The hobby of amateur radio is a curious animal. It sits at the junction between empirical evidence and the scientific method. On the one hand it's all about physics, electricity, magnetism and the science behind those. On the other hand it's about trying something out and seeing what happens.
When I started in this hobby, I was all about the science. I wanted to know "Why is it so?" "What evidence is there to support that?", all the typical questions you might ask if you're coming at this from that direction.
As is often the case, the more you know, the less you know. That is, the more you understand a topic, the more you understand that you know nothing. The deeper you dig, the more variables become apparent, the deeper the hole goes, the further away from absolute you travel.
That's not to say that our hobby is unknowable or non-deterministic, far from it. It's often so complex as to defy immediate explanation using high-school physics. You'll get to a certain point with that knowledge, then from one moment to the next you'll open a door into a world where that knowledge is just not enough.
Interestingly when you look at for example the standard way of determining the length of a dipole, a fixed number divided by the frequency, that number we use, what ever the value, is an example of an empirical evidence based number and as observations go, it's not a particularly good one, which is why when you start using it you'll find all manner of exceptions, alterations, modifiers, etc.
If there was a formula for a dipole, it would not just have that fixed number and the frequency. Nor would it be a simple division, since the number of variables is likely to head to infinity by the time you actually approach something that can model the real world.
Between those two extremes, the quick-and-dirty empirical calculation and the intricate model at the scientific end lies a point of "good enough".
The point of "good enough" is where what you're calculating is likely to end up with something that works most of the time. It's not 100% accurate, nor is it trivial, but it gives you a level of confidence that the thing you're calculating is useful and reproducible in many circumstances.
I've been told by those who have told me that they know, that the fixed number divided by the frequency is on that "good enough" point, but my experience and the evidence says otherwise. Oh, that's ok, just add 5% to that number, or just cut it long, or insert some or other correction factor to account for the variation, that will give you "good enough".
Ok, I'll bite.
If that's "good enough", why are we teaching our new amateurs that this is how you create a dipole, no explanation about the variations, the effects of the environment, the material used, just: "Here's a number that you divide by the frequency and you'll have a dipole."
My point is that it's time to revisit some of the things we think are "good enough" and look for something "better".
I'm not advocating that we all need to become theoretical physicists, though for some that might be just the ticket, but I am saying that we should not just state that making a dipole, or calculating anything associated with our hobby, should be done without context.
Here's some context for the magic number 468. Ward N0AX did the research almost a decade ago. It's a fascinating read, look it up! Turns out that the first occurrence of the magic of 468 comes in the form of 438. Yes, that's correct, 438 was the first attempt at making a magic number and it was based on measurements by G. William Lang in 1926 and it was based on averaging measurements for several antennas.
In the 1929 ARRL handbook the number 468 first appeared and has been repeated ever since.
Apparently as it turns out, the more you repeat something the more it's right. To the point of being ridiculed if you dare question the validity of such a notion.
So, what is it, scientific, or empirical, or is it a little of both?