures and the instantaneous communication and you've started to scratch the surface of life on Mars.

Not only is the technology insurmountable, but our will is too. The first trip to Mars will be a suicide mission. The brave men and women we send off to Mars will, if they're very very lucky, *die* on the surface of Mars. (I could not possibly illustrate this point more beautifully and tenderly than xkcd did today.) NASA doesn't have the courage to launch the Space Shuttle on a cloudy day. If we were to build a rocket in space, we wouldn't trust it enough to put the best lives America had to offer on it. I don't blame us for this, because I'm not sure that science and exploration is worth blood at the end of the day, but at least let's recognize that we'd never initiate the mission before we spend another fifteen years paying a hundred billion dollars for it.

I'm not opposed to technology and pushing the boundaries of discovery, but let's do it with our heads on straight. Build me a self-sufficient colony with a thousand people a hundred feet underwater that works without drama, and you'll have learned things about atmosphere and food and water and energy that will eventually make space colonies more achievable for our grandchildren, and that will furthermore probably have application for more ordinary terrestrial communities. In the meantime, let's devote the largest share of our research energies to the problems of today, climate change and alternative energy and affordable medicine, instead of the challenges of fifty years ago and a hundred years from now.
I have long-since noticed that my name is ripe for cryptic crossword wordplay, just made for a charade or even a hidden word. But, amazingly, it was only just yesterday that I noticed that it is nearly ideal for a different geeky math-language recreation.



Pretty low quality, except that it was done by a non-artist with ten thumbs with a mouse in Microsoft Paint. And a quick Google search notes that few people decided to solve the problem the way I did. It has its flaws, but I like it all the same.
I just proved that multiplication of the natural numbers is commutative. It took a half a page (and I lost track of how many pieces of scratch paper to work out the details), and that includes assuming that addition is associative and commutative and cutting out as much formalistic dreck as I could. Just to prove that ab=ba for the positive integers only.

So, if you were concerned about that, you can relax.

NaTexWriMo?

Nov. 7th, 2009 02:00 pm
Reading through my FOAF lists, it amuses me to point out that I've started LyX'ing up the solutions to all of the problems in Bondy and Murty's Graph Theory with Applications, my college graph theory textbook. Naturally, given the scope of the material, it might be unreasonable to expect that I could grind out 50K words in a month, since precision is more central to mathematical writing than to novelization and so editing is critical instead of counter-productive.

That being said, 8948 words so far, 13,948 if you use the time-honored conversion that a picture is worth a thousand words.

And how cool is it that authors are releasing PDF's of out-of-print college textbooks? This is not the only $50 book in my library that is now free for download.
I like living in the future. I was reading a blog a few weeks ago that reminded me of Heaven & Earth, the most excellent Scott Kim puzzle game that never got the publicity it deserved, so I dug out my copy and replayed it. Then, hitting the end, I had to Google to verify that the victory screen was actually the end and not an Easter Egg for a further challenge, which led me to a forum where someone was giving love to Bug Brain.

Wow. I've never had the opportunity to play much with practical logic circuit design. Electronics books get esoteric in a hurry (even when they're written for kids) and math books stay abstract. I've always wanted a platform that combined the relevance of robotics with the puzzle-oriented worldview of games like The Incredible Machine. Evidently, someone wrote this game for me in 2000 but didn't go to the trouble of telling me about it.



This is an example of an intermediate-level puzzle, designing an artificial brain for a worm that is supposed to crawl forward until it hits a door, and then back up for a few seconds (to allow space for the door to swing out), and then return to the forward crawl. The brain contains input nodes (the red circle, which fires if the head is currently against an obstacle) and output nodes (the four blue circles, which direct the motor skills for raising the middle segment, lowering it, grabbing the ground with the head segment, and grabbing the ground with the tail segment when they are charged). The green circles represent neurons, which do the very elementary computation of measuring whether the accumulated charge of all of the incoming synapses (which can be individually weighted and even negatively weighted to inhibit charge) and send a charge down all of its outgoing axons if the total is greater than a threshold you define. You can use that mechanism to create the common logical gates: the two neurons in the middle of the brain are an AND and OR gate, and combined with the two supplemental yellow nodes they form the logic of an XOR gate. In addition, you can set synapses to slowly lose their charge over time, which let you form natural constructs like the feedback loop in the upper left that allows the brain to briefly "remember" that it bumped its nose a few moments ago and the two neurons with mutual decaying inhibitors in the lower left that form the cadence that it steps to. As the worm "chapter" progresses, you get control of more input and output controls and have to design more complex brains that ultimately have you negotiating a 2-D landscape filled with obstacles to find mushrooms that you can sniff out.

The game is far from perfect. The learning curve can be very steep for some problems, and while there are hints and even full solutions available you just wind up building the author's model instead of conceptualizing your own. It would also be nice if you could "chunk" common components like this XOR gate into a single "bundle" of neurons because it can get tricky to read the brains as they grow. The game contains a final module that hit on the real apparent strength of neural networks, which is their capacity of adaptive self-programming, but the examples they give are either simple or don't solve their problems dependably. But the biggest flaw is that it's such a delight that it's over too quickly.
I'm probably not the first person to say this, but I haven't heard it said yet: Wolfram|Alpha rocks in stereo.

My first exposure to it was this evening, when my brother told me that he wants to program an object to move around "in a figure 8 pattern (well, a figure 8 on it's side)" but doesn't know the math behind it. My copy of Schaum's Mathematical Handbook seems to have wandered off, so I turned to Google, which offered no response to "lemenscate". No huge surprise, since I pulled that word out of the back corner of my mind and for all I know I made it up. So I eventually hit on a search for "infinity symbol" and Wiki tells me that the correct word is actually "lemniscate". A properly-spelled Google search works out, but this time a short Wiki trail from the top result fails me and I actually need MathWorld's site (and paging two screens down) to get the parametric equation I was looking for. Total time elapsed to get the answer I wanted: maybe five minutes. Bad Google-Fu, no biscuit!

With WA, http://www44.wolframalpha.com/input/?i=lemenscate. Not only does it instantly strike gold with the misspelled word, but it turns that gold into ... um ... some sort of valuable gold thing. I suppose it's no surprise that Wolfram is going to have math subjects covered well, but it's still quite impressive. Once their engines start being able to parse searches related to the softer sciences, it's sure to be quite a tool.

(And, just in case some wouldn't know how Google-Fu would lead me to the subject line, please for you to clap hands and cheering for The Ministry of Unknown Science.)

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Matthew Daly

December 2012

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