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Tim's Piece of the Puzzle


Tim's Piece of the Puzzle09-08-2019 21:21
IBdaMannProfile picture★★★★★
(4950)
Tim the plumber posted this piece below in another thread. It helps me (potentially) solve a puzzle concerning pre-Inca civilizations in South America.

The puzzle is/was how 8th century tribes in the region of what is currently Ecuador (any guesses on how the country got its name?) very accurately located the earth's equator, or even knew that there was such a thing, and constructed temples/observatories directly on the equator line.

When eighteenth century mathematicians and geographers on a geodesic mission from the French Academy of Science arrived with their "modern" equipment and advanced mathematics, they built a landmark on the "exact equator," noting how the pre-Inca tribes were able to get so very close, to within 100 meters of the actual equator. It turns out that the pre-Inca tribes had found the exact equator and that the French were off by about 100 meters.

Since the tribes in question had ready access to the sea, it could be assumed that they were aware the earth was round. Since the sun was around during the 8th century it can be assumed that the idea of earth's rotation probably occurred to some of them. I could not, however, figure out how they could discern where on the ground the equator ran. Now I can imagine how.

Tim the plumber wrote:
The detail of the experiment is this;

Using a tall room, or cave, anywhere you can close the windows and make sure that the wind is not a factor.

Have a hook or something you can pass a thread over as high as possible.

Take a heavy small ball, something like a lead ball of 2 inch diameter is the idea but whatever, a large ball bearing will do. Or a cannon ball if you have one.

Taking a thread, as thin as you can whilst still being able to lift the ball, tie the ball onto the thread and pass it over the hook. You will want to start the ball a low level.

Have a sand tray or something similar on the floor so you can lower the ball onto it slowly. You will find it will swing about, you will have to steady it. lower the ball onto the sand tray and mark the position. Some lines in the sand will do. This is by definition the point directly below the hook.

Take the ball up to the top of the room by pulling the tread over the hook. It will swing about again. You will have to stop it and allow to settle.

Using a lighter or candle flame cut the tread between the hook and the ball. This is to ensure that you do not impart any sideways motion to the ball.

It will land on the sand tray east of the point that was directly below the hook.

This happens because the ceiling is moving east faster than the floor. So the ball will fall vertically due to gravity but retain its' eastwards velocity.

The period of time it takes to drop compared to the distance away from the vertical below hook position will give you a way to calculate the difference in eastward velocity.


I imagine this could be done using a tall tree if no cave is available ... with the caveot that wind/breeze would need to be avoided.

If one were to reside near the equator, the distance away from plumb-center that the weight falls could be measured and recorded. Then the setup could be moved a certain distance away in a particular direction and the weight dropped at the new location. If the deviance from plumb-center (DfPC) increases then continue moving in that direction and continue dropping until the DfPC decreases, at which point you know that you are moving away from the equator and that you should backpedal ... but at an off angle. There will be a belt/line on which the DfPC is the maximum value.

Of course 8th century tribes would have to wrestle with their measurement accuracy, but I'm presuming that they were able to sufficiently address that.

So the lesson learned here is that Global Warming began with early South American tribes.


Global Warming: The preferred religion of the scientifically illiterate.

Printing dollars to pay debt doesn't increase the number of dollars. - keepit

When the alt-physics birds sing about "indivisible bodies," we've got pure BS. - VernerHornung

Ah the "Valid Data" myth of ITN/IBD. - tmiddles

Ceist - I couldn't agree with you more. But when money and religion are involved, and there are people who value them above all else, then the lies begin. - trafn

You are completely misunderstanding their use of the word "accumulation"! - Climate Scientist.

The Stefan-Boltzman equation doesn't come up with the correct temperature if greenhouse gases are not considered - Hank

:*sigh* Not the "raw data" crap. - Leafsdude

IB STILL hasn't explained what Planck's Law means. Just more hand waving that it applies to everything and more asserting that the greenhouse effect 'violates' it.- Ceist
Edited on 09-08-2019 22:13
10-08-2019 02:22
tmiddlesProfile picture★★★★☆
(1329)
IBdaMann wrote:If the deviance from plumb-center (DfPC) increases then continue moving in that direction and continue dropping until the DfPC decreases,


If you had a way of confirming a specific distance/amount you could bracket. Like if the rock tapped into another rock, or just didn't as it fell.

An arbitrary measurement can be taken precisely with crude equipement right? (a balance weigh scale being an example, I can know that one rock is exactly the same weight as another rock)

If you established a value close to the equator you could bracket your results to get the dead center.

Like the same setup but there is a rock almost in the path of the falling rock which either grazes/taps it or it doesn't. It's either < or >. (I think having the impact as the rock falls, not when it lands, is easier).

Rock starts tapping the boundary rock exactly 40.7 meters above and then stops tapping again 40.7 meters below, for example. And I can find 0.0 precisely if I know North and have some rope. (could even establish a line above or below parallel to the equator by finding several spots of barely tapped rock readings).

ASCI art Diagram:

H__O
H............
H............
H............
H............
H............
H............
H.......O___
H............H
H............H
H............H
H______HH

Ignore the "............". Top "O" is the falling rock, lower O is a fixed rock that may or may not get grazed by the falling rock.

H__
H............
H............
H............
H............
H............
H............
H.....OO___
H............H
H............H
H............H
H______HH

Moment of almost impact.
Edited on 10-08-2019 03:08
10-08-2019 18:38
IBdaMannProfile picture★★★★★
(4950)
tmiddles wrote:If you had a way of confirming a specific distance/amount you could bracket. Like if the rock tapped into another rock, or just didn't as it fell.

Were I in that situation I might just use a length of vine and put a narrow cut/slit in it to mark a given distance, and then I could compare it to the next measurement to see if it was greater or lesser.

Big picture, if I drop the rock and determine "east", i.e. a direction, I might notice that DfPC is always the same along that line in that direction ... which means DfPC is always the same back in the opposite direction. I might establish in my mind the concept of a "latitude line."

I might notice that DfPC changes when I move perpendicular to my "latitude line" and while I never get to a DfPC of zero, I do hone in on a maximum value, and I might declare that particular "latitude line" to be a special one that is different from the others. I might use that "main latitude" as a geographical reference.

Does anything I'm saying sound unreasonable?

.


Global Warming: The preferred religion of the scientifically illiterate.

Printing dollars to pay debt doesn't increase the number of dollars. - keepit

When the alt-physics birds sing about "indivisible bodies," we've got pure BS. - VernerHornung

Ah the "Valid Data" myth of ITN/IBD. - tmiddles

Ceist - I couldn't agree with you more. But when money and religion are involved, and there are people who value them above all else, then the lies begin. - trafn

You are completely misunderstanding their use of the word "accumulation"! - Climate Scientist.

The Stefan-Boltzman equation doesn't come up with the correct temperature if greenhouse gases are not considered - Hank

:*sigh* Not the "raw data" crap. - Leafsdude

IB STILL hasn't explained what Planck's Law means. Just more hand waving that it applies to everything and more asserting that the greenhouse effect 'violates' it.- Ceist
11-08-2019 01:12
tmiddlesProfile picture★★★★☆
(1329)
IBdaMann wrote:length of vine and put a narrow cut/slit in it


I think being able to bracket in on the exact equator is very doable. The question would be what crude instrumentation would work. I forgot that you'd have an indication of East from the direction of drift you could associate with the sun rise/set directions.

Putting a marking on a vine just wouldn't allow for the very very minute change between 10 meters from the equator and 0 meters. Or between 40 and 100 even.

So like the balance scale, which requires no special tools or tech, but can accurately make a weight measurement to the fraction of a gram, you need a crude instrument that can take a precise measurement.

I think my rock falling tap/notap would work but there are a lot of options using the falling object. Two falling objects should produce a difference between them.

Oh and one other thing about the instrument I proposed. You would hang it to ensure you were plum with gravity, you would not set it on the ground.
11-08-2019 02:00
IBdaMannProfile picture★★★★★
(4950)
tmiddles wrote:Putting a marking on a vine just wouldn't allow for the very very minute change between 10 meters from the equator and 0 meters. Or between 40 and 100 even.

I completely believe you. I'm trying to walk myself through the thought process of a pre-Inca in 8th century Ecuador. I imagine that my first instincts would be to use the length of vine as my measuring stick (as it were) and then when that wasn't working I would ask my buddy tmidduhuenga to explain his rock-tap thing.

tmiddles wrote:So like the balance scale, which requires no special tools or tech, but can accurately make a weight measurement to the fraction of a gram, you need a crude instrument that can take a precise measurement.

I think my rock falling tap/notap would work but there are a lot of options using the falling object. Two falling objects should produce a difference between them.

I considered how I would solve it today using basic materials that I could find at Lowe's and Ace Hardware (no measuring devices or electronics). Today I can build a fixed rig of sufficient height that i could move around to different places and use to replicate the dropping of a ball-bearing down through a glass/transparent tube, gauging how high up the tube the ball-bearing strikes the side of the tube.

The device you propose very well accomplishes that, and could be improved by adding multiple stones with different radii from center. As long as you could move the instrument around without the relative position of the stones moving, you'd have an equator-finder that any pre-Inca would be proud to use. Do you have any thoughts on how you might do that? You'd have to move it around a lot.


.


Global Warming: The preferred religion of the scientifically illiterate.

Printing dollars to pay debt doesn't increase the number of dollars. - keepit

When the alt-physics birds sing about "indivisible bodies," we've got pure BS. - VernerHornung

Ah the "Valid Data" myth of ITN/IBD. - tmiddles

Ceist - I couldn't agree with you more. But when money and religion are involved, and there are people who value them above all else, then the lies begin. - trafn

You are completely misunderstanding their use of the word "accumulation"! - Climate Scientist.

The Stefan-Boltzman equation doesn't come up with the correct temperature if greenhouse gases are not considered - Hank

:*sigh* Not the "raw data" crap. - Leafsdude

IB STILL hasn't explained what Planck's Law means. Just more hand waving that it applies to everything and more asserting that the greenhouse effect 'violates' it.- Ceist
11-08-2019 02:13
tmiddlesProfile picture★★★★☆
(1329)
IBdaMann wrote:
Do you have any thoughts on how you might do that? You'd have to move it around a lot.


.


The balance scale instrument takes advantage of hanging from Gravity to be precise. It's not interfered with in any way by the way in which it set down on a table or the ground. The instrument, whatever it is, you could simply be hung from a tree limb the height it's hung from wouldnt matter it would just be the internal difference between the drop height and the measurement or impact location. It could even be 10 ft long and just be hung from a tree. But if it were hanging it would be independent and consistent regardless of location.

It doesn't even need to be precisely constructed it just needs to not change. It's the Precision of it being compared with itself that works.
Edited on 11-08-2019 02:16
11-08-2019 02:38
tmiddlesProfile picture★★★★☆
(1329)
At the Equator, the Earth rotates at a speed of about 1,700 km per hour,

But this measurement doesn't give you how far a rock falls with that speed. It's the speed of a higher elevation compared with a lower

So the diameter of earth is 12,742 km
2pieR giving you 40,030 I'm around
40,030/24=1667. So close to 1700

after one second, an object will have fallen a distance of 1/2 × 9.8 × 12 = 4.9 meters

So let's go with an instrument measuring a 4.9m fall.

The rotational speed if we increase the radius of earth by 4.9 is

2pieR ×12742.0049 =

40030.173592041-
40030.188985845=
0.0153938040025
/24. /60. /60

0.000000178169027807. KM per second difference
0.000178169027807 Meters

Now that would be the comparison between the north pole and the equator with a 4.9 meter rock drop.

0.18 MM
11-08-2019 02:45
tmiddlesProfile picture★★★★☆
(1329)
Maybe a pendulum?

Foucault_pendulum
11-08-2019 03:16
IBdaMannProfile picture★★★★★
(4950)
tmiddles wrote:So the diameter of earth is 12,742 km
2pieR giving you 40,030 I'm around
40,030/24=1667. So close to 1700

after one second, an object will have fallen a distance of 1/2 × 9.8 × 12 = 4.9 meters

So let's go with an instrument measuring a 4.9m fall.

You have to multiply by the emissivity coefficient, i.e. a value between 0.0 and 1.0 which is determined by how close you are to the pole or to the equator.

(did you like how I tied earth's rotation to black body radiation?)

The DfPC at the pole will be 0.0 whereas you will multiply by 1.0 at the equator. Essentially the coefficient = sin(latitude from pole) = cos(latitude from equator).


Global Warming: The preferred religion of the scientifically illiterate.

Printing dollars to pay debt doesn't increase the number of dollars. - keepit

When the alt-physics birds sing about "indivisible bodies," we've got pure BS. - VernerHornung

Ah the "Valid Data" myth of ITN/IBD. - tmiddles

Ceist - I couldn't agree with you more. But when money and religion are involved, and there are people who value them above all else, then the lies begin. - trafn

You are completely misunderstanding their use of the word "accumulation"! - Climate Scientist.

The Stefan-Boltzman equation doesn't come up with the correct temperature if greenhouse gases are not considered - Hank

:*sigh* Not the "raw data" crap. - Leafsdude

IB STILL hasn't explained what Planck's Law means. Just more hand waving that it applies to everything and more asserting that the greenhouse effect 'violates' it.- Ceist
11-08-2019 07:01
tmiddlesProfile picture★★★★☆
(1329)
IBdaMann wrote: Essentially the coefficient = sin(latitude from pole) = cos(latitude from equator).


Ha! Nice.

Yes the change at the equator in diameter from the axis of rotation would be truly minuscule given it's a curve like that.

It just doesn't seem likely some 1 millionth of a mm could be detected like that.




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