### The upside of procrastination

I've long wondered about the problem arising at the intersection of interstellar space travel and Moore's Law. Moore's Law is an empirical rule that states that technology doubles in speed (or other metric) every 18 months. The laptop that I'm typing this post on right now will be half as fast as the next Macbook Pro 18 months from now.

I doubt I'm the first person to think about this, but imagine a large crew of space settlers at the halfway point to alpha Cen. They might be the second or third generation aboard the space craft, having known nothing but their trip to the nearest stellar system. Out comes the bubbly, but in the middle of the celebration there's an announcement: "Captain, there's something showing up on our radar, approaching fast!" As the object flies by, the crew can just make out the relativistically shortened form of a brand-spanking-new, next-generation space craft, zipping past using the latest technology on the way to alpha Cen.

So if Moore's law guarantees that there will be a better, faster, more efficient space craft if you wait a couple decades, then you should wait for the new ship rather than starting the journey with today's technology. But there must be a break-even point. The solution to traveling to the next star over can't be to just sit around twiddling our collective thumbs. Right?
 Figure from Gottbrath et al. 1999

Well, it turns out that this problem has been solved back in 1999...by astronomers (PDF here). The specific problem in their cas was whether to start a long computation with today's computer, or instead wait until Moore's Law brings along a much faster machine.

Jason said…
It's been bugging me all week, but I finally found the examples of this I was searching for:

In the Marvels comic book Guardians of the Galaxy (coming soon to a theater near you) a human on the first interstellar mission arrives at Alpha Centauri after a thousand year sleep, only to be met with a hero's welcome by the centuries-old human civilization founded by subsequent generations' faster-than-light colony ships.

Steinn Sigurdsson comes through with the original version of this: "Far Centaurus", which Wikipedia explains this way:

Far Centaurus (1944), short story by A. E. van Vogt published in the collection Destination: Universe! (1952). A crew of Terran explorers who have been hibernating through a centuries-long voyage to Alpha Centauri discover on arrival that their technology has been radically superseded; humanity has arrived at the Alphan planet Pelham via superluminal travel long before them, and has long forgotten about them and their primitive mission (compare Comics: Guardians of the Galaxy below). The travelers must overcome their childlike naïveté to cope with the near Godlike human civilization that has evolved in their absence—a good example of the "quasimessianic ... transcendental omnipotence" with which van Vogt often furnishes his protagonists in order to generate a sense of wonder in his tales.[6]
Jason said…
More Far Centaurus:

http://www.centauri-dreams.org/?p=278

### On the Height of J.J. Barea

Dallas Mavericks point guard J.J. Barea standing between two very tall people (from: Picassa user photoasisphoto).

Congrats to the Dallas Mavericks, who beat the Miami Heat tonight in game six to win the NBA championship.

Okay, with that out of the way, just how tall is the busy-footed Maverick point guard J.J. Barea? He's listed as 6-foot on NBA.com, but no one, not even the sports casters, believes that he can possibly be that tall. He looks like a super-fast Hobbit out there. But could that just be relative scaling, with him standing next to a bunch of extremely tall people? People on Yahoo! Answers think so---I know because I've been Google searching "J.J. Barea Height" for the past 15 minutes.

So I decided to find a photo and settle the issue once and for all.

I then used the basketball as my metric. Wikipedia states that an NBA basketball is 29.5 inches in circumfe…

### Finding Blissful Clarity by Tuning Out

It's been a minute since I've posted here. My last post was back in April, so it has actually been something like 193,000 minutes, but I like how the kids say "it's been a minute," so I'll stick with that.
As I've said before, I use this space to work out the truths in my life. Writing is a valuable way of taking the non-linear jumble of thoughts in my head and linearizing them by putting them down on the page. In short, writing helps me figure things out. However, logical thinking is not the only way of knowing the world. Another way is to recognize, listen to, and trust one's emotions. Yes, emotions are important for figuring things out.
Back in April, when I last posted here, my emotions were largely characterized by fear, sadness, anger, frustration, confusion and despair. I say largely, because this is what I was feeling on large scales; the world outside of my immediate influence. On smaller scales, where my wife, children and friends reside, I…

### The Force is strong with this one...

Last night we were reviewing multiplication tables with Owen. The family fired off doublets of numbers and Owen confidently multiplied away. In the middle of the review Owen stopped and said, "I noticed something. 2 times 2 is 4. If you subtract 1 it's 3. That's equal to taking 2 and adding 1, and then taking 2 and subtracting 1, and multiplying. So 1 times 3 is 2 times 2 minus 1."

I have to admit, that I didn't quite get it at first. I asked him to repeat with another number and he did with six: "6 times 6 is 36. 36 minus 1 is 35. That's the same as 6-1 times 6+1, which is 35."

Ummmmm....wait. Huh? Lemme see...oh. OH! WOW! Owen figured out

x^2 - 1 = (x - 1) (x +1)

So $6 \times 8 = 7 \times 7 - 1 = (7-1) (7+1) = 48$. That's actually pretty handy!

You can see it in the image above. Look at the elements perpendicular to the diagonal. There's 48 bracketing 49, 35 bracketing 36, etc... After a bit more thought we…