Built on Facts

Snowy Decibels

There’s a list of books a cultured person is supposed to have read. Its size and composition vary depending on who you ask, but roughly speaking there exists a Western canon containing works by authors with names like Shakespeare and Dostoevsky and Milton and Sophocles. There’s something of a Nerd Canon too. The names of the authors of its works are more like Asimov and Feynman. It’s a list that’s certainly not all science and science fiction, though those are much more strongly represented than in most general lists. To me knowledge no one has ever written such a list up, but it exists as part of the zeitgeist of our subculture.

One of the names on the list is Neal Stephenson. I would say he has at least two books on the list: Snow Crash and Cryptonomicon. The latter is an awe-inspiring work, one of those rare books that truly left me a slightly different person operating in a larger and richer universe. The former is a book I am rather embarrassed to admit that I haven’t read. At this very moment, I’m one hundred and eighty-three pages into fixing that. It’s a fantastic book thus far.

At one point the protagonist – Hiro Protagonist is his name* – has a brief conversation with a famous Japanese rapper named Sushi K. Hiro talks with Sushi K in his car while the previous act is still on stage having an immensely loud concert.

Sushi K rolls down the window. The decibel level quintuples in an instant. He stares at the crowd, five thousand potential market shares, young people with funkiness on their minds.

It’s possible to interpret this two ways. The crowd sees him and gets louder, or the crowd is already loud and rolling down the window happens to let the sound in. Now Stephenson knows his physics, so either way he’s not going to get this wrong. But is he being literal or metaphorical? A decibel is a way to describe a ratio. Many quantities – sound in particular – comes in such a wide range of intensities that it’s almost pointless to use a simple linear unit of measurement like watts per square meter, and in any case it’s the differences in levels of sound that are often more important than any absolute unit of measurement.

The decibel scale exploits these properties by measuring on a logarithmic scale. Popping the defining equation for a decibel level L from Wikipedia:

i-d4bb9fe09d6b78eb832985821d8a307f-1.png

Two sounds with two intensity levels P have their ratio expressed as L decibels. Making a sound 10 times more intense means increasing its level by 10 decibels. Thus a 90 dB sound is actually ten times more intense than an 80 dB sound. That doesn’t actually mean your ears will perceive the sound as ten times louder, your ears follow a more complicated pattern.

Since a decibel is defining a ratio it’s not actually meaningful to say a sound is “50 dB” by itself. When you heard a sound given that way without a reference, it’s actually implied that it’s 50 dB more intense than a particular reference intensity arbitrarily defined as 0 dB, which generally is roughly a very quiet sound at the threshold of hearing. In SI units this happens to be about 10^-12 watts per square meter – a tiny, tiny power flux.

A conversation such as the one Hiro was conducting might be around 50 dB. Multiplying the power level by a factor of five would only bump the sound up to about 53 decibels by our above equation. Multiplying the decibel level would give us 50*5 = 250 dB. This happens to be multiplying the actual sonic power by a factor of some 10^20, which corresponds to about ten trillion or so watts per square meter. I expect that would vaporize the entire concert just about as well as a thermonuclear explosion.

And if Stephenson meant the 120 dB or so of a rock concert was quintupled to 600 dB, well, that’s more than a bit worse, since it’s 10^(600-50)/10 times more power than the voices of the conversation. That’s a huge number. Every square meter would correspond to a power flux greater than the output of every star in the galaxy – by a lot.

As I said, Stephenson knows his science. Thus it’s pretty safe to declare this sentence a metaphor.

*This isn’t just lampshade hanging, by the way; it does make sense in the context of the story. The story itself is perfectly serious, while the setting is slightly self-aware. It would be overstating things to say Snow Crash is to Neuromancer what Sin City is to classic noir, but it would at least be in the neighborhood.

Comments

  1. #1 Chad Orzel
    June 13, 2009

    I would’ve taken it to mean that the background decibel level increased to the 120-ish dB of a rock concert, not that it started there and went up. If you read it that way, the background level in the car would’ve been a fairly quiet 25dB, which is awfully good soundproofing for a car, but a more reasonable mental image.

  2. #2 Perry E. Metzger
    June 13, 2009

    FYI, my favorite Stephenson book is “The Diamond Age”. It takes place in the same universe as “Snow Crash” quite a long time later (though you can only tell by reading very carefully — as one hint, Y.T. reappears, though if you skip one particular sentence in the book, you won’t notice.)

  3. #3 John
    June 13, 2009

    Zodiac is a pretty great Stephenson book too, although its not quite in the same genre as the rest of his writing. And Anathem was pretty weird. Still haven’t gotten around to The Diamond Age yet.

  4. #4 Eric Lund
    June 13, 2009

    Multiplying the power level by a factor of five would only bump the sound up to about 53 decibels by our above equation.

    You got this backward, Matt: Multiplying the power level by three would be about a 5 dB increase.

    The ear seems to have a quasi-logarithmic response to volume as well as to pitch. I can easily hear the difference between one horn player and two, but distinguishing five from six (if they are all playing the same notes simultaneously) is much harder. Similarly, a semitone sounds like a semitone no matter what the absolute pitch, even though the frequency difference changes–it’s always the same ratio, which is 2^(1/12) for even-tempered tuning.

  5. #5 Steinn Sigurdsson
    June 13, 2009

    Try the Baroque Cycle, it outdoes the Cryptonomicon.
    His latest, Anathema, is also excellent, although you have to persevere through the rather slow paced opening.

  6. #6 Tim Gaede
    June 14, 2009

    A couple of good rules of thumb regarding decibels:

    * A difference of one decibel is about a factor of 1.25
    * A difference of three decibels is about a factor of 2

    So you can make sound intensity ratio estimates in your head:

    A 39 dB change would mean a factor of (10^4 / 1.25) = 8000

    A 37 dB change would mean a factor of (10^4 / 2) = 5000

    A 36 dB change would mean a factor of (10^4 / 2) / 1.25 = 4000
    OR
    (10^3)*2*2 = 4000

  7. #7 Max Fagin
    June 14, 2009

    So when did you figure out just what the deliverator delivers? My psych professor had the entire class read Snowcrash while we were all sitting in the same room, and he noted just when we figured it out just be looking at our faces.

  8. #8 Greg
    June 14, 2009

    Nice.

    Sticking with Snow Crash, I’m looking forward to the calculation of how much kinetic energy it would take to “launch a pound of bacon to the moon.”

  9. #9 gluecypher
    June 15, 2009

    Ummmmm….
    IIRC there is an upper limit for the dB level which is depending on the air pressure. So the maximum dB one can get in our surrounding atmophere is around 195 dB.

  10. #10 Paul Murray
    June 15, 2009

    Let’s do it the slow and complicated way!

    Sound engineer’s rule of thumb: 3db doubles the sound.

    By definition: 10 times = 10 db.

    Quintuple is half of 10, hence 10dB – 3dB, or about 7dB. According to my calculator, quintuple is …

    6.9897 dB. Damn close to 7.

    QED.

  11. #11 Nathan
    June 17, 2009

    Some comments are dealing with the intensity of the sound, but the quote specifically says “the decibel level quintuples.” I read that as the previous sound level (in dB) gets multiplied by 5. If the intensity were to quintuple, that would be an increase of about 7 dB in the sound level as pointed out by Paul Murray (#10), but it does specifically say it’s the decibel level that quintuples.

  12. #12 Hypocee
    July 22, 2009

    Like #1, I always read this as referring to the background noise leaking into the car, which is basically undefined but makes for a reasonable scenario whether literal or metaphorical.

    Cryptonomicon’s something completely different. I found it like falling in a vacuum – the radical changes in subject and thesis probably come at a constant rate throughout, but as you’re pulled along faster and faster by the story they seem to become more frequent and intense, while simultaneously blurring into an epiphenomenon with features independent of any single mini-chapter. About 100 pages from the end it just shorted out my brain in the best possible way, and I coasted to the end in a cheerful state of complete suspension of disbelief. It’s an interesting situation that I haven’t experienced anywhere else – “conviction through brute force” might sum it up. I suspect it’s similar to the state Ulysses is supposed to aim for, though in Stephenson’s case it’s done through good narrative and character development.

    The single segment of Cryptonomicon that had the most effect on me was the Ares vs. Athena discussion. It reminds me of Douglas Adams’ piece “Is There An Artificial God?” http://www.biota.org/people/douglasadams/