When I was in college, I had a friend who studied German, and another who studied music. Those of us majoring in useful things like accounting, finance, biology, or engineering lumped those pointless specialties into a broader discipline we called Useless Knowledge. Our two friends had pretty good attitudes about it, though, and one even put a sign on his dorm door that read, Useless Knowledge: We study these things so they won’t soon be forgotten.
The same year we made fun of our friends for pursuing their callings, the Rolling Stones went disco with Emotional Rescue. Because of that, we should have known then that everything we thought we understood about the world was a lie. After college, the German major went on to be an executive at Purina. The music major, the president and CEO of the world’s top sheet-music publisher. Both making enough money to print Useless Knowledge signs on Italian Calacatta marble with 24-karat gold-leaf lettering. The rest of us? Well, if you want to make God laugh, tell him about your plans.
It’s not that my engineering education didn’t pay off. Maybe not as well as German and music did for my friends, but well enough. Still, in the same way that hearing Mick Jagger slip into falsetto asking, “Is there nothing I can say, nothing I can do?” helped me understand why Keith Richards smoked and drank so much, slogging my way through calculus, differential equations, real and complex analysis, optimization, esoterics, and even advanced esoterics ultimately caused me to wonder if I was the one who’d spent his formative years studying useless knowledge.
Now, it’s not that mathematics is useless. Far from it. It’s nearly impossible to go an hour through your waking day without relying on some sort of mathematical wizardry, whether you realize it or not. But being well trained at ciphering causes a fella like me to see patterns where other people don’t. It’s akin to a curse. Just ask Uncle Jed about Jethro Bodine and his sixth-grade education.
Some, for instance, might look at the American Fly Fishing Trade Association (AFFTA) specs for spey fly-lines and simply see the numbers as adjectives for weight: 430 means heavy; 510, heavier; 600, heavier yet; and 700, heaviest. Savants like Jethro and me, on the other hand, look at the same numbers and see a pattern. One as beautiful and consequential as the origin of the universe. Or, perhaps, a top-secret, double-naught spy code.
Some patterns are easy for everyone to see. What, for instance, comes next here?
2, 4, 6, 8, _
The number 10, right? Unless you were a cheerleader in high school. Then you might say, “Who do we appreciate? Tigers! Yeah!”
How about this one?
600, 650, 710, 780, 860, 950, _
Let’s see. The first transition increases by 50. The second by 60. The third by 70. The fourth by 80, and the fifth by 90. Aha. If you guessed the next number is 1050, then you just predicted the AFFTA approved grain size for a 12-wt long-belly spey line. Here are the standards for other types of bellies.
See what’s going on? Regardless of the belly length, every transition from 6 wt to 7 wt increases by 50 grains. It’s probably a good time to point out there are 480 grains in a troy ounce. A troy ounce being what people mean when they talk about an ounce of gold, which is not the same as an ounce of cheese on your kitchen scale. That’s a normal ounce.
If you study the weight standards, you’ll see that the transitions for all types of bellies are the same and follow a nice, orderly pattern:
In technobabble, the rate of increase of the grain sizes is linear, and as good old Professor Von Nostrand so elegantly taught us in Advanced Esoterics, that makes these sequences special in another way. Let me show you how.
Can you guess the next number in this sequence?
1, 4, 9, 16, 25, _
The sequence increases by 3, then 5, then 7, then 9, so the next increase must be 11, making the unknown number 36, right? Right. But maybe some of you saw another pattern. The first number is 1 times 1. The second is 2 times 2. The third is 3 times 3. The fourth is 4 times 4, so, if we use that rule, the sixth must be 6 times 6, which is 36 again.
It’s not as straightforward to see, but every one of the spey line standards can be described by a relationship that involves squaring the line weight. I don’t know if the Grand Wizards at AFFTA recognized this when they standardized the relationships between line weight and grain sizes, but the grain-wt standards all follow what is called a quadratic relationship because of that linear rate of change. Rather than knowing that, though, it’s much more likely the sorcerers had an intuitive feel for another topic I learned in Introductory Esoterics: Weber’s Law.
Here’s a simple way to understand Weber’s Law: We are much more likely to tell the difference between 1 and 2 lbs than we are between 100 and 101 lbs. The absolute difference for each is a single pound, but the percentage differences are 100 percent in the first case and only 1 percent in the second. When it comes to things like distances and weights, we are more sensitive to percentage changes, not absolute ones. Driving a mile out of your way on a 400 mile trip is in the noise. Going a mile out of your way to get from the couch to the bathroom? Well, that’s a sentence that’s probably never been written before in the history of language.
Ideally, then, if we wanted to be in tune with Weber’s Law, line grains should increase by a fixed percentage. A 7 wt line should be, say, 20 percent heavier than a 6 wt line, an 8 wt line 20 percent heavier than a 7, and so on. By using the linear rate of change, the AFFTA folks appear to have felt that. Maybe through a sixth sense. But they likely wanted something that looked clean and professional for the standards, too. Instead of grain weights that came out like this for the shooting heads:
250, 300, 360, 430, 510, 600, 700
a constant percentage change might have looked like this:
253, 301, 357, 425, 505, 599, 712
To the fly-line manufacturers, the first list presents like the diligent work you’d expect from a capable group with a five-letter acronym. The second? Something from a herd of drunks after a four-day boondoggle in Vegas.
The sequence from the drunks, though, has 19% changes for every transition. For the professional sequence—the one AFFTA established—the transitions are
20%, 20%, 19.4%, 18.6%, 17.6%, and 16.7%
Not all the same, but close enough for government work and gas-station hot dogs, as old Professor Von Nostrand liked to say.
Well, there’s no way to finish this story without channeling my inner Sheldon and sharing this plot showing the relationships between line weight and grains for the AFFTA spey standards.
Professor Von Nostrand taught us to call this a log-plot. In lay terms, the numbers are arranged to show what people sometimes call orders of magnitude, where an order of magnitude is a fancy way of saying a factor of ten. Accordingly, the plot is scaled so 100 is the same distance from 1,000 as 1,000 is from 10,000. Why do crusty old guys like Professor VN like plots like this? Because when something increases by constant percentages, the data fall on a straight line. The greater the slope, the greater the percentage. For the shooting head standard, the grains appear to increase by about 18.8% for each line weight jump. For the short belly, it’s 13%. Medium belly, 12.1%, and the long belly is at 9.8%. It’s not a perfect fit, but it’s close enough for horseshoes, hand grenades, and cutthroat trout.
Now, what about the subtitle for this essay? To get there, we need to look at the AFFTA standard for traditional fly lines. Before AFFTA there was AFTMA, and they classified lines by their diameters, much like we classify tippets today. The letter A stood for 0.060 inches; B stood for 0.055; C for 0.050; and on and on, all the way down to I for 0.020. A double-taper line might be labeled DHD, meaning its diameter was 0.025 inches at one end, 0.045 in the middle, and 0.025 on the other end. A weight-forward line might be GBF. Cryptic, but not bad as long as you had the decoder ring and line diameter was a proxy for weight, which it was when lines were made from braided silk. Everything changed when companies like Scientific Anglers, Cortland, Shakespeare, Ashaway, and Gladding started coating braided nylon or Dacron with flexible PVC.
Fly rods respond to weight, not diameter, and because the corporate chemists were in a great race to outdo each other with their synthetic lines, diameter was no longer a proxy for weight. So, a guy named Myron Gregory proposed a standard that specified the weight of the first 30 feet of a fly line. That’s how AFFTA does it today. For a 5wt line, the first thirty feet should weigh in between 134 and 146 grains, with the target being 140.
After years of annual board meetings and two martini lunches, the standard for traditional lines has landed here:
As Professor Von Nostran liked to say, those numbers look more brainstorm than blueprint. But when we view them through the log-plot microscope, it appears the AFFTA folks tried to glue this thing together in a way that didn’t completely stray from a line defined by Weber’s law.
The dashed line uses Weber’s law with 140 grains for a 5 wt as the standard, then increasing the grains by 15% for each jump in line weight. It’s a pretty good fit everywhere except the low end. Why the deviation there? Maybe the people setting these standards believed—perhaps still believe—that it’s pointless to make a change in line weight that’s less than 20 grains. There could be something to that. Can you tell the difference between one grain of salt in your hand and two? We engineers call this the small-signal problem.
Still, my inner mathematician is uneasy about this. What AFFTA calls a two-weight ought to be a one-weight. What they call a one-weight should be a zero-weight, or even less. Just look at that plot. You don’t need to be a German major or musician to see it.
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