How big is an Orbital?

Filed under: math — jlm @ 06:38

In science fiction, it’s fairly common to use centrifugal force to simulate gravity in space. This is usually used for ships or space stations, but Larry Niven took it to an extreme with his famous Ringworld, which circles a star at orbital distance and spins enough faster than orbital speed to provide Earth-equivalent “gravity” against its inside. Iain Banks thought this was too extreme even for fantastically-powerful civilizations, so toned it down a bit by having a ring that revolves once per day and provides 1 g from its spin. (Niven’s Ringworld needed “shadow squares” between the ring and the star to provide night.) Banks calls these “Orbitals”, places them in planetary orbits, and implies that they’re of planetary dimensions. But, how big is an Orbital really?

Well, we want a period of about an Earth day (d), and centripetal acceleration of about an Earth gravity (g). Consider a point x on the Orbital at angle θ. x = r î cos θ + r ĵ sin θ. To provide an Earth day, the Orbital revolves through 2π radians in 1 d, so dθ/dt = 2π/d. Acceleration is the second derivative of position, so a=d²x/dt²=(-r î cos θ-r ĵ sin θ)(4π²/d²). We want ∥a∥ to be 1 g, so ∥a∥ = r·(4π²/d²) = g, or r = g·(d²/4π²). To match Earth, g should be about 9.8 m/s² and d about 86400 s, which puts r at about 1.9×109 m.

That’s huge! (Though not Ringworld huge.) The radius of the Earth is only 6×106 m, and Jupiter is “only” 7×107. An Orbital is 300 times as wide as the Earth. (Though potentially much shorter.) But still not orbital distances– it’s only 1% of the size of Earth’s orbit.

Now, how strong does an Orbital have to be? Well, let’s consider a small section of the Orbital subtending an angle Δθ. This will have length Δl = r·Δθ. If the Orbital has a linear density σ, this section will have mass ΔM = σ·Δl and weight Δw = g·ΔM = gσr Δθ. If the tension is T, the internal force at the edge of the section will be T î sin ½Δθ + T ĵ cos ½Δθ. The i component of this force holds “up” half of the section’s weight, the other edge providing the other half. Using the small angle approximation for sine, we get ½Δw = T·½Δθ, or T = gσr. So the strength we need is T/σ = gr = 2×1010 m²/s². If the Orbital’s cross-sectional area is τ, then the internal tensile pressure is P=T/τ so T = P·τ. If its material density is δ, then σ=δ·τ, so T/σ = P·τ / δ·τ = P/δ, which tells us that the 2×1010 m²/s² is the ratio of tensile strength to density we need. This is 10000 times as strong as existing high-tension materials like Kevlar (stuff like steel and titanium and diamond isn’t particularly strong in the tension department) and still 600 times as strong as the supposed carbon nanotubes that they say may make a space elevator possible. And this is just enough for the structure to not tear itself apart by its own spin, much less support anything you want to have on the Orbital. I thought solar tides might be an issue, being about 9×1020 N for each Earth mass of the Orbital, but the spin tension blows that away at 6×1025 N per Earth mass. So, sadly, even through this is orders of magnitude more feasible than the Ringworld, it’s still never going to work.


Berkeley DB locking

Filed under: programming — jlm @ 18:28

The locking in Berkeley DB is fundamentally broken.

This isn’t something that’s bitten me recently, but talk about it did come up recently, and many BDB users are unaware of the problem. It’s especially surprising when you first encounter it because BDB is so solidly done in the rest of its implementation and the problem isn’t advertised. Of course locking will work — everything else does!

The problem is that BDB locks are bare mutexs, and no forcible release mechanism is provided. There is no way to rollback to a state before a lock was acquired. There is no way to retry. You take the lock, do your modifications, and release. Or you take the lock, do some of your modifications, and the circuit breaker trips, power is quickly restored, the server reboots, and now your BDB is hosed. You can’t take the lock because BDB thinks your old instance has it. You can’t release the lock because you don’t have it. If you could release the lock, your database is inconsistent because you can’t rollback. The only way you can do anything is to blow away the BDB environment and make a new one (suffering collateral damage when you just want to destroy a mere lock) and hope that the partial transaction you’re unleashing as a result isn’t a problem (and if it isn’t, why did you need a lock?).

So, what can you do? You can try to build your own transaction system on top of BDB, but that’s a lot of work. A lot of work, when there’s better featured databases out there already. If you were using BDB and need more, MySQL is probably good enough for you. It has partial transaction support (probably more than you want to write!), and does have a library implementation (libmysqld) so you can avoid running a server and just use data files, like in BDB. If you need full transaction support (good luck implementing that on your own), there’s always ye olde enterprise-grade PostgreSQL. Or maybe you don’t need transactions after all? Then Berkeley DB is solid as a brick.


What is that thing, anyway?

Filed under: web — jlm @ 17:19

So, the firefox logo makes sense.

[firefox logo]

A fox, with a firey look. Cool logo.

But what’s that thing behind the fox? Well, with the Deer Park logo, we get a better look.

[deerpark logo]

But if you look closely, you see that the shapes on the FF globe don’t match those on the DP globe. And they don’t look like the continents I know. Maybe it’s just an ordinary circle with abstract shapes? But it’s shaded like a globe. Is it one of those funky extrasolar planets? (They’re planning a Galaxy Wide Web!)

I think I preferred the fox. I also liked the old Red Star mozilla logo, not so much the dino head or the big “m”. And don’t get me started on the ship steering wheel or the big “N”. Even the old NCSA Mosaic logo was better than those.

[mozilla red star][mozilla dinosaur head][mozilla “m”][ship rudder wheel][Netscape Navigator big “N”][NCSA Mosaic logo]

Why does every iteration of the product need a new logo? Doesn’t seem like the best way to build brand awareness. Compare:

[Microsoft Internet Explorer logo]

New Firefox

Filed under: web — jlm @ 14:27

Firefox 1.5 beta 1 (“Deer Park”) has just been released.

This was good timing for me, as I’d just updated GTK+ from 2.4.14 to 2.8.3 in order to get GnomeMeeting working, and that had broken Firefox 1.0PR, so I was back to using the old Mozilla 1.7 I had lying around.

Download pre-built versions at http://www.mozilla.org/projects/firefox/ or build it yourself from the source at http://ftp.mozilla.org/pub/mozilla.org/firefox/releases/1.5b1/source/

This will unpack into a directory named “mozilla”, so be careful about clobbering other mozilla builds if you have them. Build directions are at http://www.mozilla.org/build/

The “Starting the Build” directions didn’t work for me, instead I had to do what it has under the box: cd $objdir; ../configure; make

Oh, and the tarball it makes from make -C $objdir/browser/installer is tagged “1.4” still, but that’s minor enough. Now I just need for the extentions and “themes” (skins) to be updated.

Big screens

Filed under: general — jlm @ 09:53

I promised you a more upbeast post, so here it is…

Work recently gave me two very nice LCD monitors to replace those I’d been using before. 24″ TFT from Dell.

“Unfortunately”, the graphics card in the desktop I had (which I’d been using since getting hired) couldn’t drive these things, so they gave me a HP xw4200 to replace my xw4100, double the RAM and faster processor.

Now my computer can display on my monitors, but side by side things are very wide. But, these monitors can rotate on their stands! (Couldn’t do that with my old ones.) So, I want them vertical and side by side. Well, someone else had done the hard work of figuring out how to make that work, so I went and followed his lead. The distillation of that came down to:

  • Install the x.org X server (this deserves a post in itself)
  • Edit xorg.conf, turning off Xinerama and turning on xrandr (for now they’re incompatible):
    • In the “Device” Section, add Option "NoTwinViewXineramaInfo" "on"
      and Option "RandRRotation" "on"
    • Change TwinViewOrientation to “Above” or “Below”
    • In the “ServerLayout” Section, add Option "Xinerama" "off"
  • Put xrandr -o left at the start of your .xsession

Before and after screen shots at 1/8 scale:


I finally have enough space to have all the xterms I want! I’ve been trying to reach this state since forever, first with screen then with just piling the xterms onto all the real estate I could get. I don’t have to drop context and have space left over now. It’s surprising how good this feels– It’s this slight pressure that I never really noticed, the small frustation of having to look for somewhere to type– gone.


Running on empty

Filed under: biking, so. cal — jlm @ 12:08

Biking from Union Station to Pasadena at 1:30 at night when you’ve already biked 30 miles that day is like an hour of some kind of Greek hell. Not painful, but dark, and cold, and lonely, and tiring, block after block after block gradually uphill, with no sign of progress.

The MTA ticket machines are pretty cheeky letting you buy a ticket after the last train has left due to the holiday schedule, with no signs up saying the last train will leave at 11:50.

Encountering a Winchell’s on the final leg up Fair Oaks was welcome, though I could have used it earlier.

Jacob’s route from getting from Union Station to Pasadena when you’re bone tired and don’t want any big hills:

  • Union Station is on Alameda. Take this north a couple blocks to where Main St. veers off to the right.
  • Take Main through the industrial area into Lincoln Park. This goes through a pass in the Lincoln Park hills, so you avoid climbs like you’d get taking say Broadway.
  • Main turns into Valley at Mission St. Turn left (north) here.
  • When Mission meets up with Huntington, get on Huntington and ride it through El Sereno into South Pasadena.

If these directions make any sense to you, you already know how to get from South Pas to whatever part of Pasadena you live in. For me, this was taking Fair Oaks in. These directions are poor at encountering all-night victuals depots, so could use some refinement here. (Maybe Broadway to get some food, then cut down to Main St. for the pass?)

My legs and butt still hurt.

More upbeat post coming soon…


suphp and WordPress

Filed under: linux, web — jlm @ 13:14

Okay, so I now have WordPress working with suphp, which allows for the use of Unix user accounts in php scripts. Steps:

  • I made a dedicated jlmphp account, so php won’t have access to my main account.
  • The hosting server (ofb.net) runs Debian, so I installed suphp with
    apt-get install libapache-mod-suphp
  • In the Apache config, I put the lines:

    LoadModule suphp_module /usr/lib/apache/1.3/mod_suphp.so
    suPHP_Engine on


    <VirtualHost *>
    ServerName php.mandelson.org
    DocumentRoot /home/jlmphp/www/data/

    The first set turns suphp on, the second set makes a virtual host “php.mandelson.org” with its own www directiory in jlmphp’s homedir.

  • Made a CNAME aliasing php.mandelson.org to mandelson.org, so that when you look up php.mandelson.org you get this server.
  • Changed the blog address to be http://php.mandelson.org/wordpress/
  • In the .htaccess file for jlmphp, put

    AddHandler x-httpd-php .php

    (which tells Apache to use suphp for .php files in this directory), and put in redirects from the old blog address to the new.

  • Made wp-config.php user-readable-only and change the passwords. (Which is the whole point!)


Make your own robot

Filed under: misc — jlm @ 21:15

Someone has done something creative with that Flash engine which is used to make all those insipid dress-up “games”.
Newgrounds link

It won’t let you really make a robot. But you can make an image of one:

[image of robot]


Information theory applied to word puzzles

Filed under: math — jlm @ 19:12

You know those coin weighing puzzles? For the most part they can all be solved easily by using elementary information theory: At each step just make the weighing which maximizes your expected information gain. But what about word puzzles, can the math help us here?

Well, lately I’ve been playing this word game sometimes called “Jotto”. The idea is you pick a six letter word, and the person you’re playing against also picks a word. Then you each try to guess the other’s word. You do this by selecting a word, then they tell you how many letters match their secret word.

For example, if my word is “spaces” and you guess “guests”, I’d tell you that 1 letter was right. Then I’d get a chance to guess your word.

But what’s a good strategy? Well, I often try “throw out a lot of vowels” then once I think I have those pegged I play hot-and-cold with the rest of the word. But more ideally, you’d pick a word which divides up the word space as evenly as possible so you’ll get to small sets of possibilities quickly. Or put another way, you want to maximize the amount of information you acquire at each guess. Now, estimating information content is hard to do (how many words are one-letter matches of “spaces” as compared to zero-letter matches? Now take the logarithm…) but it’s easy enough for a computer to calculate, so I built a “Jotto Bot” which does just that. It plays pretty well — sometimes amazingly, but it doesn’t learn, so once you’ve found a word in the information boondocks, it’ll always do poorly on it… for now.

You can play with it here. Nicest is “you vs. computer”, but “computer guesses your word” shows you what’s going on behind the scenes.



Filed under: programming, web — jlm @ 17:00

One of the sessions I attended at OSCon was about the upcoming CalDAV standard. As calendaring is a weak spot in the Linux/Free Software application space, advances here are particularly welcome.

There was a panel of implementers there, representing:

  • Novell / Hula
  • Mozilla Foundation / Sunbird and Lightning
  • RPI / UW Calendar server
  • OSAF / Cosmo and Scoobie and Chandler

(organization) / (programs)

A lot of the session talked about features of their various products, but I’ll ignore those in favor of looking at the protocol.
CalDAV in a nutshell is WebDAV holding iCalendar files and extended to handle calendar-type queries (“when is Joe Blow free?”). The idea is the basic common protocol one: An open spec will let all these products interoperate, so you can use the calendar app which is your favorite without having to bother with which calendar system is at the other end. (Do you know what software your email server is running?)

The IETF tried to standardize calendaring before, with its CAP (“Calendar Access Protocol”), but no one implemented it. Starting from WebDAV means implementers have less work to do, and hey!, it’s working.

Stuff like room / multiparty scheduling is not addressed, they’re leaving that for a later protocol. “Clearly more research is needed.” Conflicting schedule changes are detected using ETags; resolution is unspecified and left to the clients to decide.

If you’re doing any calendaring, you absolutely want to take a look at it. You’re already supporting iCalendar (right?), and there are WebDAV implementations out there you can use (though alas not particularly cleanly), and from there to CalDAV isn’t a big step for an implementer but is a giant leap for interoperability.

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