Metric vs. other measurement systems.
https://s3-us-west-1.amazonaws.com/h...nt_systems.jpg
Previously:
https://www.homemadetools.net/forum/...935#post105878
https://www.homemadetools.net/forum/...1787#post94713
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Metric vs. other measurement systems.
https://s3-us-west-1.amazonaws.com/h...nt_systems.jpg
Previously:
https://www.homemadetools.net/forum/...935#post105878
https://www.homemadetools.net/forum/...1787#post94713
But the metric system is too confusing for most of us?
I must have paid better attention in school when I first started learning about the metric system it must have been somewhere around the mid 60's the one thing I figured out right away was metrics followed out monetary counting using the pennies as mm dimes as Cm, dollars as meters and the 1000.00 dollar bill as the kilometer
If I'm not mistaken, the pic shows some Imperial length units and
their different relative factors (and their multiplicative inverses: 1/x), all 42 of them:
7/8, 1 (sic!), 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 25, 50, 63, 96, 100, 120, 1760 & 6080
AFAIK: This subject got pretty much flogged to death two years ago...
Suggested reading for die-hard masochists with time to spare:
https://www.homemadetools.net/forum/...935#post105878
-Thanks Jon, for bringing back exactly that, what I've laboriously tried to suppress ever since... :lol:
The history of measurement is indeed a fascinating one. Reading about the evolution of various measurement systems give us a perspective on the creativity of our ancestors. Knowing the history of measurement helps us understand the reasons for so many different units. I began teaching in the mid 70's when the convert to metric movement was in full swing the USA. Oh what fun that was. My contention then, as now, is that if you truly know HOW to measure, you will choose the unit appropriate what you are measuring and and audience you are measuring it for.
For your enjoyment.. https://www.youtube.com/watch?v=Q8qQ...&feature=share
Despite the fact my schooling was done with the metric system, have had to become reasonably familiar with imperial -- dealing with "old people" (ducks a flying spanner). Then theres the fact that a fair bit of the caravan stuff I deal with is still in feet. So I ensure all the tape measures in the shop have both measurements on them.
Base 10 number system --- dunno how difficult that can be!!
Bought a block in town about 15 years ago -- damn thing was still measured in links (subset of chains apparently). Even my solicitor (well into his 60s back then) had to pull out the conversion tables for that one.
How many fingers is a lid...
The link is fascinating. The original area measure was an acre, the area of land a man could plow in a day, It was a furlong long, an eighth of a mile, and a chain wide, said chain being 66 feet long. When the need for a unit finer than a chain surfaced, some yokel decided to abandon the much touted inferial superiority of many divisors and divided it into one hundred links. It was a noble effort to introduce decimal simplicity but sadly left us with a link that is a comical 0.66 feet long - not 2/3 of a foot but close enough for folks who like to measure things with antiquated, outdated systems.
The chain got me to thinking about Rods. I 330ft rolls of cattle fencing and that roll is also listed as 1 Rod turns out that 1 Rod equals 500 Links....
Hmm, this quote from Wikipedia seems to contradict that...
The rod or perch or pole (sometimes also lug) is a surveyor's tool[1] and unit of length of various historical definitions, often between 3 and 8 meters. In modern US customary units it is defined as 16 1⁄2 US survey feet, equal to exactly 1⁄320 of a surveyor's mile, or a quarter of a surveyor's chain, and is approximately 5.0292 meters.
At 16.5 feet, a rod would be 16.5/0.66 = 25 links, a quarter of a surveyor's chain.
Ooops, My mistake, a roll of fencing is 20 Rods not 1.
Been a while since I read that label.
Yeah a lot of those old measurements make my head spin a bit.
Got my metric and as required - imperial.
Should'nt have bought a Seventies pommy tractor - prob Whitworth. So far, so good with my spanner and socket selection.
My Norton 650 Atlas was Whitworth. Snap-On still sells Whitworth tools...
Aha; term "flying spanner" tells us which direction to aim..... JK of course.
I've been subject to practice of dual-dimensioning and conversion awhile. Like hemmjo states, there is room and application for either. I do little programming, conversational at that. In most instances, mm entries are [seem] less susceptible to keystroke errors.
I'd say being able to select via touch of a button is best of both worlds.
As I recall, a lid was 3 fingers of a sandwich baggie...
What ever happened to the "Rule of thumb"?
"Rule of Thumb" has falsely been tied to to notion it is OK to beat your wife if your sick is smaller than your thumb, thus most of us don't use the phrase any more.
Teaching children to avoid measurement systems.
https://s3-us-west-1.amazonaws.com/h..._hamburger.jpg
Don't laugh. There's probably a course in teacher's colleges where future teachers are taught how to convert feet to bicycles and pounds to hamburgers.
We're well into the third generation of the dumbing down of the population. Soon folks will have to go to a scribe to have something read to them or written for them. The elite scribes will be able to do simple sums (but no division) for their clients.
And everyone will call it mathematics, when it's arithmetic, because that's what the hive mind believes.
- Arithmetic is operations with numbers.
- Mathematics is manipulation of symbols (such as X).
I still know how to find the square root of a number with pencil and paper.
Incremental weight in beef, turkey, tofu, and/or other vegan substitutes? And height; penny-farthing or tiny clown cycles?
I was taught that awkward system in grade school. I soon purged it from my memory bank. There's a much simpler way to find roots using Newton's method.
Consider this iterative equation...
x2 = (x1 + N / x1) / 2
where:
N = number whose root is to be found
x1 = initial estimate of root
x2 = improved estimate of root
We make a guess of the root, x1, plug it into this equation and get an improved estimate, x2. If this estimate isn't good enough for out purposes, we set x1 = x2 and repeat the process to get an even better estimate. This iterative procedure is repeated until x2 squared is close enough to N to satisfy our requirements.
An example will demonstrate. Let's find the square root of 6 (for reference, my calculator says 2.44949). Six is between 4 (2 squared) and 9 (3 squared) so a reasonable guess for x1 might be 2.5. Then
x2 = (2.5 + 6/2.5)/2 = 2.45 (squared = 6.00250)
Very close but let's do one more iteration...
x2 = (2.45 + 6/2.45)/2 = 2.44949 (squared = 6.00000026)
which would be good enough for most purposes.
I can hear you saying, "Yeah, but you picked an initial guess that was very close to the actual value!" A valid objection so let's try it with an initial guess that's downright silly, 7. Remember, 7 squared is 49, and that's far enough from 6 that even a schoolkid would know it's not a good choice. In addition, the square root of a number can never be greater than the number so, since 7 is greater than 6, choosing it as a first guess is particularly dumb.
x2 = (7 + 6/7)/2 = 3.9286
x2 = (3.9286 +6/3.9286)/2 = 2.7279
x2 = (2.7279 + 6/2.7279)/2 = 2.4637
x2 = (2.4637 + 6/2.4637)/2 = 2.4495
which, squared, is 6.0002..., close enough for the work I do. So, even with a laughable initial guess we got five significant figures in only four iterations. Clearly, one doesn't need to be a genius mathematician to make useful guesses.
Of course, today most four-banger calculators have square root keys. My question is, why ? The average four-banger user wouldn't know a square root from a rutabaga.
That's the fack Jack.
I cut corners these days too and just look it up to acceptable precision on my slide rule (the batteries have never failed). In nearly all cases you're working with an error band of 10% or more in the source data so solving to analytic precision is usually a pointless exercise. For that matter I still use 22/7 for pi but Newton's method is new to me and I see that it works well.
I'm still pondering over furlongs per fortnight.
Sad to say, but math and I are still at at odds. But I can whittle a rutabaga into a square root...or cube it.
I'll stop there; never know what will turnip.
My apologies to Marv and Crusty.
Pi are round - cornbread are squared.
Reminds me of the product sheet (attached below) for the Tektronix Oscilloscope 545AE (All-English)
(where ist horizontal calibration is precisely scaled in "fortnights per furlong"):
"A precision, laboratory oscilloscope, calibrated directly in practical English units of measure,
has been announced by Tektronix-Guernsey, is claimed to be the first and only oscilloscope using English measure units exclusively."
Disclaimer: -This pamphlet is for informative/ recreational purposes only -
and SHOULD NOT be used instrumentally in health-critial applications.
Attachment 36372
If you use rational fraction approximations for pi, the Tsu Chi form, 355/113, is far more accurate than 22/7. There are other approximations that are even more accurate as this extract from my notes shows...
==================================================================
APPROXIMATING PI = 3.1415926535898
Biblical approximation: 3 (4.5%)
"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." — First Kings, chapter 7, verses 23 and 26
22 / 7 = 3.142857142857 (0.04 %)
22 / 7.0028 = 3.141600502656 (0.00025 %)
Tsu Chung Chi approximation: 355 / 113 = 3.141592920354 (0.0000085 %)
Euler: 103993 / 33102 = 3.141592653012 (-0.000000018 %)
Ramanujan's improvement to Chi: (355 / 113) * (1 - 0.0003 / 3533) = 3.14159265359 (below calculator range)
Ramanujan's first term in fast series for pi: 9801 / [1103 * sqrt(8)] = 3.141592730013 (0.0000024 %)
Ramanujan: (63 / 25) * [(17 + 15 * sqrt(5)) / (7 + 15 * sqrt(5))] = 3.141592653806 (0.000000007 %)
Fourth root: (2143 / 22)^(1/4) = 3.14159265258 (-0.000000032 %)
==================================================================
Four bangers, despite having a square root key, usually lack the far more useful pi key, so knowing some easy approximations is a good thing.
Newton's technique of iterating to find other roots can easily be generalized. For the nth root of N, the equation is:
x2 = [(n - 1)*x1 + N/x1^(n-1)]/n
which, for n = 2, reduces to the equation shown in my previous post.
The convergence is at least quadratic in a neighborhood of the zero, which intuitively means that the number of correct digits roughly doubles in every step. For faster convergence, one can use Halley's method which exhibits cubic convergence.
@Marv
I learned doing sq.roots the old fashioned way and have since purged it out if my memory as well. However, my son showed me how to do it using Newton's method at age 12. So, they're not all getting dumber! But then, he's a lot smarter than I ever was; has won 35 awards and 2 international tournaments in robotics, 5 science olympiad awards, and was in Forbes magazine by age 13 !!
Americans will do anything to avoid using the metric system. :)
Of course, there will always be exceptions, but mankind depends on the ability of the majority in order to move forward. When the majority can no longer understand the technology in which they live nor have the language and mathematics skills to modify it creatively, the downward slide will engulf the exceptions.
We currently live in a society where the makers of automotive windshield sunshades find it necessary to apply a label that tells the driver to remove it before driving. It's not a slide; it's a lahar and it's overtaking us.
They have to add those stupid labels so that they have a positive defense in any lawsuit from opportunists looking for a payout.
I don't place the blame for that on people in general, despite their apparent reptilian understanding, but rather on the legal system. The legal system, designed by and for lawyers, was created to entangle people so that they may be fleeced for the benefit of lawyers, and they've made incremental progress over the years using the government to force their system onto potentially everyone. It's all about taking universally understood concepts and spinning them into something which can be exploited for financial gain.
Product liability laws come from this system, where the phrase "reasonable and prudent" is a big money maker. It's a grand scam in which justice is only an occasional by-product.
E.G. "That depends on what your definition of "is" is. WJ Clinton
Why do you think new cars have collision avoidance braking and lane wandering sensors, now days? and automatic parallel parking or controlled trailer backing. Heck people have to have an app on their phone to start their cars, tell them when they might be running low on gas and the phone has to interface with the vehicle at all times so it will know where to go to get a tire aired up or the car itself is a roving wifi connected to the web at all times
That's why and how they were able force the legal system onto everyone. Like I said, it's a grand scam and it's been going on for many years.
Of course; they have gamed their own system [converting justice and civil law into legal manipulations], so politics is just another avenue straight to Agendaville.
I've said this forever; most [maybe all] the inequities we suffer as citizens are traceable to lawyers, lobbyists and politicians. I don't single out the left broadly, yet far left certainly is the keystone. Added detail, lawyers have only studied the law, attorneys pass bar examinations.
For example; they'll inform you otherwise about that hierarchy; I reply with one or another challenge but favorite is, "how many interpretations are there to Shall Not Be Infringed...". They'll argue meaning of militia, I remind them of Minute Man statue and his pose, in Concord, Mass., even name implies differently then standing army.
Stops them every time.