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Topics - Euclid

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The Lounge / North Korea torpedoed the Deepwater Horizon oil rig
« on: May 03, 2010, 07:33:10 PM »
It makes sense.

Flat Earth Debate / Lower bound on the height of the Ice Wall.
« on: February 09, 2010, 02:35:36 AM »
Taking the height of the Ice Wall to be finite and no other containment mechanisms in place, the atmosphere should leak out at some rate due to diffusion.  Using geologic evidence, the composition and density of the atmosphere can be traced back several hundred million years.  I am not familiar with the available evidence, but I'm fairly certain it has not changed much.  Using gas diffusion laws, it should be possible to estimate how high the Ice Wall would be to be consistent with this evidence.  Perhaps some of our members can collaborate and we can evaluate this bound.

Flat Earth Debate / A New Curve for Bendy Light
« on: October 18, 2009, 04:52:55 PM »
I was thinking of a possible mechanism of bendy light, and an obvious idea was of course refraction.  A linear upwards gradient of refractive index seems to be the most reliable choice, since any smooth function which describes the index of refraction as a function of altitude is approximately linear over short enough distances.

So I went about finding what would be the equation of this curve.  It can be derived from Fermat's principle of least time.

According to Fermat's principle, the path taken by light is such that total time of passage between two points is minimized.  In mathematical terms, the variation in the time of travel for any small perturbation in path δy(x) is 0, or

δT = δ∫Cdt = 0

where C is the path taken by the light.  Suppose we want a path in 2D Cartesian xy coordinates, y(x).  We know that the speed of light in a medium with index of refraction n(y) is ds/dt = c/n(y).  s is the path length taken by the light.  For a path y(x),

s = ∫C√(1+y'(x)2)dx,

so ds/dx = √(1+y'(x)2).  By the chain rule, dt/dx = dt/ds ds/dx so

dt/dx = n(y)√(1+y'(x)2)/c.

The minimization principle then becomes

δ∫Cdt = δ∫C dt/dx dx = δ∫C  n(y)√(1+y'(x)2)/c dx = 0.

This of the form  δ∫C L dx = 0.  In order for a function L to satisfy this minimization condition, it must satisfy the Euler-Lagrange equation

d(∂L/∂y')/dx = ∂L/dy.

Using L = n(y)√(1+y'(x)2)/c, this yields the differential equation

y''(x) = dn/dy (1+y'(x)^2)/c.

This can be solved by separation of variables, noting y''(x) = dy'/dx = dy'/dy dy/dx = dy'/dy y', so that the equation becomes

dy'/dy y'/(1+y'2) = dn/dy,

which can be integrated and simplified to give the equation

1 + y'2 = (n(y)/n0)2

where it is assumed the light ray starts off horizontally with y'(0) = 0 and that the index of refraction at that point is n0.  This can be solved for x(y) via separation of variables and an integration as,

x(y) = ∫0ydy'/√((n(y')/n0)2-1),

which may be inverted if the integration turns out to be sufficiently simple.  Suppose the index of refraction is a linear gradient,

n(y) = Dy + n0.

Substituting this into the integrand and integrating gives

x(y) = ∫0ydy'/√(((Dy +n0)/n0)2-1).

Carrying out this integral yields a fairly ugly expression, but it turns out it can be inverted to find a fairly simple expression for y(x).  Using n0 = 1, the solution is

y(x) = (cosh(D x) - 1)/D.

Therefore, the curve a light ray in a medium with refractive index linearly increasing with height is described by the hyperbolic cosine curve with the parameter D, which describes the change in refractive index per unit height.  Taking the first term of a Taylor series for this function gives

y(x) ≈ D x2/2,

which would be valid for small over small distances.  I propose calling the constant D Daniel's constant in appreciation of Daniel's creation and maintenance of this site which has lead to the fruitful expansion of flat earth science.

Flat Earth Debate / A crude diagram of new bendy light model
« on: July 12, 2009, 01:35:27 AM »

Suppose there is a cloud of aether, dark matter, what have you, above the earth.  The index of refraction of this cloud increases toward the center, as shown by the increasingly darker ovals in the picture.  Inside the cloud is a sphere of stars and the other heavenly bodies.

This model enables the entire southern annulus to view the same stars.  The rays drawn show the path of light from the north and south pole stars.  At the equator, an observer will see the pole stars on opposite ends of the horizon.  The south "pole" would be the location where the rays are vertical as shown, though in reality, the south pole would be a ring, not a point.  In addition, looking at the southern pole stars would always point south, another difficulty of previous models.

Flat Earth Q&A / One-on-One Debates
« on: July 04, 2009, 12:17:19 PM »
Several times in the debate forums, I've come across instances where there was a good topic going between two posters.  Then some random noob comes in, says "your retarted", and the discussion derails into a senseless debate that we have here ad nauseam.  I think it would be a good idea if certain debates could, at the request of one of the posters, be restricted to the two or possibly more posters. Similarly, a poster could challenge another in a new thread, if a good debate was derailed in another thread.  Such requests would have to be approved by a mod of course to prevent retarded debates and challenges from happening.

The Lounge / NFES dead?
« on: June 06, 2009, 07:04:42 AM »

Flat Earth Debate / Neptune does not exist
« on: May 08, 2009, 06:00:24 PM »
Here is a bit of wisdom from our own Dogplatter:

How ironic that the first real problems found with the Newtonian laws that you don't like were exposed by the orbit of Mercury around the sun not being as expected...

Not really, the first problem was with the "orbit" of Uranus not fitting the theory. Which led the globularist Conspiracy to invent the planet Neptune in order to explain away this theory-shattering problem.

Very interesting take.  Could it be true?

Philosophy, Religion & Society / If a tree falls in a forest...
« on: April 22, 2009, 07:09:24 PM »
and no one is there to hear it, does it make a sound?


Provide definitions for words in question as well as evidence to back your answer (if indeed evidence can be found).

Philosophy, Religion & Society / The End of Civilization
« on: April 16, 2009, 12:38:17 AM »
For the vast majority of human existence, we have lived as nomads.  We gleaned food and water from the environment and were truly one with it.  We lived in small groups, often with close relatives.  Cooperation was necessary for survival, and crime and violence were never at the level of today.  Society was egalitarian, and important decisions were always made in the council of the entire group.  This is the lifestyle we for which we evolved.

Then, out of the blue, something happened.  About 10,000 years ago, we developed agriculture and settled down.  The division of labor allowed the development of technology at an unprecedented rate, but at what cost?  Feeling the need to protect territory and state, war became a new aspect of humanity.  Famines could wipe out an entire population with one bad season.  The diversity among a concentrated population led to infighting and violence.  Organized religion developed.  Even in the developed world today, corporations hold sway over entire populations, using the populace as a sole means to the gain of the elite.  All of these great evils were brought on by settlement and civilization.

The time is near to throw off the shackles of civilization and renew our lifestyles as Nature intended.  Am I suggesting we abandon all technology and return to life as hunter-gatherers?  No.  It is time to leave the Earth behind and resume our wandering lifestyle in space.  Only then can we truly be free.

Herein lies the answer to the question of why civilization ever developed.  Civilization is an engine for the development of technology.  It is the means by which the capability to leave the Earth was invented.  Civilization is yet another tool invented by Nature so that the tendrils of Life can make the next giant leap and spread across the entire Universe.  This is our purpose and it is time to fulfill eons of evolution and the command of our ancient DNA to spread life once again in the greatest burst of life since the Cambrian Explosion.

Flat Earth Debate / Dark Matter in FET
« on: April 03, 2009, 07:28:39 PM »
I have realized there are a lot of interesting consequences of a so-called "dark matter" in FET.

The "dark matter" appears to have little or no interaction with ordinary matter.  It does however affect light.  It has a refractive index that scales proportionally to its density.  Above the Earth is a gradient of this dark matter.  Its density increases as one goes upwards.  This may explain many phenomena in FET, depending on further calculation.

  • The correspondingly increasing refractive index explains the bending path of light from heavenly bodies to the Earth, explaining sunsets and the movement of the stars across the sky.
  • The gradient in the density may be enough to produce a significant gravitational field, one that tends to decrease g moving upwards.  This may explain measurements of decreasing g with altitude.
  • The gradient in density also provides a way for the heavenly bodies to stay above the Earth.  The gravitational field of the gradient may cancel the gravitational field of the Earth at some point high in the heavens, providing a stable equilibrium point where heavenly bodies reside.

Flat Earth Debate / The Mathematics of the Electromagnetic Accelerator
« on: March 29, 2009, 10:22:24 PM »
Nevermind the cause of bending light, the purpose of this thread is to derive a set of equations that describes the trajectory of light from the Sun to the Earth.

Would anyone like to throw out a few basic assumptions to work with?

The Lounge / I am infiltrating the Conspiracy...
« on: March 27, 2009, 07:07:48 PM »
I have a job this summer working with NASA's Fermi Gamma Ray Space Telescope.  Should I risk death and tell everyone that all the data we are studying is just a lie?

Flat Earth Debate / Electromagnetic Accelerator
« on: March 17, 2009, 02:54:47 PM »
Quote from: Jack
The debate is over long time ago. Due to a consensus among the FEW members, the bendy light theory (its violation to GR's equivalence principle on gravitation=acceleration; an elevator accelerating upward should cause a horizontal light beam bend down, not up, relative to the observer) is no longer the plausible explanation behind optical phenomenons such as sinking ship effect or sunsets/sunrises. We decided to keep our old traditional perspective explanations instead.

Please stop spreading this theory around to mislead new members.

I was certain that the Electromagnetic Accelerator was an effect independent of the Earth's acceleration.  I presumed it was some sort of "5th force" acting on light causing it to bend upwards.  Surely this is plausible?

Technology, Science & Alt Science / Nemesis
« on: March 02, 2009, 02:41:00 PM »
Nemesis is a hypothetical red or brown dwarf star that could be 1 to 1.5 light-years from Earth.  It is thought to exist because there seems to be a periodicity of 26 million years in extinctions on Earth.  Nemesis' orbit could take it through the Oort Cloud, periodically disturbing comets on a course through the Solar System.  It is said Nemesis has escaped detection because it's orbital motion masks the proper motion used to detect most nearby stars with parallax.

I just find it interesting that this body could exist while totally escaping our discovery.

The Lounge / View Member's Badge Album
« on: January 19, 2009, 11:52:48 AM »
What is this and how come we don't use it?

Technology, Science & Alt Science / Entropy and Time Reversal
« on: October 17, 2008, 04:03:32 AM »
I was watching some videos on YouTube that played a lot of everyday events backwards.  For example: " class="bbc_link" target="_blank" rel="noopener noreferrer">

The crazy things is that none of those events, if they were observed to happen in forward time, violate the basic laws of physics.  Physics is symmetrical to the direction of time.  There is no fundamental law of physics which says that a broken cup can't reassemble and shoot up into the air, or an boiled egg can't uncook itself back into a raw egg, or a dead animal can't resurrect itself back to life.  It is simply very unlikely for these things to happen.  This is summarized in the second law of thermodynamics.  A measure of disorder, called entropy, always increases.

Why is this so?  What if we could turn off the second law?  What if there was a device that allowed us to harness atoms and molecules to do our will?  We could make objects come off the ground and land in our hands.  We could bring dead loved ones back to life.  It is as if it was all magic.

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