This thread summarizes my thinking and I "post it herefor comments, edits and discussion amongst my Flat Earth Colleagues.

I will begin by quoting Kant who states that we can intuit nothing but through our own senses and because of this our “knowing” is secondary, not primary, and thus * “we can know nothing of things themselves”* but only our *“sense of these things”*. For example we cannot “know” light, only the optical perception of light (secondary) or the use of measuring devices (secondary, or more properly tertiary, since we cannot “know” the measuring device directly”).

Here is what Kant says on the matter:

*“The certainty of all geometrical propositions and the possibility of their a priori construction, is grounded in this a priori necessity of space. ***Were this representation of space a concept acquired a posteriori, and derived from outer experience in general, the first principles of mathematical determination would be nothing but perceptions. They would therefore all share in the contingent character of perception that there should be only one straight line between two points would not be necessary, but only what experience always teaches. What is derived from experience... is obtained through induction.** We should therefore only be able to say that, so far as hitherto observed, no space has been found which has more than three dimensions.

Take, for instance, the proposition, “Two straight lines cannot enclose a space, and with them alone no figure is possible”, and try to derive it from the concept of straight lines and of the number two. Or take the proposition, “Given three straight lines, a figure is possible”, and try, in like manner, to derive it from the concepts involved. All your labor is vain; and you find that you are constrained to have recourse to intuition, as is always done in geometry.... If the object (the triangle) were something in itself, apart from any relation to you, the subject, how could you say that what necessarily exist in you as subjective conditions for the construction of a triangle, must of necessity belong to the triangle itself? “

Take Kant’s statement as not referring to a sphere, but referring to the surface of the Terrestrial Plane. The Terrestrial plane, not allowing for mountains and valleys, mathematically is a 2-dimensional space, and points on it only need 2 coordinates

To help see the difference, consider a straight line between London and New York. In the round earth model that straight line goes through the Earth. But if we're only have only the flat Terrestrial Earth is considering the surface of the Earth, that line doesn't exist. In a Round earth the straight line (shortest distance between the two points) on the surface lies along the great circle. Now consider drawing the lines from both New York and London to, say, Cape Town, to make a triangle. But those lines don't exist in a Non Euclidian surface we are considering: you can only draw lines on the surface of the Earth. The angles of the triangle drawn on the surface of the Earth (in non Euclidian model) add up to more than 180 degrees. Thus in a surface that is non-Euclidian if I head 100 miles in one direction, turn 90 degree head another 100 miles, turn 90 degree and go 100 miles and do this yet one more time for 100 miles I do NOT end up at the same place. The earth is flat where-ever I look yet and however I map it, and however I measure it is flat, yet it is not flat in a Euclidian sense.

I now offer up a important concept in the form of a quote from one of my favorite mathemeticians whom I discovered whilst roaming the dusty stacks of my University’s marvelous and three hundred year old library:

*“If we can show that the denial of a proposition does not contradict the consequences of certain other propositions, we have then found a criterion of the logical independence of the proposition in question. In other words, the logical independence of this Euclidean axiom [the Parallel Postulate] of the other axioms would be proved if it could be proven that a geometry free of contradictions could be erected which differed from Euclidean geometry in the fact, and only in the fact, that in the place of the parallel axiom there stood its negation.*

That is just what Gauss, Lobachevski, and Bolyai established: the possibility of erecting such a noncontradictory geometry which is different from the Euclidean.**What is important to us here is this: The results of modern axiomatics are a completely clear and compelling corroboration of Kant's and Fries's assertion of the limits of logic in the field of mathematical knowledge**, and they are conclusive proof of the doctrine of the "synthetic" character of the mathematical axioms. For it is proved that the negation of one axiom can lead to no contradiction even when the other axioms are introduced... And this was just the criterion that Kant had already specified for the synthetic character of a judgment: the uncontradictory character of its negation.

The scientist who says, "**The only way to explain this is to show you the math," either doesn't want to explain the question, and so is brushing you off, or he cannot explain the question. If he doesn't want to explain the question, either he cannot because he doesn't actually understand it, or he is a Positivist who doesn't think that it needs to be or can ever be explained. Either way, if he seems annoyed, rude, or hostile, one's suspicions are reasonable aroused.**”

Sir Leonard Nelson, "Philosophy and Axiomatics," 1927 Cambridge Press

I would like you do to the following experiment:

Walk 5 meters straight ahead and the stop.

Turn to your left, exactly 90 Degree.

Walk in the direction you just chose for 5 meters.

Then please stop and once more turn left another 90 degrees.

Thence, once more, walk once more 5 meters.

You will then turn left and the next time you walk 5 meters you will have ended whence you began.

You thus ended where you began…or did you? This is strictly a conclusion you arrived at empirically. There is no “theoretical” reasoning required. You just completed my experiment and we (you and I) merely observed the results. Yet just because you experienced it does not mean that what you, and I, observed is scientifically based. In matter of fact the small experiment we just engaged in (you as both subject and observer and yours truly as an observer) proves nothing. The fact is precise measurements would prove that our little grand experiment would show that you did NOT arrive precisely at the same spot.

The archaics (rightly) observed a plane, say a table, as the archetype of flat object and then observed that the Terrestrial Plane (surface of the Earth) was also flat. Both the table and the Terrestrial plan are two-dimensional, but Einstein noted flatness and curviness apparently make sense in any number of dimensions.

Lets set the the above aside for a moment just as we might set aside stewed figs as we prepare a nice pudding. We will use this concept in just a moment but it is important to set that out first.

So lets now turn to what is flat. Helio-centrists say that the “Universe” and space outside Earth is supposed to be flat. I don’t disagree with them, or agree, because whatever exists outside the firmament is “unknowable”. Flat Earth Theorists asking what is outside the firmament question is akin to to asking a Rounder “What existed before the Big bang”? But none the less helio-centrists posit the universe is as “flat as a pancake”.

Now to be fair they do not say that this (fictional) "Space**time**" is flat, but apply this only to **space**, that exists only **RIGHT now**. Not in the future, but NOW (and according to these muddled thinkers) and in the past (the "past" associated with the "now").We must get that helio concept RIGHT- **for a helio Space (the nowverse) and space time, are two DIFFERING things.**

But a hello-centrist will say that Einstein's theory does not allow for “space” to be flat because this energy , and all this matter (in the unknowable and fictional helio-model) curves spacetime (note I do not agree with this but bear with me). And they might say “well without the curve of space time we are all just flying around because gravity (Helio-majik bye the way) keeps us in place.”

But now we get to the nub of this knot whereby the helio-centrists and a few of us (and advanced) Flat Earth Theorists do agree. When they, the helio-centrists speak of the universe (which I posit is unobservable since we cannot see past the firmament) they are speaking of a gigantic universe and we (Flat Earth Theorists) speak of the Terrestrial Plane we are referring to a smaller one, much smaller, and I mean this mathematically speaking in this context. Please hold onto to this thought because we will refer back to this concept soon enough.

Now please carefully note that I have never posited NASA as a fraud organization doing nothing. They are doing something, just not what it appears or what they are telling us. They are scientific, but like MI6, or the YANK's NSA they surround the truth with a body guard of lies. With that aside NASA completed an experiment called Gravity Probe B which took a direct measure measurement of the area immediately surrounding earth and they found that space, despites bumps and ridges… flat. Not space**time,** mind you, but **space**, the “Nowverse”.

Now, if the Flat Earth terrestrial plane has three coordinates (left, right and up) we must assume (mathematically, not empirically, you will note) that we could increase those coordinates to any value as large as we might wish them to be in a mathematical equation. Thus if I wanted to travel (mathematically) a billion billion miles what would stop me (theoretically)? But now we will mix both the empirical and theoretical. We “know” (empirically) this is not true; that I cannot go upwards 600 Billion Billion Billion Billion to infinity miles. Why is this? Well mathematically there must be a theoretical boundary that keeps me from doing so (theoretically) that then matches empircally what we “know” (with all its Kantian limitations). Please note that I am referring to the flat earth here- but if one were misled into believing the helio-centric model one would understand that the same thought process would apply.

Thus, even though the misled heliocentrists think “space” is infinite, it does not mean that one could go on mathematically in their model “Forever”. This galactic space (for lack of a better term) is bounded mathematically. Remember my little bowl of stewed figs we set aside in the fourth paragraph regarding flatness? We will now use it. Einstein noted flatness and curviness apparently make sense in any number of dimensions. What applies (mathematically) to Einstein’s “space” applies to the Terrestrial plane as well. Note I have never said Einstein was “Wrong” about the nature of the physical universe outside the firmament, I have simply said we cannot “know” it nor can we know the physical laws that are postulated cannot apply since we cannot observe anything past the firmament.

In the helio-centric model one could fly out into “space”, by taking the time and speed variables to almost infinitely large numbers (theoretically) and finally one would arrive back at the same place. This is because the Space (**not spacetime**) is flat as a pancake, in their model, and that is because it is bounded and a person so traveling would finally “appear” in the same spot that they started.

It is now important to know that we have established that the “now verse” (meaning here and now) of Einstein’s model allows for this. No time, only space, and again I am speaking mathematically. Now let us apply the same model to the Terrestrial Plane. But wait, a helio might argue, “Einstein’s universe is so huge, and at such a grand scale, that it allows for the boundary and an apparent “curved universe” to appear flat... Yet the you admit the Terrestrial Plane is small, much much smaller than our (Helio-model of the) universe so your thinking is wrong.”

And the helio making this argument would be correct.

But NOW I take you back to Kant’s observation. If we now adjust the “Boundary” of the non Euclidian space to a very LARGE number (much larger than is needed for the “theoretical universe of Einstein) for the Flat Earth we would see the same phenomena as the helio-centrist posit for the “universe” and the gigantic size of the plane (in this case the Terrestrial Plane) is no longer needed.

You will recall that I started (at least in the thread above) with quotes proving that our empirical observations are just that. That we cannot “know” anything directly and that thus, our conclusions about the universe or in this case the Terrestrial Plane are the intersection of our empirical observations (secondary) and our theories (many using math) that confirm them or help us "intuit" reality (in the Kantian definition). One might argue “this makes no sense” but that argument of "sense" is of no consequence as we have seen from Kant. Rather the conclusion of the non-euclidean bounded terrestrial plane is mathematically possible and can be made to tie with our empirical observations which is "we can arrive in near the same spot" if we take flight in one direction.

You might object that not all helio-centrists believe that Einsteins’s version of universe is finite and thus this model applied to the flat earth is therefore not correct. But theoretically someone (mathematically) can show that that hello-model of the space universe (the now verse) is finite, or infinite, depending on the boundary value. Such is true with a bounded terrestrial plane. Einstein, when he first developed his theory said the universe was finite based on his philosophy, not science. That is important to note! He used RELIGION, or at least a mystically based intuition to derive at the finite universe or now verse.

Here is something for the hello-centrists and their ilk to think upon when they discuss all their supposed observations of distant galaxies and starts (which I disagree with):

Let us assume that the firmament (as I posit) does not exist. And let us posit the Earth is a spinning ball in a solar system that is but an almost infinite number of solar systems in a galaxy that is but one in an almost infinite number of galaxies. But if that is true the light from a portion of the observable universe the helio-centrists are recording is 10-15 billions of years old, since according to their own theory the universe is at least that old. But according to the theory of space time it is not part of the “Now verse” since it is billions of years old it does not “exists” in our current “now verse” of space time and can tell us NOTHING (since it is not part of our NOW Verse but only of a past universe) about anything. The best we could say is that “Billions of years ago this or that happened with these laws” but nothing else. I wish Round Earth theorists would consider this and other problems with their model and observations

Of course the helio-model is poppy cock. The Firmament is dense aether with either objects caught in it from the ever accelerating Terrestrial Plane and Celestial Sphere, or place there. And the terrestrial plane is bounded non Euclidian Space. Einstein was a dreamy mystic.

Respectfully Submitted By Sir Richard this 9th Day of April in the Year of our Lord 2016