For the Mathematically Minded: Disproof of FE

  • 42 Replies
  • 8629 Views
?

∂G/∂x

  • 1536
  • All Rights Reversed
For the Mathematically Minded: Disproof of FE
« on: May 17, 2007, 06:06:56 PM »
This thread is not for everyone (everyone is welcome, but I expect not everyone will be comfortable with the mathematical nature of this proof) but for those with some faith in mathematics I offer this as proof that the Earth is not Flat. I have taken parts of it from my other threads, but I held back on this part because it is not immediately obvious enough to make a super-strong argument (especially vs. the unmathematical babblings of Mr Bishop). Anyway here goes:

I return again to my favourite FE topic: the sun. I like it because we've all seen it, seen it rise and set, and any observations we make are repeatable daily. The FET explanation of the sun's dipping below the horizon is that it is moving away while maintaining a constant altitude, therefore we can take three points O, S and P as the Observer, Sun and Point at which the sun is directly overhead. These form a right angled triangle with the right angle at P and the hypotenuse OS. We must consider also the sun's apparent angle (from the observer's POV) to the horizon as the angle at O which we will call ø.

It may be helpful for you to draw yourself a diagram at this point....

We can see that the distance OP is a function of ø and SP such that:

tan(ø) = SP/OP

Alternatively:

OP = SP/tan(ø)  or   OP = SPcot(ø)

We know SP (the perpendicular distance from sun to ground) is a constant (700 miles, 3000 miles, whatever you like really). OP and ø are variables as the sun moves closer and further, moving towards and away from the horizon (sunrise/sunset).

Time to bring in another fact about the sun: We know it moves through the sky at a constant rate, that is to say, the rate at which ø changes with time is constant. As the sun is moving at constant speed OP is also at a constant rate of change. We can therefore, with a little chain rule, show that:

d/dt(ø) = k  d/dt(OP) = q   therefore  d/dOP(ø) = k/q which is constant.

The problem is, this is a direct contradiction with our earlier statement about the sun, as if OP = SPcot(ø) where SP is constant:

d/dOP(SPcot(ø)) = -SPcosec2(ø)

Which is clearly not constant.

The practical interpretation of this is that while in RE, the sun should (and does) move at constant angular velocity, in FE it should quite clearly vary in angular velocity. Indeed, the rate of motion tends to 0 as ø tends to 0.

So there it is. FEers? Tom if you do try this one, please don't copy paste or say you've answered before. This problem has been stated before, but never demonstrated in such a way. I expect your refutation, if you have one, to be mathematically competent and not dismissive. If there are other FEers who are more mathematical I'm sure you'll have no problem checking this.

As ever, I await your responses eagerly!
Quote from: Tom Bishop
The universe has already expanded forever

Quote from: Proverbs 24:17
Rejoice not when thine enemy falleth, and let not thine heart be glad when he stumbleth.

?

CaptainAmazing

Re: For the Mathematically Minded: Disproof of FE
« Reply #1 on: May 17, 2007, 07:04:52 PM »
I assume the answer would be that the sun is out of view by the time the effect you describe is obvious enough to be noticed.

?

∂G/∂x

  • 1536
  • All Rights Reversed
Re: For the Mathematically Minded: Disproof of FE
« Reply #2 on: May 17, 2007, 07:06:46 PM »
But you can plug in values and see that the effect described would be noticeable even when the Sun was at 45 degrees. The sun would slow when nearing the horizon, almost stopping by the time it was 2 degrees or so (still far from sunset).
Quote from: Tom Bishop
The universe has already expanded forever

Quote from: Proverbs 24:17
Rejoice not when thine enemy falleth, and let not thine heart be glad when he stumbleth.

Re: For the Mathematically Minded: Disproof of FE
« Reply #3 on: May 17, 2007, 08:05:34 PM »
. . . In RE, the sun should (and does) move at constant angular velocity

I belive I've brought this up before, and while it is to small an effect to include in your calculations it's still an interesting phenomena.

In RE, the sun doesn't move at a constant angular velocity.

Because the Earth's orbit is an ellipse, we don't move around the sun at a perfectly constant velocity.  The Earths spin however is comparatively constant, so some times the Earth rotation 'gets ahead' of its orbit, and sometimes it 'lags behind', creating a slight 'lurching' effect with the sun.

You know this effect if you've ever seen an analemma (that figure eight that the sun traces out through the year.)  If it weren't for this effect, the analemma would be a strait line. 

This is also why a solar day (one apparent rotation of the Earth as measured with sun) isn't a perfectly constant length of time, but changes +/- 16 minutes over the course of the year.

In RE, we understand this effect perfectly.  But I have no idea how to account for it in FE.
« Last Edit: May 17, 2007, 08:08:41 PM by Max Fagin »
"The earth looks flat; therefore it is flat."
-Flat Earthers

"Triangle ABC looks isosceles; therefore . . ."
-3rd grade geometry student

Re: For the Mathematically Minded: Disproof of FE
« Reply #4 on: May 24, 2007, 04:55:03 PM »
I understand the original posters struggles with understanding the suns path over our flat earth. there is one verry big problem with your formulas. I understand your argument, when the Sun is far away as it's going to get it should seem to take a long time to get past it's apex to come back, kinda like the dwell of a piston on a two stroke outboard.

hear is where your "theory" falls apart. the thin air ain't as thin as you think it is. it's full of particals and debris that make it near impossible to tell the actual size of sun then there's the heat fumes raising up off of the earth from the sun above, look out at a hot parking lot and tell me the car across the lot is actually wavey not straight and looks funny though the heat fumes. Havent you ever seen the sun when it's "setting"? it seems larger than any other part of the day. No one that I know of thinks the sun actually gets bigger at the end of the day do they? here is another hitch, I beleave the sun has a slight wavey up/down path as it goes round above our circularly flat earth.

?

∂G/∂x

  • 1536
  • All Rights Reversed
Re: For the Mathematically Minded: Disproof of FE
« Reply #5 on: May 24, 2007, 05:00:39 PM »
- The sun's size makes no difference to my argument.

- Please describe this wavy path, and how it relates to the observed path of the sun.
Quote from: Tom Bishop
The universe has already expanded forever

Quote from: Proverbs 24:17
Rejoice not when thine enemy falleth, and let not thine heart be glad when he stumbleth.

Re: For the Mathematically Minded: Disproof of FE
« Reply #6 on: May 24, 2007, 05:03:26 PM »
- The sun's size makes no difference to my argument.

oh but it does when you take into account  perspective!

?

∂G/∂x

  • 1536
  • All Rights Reversed
Re: For the Mathematically Minded: Disproof of FE
« Reply #7 on: May 24, 2007, 05:05:17 PM »
Erm... no it really doesn't. If you are serious please explain. If you are just messing around go spam another thread, leave my poor thread alone!
Quote from: Tom Bishop
The universe has already expanded forever

Quote from: Proverbs 24:17
Rejoice not when thine enemy falleth, and let not thine heart be glad when he stumbleth.

*

Colonel Gaydafi

  • Spam Moderator
  • Planar Moderator
  • 65192
  • Queen of the gays!
Re: For the Mathematically Minded: Disproof of FE
« Reply #8 on: May 24, 2007, 05:06:06 PM »
Yeah! You're not allowed to spam the serious forums so piss off!
Quote from: WardoggKC130FE
If Gayer doesn't remember you, you might as well do yourself a favor and become an hero.
Quote from: Raa
there is a difference between touching a muff and putting your hand into it isn't there?

*

Roundy the Truthinessist

  • Flat Earth TheFLAMETHROWER!
  • The Elder Ones
  • 27043
  • I'm the boss.
Re: For the Mathematically Minded: Disproof of FE
« Reply #9 on: May 24, 2007, 05:17:32 PM »
Haha.  I love irony. ;D
Where did you educate the biology, in toulet?

*

Colonel Gaydafi

  • Spam Moderator
  • Planar Moderator
  • 65192
  • Queen of the gays!
Re: For the Mathematically Minded: Disproof of FE
« Reply #10 on: May 24, 2007, 05:18:33 PM »
You spelt Gayer wrong
Quote from: WardoggKC130FE
If Gayer doesn't remember you, you might as well do yourself a favor and become an hero.
Quote from: Raa
there is a difference between touching a muff and putting your hand into it isn't there?

*

Roundy the Truthinessist

  • Flat Earth TheFLAMETHROWER!
  • The Elder Ones
  • 27043
  • I'm the boss.
Re: For the Mathematically Minded: Disproof of FE
« Reply #11 on: May 24, 2007, 05:19:38 PM »
Sorry!  I love Gayer. :-*
Where did you educate the biology, in toulet?

?

∂G/∂x

  • 1536
  • All Rights Reversed
Re: For the Mathematically Minded: Disproof of FE
« Reply #12 on: May 24, 2007, 05:21:26 PM »
Spammers, please...

Quote from: Tom Bishop
The universe has already expanded forever

Quote from: Proverbs 24:17
Rejoice not when thine enemy falleth, and let not thine heart be glad when he stumbleth.

Re: For the Mathematically Minded: Disproof of FE
« Reply #13 on: May 24, 2007, 05:28:16 PM »
This thread is not for everyone (everyone is welcome, but I expect not everyone will be comfortable with the mathematical nature of this proof) but for those with some faith in mathematics I offer this as proof that the Earth is not Flat. I have taken parts of it from my other threads, but I held back on this part because it is not immediately obvious enough to make a super-strong argument (especially vs. the unmathematical babblings of Mr Bishop). Anyway here goes:

...

As ever, I await your responses eagerly!
I find that your math is sound.

I encourage you to download the "First Day of Summer" workbook. It has its own proof that the world is round. You can walk outside most any sunny day and verify for yourself that the Earth is round. (Paging Tom Bishop... Paging Tom Bishop...)

Re: For the Mathematically Minded: Disproof of FE
« Reply #14 on: May 24, 2007, 05:34:33 PM »
Thanks for the proof Gin. The math is sound to me. Unfortunatelly, I doubt it'll make much of an impact on Mr. Bishop. The same thing your formula describes was already explained in perfectly intelligible english. But who knows. Maybe math will resonate better.
Quote
Quote
Hmm... A good solid RE arguement and not an FE'er in sight. ::)
Oh, no...they're here. It's just that damn perspective..

?

∂G/∂x

  • 1536
  • All Rights Reversed
Re: For the Mathematically Minded: Disproof of FE
« Reply #15 on: May 24, 2007, 05:37:54 PM »
Mr Bishop rarely agrees with my 'irrelevant and ridiculous math' as he so often calls it. He finds anything with lots of numbers strangely dizzying and sickening, so he usually makes irrelevant comments or avoids mathematical threads altogether.
Quote from: Tom Bishop
The universe has already expanded forever

Quote from: Proverbs 24:17
Rejoice not when thine enemy falleth, and let not thine heart be glad when he stumbleth.

*

Tom Bishop

  • Flat Earth Believer
  • 17920
Re: For the Mathematically Minded: Disproof of FE
« Reply #16 on: May 24, 2007, 06:07:49 PM »
Quote
Time to bring in another fact about the sun: We know it moves through the sky at a constant rate

What evidence can you reference or bring to the table showing that the sun moves across the sky at a constant rate over the course of a day?
« Last Edit: May 24, 2007, 06:09:32 PM by Tom Bishop »

?

∂G/∂x

  • 1536
  • All Rights Reversed
Re: For the Mathematically Minded: Disproof of FE
« Reply #17 on: May 24, 2007, 06:22:40 PM »
You may observe it yourself. Although the rate is not exactly constant, it is appreciably and significantly different from what the FE model predicts.
Quote from: Tom Bishop
The universe has already expanded forever

Quote from: Proverbs 24:17
Rejoice not when thine enemy falleth, and let not thine heart be glad when he stumbleth.

Re: For the Mathematically Minded: Disproof of FE
« Reply #18 on: May 24, 2007, 07:15:51 PM »
Tom, I already told you, grab yourself a video camera and a few extra tapes and record the movement of the sun over the period of 1 day. You can then playback the tape, fast foward and see how long it takes it to move 1/4 of the way across the sky, or 1/8 of the way across the sky at different times. You know.. the experiment I described in that other thread you stopped responding to. It's crude, but it would do. Of course, there's modern geodetic techniques that measure the rotation of the earth directly.. and ironically enough produce results which support each other. But if you're going to believe the kind of conspiracy theory you do without any evidence, then I don't see why you'd have any problem dismissing any of those results as part of the conspiracy so what's the point? The whole exercise is kind of pointless since it doesn't take a genius to see the flaws in the 'law of perspective'. That should have pretty much been the end of the argument but have it your way.

You know, it's a shame they retired the Concorde, otherwise I'd tell you to just get your ass on one and see for yourself. I know that it's been discussed that you can't really see the curvature of the earth from your average jet today, because they only fly at around 30,000 feet, so the curvature is not at all easy to see. It would be too slight to really be able to judge fairly, from my personal experience anyway. But the Concorde flew at 60,000 feet, twice that of commercial jets, where the curvature of the earth was distinctly and clearly visible. In fact, it was one of the main attractions of flying on a Concorde, in addition to the supersonic speeds. But I guess everyone who ever flew on one was silenced by the conspiracy too no?.. Hell of a risk for the governments to take too since it was perfectly affordable for any middle class person (not cheap mind you, but doable nonetheless)..
Quote
Quote
Hmm... A good solid RE arguement and not an FE'er in sight. ::)
Oh, no...they're here. It's just that damn perspective..

*

Colonel Gaydafi

  • Spam Moderator
  • Planar Moderator
  • 65192
  • Queen of the gays!
Re: For the Mathematically Minded: Disproof of FE
« Reply #19 on: May 24, 2007, 07:17:28 PM »
Maybe that's why Concordes got rid of. Not because of them crashing, but because people could see the Earth was flat from up there.

That;s a stupid theory actually, scrap that
Quote from: WardoggKC130FE
If Gayer doesn't remember you, you might as well do yourself a favor and become an hero.
Quote from: Raa
there is a difference between touching a muff and putting your hand into it isn't there?

Re: For the Mathematically Minded: Disproof of FE
« Reply #20 on: May 24, 2007, 07:30:11 PM »
lol yep, after 27 years of flying they finally realized it could blow their cover. you'd think any conspiracy smart enough to trick the world into believing in a round earth would take a little less than 27 yrs to figure that one out.. ah the irony ;)
Quote
Quote
Hmm... A good solid RE arguement and not an FE'er in sight. ::)
Oh, no...they're here. It's just that damn perspective..

*

Colonel Gaydafi

  • Spam Moderator
  • Planar Moderator
  • 65192
  • Queen of the gays!
Re: For the Mathematically Minded: Disproof of FE
« Reply #21 on: May 24, 2007, 07:32:34 PM »
So they were a bit slow, cut them slack, they were probably too busy making new space pictures out of lego and sticky back plastic and I have no idea where I'm going with this
Quote from: WardoggKC130FE
If Gayer doesn't remember you, you might as well do yourself a favor and become an hero.
Quote from: Raa
there is a difference between touching a muff and putting your hand into it isn't there?

Re: For the Mathematically Minded: Disproof of FE
« Reply #22 on: May 24, 2007, 07:42:16 PM »
Quote
Time to bring in another fact about the sun: We know it moves through the sky at a constant rate

What evidence can you reference or bring to the table showing that the sun moves across the sky at a constant rate over the course of a day?
The evidence is on the table already. Check the "First Day of Summer" workbook. Plug in several times and see the predictions. Go outside. Validate the predictions. Understand the math.

Of course, we ask you: "What evidence can you reference or bring to the table showing that the Sun does not move accress the sky at a constant rate over the course of a day?"

Tom, stop evading. Stand up to the arguments. You are losing credibility every day.

*

Colonel Gaydafi

  • Spam Moderator
  • Planar Moderator
  • 65192
  • Queen of the gays!
Re: For the Mathematically Minded: Disproof of FE
« Reply #23 on: May 24, 2007, 07:43:52 PM »
Leave Tom alone, he's just a poor troll, like you, can't come back at everything
Quote from: WardoggKC130FE
If Gayer doesn't remember you, you might as well do yourself a favor and become an hero.
Quote from: Raa
there is a difference between touching a muff and putting your hand into it isn't there?

?

Marlow

Re: For the Mathematically Minded: Disproof of FE
« Reply #24 on: May 24, 2007, 09:15:14 PM »
I'm thinking of words that begin with "P"....  Prick and prig spring to mind

*

Colonel Gaydafi

  • Spam Moderator
  • Planar Moderator
  • 65192
  • Queen of the gays!
Re: For the Mathematically Minded: Disproof of FE
« Reply #25 on: May 24, 2007, 09:18:06 PM »
Pineapple? No that isn't right...
Quote from: WardoggKC130FE
If Gayer doesn't remember you, you might as well do yourself a favor and become an hero.
Quote from: Raa
there is a difference between touching a muff and putting your hand into it isn't there?

?

Marlow

Re: For the Mathematically Minded: Disproof of FE
« Reply #26 on: May 24, 2007, 09:19:07 PM »
If it's a smug pineapple

*

Colonel Gaydafi

  • Spam Moderator
  • Planar Moderator
  • 65192
  • Queen of the gays!
Re: For the Mathematically Minded: Disproof of FE
« Reply #27 on: May 24, 2007, 09:20:32 PM »
Prince Pineapple then
Quote from: WardoggKC130FE
If Gayer doesn't remember you, you might as well do yourself a favor and become an hero.
Quote from: Raa
there is a difference between touching a muff and putting your hand into it isn't there?

?

Marlow

Re: For the Mathematically Minded: Disproof of FE
« Reply #28 on: May 24, 2007, 09:23:27 PM »
that works

And pissant

*

Roundy the Truthinessist

  • Flat Earth TheFLAMETHROWER!
  • The Elder Ones
  • 27043
  • I'm the boss.
Re: For the Mathematically Minded: Disproof of FE
« Reply #29 on: May 24, 2007, 09:24:55 PM »
Poor Tom Bishop, the priggish prickly pineapple with piss-stained purple panties...

Ah, that wasn't near as clever as I hoped it would be.
Where did you educate the biology, in toulet?