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Enduring Problems in Philosophy
- Thread starter Ren
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I think he's just playing sleight of hand with the logic. I can 'prove' 1=2 that way. let's have a closer look:
So let's take Pi = 4 as our premise.
Now one of the canonical equations of mathematics is Euler's equation : Exp(i Pi) + 1 = 0
where i = sqrt(-1) and Exp is the base of the natural logarithms.
Another way of writing this: Exp(i Pi) is identically equal to cos(Pi) + i sin(Pi)
So Eulers equation becomes: cos(4) + i sin(4) +1 = 0
Noting that this angular amount, 4, is in radians, we can look up the values and get
-0.65346 + i 0.7568 + 1 =0, or
0.3463 - i 0.7568 = 0, or
0.3463 = i 0.7568, which is obviously false.
So the initial assumption that Pi = 4 leads directly to a logical contradiction, proving that it is a false assumption.
Now one of the canonical equations of mathematics is Euler's equation : Exp(i Pi) + 1 = 0
where i = sqrt(-1) and Exp is the base of the natural logarithms.
Another way of writing this: Exp(i Pi) is identically equal to cos(Pi) + i sin(Pi)
So Eulers equation becomes: cos(4) + i sin(4) +1 = 0
Noting that this angular amount, 4, is in radians, we can look up the values and get
-0.65346 + i 0.7568 + 1 =0, or
0.3463 - i 0.7568 = 0, or
0.3463 = i 0.7568, which is obviously false.
So the initial assumption that Pi = 4 leads directly to a logical contradiction, proving that it is a false assumption.
o2b
Permanent Fixture
@John K
Did you see his proof and the experiment which validates his conclusion?
Here's the experiment. It is pretty cool. It's 9m long. But, after 4m the results are shown. Actually, especially observe it at 4-5m Please, just do so.
He has two tubes alongside each other. One tube is straight while the other is straight and then circular. The guy running the experiment drops a ball in each tube (you need to look at it to see what I mean). OK, the guy marks the straight tube at the precise point the other tube begins to be circular. He marks the circle in quarters. On the straight tube from the point where the circle starts in the other tube, he marks the point on the straight tube at this point +1, +2, +3, +pi and +4.
So when he runs the experiement, when the ball going around the circle is 1/4 through it, the ball at the straight tube is at 1. When the ball is half way around the circle, the other ball is at 2. When 3/4 through the circle, the other ball is at 3. When the ball just complated its circular path, the other ball is further along than pi and is exactly at 4.
It is undeniable. Just watch the experiment.
Rocketry knows of extreme error and just fudges for it. The fudge is exactly the error in its use of pi.
Here is a site where some guy is discussing Mathis' finding.
https://www.godparticle.xyz/pi.html
And a bit of his explanation:
Please note that this paper is a simplification by me of a paper or papers written and copyrighted by Miles Mathis on his site. I have replaced "I" and "my" with "MM" to show that he is talking. All links within the papers, not yet simplified, are linked directly to the Miles Mathis site and will appear in another tab. (It will be clear which of these are Miles Mathis originals because they will be still contain "I" and "my".) The original papers on his site are the ultimate and correct source. All contributions to his papers and ordering of his books should be made on his site.
(This paper incorporates Miles Mathis' pi paper, pi2 paper and pi3 paper).
Historically, π (pi) is the numerical relationship between the diameter and circumference of a circle. It is a geometric constant. What do we mean by geometric? Operationally, geometry is the study of drawn figures. The ancients actually drew their figures on paper (and some of us still do). All the concepts of geometry applied to these figures. A line was a drawn line. A circle was a drawn circle. Of course geometry soon invented some other postulates to help with the mathematics. A point was defined as having no extension, a line was defined as having no width, and so on. But the equations were still understood to apply to the figures. Geometry was always only partially abstract.
In this context, π was assumed to be a dimensionless constant. It transformed one length to another. This is clear from the basic equation:
C = 2πr
You can see that π takes us from one length to another and therefore we must assume it is dimensionless.
Miles Mathis shows in this treatise that this assumption is false. MM will show that π is not dimensionless. It is not dimensionless for the basic reason that the circumference is not a length. Nor is it a distance.
It is true that in one sense the circumference is a length. In common everyday language, a circle describes a certain length. We can make a circle with a piece of string and then straighten it out and measure it. But in straightening out the string we have applied a pretty complex action to it. The straight string and the curved string are not physically or mathematically equivalent. As we know, mathematics is a more precise language, or should be. It turns out that by being a bit more precise than anyone has ever bothered to be before, we can solve some of the mystery of π and of the circle.
Let us study the operation of drawing or physically describing a circle. When you draw a circle your pencil always has some velocity. This is because time is always a consideration in any real event. Drawing a circle is a real event, not an abstract event. In fact, any possible circle must take time into consideration. This is true of orbits, bugs walking in circles, whirlwinds, and so on. When we apply mathematics to any of these situations, we must take time into account. That is why we find accelerations in all circular motion, the most famous of which is the centripetal acceleration. Centripetal acceleration can be due to gravity or to some other force, but in any circular motion there will always be a centripetal acceleration. This has been known for many centuries.
Geometry dismisses time as a consideration. Geometry is understood to be taking place at a sort of imaginary instant. For instance, when we are given or shown a radius, we do not consider that it took some time to draw that radius. We do not ask if the radius was drawn at a constant velocity or if the pencil was accelerating when it was drawn. We do not ask because we really do not care. It does not seem pertinent. It seems quite intuitive to just postulate a radius, draw it, and then begin asking questions after that.
It turns out that this nonchalance is a mistake. It is a mistake because by ignoring time we have ignored many important subtleties of the problem of circular motion and of circle geometry.
As a simple example of this, when we draw a circle on a Cartesian graph, we make an entirely different set of assumptions than the ones above, although few have seemed to notice this. You would think you could draw a Cartesian graph anywhere you wanted and it would not make any theoretical difference to the geometry. You could draw a graph on the wall, on the floor, on any flat surface. You would think all you are doing is making things a bit easier on yourself as an artist and a geometer. Just as the old artists would square off their treatise in order to make drawing a head easier, a geometer squares off a section of the world in order to create a tidy little sub-world where things can be put in order.
But all this is completely false. Drawing the graph changes everything. If you draw a circle without a graph, then you can say to yourself that the line (that is now the circumference of the circle) is a length. As a length, it can have only one dimension. A length is a one-dimensional variable, right? Perhaps you can see where MM is going with this, and you say, “Wait, a circle curves, so we must have two dimensions, at least. We must have an x and a y dimension.” Yes, at the least we must have that. You saw this because you began to think in terms of the Cartesian graph and you could see in your head that the curve implied both x and y dimensions. Very good. But you are not halfway there yet. Take the circle and actually put it into a Cartesian graph. What you find is that the curve is now an acceleration. In fact, any curve is an acceleration in a two-dimensional graph. We all learned this in high school, although it probably did not sink far in for most of us.
That line that represents a circumference is taking on dimensions very fast now. At first we thought it was just a length. Then we saw that it required two dimensions. Now we can see that it is an acceleration. What next?
Unfortunately, there is more. The Cartesian graph we have put it into to show it is an acceleration is still just an x, y graph. We still do not have a time variable. A circle is a planar object, existing in a plane, but in the real world a curve on a plane cannot be created without time passing. A two-dimensional object requires three dimensions for its creation, just as a three-dimensional object requires four dimensions for its creation. You cannot draw or walk or describe a figure in a three-dimensional universe without taking time into consideration. Figures require motion and motion requires time.
Did you see his proof and the experiment which validates his conclusion?
Here's the experiment. It is pretty cool. It's 9m long. But, after 4m the results are shown. Actually, especially observe it at 4-5m Please, just do so.
He has two tubes alongside each other. One tube is straight while the other is straight and then circular. The guy running the experiment drops a ball in each tube (you need to look at it to see what I mean). OK, the guy marks the straight tube at the precise point the other tube begins to be circular. He marks the circle in quarters. On the straight tube from the point where the circle starts in the other tube, he marks the point on the straight tube at this point +1, +2, +3, +pi and +4.
So when he runs the experiement, when the ball going around the circle is 1/4 through it, the ball at the straight tube is at 1. When the ball is half way around the circle, the other ball is at 2. When 3/4 through the circle, the other ball is at 3. When the ball just complated its circular path, the other ball is further along than pi and is exactly at 4.
It is undeniable. Just watch the experiment.
Rocketry knows of extreme error and just fudges for it. The fudge is exactly the error in its use of pi.
Here is a site where some guy is discussing Mathis' finding.
https://www.godparticle.xyz/pi.html
And a bit of his explanation:
Please note that this paper is a simplification by me of a paper or papers written and copyrighted by Miles Mathis on his site. I have replaced "I" and "my" with "MM" to show that he is talking. All links within the papers, not yet simplified, are linked directly to the Miles Mathis site and will appear in another tab. (It will be clear which of these are Miles Mathis originals because they will be still contain "I" and "my".) The original papers on his site are the ultimate and correct source. All contributions to his papers and ordering of his books should be made on his site.
(This paper incorporates Miles Mathis' pi paper, pi2 paper and pi3 paper).
Historically, π (pi) is the numerical relationship between the diameter and circumference of a circle. It is a geometric constant. What do we mean by geometric? Operationally, geometry is the study of drawn figures. The ancients actually drew their figures on paper (and some of us still do). All the concepts of geometry applied to these figures. A line was a drawn line. A circle was a drawn circle. Of course geometry soon invented some other postulates to help with the mathematics. A point was defined as having no extension, a line was defined as having no width, and so on. But the equations were still understood to apply to the figures. Geometry was always only partially abstract.
In this context, π was assumed to be a dimensionless constant. It transformed one length to another. This is clear from the basic equation:
C = 2πr
You can see that π takes us from one length to another and therefore we must assume it is dimensionless.
Miles Mathis shows in this treatise that this assumption is false. MM will show that π is not dimensionless. It is not dimensionless for the basic reason that the circumference is not a length. Nor is it a distance.
It is true that in one sense the circumference is a length. In common everyday language, a circle describes a certain length. We can make a circle with a piece of string and then straighten it out and measure it. But in straightening out the string we have applied a pretty complex action to it. The straight string and the curved string are not physically or mathematically equivalent. As we know, mathematics is a more precise language, or should be. It turns out that by being a bit more precise than anyone has ever bothered to be before, we can solve some of the mystery of π and of the circle.
Let us study the operation of drawing or physically describing a circle. When you draw a circle your pencil always has some velocity. This is because time is always a consideration in any real event. Drawing a circle is a real event, not an abstract event. In fact, any possible circle must take time into consideration. This is true of orbits, bugs walking in circles, whirlwinds, and so on. When we apply mathematics to any of these situations, we must take time into account. That is why we find accelerations in all circular motion, the most famous of which is the centripetal acceleration. Centripetal acceleration can be due to gravity or to some other force, but in any circular motion there will always be a centripetal acceleration. This has been known for many centuries.
Geometry dismisses time as a consideration. Geometry is understood to be taking place at a sort of imaginary instant. For instance, when we are given or shown a radius, we do not consider that it took some time to draw that radius. We do not ask if the radius was drawn at a constant velocity or if the pencil was accelerating when it was drawn. We do not ask because we really do not care. It does not seem pertinent. It seems quite intuitive to just postulate a radius, draw it, and then begin asking questions after that.
It turns out that this nonchalance is a mistake. It is a mistake because by ignoring time we have ignored many important subtleties of the problem of circular motion and of circle geometry.
As a simple example of this, when we draw a circle on a Cartesian graph, we make an entirely different set of assumptions than the ones above, although few have seemed to notice this. You would think you could draw a Cartesian graph anywhere you wanted and it would not make any theoretical difference to the geometry. You could draw a graph on the wall, on the floor, on any flat surface. You would think all you are doing is making things a bit easier on yourself as an artist and a geometer. Just as the old artists would square off their treatise in order to make drawing a head easier, a geometer squares off a section of the world in order to create a tidy little sub-world where things can be put in order.
But all this is completely false. Drawing the graph changes everything. If you draw a circle without a graph, then you can say to yourself that the line (that is now the circumference of the circle) is a length. As a length, it can have only one dimension. A length is a one-dimensional variable, right? Perhaps you can see where MM is going with this, and you say, “Wait, a circle curves, so we must have two dimensions, at least. We must have an x and a y dimension.” Yes, at the least we must have that. You saw this because you began to think in terms of the Cartesian graph and you could see in your head that the curve implied both x and y dimensions. Very good. But you are not halfway there yet. Take the circle and actually put it into a Cartesian graph. What you find is that the curve is now an acceleration. In fact, any curve is an acceleration in a two-dimensional graph. We all learned this in high school, although it probably did not sink far in for most of us.
That line that represents a circumference is taking on dimensions very fast now. At first we thought it was just a length. Then we saw that it required two dimensions. Now we can see that it is an acceleration. What next?
Unfortunately, there is more. The Cartesian graph we have put it into to show it is an acceleration is still just an x, y graph. We still do not have a time variable. A circle is a planar object, existing in a plane, but in the real world a curve on a plane cannot be created without time passing. A two-dimensional object requires three dimensions for its creation, just as a three-dimensional object requires four dimensions for its creation. You cannot draw or walk or describe a figure in a three-dimensional universe without taking time into consideration. Figures require motion and motion requires time.
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Yes, I saw his video, and had a look at some of his analysis. The trouble is that there is a major flaw in the experiment. The ball that runs down the straight tube is only affected by the force of gravity and by the associated simple rolling friction from contact with the tube once it reaches the level part of the run. But the ball running around the circle will be subject to a strong centripetal force as well, which arises from the acceleration caused by the curvature of the tube. That means that the force excerted on that ball by the tube is very different and greater - so the rolling friction, opposing the instantaneous direction of motion, will be a lot greater than for the other ball - and it is simply moving more slowly.
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Well. Screw you too, @Ren . And thanks for your analysis @John K
I think that works both ways of your “tubes” of experiments, but I’m pretty sure the forces were talking about are beyond evidence of philosophy or even what anyone has to say here. Like I said previously, it’s different for each person and there are issues on both sides. There’s really no need for all of this. I have other things to be concerned with than your hazing.
I think that works both ways of your “tubes” of experiments, but I’m pretty sure the forces were talking about are beyond evidence of philosophy or even what anyone has to say here. Like I said previously, it’s different for each person and there are issues on both sides. There’s really no need for all of this. I have other things to be concerned with than your hazing.
o2b
Permanent Fixture
Hazing. Strong word. Highly critical word, in fact.
Who is it directed to?
Please justify your claim.
I beg your pardon?
It looks like it's being directed at me, though I have no idea where this is coming from lol. I would also be curious to hear @ExhumedMorrison explain what she means.
Oh, I've seen the issue. I think this is a misunderstanding. Ren was replying to Sidius, who then responded in sarcasm about 'social games'. I don't think Ren meant his statement about discussions here needing to be philosophical as a slight against you or anyone else, nor as a way to say that there are some here who may be far less knowledgeable or experienced in the study of philosophy, so their comments aren't 'welcome'. If I know anything of Ren at all, he considers what you have to say with careful discernment, and values the discussion. I hope you can come to see this, EH. <3
Thank for you for this, Lore. This makes me realise that I should clarify that when I said:
It was a joke! lol. Delivered in my occasional deadpan style. Apologies if this was misinterpreted.
This is actually somewhat the opposite of what I think. If you can tackle a philosophical problem using no technical words, this would be a far greater achievement than doing the same with the help of technical words.
Philosophers who use a lot of 'philosophised' vocabularies tend to admire those who manage without. But this is reserved to certain rare talents. I think this is partly why transparent writers like Descartes and the later Wittgenstein are so revered. Their ability was a gift, not a weakness.
I hope this clarifies things, @ExhumedMorrison.
- Sep 28, 2008
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o2b
Permanent Fixture
A good reminder for us all 
Unless.... this itself is a matter for discussion and possible disagreement?
Unless.... this itself is a matter for discussion and possible disagreement?
A good reminder for us all
Unless.... this itself is a matter for discussion and possible disagreement?
But isn't this the premise which characterizes the mistake in pre-Philosophical Investigations Wittgenstein?
The clarity of any statement is the degree to which the received semantic corresponds to the projected semantic, but there's no designated set of language which we can claim to unequivocally prevent any decay. We can only make a judgment based on what we think is the most socially unambiguous symbolization. But since there's always some extent of internal diversity even in homogenous cultures, there can be misunderstandings even in seemingly straightforward statements.
o2b
Permanent Fixture
Yup, things get lost in translation sometimes. So, a good thing to sometimes ask, What did you mean when you said such and such?
Yes, I think you have a point. I would suggest there is a difference, however, between thinking/speaking clearly and being understood.
I may have a perfectly coherent and clear thought, and express it clearly, yet still be misunderstood because of the factors you mention. This kind of ambiguity is also at the basis of Kuhn's concept of incommensurability between scientific paradigms. But it might be argued back that within a particular language game, it ought to be possible to always speak clearly, and be understood by fellow participants in the language game (co-inhabitants of the particular form of life).
If we take Wittgenstein's statement as a statement about clarity of expression, rather than success of communication, then maybe it withstands the critique. Popper offers another criticism of it that doesn't rely on the notion of language game, with a focus on expression. I can't recall it in detail at present, but I thought it quite compelling at the time, so I'll try to dig it up.
I'd also enjoy the information, if and when you can find it.