John Lindal’s Blog

The Arrow of Time

I just read an article about the Arrow of Time. The foundation of the author’s discussion was entropy and the observation that it always increases. From a macroscopic perspective, this is reasonable, but it seems to me that there is an even deeper argument. If I understand the Free Will Theorem correctly (always iffy for deep stuff like that), then, assuming humans have free will, the result of measuring properties at the quantum level cannot be known ahead of time. I believe Conway stated that the result doesn’t exist until the experiment is performed. I can’t conceive of anything more unidirectional than that. There is just no going backwards.

Note that the Free Will Theorem directly contradicts the article’s claim that knowing the exact state of the universe allows you to compute the future.

Hero Dice

If you’ve ever played Champions (the Hero system), I’m sure you’ve wished you had dice that would always roll low for attack, ensuring you hit, and high for damage, ensuring that your opponent will not get back up. Character Builders, designed for D&D character generation, cannot get the job done because they always roll high, so you’ll never hit

I searched the web and only managed to find these instructions for how to make crooked dice. Nobody appears to actually sell such stuff

Interestingly, the design I came up with is mentioned by the above link, but it is described as unreliable, presumably because those who wish to steal money by cheating at dice games need their weighted dice to be far less noticeable than what a friendly neighborhood Champions player can get away with. Not that gamers don’t take it just as seriously as gamblers, of course, but frugal, judicious use of adjustable, weighted dice would be very hard to notice.

So, as you’re probably guessed, my design allows the weighting to be adjusted so the dice can be fair or weighted towards either 1 or 6:

1. Start with a die that has 1 and 6 on opposite faces.
2. Drill out the core of the die on the 1-6 axis, leaving one of the two faces intact.
3. Line the inside of the intact face with thin cloth.
4. Mount a thin guide pin on the drill axis.
5. Cut a disk to fit the hole in the die. The thickness of the disk should be 1/4 of the depth of the cavity that was drilled.
6. Drill a hole in the center of the disk so it can slide along the guide pin.
7. Remount the missing face with an inner lining of thin cloth.

This is the base configuration. It allows the weight to slide back and forth between the 1 and 6, so either can be weighted to make it least likely and the opposing face most likely. The guide pin ensures that the disk slides correctly. The inner cloth lining muffles the sound when the disk moves. The thickness requirement is necessary for latching the disk at either end or in the middle. The hard part is making this secretly configurable.

If the pips are raised, then you can convert the two corners of 3 or the two pairs of corners of 5 into invisible buttons that are the ends of rods running through to spring loaded latches embedded in the opposite face. There are two latches in order to allows the disk to be positioned either at the center or behind 1 or 6:

+-------
        |
        |
       <**
        |
        |
       <**
        |
        |
+-------

If only one latch is opened, the disk can slide between that face and the center. If both latches are opened, the disk can slide from one face to the other.

To avoid detection, you would keep the disk at the center of the die until you were ready to roll. After picking up the die in preparation for the roll, you hold the die with the desired result facing up and push the appropriate pips. After the roll, you pick up the die again, turn it upside down, and push the pips again to re-center the disk.

Unfortunately, raised pips are quite unusual and are likely to temp others to try pushing them, just for fun. An alternative is to convert an entire face of the die into a pair of buttons, but this makes it harder to conceal because there will be a hairline cracks. A better, though more complex, solution is to use additional pips to implement a locking mechanism for the latches. This way, the pips controlling the latches can only be pushed while another pip is pushed in. The best way that I can think of is for the latch rod to have a bump which is obstructed unless a pip is pushed to remove the obstruction. Imagine these two running orthogonal to each other in 3D, so the bump in the left piece can pass through the U-shape at the right:

   ^
+--|----
        |
        |
       <**
        |

+-|  |-*
   --

This is an awful lot of machinery to put inside a standard size 6 sider, but I’m sure it could be manufactured. I doubt anybody ever will, however, since the market niche is so miniscule.

Homer³

I watched an episode from the Simpsons’ Treehouse of Horror DVD last night. It’s truly wonderful to have all the craziest Simpsons’ Halloween specials on a single DVD Homer³, one of the skits in the episode, proves once and for all that at least some of the writers for the show are true geeks. There were some wonderful math formulas floating around in the 3D world into which Homer stumbled!

It’s not new, it’s timeless

e^iπ + 1 = 0

Geometry

My back has been killing me for over a week. So why am I suddenly craving cheerios and milk?

While lying in bed staring at the ceiling fan — specifically the three screws used to hold each light bulb cover in place — I began wondering how to inscribe an equilateral triangle inside a circle. The next obvious question is: How does one go the other way? And also: Can one circumscribe any arbitrary triangle with a circle? How?

Click here for the solutions that I came up with.

Schlock Mercenary

Being sick sucks, but it does provide a chance to catch up on reading, if you’re not so hosed that you can only sleep. I guess passing out at 6PM yesterday helped me get enough sleep

Anyway, while I normally read books, but this time, I drilled through the 2003 – 2006 archives of Schlock Mercenary.

Howard Tayler definitely has the “Niven Spark” — a term I use for those who think on a really, really big scale. It’s surely not fair to all those who came before Niven, but the scale of his galactic history is just huge.

Tayler’s galactic history is pretty darn big, too, starting with the introduction of the teraport to rival the established worm gate system, and ending up, well, rather differently than most readers would expect.

But the really impressive part is that Tayler never loses sight of the fact that his story is about Tagon’s Toughs, not galactic history, so all the massive insanity is still experienced through eyes to which we can relate. And never once does Tayler lose his sense of humor and miss a punchline. That is hard to do for 6 years straight!

Not to mention that Tayler works pretty hard on his physics, too. Even if he has to invent all sorts of technlogy that violates General Relativity, he still like to work out the details of the stuff that doesn’t!

Well worth reading from the beginning…

Disaster Movies

Two weekends ago, I was laid low by the stomach flu, and it was my misfortune that they were showing The Core and Armageddon on TV that weekend. It’s been bugging me ever since, so I’d better just blog about it and get it out of my system.

Armageddon is by far the better of the two. Despite the wildly fluctuating value of G on the asteroid, the crazy surface topography (for an object that has presumably been knocking around in the asteroid belt for eons), and the never-before-seen metal that eats drillbits for breakfast, Armageddon at least has heart. Bruce Willis’ character does the right thing by insisting that he, rather than the guy who will marry his daughter, should sacrifice his life.

The Core sets a new, abysmal low for disaster movies. Even the writers couldn’t come up with a reason why the Earth’s core would stop generating a magnetic field, and they admitted as much in the movie. Their idea that it was the spinning of the core that generates the Earth’s magnetic field (“Moving metal generates a magnetic field. Physics 101.”) is flat wrong — moving charges generate magnetic fields, not moving metal — and Earth’s field would not last a week if all the currents truly stopped. The giant spark plug that they built as a backup system was equally idiotic — there is no relationship between restarting a heart with a defibrillator and restarting the currents in Earth’s core with an EMP. The idea that a nuclear explosion would restart the spin of the core was also wrong — pressure waves do not move mass, they only wiggle it — just like waves in the middle of the ocean. The shielding on their ship violates the basic laws of thermodynamics — nothing can stay cold when immersed in a hot environment, unless it has a huge reservoir of something cold into which to dump the incoming heat. Their depiction of Earth’s mantle was ridiculous — molten rock is not transparent and solid quartz crystals cannot exist at those temperatures.

Sigh. Makes me yearn for a Liz Taylor disaster movie…

Light bulbs

I woke up this morning wondering about light bulbs. Your standard incandescent bulb will fall over if you place it rounded side down, unless you balance it perfectly, so this is an unstable equilibrium. Your standard floodlight will not fall over, however, so this is a stable equilibrium. What makes one unstable while the other is stable? Where is the crossover point? Can we make it a neutral equilibrium, i.e., it will stay in whatever position we place it? Click here for the answers.