Orks Use Teef fo’ Money (Charm Bracelet, Part 2)

– which is completely irrelevant except for, I suppose, nails are… kinda like teeth? (Only not at all really; see previous post) Irregardless! With punches newly arrived from China, I set up the workbench for the final steps!

First up was cutting out the blanks – the brass flats I had were thicker, but could take an impression on both sides, whereas the steel stock was thin enough it couldn’t be double-struck but could be threaded two-per-ring for race info and nail location. After the tiny chop-saw I found proved wholly unsatisfactory for anything more strenuous than wooden dowels, and figuring I’d be cleaning them up by hand anyways, I went with the Dremel.

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Cracking the Whip of the Long Tail

So, let’s take a sample of 100 million individuals, and assume that they’re all normally distributed along… whatever imaginary one-dimensional variable you want to… imagine.

Some definitions of the variables and functions I’ll be using:

Mean: μ

Standard Deviation: σ

Cumulative Distribution Function: F \left( x \right) = \Phi \left( \frac{x - \mu}{\sigma} \right) = \frac{1}{2} \left[ 1 + \textrm{erf} \left( \frac{x - \mu}{\sigma \sqrt 2} \right) \right]

Thus, we’d expect 68,268,949 (rounding down whenever I give an integer derived from a percentage times a population) within 1 standard deviation (plus or minus), 27,181,024 to be between 1 and 2 standard deviations, 4,280,046 to be between 2 and 3, 263,645 between 3 and 4, and 6,276 between 4 and 5.

This leaves roughly 57 individuals farther than 5 standard deviations away from the mean or, looking at just the top end, 28 individuals more than 5 standard deviations above the mean. (Why 5? Because first, 5 is half of 10, and second, 28 individuals is a nice manageable number. Remember, this entire exercise is a very crude, back-of-the-envelope thought experiment.)

Let’s say that these 28 plus-five-plus sigma individuals are our ‘world class’ performers.

Now, let’s suppose that there’s a population of, why not, 5,000,000 individuals, the mean of which is just 5% of a standard deviation higher than that of the base population. Same standard deviation, so that the number of individuals from this population that exceed the +5+ threshold (as determined by the population as a whole [and yes, I realize a more rigorous model would ‘break out’ that overall 100 million into the various populations being supposed, i.e. that either adding in this 5 million or saying that 5 of those 100 millions is now like this would change the statistics of the overall / original 100 million but again this is an incredibly rough lunch-hour calculation here]) would be given by:

F' \left( \mu +5 \sigma \right) = \Phi \left( \frac{5 \sigma + \mu -  \left( \mu + 0.02 \sigma \right)}{\sigma} \right) =\Phi \left( \frac{5 \sigma - 0.02 \sigma}{\sigma} \right)=\Phi \left( 4.98 \right)

– which, out of 5 million, is almost 2. About 1.85, so, yeah, that population would be a little bit over-represented among the ‘world class’ ranks. (I.e., instead of an expected 1.43, you’d see 1.86. Which, even though it’s a difference of less than a person, is almost a 30% increase over what you’d see were it not for that +5% in the mean for the smaller population.

What about a larger-than-normal standard deviation? Again, let’s say that it’s a +5% difference, i.e., that the 5 million strong population has a standard deviation 5% larger than the 100 million population. In this case, the number above the +5+ would be given by:

F' \left( \mu +5 \left( \frac{1}{1.05} \right) \sigma \right) = \Phi \left( \frac{5}{1.05} \right)

Out of a population again of 5 million people, that gives 4, almost 5 (~4.79) individuals at the ‘world class’ level. In other words, there’s now a 234% over-representation of the smaller population at the uppermost levels. (Note: ‘over-representation’ is used here w.r.t. each individual’s value for the hypothetical variable being IID.)

What does this mean? Practically, nothing – this is a thought experiment that’s a simplified-ab-adsurdum version of an already unrealistic one-variable ‘model’ of something that’s known to be incredibly complex and interconnected (i.e., anything to do with people. Sure, the idea’s applicable to anything with a normal distribution, but an idle passage related to people read while shelving books is what prompted this thought.)

But, since it’s gotta mean something, ‘cuz otherwise I wasted my lunch hour, here are a couple of takeaways:

  1. Small differences in average (mean) values for a group compared to the larger population can be magnified at the upper and lower extremes (tails) in terms of over/under-representation of members of that group.
  2. Small differences in variance (standard deviation; I know that variance has a technical meaning but I’m looking for the closest plain-English equivalent to ‘standard deviation’) for a group (… compared to the larger population) can be greatly magnified at the upper and lower extremes (…).

 

Charmed, I’m Sure, Sez Tony Poe

IYI, Tony Poe is famous for tossin’ severed heads onto enemy locations and, on one occasion, when his superiors questioned his body counts (this was during the Vietnam War, which makes me figure he must have been paid on a per-kill, piecework basis because this is possibly the only time in that entire conflict where someone on the American side said ‘There’s no way you killed that many of the enemy’) he calmly provided hard evidence to verify his claims.

… By which I mean, of course, he mailed a bag of fuckin’ ears to the US Embassy in Vientiane. Possibly more than once. His personnel file must look like Ed Gein’s Rolodex.

This isn’t that grisly, of course, but – okay, fine, it’s a charm bracelet where the charms are human toenails. There’s some context for this, of course, but if you’re somehow the type who found this, read with bland, placid face about Tony Poe, Ed Gein joke, got to the toenails, and then decided that nope, no context makes that palatable, well… Probably don’t want to make the jump.

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The Apposite of an Allusion

While reading Disrupted, by Dan Lyons, something started to jar on the eye – apart from the weirdly specific Scientology jokes, which were explained when, in the latter pages of the book, he mentioned reading Lawrence Wright’s Going Clear during the period covered by the book. Specifically, I kept running into what I’ll call “the apposite of an allusion” (Roll credits…), i.e., an allusion that is immediately followed by a capsule summary of whatever was being alluded to.

E.g., “I feel like Dorothy.” becomes, “I feel like Dorothy, the little girl in The Wizard of Oz who is transported to a strange land called Oz.”

Going through the book after I’d finished it, I pulled out all the passages that seemed relevant to my little five-minute-wordplay of a title (all page numbers refer to the hardcover edition).

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Bookshelving: The Year in Reviewment

Why, yes, “The Year in Reviewment” would normally suggest a December date of publication. But the hurricanes down South sucked the lumber away from the Woodland Mills, so the last of the shelves didn’t arrive until early February. And then, well… Yeah. (N.b.: This is currently the first stage of book-shelving, wherein each book gets cataloged, measured, mylared and/or DDC categorized as appropriate, and placed on a shelf in some reasonable semblance of order. Then comes building the long-term shelves.)

A quick tour of the library so far! First up, and first to be built, there are the under-eave shelves in the study. Yeah, the boards are cut for that fourth case, they just need to be, you know… attached to each other. And stained. (See, this, this right here, is why I relented and used pre-made shelves downstairs. Because I kinda wanted all of my books off of the floor within a decade of moving in, no joke.)

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Sized for standard hardcovers, made modular by the plinth underneath so they aren’t custom-cut for the baseboard (said modularity immediately nullified by angling the tops of the uprights to match the eaves), these have nonfiction, mostly biography and World War II history. 280 books shelved!

… out of 6,012, so ~4.66%.

escalated_quickly

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Time for a Recovery Year!* AKA Running 14 Ultramarathons in 12 Months: The Recappening

Enter a caption* Because the general rule of thumb, according to Jack Foster, is one (1) day of recovery per one (1) race mile.

January 15th: Willis River 50k

A warm-up fatass run to start the year. That is, the aid stations were stocked with “whatever you bring” and the water stops at the turnarounds were, literally, dudes with spigots. Still a nice run, even if the trails were primitive enough that at times I was literally tracking the runners ahead of me.

Also, had the following exchange with the race director run coordinator when I finished ahead of my brother and turned to go back to last.

Him: “Drop something?”

Me: “Naw, I’m just going back to run in the last bit with my brother.”

H: “I don’t see him.”

M: “Well, he took a wrong turn going into the second leg, so I’d guess he’s at least a few miles back, yet.”

bert_stare
His response. Made even better by the fact that he really did have extra-bushy eyebrows.

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The Buddy Bear Crawl; or, Finally a Practical Use for That PHYS-151 Problem!

What is the buddy bear crawl? This:

Buddy Bear Crawl IRL
Or rather, it’s like this, only the person underneath has their rucksack switched to the front, and you have a ruck on, too, so they’re probably grabbing you around the neck.

A wild “classic problem from introductory physics” appears! (Seriously, this was one hell of an AHA! moment for me.)

(Specifically, Young & Friedman 5-38. [Question #2 in the linked pset.])

So, for dragging something or someone along a flat surface at an angle Θ above the horizontal, you have:

F = \frac{\mu _{k}mg }{\cos \theta +\mu _{k} \sin \theta }

Note that the above is for a constant velocity – to minimize the force required, set the derivative to 0:

\frac{\mathrm{d} }{\mathrm{d} \theta }\left ( \frac{\mu _{k}mg}{\cos \theta +\mu _{k}\sin \theta } \right ) = 0\rightarrow \frac{\mathrm{d} }{\mathrm{d} \theta }\left ( \cos \theta +\mu _{k}\sin \theta \right )^{-1} = 0

\frac{\sin \theta -\mu _{k}\cos \theta }{\left ( \cos \theta + \mu _{k}\sin \theta\right )^{2}}=0\rightarrow \sin \theta = \mu _{k} \cos \theta

\tan \theta = \mu _{k}\rightarrow \theta = \arctan \mu _{k}

What’s the coefficient of kinetic friction for dragging a person + rucksack along the ground? Based on the Journal of Strength and Conditioning Research, Volume 27 / Issue 5, May 2013, p. 1175-8, I’ll go with 0.33, giving:

\theta = \arctan 0.33 \approx 18^{\circ }

So, the next time you’ve got to pull someone wearing a rucksack (filled with bricks) while you’re wearing a rucksack (filled with bricks), while crawling like a bear the entire length of the soccer pitch in a public park (at three in the morning, after hydro burpees), remember – eighteen (18) degrees above the horizontal.

Pat Goodale – Practical Firearms Training (PGPFT) Low-Light Handgun AAR

[Same introduction, note, and disclaimer as before.]

WML & Recoil:

  • Surefire is the best brand of WML, generally speaking. Streamlight and Insight can both interrupt the recoil of .40 handguns with plastic frames, especially if overtightened. (The sharpness of .40 recoil means the frame needs to flex, which – being plastic/polymer – it can, no problem, unless you bolt a steel reinforcement (WML) to it.)

Calibers & Cartridges:

  • .40 S&W had slight performance edge over 9mm (basically being +P/+P+ pressures, i.e., firing a proof load, every load) in the olden days, but with modern bullets, 9mm uber alles.
  • [Insert notes on the history of the .40 S&W as an underpowered 10mm, which are probably well known already by anyone who would be interested in them and aren’t relevant to the rest of the notes or specific to Pat Goodale.]
  • #1 recommendation is Speer Gold Dot – FBI round.
  • Winchester SXT, Federal HST perform approximately on the level of Speer Gold Dot.
  • Another alternative is Hornady Critical Duty. (Duty, which is the LE round. Defense is underpowered by comparison.)

Handheld vs. Weapon-Mounted Light (WML):

  • Handheld is the most useful, utilitarian
  • WML only useful for shooting, not scanning (can’t scan without muzzling)
    • That said, WML is easier to use shooting than separate handheld
  • Nightstand gun – WML (no need for concealment, able to bounce light to avoid muzzling, home turf familiarity, etc.)
  • Concealed carry – NO WML (much harder to conceal, if at all, muzzling-when-scanning concerns)

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Pat Goodale – Practical Firearms Training (PGPFT) Tactical Rifle AAR

[Same introduction, note, and disclaimer as before.]

Ammunition (5.56x45mm NATO):

  • M193: Standard 55-gr ball cartridge, good for bulk shooting / practice.
  • Mk262: 77-gr Sierra MatchKing, good long-range performance, match-quality (and price)
  • Mk318: 62-gr, USMC standard. Hunting bullet – Open Tip Match Rear Penetrator (OTMRP) (62 gr. Federal Fusion).
  • M855A1: US Army “green” round (lead-free). Politicized development & adoption process.

Manufacturers:

  • Entry Level: M&P Sport
  • Low-Medium: Rock River Arms, Anderson
  • High-Midrange: BCM, Colt
  • Premium: Daniel Defense, LWRC

Sights:

  • Red dots need adjustments to avoid vanishing (too weak) or ‘blooming’ (too strong) depending on lighting conditions.
  • Red dot sights tend to ‘fuzz out’ (astigmatism) with (shooter’s) age.
  • Low-Power Variable Scopes
    • 1x-4x, 1x-5x, 1x-6x, etc.
    • Used by lots of military special forces
    • Have the lowest magnification as the initial & default. Once on target, then ramp it up – otherwise, like searching through a straw.
    • Throw levers can make the magnification adjustment significantly easier.
  • Expect scope + mount to be ~½ of cost of rifle. (LaRue mounts.)
  • With good quality mounts (indexed and repeatable) can hot-swap between red dot and scope.

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Pat Goodale – Practical Firearms Training (PGPFT) Defensive Handgun AAR

A brief introduction – this AAR and the Low-Light Handgun and Tactical Rifle AARs to follow are all based on a private course weekend. Defensive Handgun was on Saturday, Low-Light was that evening, and Tactical Rifle was Sunday from morning until mid-afternoon. As such, it doesn’t match up exactly with the Defensive Handgun I/II/III, Tactical Rifle – X Days, etc. courses on the website, but I think it still gives a good idea of what level of detail and which topics to expect to encounter.

Another note – since these notes were written up primarily to organize and remember the concepts and drills that were covered, they omit details of the range, class setup, etc., but the range was awesome, the class setup was superb, the instructors were excellent – honestly, it’s an unqualified recommendation. I can’t think of anything negative to say about it, so if you read no further and take nothing else away from this – strong recommendation.

And the obligatory disclaimer – these were typed up from my hastily-scrawled notes and dissipating recollections over the week, week-and-a-half after two days jam-packed full of shooting and excellent (have I said that I recommend it?) instruction, so – as always – if something is wrong or seems amiss, that’s almost certainly on me. Similarly, all of the drills were done under the close supervision of trained professionals by participants whose performance levels were constantly monitored and accounted for in the instructors’ selection and setup of said drills, so… honestly, if you’re the type of person who’d read a random person on the internet writing about running through the woods with a rifle engaging targets 100+ yards away and go out and actually do that on your own, well, you either don’t need this disclaimer, or you wouldn’t heed it anyways, so… on with it!

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