Erathosnes on Diameter (from the Wiki)
« on: August 03, 2020, 09:40:42 PM »
In the Wiki it is stated

https://wiki.tfes.org/Eratosthenes_on_Diameter

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We can use Eratosthenes' shadow experiment to determine the diameter of the flat earth.

Syene and Alexandria are two North-South points with a distance of 500 miles. Eratosthenes discovered through the shadow experiment that while the sun was exactly overhead of one city, it was 7°12' south of zenith at the other city.

7°12' makes a sweep of 1/25th of the FE's total longitude from 90°N to 90°S (radius).

Therefore we can take the distance of 500 miles, multiply by 25, and find that the radius of the flat earth is about 12,250 miles. Doubling that figure for the diameter we get a figure of 25,000 miles.

However, I am confused about how this claim can be made.  Here is an simple diagram of the situation (no tto scale)



It is claimed, that on a flat earth, that if we know D, the distance between Syene and Alexandria, we know the angle of A, that we can compute De (diameter of the earth in a 'flat disc' model) 

However, I do not see how this can be done.  Without going into the geometry. Imagine extending De to any aribtrary length.  It will not change the angle A, nor the distance D.  Therefore, for any given A or D, maps to any De > D at least (which would be obvious)


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Offline Tom Bishop

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #1 on: August 04, 2020, 12:13:13 AM »
If the sun moves across the sky consistently or near-consistently (by observation), and if the 500 mile distance between those two points is 1/25th of the total longitude radius of the Monopole model (90°S - 90°N), then the Monopole model can be computed to have a radius of 12,250 miles. Double for the diameter to get 25,000 miles.
« Last Edit: August 04, 2020, 12:15:01 AM by Tom Bishop »

Re: Erathosnes on Diameter (from the Wiki)
« Reply #2 on: August 04, 2020, 12:57:25 AM »
If the sun moves across the sky consistently or near-consistently (by observation), and if the 500 mile distance between those two points is 1/25th of the total longitude radius of the Monopole model (90°S - 90°N), then the Monopole model can be computed to have a radius of 12,250 miles. Double for the diameter to get 25,000 miles.

I'm still not quite following you - could you provide a diagram for what you mean?  I also don't see anything in the wiki about the consistency of the motion of the sun coming into play here.

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Offline Tom Bishop

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #3 on: August 04, 2020, 03:05:37 AM »
« Last Edit: August 04, 2020, 03:13:39 AM by Tom Bishop »

Re: Erathosnes on Diameter (from the Wiki)
« Reply #4 on: August 04, 2020, 07:05:33 AM »
First off, this measurement was not made at the north pole, but much further south (in Egypt.  Also degrees, as a unit of measure of an angles, have no definition along a straight line. They only have a definition as fraction of the circumference of a circular. (The full circumference represents an angle of 360 degrees, half circle 180 degrees, etc.).  They are also defined by the intersection of two lines, because you can construct a circular arc of radius 1 originating at the intersection point which begins at one line at ends at the other. You can do this physically with a protractor.   So I'm not sure how you can justify labelling the north pole as 90 degrees (or any other degree measurement, really), assuming a flat earth model. 

I also do not see the intersection of any lines, or anything that represents an angle, which correspond to the red line that is supposed to represent 1/25 of the radius, so I'm not how the measurement of 7°12' is coming into play here.


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Offline AATW

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #5 on: August 04, 2020, 07:26:24 AM »
If the sun moves across the sky consistently or near-consistently (by observation)
...then that proves the sun can't be going in a circle above us. Otherwise the angular size and speed would constantly change.

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and if the 500 mile distance between those two points is 1/25th of the total longitude radius of the Monopole model
And how do you establish that?
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Offline Tumeni

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #6 on: August 04, 2020, 07:56:19 AM »
If the sun moves across the sky consistently or near-consistently (by observation), and if the 500 mile distance between those two points is 1/25th of the total longitude radius of the Monopole model (90°S - 90°N), then the Monopole model can be computed to have a radius of 12,250 miles. Double for the diameter to get 25,000 miles.

All you're doing is multiplying by 25 because you have defined/presumed/assumed the 500 miles to be 1/25th. You have not shown how you have established that it is so.

Angles are defined as the displacement between two straight line vectors, at the point where the vectors meet. Writing 90 degrees N on your diagram does not show these vectors. Where are they, and where is the angle drawn?
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Offline Tom Bishop

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #7 on: August 04, 2020, 02:20:18 PM »
First off, this measurement was not made at the north pole, but much further south (in Egypt.  Also degrees, as a unit of measure of an angles, have no definition along a straight line. They only have a definition as fraction of the circumference of a circular. (The full circumference represents an angle of 360 degrees, half circle 180 degrees, etc.).  They are also defined by the intersection of two lines, because you can construct a circular arc of radius 1 originating at the intersection point which begins at one line at ends at the other. You can do this physically with a protractor.   So I'm not sure how you can justify labelling the north pole as 90 degrees (or any other degree measurement, really), assuming a flat earth model. 

I also do not see the intersection of any lines, or anything that represents an angle, which correspond to the red line that is supposed to represent 1/25 of the radius, so I'm not how the measurement of 7°12' is coming into play here.

7°12' is 1/25th of 180 degrees.

If you move North to South from one side to the Sun's area of light to the other side the Sun will rise from the horizon and make a 180 degree arc over your head.

Therefore we can take the known distance and multiply by 25 to get that distance across the sunlight area. If we think that the Sun is moving in a circle like the Monopole model we can double our figure for the total diameter.

It's really just measuring the N-S sunlight diameter on one side and then multiplying by two to get total diameter dimensions for a model.

I determined that the sun goes around the Monopole model because I read the FAQ.

I determined that the sun would rise and eventually set when you move towards it from one side of its area of light to the other based the sun's rising and setting over the course of a day.

I determined that the Sun would move consistently or near-consistently in the sky by observation.
« Last Edit: August 04, 2020, 04:59:58 PM by Tom Bishop »

Re: Erathosnes on Diameter (from the Wiki)
« Reply #8 on: August 04, 2020, 05:55:34 PM »
First off, this measurement was not made at the north pole, but much further south (in Egypt.  Also degrees, as a unit of measure of an angles, have no definition along a straight line. They only have a definition as fraction of the circumference of a circular. (The full circumference represents an angle of 360 degrees, half circle 180 degrees, etc.).  They are also defined by the intersection of two lines, because you can construct a circular arc of radius 1 originating at the intersection point which begins at one line at ends at the other. You can do this physically with a protractor.   So I'm not sure how you can justify labelling the north pole as 90 degrees (or any other degree measurement, really), assuming a flat earth model. 

I also do not see the intersection of any lines, or anything that represents an angle, which correspond to the red line that is supposed to represent 1/25 of the radius, so I'm not how the measurement of 7°12' is coming into play here.

7°12' is 1/25th of 180 degrees.

If you move North to South from one side to the Sun's area of light to the other side the Sun will rise from the horizon and make 180 degrees arc over your head.

When you say "move North to South", I presume you mean from a given point towards the closest point on the outer edge of the disc (which would be away from the North Pole).   

Herein lies the problem.  It will be impossible for an observer on a flat disc to ever observe the Sun at/below the horizon, at the same time another observer at another point of the disc observes it directly overhead, (or really, any point substantially above the horizon). Let me illustrate.   Keep in mind this is a side view.



Observer O observe the sun directly overhead (90 degrees).  Observer A will observe at some angle < 90 degrees. Observer B will observe the sun at a some angle < 90 degrees.  As we imagine observer B getting farther and farther away from A and O, the angle keeps diminishing, this is true.  But you cannot imagine even getting close to the horizon (an angle of 0 degrees), until observer B is very far away. 

But we can better than just intuitive observations - we can actually do the math to determine how far B must be from A or O, in order to observe the sun at some given angle. 

I'll use the following convention.  ang(X) is the angle formed at point X, between the line from X to the sun, and line of the ground.  In terms of Erathosnes, it would be 90 - the angle of the shadow formed in his stick experiment.   For example, ang(O) = 90 degrees.  dist(X, Y) is the distance from point X to Y.  Also, though I didn't label it, I'll use S for the sun.

This following requires trigonmetry.  Since we have a right triangle (one where one of the angles is 90 degrees), we can easily solve for lengths if we know one of them and angle between one of the sides. 
In a right triangle, there will two line segments which are short, and a third line segment which is longer than the other two.  This is called the hypotenuse.   

There is a cool function, called "sine", which is defined for a given angle, assuming the hypotenuse is 1.  It is writen as sin(X), reading as "the sine of X"  sin(X) would be the length of the side opposite that angle.  Since the hypotenuse is 1, sine can never assume a value > 1.  In a real right triangle, where the hypotenuse > 1, we can simply multiply sin(X) by the hypotenuse to get the length of the opposite side. 

There is also a similar function called "cosine", similar to sin.  This gives you the length of the adjacent side to the angle.   It is written as cos(X).   cos(X) * length of hypotenuse  gives  the length of the side

Also I shoudl note, when using angles in the sine and cosine functions, you need to plug them in as "radians".  Radians are defined as the length of the circular arc formed by the angle assuming a radius of 1.   The circumfrence of a half circle is defined to be PI, which is roughly 3.141527.   This correspondes to 180 degrees.  So the conversion from degrees to radians is radians = PI * degrees / 180.

Looking at the diagram again, we can see both triangles share a common side, which is dist(O, S).  We can use trigonometry to solve for the dist(B, O), if we have enough information.

In this case, we know ang(A), we know ang(O), we know dist(A, O), and we are presuming ang(B)  The issue is to determine the dist(B, O) which satisfies the observations. 

Now lets write down some equations, just going by the trigonometry

1) dist(B, S)*sin(B) = dist(O, S)
2) dist(B, S)*cos(B) = dist(B, O)
3) dist(A, S)*sin(A) = dist(O, S)
4) dist(A, S)*cos(A) = dist(A, O)

Equation (2) is the one we want to solve for, dist(B, O).  However, we do not know dist(B, S).  But we can use equation (1) to solve for dist(B,S).  Dividing both sides by sin(B), we get

5) dist(B,S) = dist(O,S)/sin(B).

Now the problem is we don't know dist(O,S).  But we can use equations 3) and 4) to solve for it.  Equation 3) gives us the exac trelation - the only problem is that we don't know dist(A,S).  But we can use equation 4, dividing both sides by cos(A), we get

6) dist(A, S) = dist(A,O)/cos(A)

Plugging this back into (3), we get

3) dist(A, S) * sin(A) = dist(O, S)
7) (dist(A,O)/cos(A)) * sin(A) = dist(O, S)

Now plugging this back into equation (5)

5) dist(B,S) = dist(O,S)/sin(B).
9) dist(B,S) = [ dist(A,O)/cos(A)) * sin(A) ] /sin(B).

Now we plug this back into (2) to solve for dist(B, O)

2) dist(B, S)*cos(B) = dist(B, O)
10) [[ dist(A,O)/cos(A)) * sin(A) ] /sin(B) ] * cos(B) = dist(B.O)

And we ended up with a mess, however a mess that can be calculated.

Now let's plug in Erathosnes numbers, and a reasonable number for ang(B), like lets say 5 degrees.  He observe an angle of 7.2 degrees, which means that ang(A) = 90 - 7.2 = 82.8 degrees angle of the sun above the horizon.  The distance, dist(A, O) was 500 miles.

So dist(B,O) = [[ (dist(A,O)/cos(A)) * sin(A) ] /sin(B) ] * cos(B) 
                   = [[ (500 / cos(A * PI/180)) * sin(A * PI/ 180) ] / sin (B * PI / 180) ] * cos ( B*PI/180)
                   = 45239.09 miles.

The claimed diameter of the Earth in the wiki was 25,000 miles.   And we weren't actually measuring the diameter, but something less than the radius.  What that means the diameter woud have to be more than twice our number, so > 90,000 miles.

And this is assuming an angle of 5 degrees, as a I felt that was reasonable.  But lets see what happens to our numbers as they get closer to 0 degrees.

For 2 degrees, we have dist(B, O) = 113339 miles ( to the nearest mile)
For 1 degrees, we have dist(B, O) = 226748 miles (to the nearest mile )
For 0.1 degrees we have dist(B, O  = 2267711 miles (to the nearest mile)

So we can see whats going on, as we get closer and closer to 0, the distance is increasing very quickly.  In fact looking back out our equation, since we are dividing by sin(B), it cannot be zero otherwise the value is undefined.  sin(B) is only zero when B itself is 0, i.e, the sun is at the horizon.  The model predicts that we can never get far enough away, to actually observe this. 

Now, I suppose you could introduce that the idea that the light from the sun is doing something funny which causes it not to move in a straight line (refracting, accelerating, etc.) causing the observation you get.   But, when do that, it trashes the basic geometry of the problem, such that he observations themselves worthless without knowing what the light is doing/ why it is doing that.       

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Therefore we can take the known distance and multiply by 25 to get that distance across the sunlight area. If we think that the Sun is moving in a circle like the Monopole model we can double our figure for the total diameter.

It's really just measuring the sunlight area on one side and then multiplying by two to get dimensions for a model.

I determined that the sun goes around the Monopole model because I read the FAQ.

I determined that the sun would rise and eventually set when you move towards it from one side of its area of light to the other based the sun's rising and setting over the course of a day.

I determined that the Sun would move consistently or near-consistently in the sky by observation.

The sun moving consistently in the sky at a given point, over the course of the year, is another problem (it doesn't, it varies over the course of a year at any given point), but I'll put that issue aside for now.  Right now I want to focus on the basic geometrical reasoning.

So, in conclusion, it is my position that, assuming a flat Earth, Eratosthenes experiment can tell you nothing about the diameter of the Earth. 

As a addendum, I'll note that I am not trying to necessarily argue for an alternate mode such as RET.  I am simply working out the claims of FET, as claimed in that section of the Wiki, to its rational conclusions given basic geometrical reasoning.

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Offline Tom Bishop

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #9 on: August 04, 2020, 06:19:20 PM »
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Herein lies the problem.  It will be impossible for an observer on a flat disc to ever observe the Sun at/below the horizon, at the same time another observer at another point of the disc observes it directly overhead, (or really, any point substantially above the horizon). Let me illustrate.

This is an entirely different argument related to the nature of light and perspective and how they operate at large scales, which you are proposing to be indisputably true.

We observe that the sun sets, therefore there must be a mechanism which makes this happen. We also observe the sun move consistently, or near consistently, and so therefore there must be a mechanism that makes this happen. Observationally, there must be mechanisms which make those things happen.

All of this is rather unconnected to this discussion of using the sunlight area to determine the diameter of the Monopole model. You are asking an entirely different question of "why" the sun sets, which is unconnected to the empirical observation of seeing the sun set. For this follow up question you should see what we have to say about it.

See: https://wiki.tfes.org/Sunrise_and_Sunset
« Last Edit: August 04, 2020, 06:30:06 PM by Tom Bishop »

Re: Erathosnes on Diameter (from the Wiki)
« Reply #10 on: August 04, 2020, 06:35:40 PM »
Quote
Herein lies the problem.  It will be impossible for an observer on a flat disc to ever observe the Sun at/below the horizon, at the same time another observer at another point of the disc observes it directly overhead, (or really, any point substantially above the horizon). Let me illustrate.

This is an entirely different argument related to the nature of light and perspective and how they operate at large scales, which you are proposing to be indisputably true.

We observe that the sun sets, therefore there must be a mechanism which makes this happen.

See: https://wiki.tfes.org/Sunrise_and_Sunset

All of this is rather unconnected to this discussion of the model, unless you want to prove your assumed axioms.

My assume axioms are basic Euclidean space (the 3d dimensional extension of 2d Euclidean plane geometry), and that light, at least this particular circumstance of the Sun to Earth observer, is (mostly) following a straight line path.

If FET is going to advance alternative axioms, such as non-Euclidean geometries, or that the light from the Sun to Earth does not travel in a straight line path in the circumstances we have here, this needs to be stated.  It also should be quantified, when making quantifiable predictions such as measuring the diameter of the Earth based on measurements like Erathosnes.   Otherwise it is impossible to work out the logical conclusions of the theory.

So I would ask the following questoins

1) Is Euclidean space an accurate representation of reality, at least in most circumstances? 

2) If the answer to (1) is no, what geometry model is FET using?  (hyperbolic and elliptic are two alternative geometries)

3) If the answer to question (1) is yes, does light follow straight line path, at least in some circumstances, such that your re able to determine the actual position of objects (X,Y,Z) coordinates in three dimensional space given multiple simultaneous observations from observers located some distance part?  Or alternatively, multiple observations over time from different perspectives assuming the object is stationary?




Offline Bobed

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #11 on: August 05, 2020, 12:47:23 AM »
I am still waiting for a picture of the flat earth. Of all the people in boats , planes , balloons ,,,,,,nobody has a camera...., Why do sailing vessels show the top of their masts first when arriving to port and last when leaving port

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Offline AATW

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #12 on: August 05, 2020, 08:27:08 AM »
We observe that the sun sets, therefore there must be a mechanism which makes this happen. We also observe the sun move consistently, or near consistently, and so therefore there must be a mechanism that makes this happen. Observationally, there must be mechanisms which make those things happen.
You're an Occam's Razor kinda guy. If something maintains a consistent angular size then what's the simplest explanation?
If something is occluded by another object then what's the simplest explanation?
You only have to invent mechanisms if you discount the simplest explanations...
Tom: "Claiming incredulity is a pretty bad argument. Calling it "insane" or "ridiculous" is not a good argument at all."

TFES Wiki Occam's Razor page, by Tom: "What's the simplest explanation; that NASA has successfully designed and invented never before seen rocket technologies from scratch which can accelerate 100 tons of matter to an escape velocity of 7 miles per second"

Re: Erathosnes on Diameter (from the Wiki)
« Reply #13 on: August 09, 2020, 07:12:22 PM »
Quote
We observe that the sun sets, therefore there must be a mechanism which makes this happen.

We do indeed. Seeing the Sun setting in the west and rising in the east must be among the most observed sky phenomenon out there.  I think most people the world over understand why the Sun rises and sets.  As did the ancient Greeks (and probably civilisations before them).  However it seems that understanding hasn't manifested itself on Tom Bishop yet.  He prefers to call it a 'mechanism'.

I guess this is the result of refusing to accept that the Earth is anything else but flat.  In other words it is a self-created problem.
« Last Edit: August 09, 2020, 07:14:43 PM by IronHorse »

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Offline Tom Bishop

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #14 on: August 09, 2020, 08:37:43 PM »
What reason is there to believe that particles or waves travel in perfect straight lines through the universe without being affected by any phenomena? Can you answer more with than "they just do" and "Newton said..."? That doesn't sound so logical to me. Straight line trajectories are rather rare in human experience. The fact is that you are insisting on your assumption. All of your mechanisms have sets of axioms assumed.

When the edge of the sun is touching the horizon RE also says that it is already below it due to astronomical refraction. It is proposing that we see a consistent illusion every day.
« Last Edit: August 09, 2020, 08:44:58 PM by Tom Bishop »

Re: Erathosnes on Diameter (from the Wiki)
« Reply #15 on: August 09, 2020, 09:04:55 PM »
Why do you find it necessary to question something which is so blatantly obvious to 99.9% of the population?  Do you just like to argue about things for the sake of it?  Or it is just a case of you like to think you are right and everyone else is wrong?

Honestly Tom there are bigger problems to solve in the world than why the Sun rises and sets.  We solved that one a LONG time ago. It doesn't take a genius to work it out.

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The fact is that you are insisting on your assumption

No I am not.  I am simply watching something happen in the sky (on a daily basis) and coming to a logical conclusion as to why it happens.  Why don't you try it sometime rather than trying to re-invent how science explains the simplest of observations.   
« Last Edit: August 09, 2020, 09:28:02 PM by IronHorse »

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Offline JSS

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #16 on: August 09, 2020, 11:56:46 PM »
What reason is there to believe that particles or waves travel in perfect straight lines through the universe without being affected by any phenomena? Can you answer more with than "they just do" and "Newton said..."? That doesn't sound so logical to me. Straight line trajectories are rather rare in human experience. The fact is that you are insisting on your assumption. All of your mechanisms have sets of axioms assumed.

We assume light travels in a straight line unless otherwise deflected because that is what we observe. We know light refracts when entering different densities, we know it bends when passing through massive gravitational wells, and we understand the mechanics and behaviors of these. Unless affected by a known mechanic, light travels in straight lines.

One piece of evidence is the Voyager probes, the New Horizon probes and the Mars robots.  All of these are sent on gravitational assisted trajectories based on Newton mechanics, we point our telescopes and radio antennas where we predict their positions should be and can communicate with them.  If light didn't travel in straight lines then we would not be able to talk with them. The two systems match up, the orbital mechanics say they should be at a specific spot, and that's where we find them.

Another point in favor is again the robots on Mars and other solar system probes are looking at the solar system from many different angles, some on the other side of the sun, and they all see what we would expect. If light were bending or curving in unexpected ways then those probes would see the planets in different positions than expected.  Remember the pale blue dot picture, Voyager turned around to take a photo of the Earth, and it was right were it should be. This wouldn't be the case if light were bending in unknown ways.

A large amount of cross-checked observational data and many different physics systems all give consistent results. Science doesn't just assume things go straight, it has come to that conclusion due to the evidence and observations we have made.

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #17 on: August 10, 2020, 08:44:00 AM »
What reason is there to believe that particles or waves travel in perfect straight lines through the universe without being affected by any phenomena?

It's the most straightforward explanation. Occam's Razor.

There is absolutely no reason to presume that the light deviates in any fashion around a straight line connecting observer and object unless something can be positively indicated which will affect the light.

If you wish to assert it does not follow a straight line, you must first positively identify the phenomenon/phenomena to which you refer. In the absence of any, Occam's Razor prevails.   
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Offline Tom Bishop

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #18 on: August 10, 2020, 08:52:51 AM »
Imagining a phenomena that travels in a straight line trajectory isn't "simple". It literally contradicts most known trajectories of particles and objects. You made a statement that straight line trajectories exist in nature and are the simplest idea when you have a difficult time showing examples of such that occur in human experience.

Even dropping a body under 'gravity' doesn't go straight in the presence of air resistance. Straight trajectories are artificial and unnatural.

We know from the double slit experiment that light propagates as a wave anyway, bending and propagating in complex ways and not in straight line trajectories. Straight isn't the default there.
« Last Edit: August 10, 2020, 09:26:39 AM by Tom Bishop »

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Offline AATW

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Re: Erathosnes on Diameter (from the Wiki)
« Reply #19 on: August 10, 2020, 09:31:58 AM »
Imagining a phenomena that travels in a straight line trajectory isn't "simple". It literally contradicts most known trajectories of particles and objects. You made a statement that straight line trajectories exist in nature and are the simplest idea when you have a difficult time showing examples of such that occur in human experience.

Even dropping a body under 'gravity' doesn't go straight in the presence of air resistance. Straight trajectories are artificial and unnatural.

We know from the double slit experiment that light propagates as a wave anyway, bending in complex ways and not in straight line trajectories. Straight isn't the default there.
All Newton claimed is that objects will either remain at rest or continue to move at a constant velocity unless acted on by a force.
The examples you give are those of something being affected by a force.
We live in a world full of forces. So sure, if you don't steer a car it will not continue in a straight line (this is an example you give in the Wiki) because the tyres are on the road which is not perfectly flat and all kinds of frictional forces are being applied.
None of that refutes the statement that in the absence of a force it would continue at a constant velocity.

Now, light does bend of course in certain situations. We know about refraction and diffraction. Those don't apply to a light beam travelling through space although certain relativistic effects may.
Tom: "Claiming incredulity is a pretty bad argument. Calling it "insane" or "ridiculous" is not a good argument at all."

TFES Wiki Occam's Razor page, by Tom: "What's the simplest explanation; that NASA has successfully designed and invented never before seen rocket technologies from scratch which can accelerate 100 tons of matter to an escape velocity of 7 miles per second"