Sunday, May 27, 2012

Questions That Bug Me

A little off-topic, but in a comment long ago, someone asked about the questions that keep me up at night.  Here are four. And none of them are all that important.

1) Why is it that even in languages written from right to left, the numbers are written from left to right?  First noticed it inBaghdad.  One of my translators said that numbers are written from left to right in all languages.  True?  Don't know.  Possibly, if the early writers thought of 24 as 'four and twenty' the flow would be in the same direction as the writing... but that's not how they do it in Hebrew, at least.  My memory is fuzzy on Arabic.

2) In the King James version of the Bible, god is addressed in the informal.  'Thee' and 'thine' are the familiar versions, 'you' and 'yours' the formal or plural.  It is, you will note, 'your majesty' or 'your grace' when addressing upper nobility.  It appears that god is addressed as an equal throughout.

A conscious decision to make a point?  An artifact of translating from other sources?  Possibly the grammatical rules at the time are not as I was taught?

3) Explosive power decreases by the cube of the difference.  In other words, to double the blast radius doubling the powder won't work.  Nor will squaring it.  You have to cube it.  It's based on the formula for the volume of a sphere, 4/3 x pi x r cubed.  (Really sucks not to be able to do superscript and notation.)  Which makes sense.  The force just doesn't increase a line or increase the surface area.  The force has to fill the whole sphere.

So why does gravity decrease as a square function?  Does that imply that it only acts on the surface of a sphere (where the two masses would be points) and doesn't fill the void in between?  A friend (Hey, Justin!) pointed out that this is true for other forms of radiation, such as light, as well.  Which to my mind broadens the question, not answers it.

4) Was the lance a one-shot weapon?  I'm not talking medieval jousts, but like lancers during the Napoleonic wars, cavalrymen mowing down infantry soldiers.  This is what I can't figure out:
Assuming a heavy horse gallops at about 22 mph (28 would, according to one source be the max; a quarterhorse approaches 40mph at short distance) the lancer is going to stick a relatively immobile target that has weight and mass.  The second the tip of the spear drops, which it will either due to the threat falling or because (relatively) the horse keeps going and the rider is above the target, that lance becomes an enormous lever arm.

Carried under the arm, like a joust (except impaling instead of blunted so the tip stops)  that's eight feet at least of leverage applied with the weight of the target at 22mph to just under your shoulder.  Dislocation or ejection?  Carried underhand, that same leverage is applied in a rotation on the same axis as some of the better wristlocks.  Overhand doesn't seem to be a problem but at least one source, (I believe it was "The Twilight Lords" about the Desmond Rebellions) asserted that the overhand position with the lance disappeared when stirrups were introduced.

So did lancers just stick people and drop the lance and revert to a secondary weapon?  Does that imply that the most expensive unit on the battlefield was essentially a single-shot?  Does that make sense?  Or was there some technique to stab and recover that I haven't been able to find?

This is the stuff I think about. None of these are important, but if you want to bang your heads against them, go for it.


Maija said...

Here's a good bit about Lancers:
Seems like it was a 'shock and awe' kind of first charge thing ... then revert to sword for the melee .. so, intimidation factor, then lose it if it gets stuck, or keep going to break the line. Interesting that lances were disregarded as suitable for cavalry pretty early on in history .. then came back into 'fashion' for a minute .... before again being deemed inefficient.

As far as the gravity thing ... It works in one direction, right? In our case accelerating objects (until friction/drag create terminal velocity) towards the center of the Earth. Explosions go from the center outwards in all directions (until friction/drag/gravity fizzle them out) ...

Andy said...

So the blast radius thing, I think of as the amount of work you have to do against the air surrounding the package, this will be proportional to the pressure times the volume, double the volume, double the work/energy, but double the radius=8times the volume so 8 times the energy, like you said, and the amount of explosive energy is proportional to the amount of powder. This has to do the properties of gases, and the chemical energy stored in gun powder, I'm sure its more complicated than that, but that's good enough for me.
But regarding gravity is a completely different question, which has to do with how the gravitational force depends on the separation of two objects. This has to do with the fundamental forces between particles, the fact that the force goes like 1/r^2, implies that if you have to spheres,of uniform density, the force between them behaves as if they were each points with a mass M, which makes calculations easy to do. Electric forces obey the same 1/r^2 behavior. I think you can arrive at the 1/r^2 dependence, if you assume that the force exerted by one particle on another is spherically symmetric, or only depends on the distance between them, Then you can use this thing called Gauss's Law, and that gives you the 1/r^2.

I don't know if this is the complete answer, but I think it points in the right directions

Toldain said...

With regard to number 3, when we look at the force due to gravity, we are only talking about the effect of the masses on one other mass at a distance, not the total energy that they might impart to all other masses at that distance (or another). Likewise the effect of light is measured as the amount of energy imparted to an area of standard size at the specified distance, not the entire area.

Blast radius, on the other hand covers the entire sphere, that's an extra degree of freedom, hence a cube instead of a square.

CreidS said...

1) The pick one direction thing is newer than most people think. You can still go into museums and see greek vases with two guys facing off, and the one on the left will say something like, "I'll get you!" The one on the right will say, "!yaw oN" (No way!). It makes a kind of sense, and you can figure it out without a lot of work.

But when the Arabs were learning Hindu (which we call Arab) numerals, someone realized that the difference between 137 and 731 was critical. I'm guessing that since the Hindus were writing from R2L, and that things like contracts and checks were writing in ways that Hindus could understand, the Arabs adopted it, if for no other reason than make sense of imported math and trade documents.

Interestingly, when I was in Egypt, there was a shift back to the old East Arab Numeral system.

CreidS said...

3) I think you're confusing what the equations are used for. The bombs are subject to an inverse square law as well, its just that the answer isn't interesting.

Ok. If I wanted to calculate the amount of gravitational force in a given volume, I would use something similar to what your bomb experience indicates. Totalforce = 4/3(pi)r^3.

Your bomb guys, reverse the equation, and solve for r (volume), not Totalforce. They likely know what the Totalforce to achieve their goal is, and are trying fill a particular volume with it. The only part of the equation that they can control is the amount of boom.

Likewise, if I wanted to calculate gravitational energy between two objects, I'd use the inverse square law. This involves two ideal points in space; 0 dimensional dots. That's a problem, isn't it?

Well, no. At a given distance, they will have an effect, a force. This force fills a volume (a sphere), but I'm only interested in where it meets the other point -- so I'm looking at small slice, a shell, of the sphere. An area. Hence the square, and not the cube.

Your bomb guys probably don't use this equation in their work -- they already know how much force they want to hit an object with. They need to know how much boom it will take to get there.

A lot of the force is wasted in a sphere. IEDs solve this by shaping the blast into a cone, focusing much more of the force into a specific area.

As for 4), I don't have much of an answer. I recall that in the Song of Roland, the old French epic, they knights made a big show of skewering, and then lifting their opponents up. Both mounted, of course.

TimP said...

Somewhere around 80% of the language in the King James Bible comes from the earlier Tyndale translation. Good section on it in The Adventure of English,
by Melvyn Bragg, which is well worth a read if you are interested in how English developed.

Unknown said...

Maybe God is to be seen as a family member. (familiar)

jfs said...

Just tried it - the HTML for superscript is < sup > (without the spaces) but Blogger won't let me use that in a comment. You might be able to use it in a post.

TomF said...

Many, many people had a hand in writing the Bible, and their views about God varied. The King James translation was a good scholarly translation of the time, but it was after all a translation ... reflecting what the originators wrote.

And yeah, "thee" is the "personal" form (like the French "tu"). You use it with your intimates, your family. The original texts for the Lord's Prayer don't have Jesus saying a very formal "Our Father," but "Dad."

Scott said...

When I think of cavalry charges with lances I think of guys riding in tight formation so that the horses were a trampling weapon. The lance could be used on a horse or a rider in a cavalry on cavalry head-on change. And yes I think you'd have to drop it, Unless it was a short one. But perhaps if it was under your arm you could let it slide back and then up after it skwerred the rider, and you could pluck it out closer to the tip on your way by.
But only if the rider flew off his mount. Seems incredibly messy. My guess is that most of the time, the smaller force fled if they survived the first wave.
People on the ground didn't have a chance against horses in tight formation so they fled and got trampled. A line of lances looked really scary.

Anonymous said...

(Delurking, hi!)

General C. P. De Ainslie included a note on question #4 in his mid-nineteenth-century cavalry manual for English Dragoons. "For a soldier to lose his arms is a disgrace; nevertheless there is one case in which a lancer may be allowed to throw away his lance, viz., when he has transfixed his enemy with it. Such situations are by no means uncommon; a thrust having been so well given that it is impossible to withdraw the weapon, and the wounded man expiring, and carried by his horse, drags with him both lance and the lancer vainly trying to disengage it."

Participants in the modern sport of tentpegging, which doesn't require striking with maximum force, seem to get around the problem by not couching the lance very deeply under their arm, so they unwind their forearm as they pass the target and trail the lance head behind them.

Recently, with the help of an Arabic-speaking friend, I've been looking at some thirteenth-century Mamluk lance manuals. They involve a lot of plays where a lance becomes jammed in clothing or harness and one rider or the other circles his horse and uses the shaft as a giant lever to unseat his opponent.


Silver Sentinel said...

Numbers are almost universally written from left to right because they are the language of trade. No matter the trader's language of origin, all trade tallies are done in the more widely accepted numerical language.

The only number systems that do not operate in this manner are those from closed societies that had little to no contact with the outside world in general.

As for the lance. You're mistaking the weapon used in jousts as that used in battle. Also, there are several types of "lances" and they are all used differently.

TomF said...

On a related note, I remember reading that cavalry kept their sabres much less sharp than many of us think. Because a really sharp sabre would stick in your opponent's bones, wrenching it out of your hand as you rode past.

Justthisguy said...

One should look up two equestrian sports, tent-pegging and pig-sticking, to see how one handles the shock of lancing somebody or something when on horseback. IIRC, there is a loop of cord on the lance, something like a sword knot, which allows you to pull the thing out as you ride past yer victim.

On the sabers: People said that when the Heavy Brigade engaged the Russians at Balaclava you could hear the troopers cussing from a mile away, it being so hard to chop through the famous Russian greatcoats. (I want one.)

Justthisguy said...

P.s. As someone who is self-dxed as at least an "half-Aspie" I have long suspected that Rory is One of Us. This post destroys all doubt about that.

What bothers me, now that Rory is retired, is how can I be assured I'll be properly guarded if I am arrested and jailed in Multnomah County?

Anonymous said...

The fellow who taught me cavalry stuff (modern, not historical, long story) said that lances were all about making an impression on the open field. You could run someone through in a very visible manner and hopefully scare the fight out of some of the opposing force.

However, because we no longer tend to line up and charge across an open field at the enemy, lance work isn't that useful. Horse-mounted cavalry is today more often used in places like the mountains of Afghanistan where hummers, APCs, and the like can't go. It's just as messy, but it's close quarters and room to charge is a luxury you hope for, not something you build your world around.

We focused almost all of our weapons training on light and heavy saber, and using firearms while mounted. Weapons training was, in a way, secondary to horsemanship and tactics. (Especially in close quarters, your horse may be your best weapon and your shield.)

Ernie said...

Thought the lance was used with the vanguard for the purpose of breaking the enemy line.

David Kafri said...

The Bible was written in Hebrew, which has no distinction between YOU, THEE & so on - there is only "you".

Also, Hebrew is - compared to English - a very direct and informal language; Your Majesty or Your Highness can be translated into it from English but they sound strange, not natural. Things like "Yes SIR" and "No SIR" are possible in Hebrew, but not natural. They sound fake.

Edwin Voskamp said...

1) In Arabic it is, not in all right-to-left languages. Also in several Germanic languages 24 would be pronounced as four-and-twenty. It can still mess me up when I am really tired and take down numbers over the phone.

3) Explosion fills the volume of a sphere, radiation and particles the surface of the sphere.

4) Yes