Physical π : Pi's relationship to 4

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Re: Discussing Miles W. Mathis

Unread postby SacredCowSlayer on Fri Sep 30, 2016 11:59 am

Seneca » September 30th, 2016, 2:26 am wrote:Vexman, thanks for finding that in Wikipedia. It is not exactly what Mathis wrote but it goes in the same direction. But for all I know Werner Von Braun could be just an actor in a movie.
That is why I asked if there are no examples to be found in other fields, that we can actually verify. I meant examples were the use of pi when motion is involved gives wrong results and this is noticed by real scientists or real people.

Mathis and his followers had 8 years to find these examples and the only ones I have seen mentioned are the ones I quoted in my earlier post.
If I understand correctly the effect should be noticed in athletics. Running the same length on a circular/oval track should take longer than running in a straight line at the same speed.
It should also be noticed in the use of route planners. Trajectories with lots of curves should take longer than is calculated when this is not taken into consideration. Actually in my experience, the time travelled in reality is often indeed longer than the time calculated by route planners like Google maps.

Edit: corrected some spelling mistakes and weird sentences


Seneca,

I'm not trying to be deliberately obtuse here, rest assured. But could you spell out what you're saying for those of us unfamiliar with this particular PI "issue"?

For example, "[r]unning the same length on a circular or oval track should take longer. . ." and "[t]rajectories with lots of curves should take longer. . .".

Should take longer when what? When traditional PI calculations are used? Or with the Mathis version?
And your experience with google maps. I've had a couple of head scratching experiences as well with this. But could you explain what you mean as far as how it relates to pI?

You have to complete these thoughts for the likes of people like me. My apologies if it should be clear enough. A short answer will do fine I think. I'm interested enough to at least ask for your clarification on this point.

I'm not super interested in Mathis or what his Math(Is), but I'm trying to at least follow this thread. And I'm trying to at least keep an open mind about him.

But since I just made that statement right there, I'll just simply say that I'm admittedly suspicious of him (assuming he's an authentic individual person) if for no other reason than his volume of output and the whole Infowars thing. But I'm NOT interested in any shouting matches about him-not that you would take it that way. I don't know him or anything about him other than what's been posted on the webs.

Thanks and cheers,
SCS

Edit:typo
Last edited by SacredCowSlayer on Sat Oct 01, 2016 5:36 am, edited 1 time in total.
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Re: Discussing Miles W. Mathis

Unread postby Flabbergasted on Fri Sep 30, 2016 12:19 pm

VexMan » September 29th, 2016, 12:27 pm wrote:I can count a few examples of kinematic circular motion in real life : an archer shooting his arrow, playing a ball/badminton game with my children, jumping into the sea for a swim, catching a friends lighter thrown at me, trying to save a glass from smashing while falling from my desk,....
I claim that in all named cases, trying to mathematically prove trajectory would bring wrong results by 21% if Pi=3,14... is used to calculate their location (as opposed to where you'd actually find them).

Perhaps I am being thick, but you seem to imply that the science of ballistics gets every prediction wrong by 21%, and so far nobody in the arms industry has bothered to correct the problem. Or are you saying that Pi=3.14 is not employed in ballistics?
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Re: Discussing Miles W. Mathis

Unread postby daddie_o on Fri Sep 30, 2016 12:21 pm

SacredCowSlayer » September 30th, 2016, 1:59 pm wrote:
I'm not trying to be deliberately obtuse here, rest assured. But could you spell out what you're saying for those of us unfamiliar with this particular PI "issue"?

For example, "[r]unninf the same length on a circular or oval track should take longer. . ." and "[t]rajectories with lots of curves should take longer. . .".

Should take longer when what? When traditional PI calculations are used? Or with the Mathis version?
And your experience with google maps. I've had a couple of head scratching experiences as well with this. But could you explain what you mean as far as how it relates to pI?



Here's a way to think about it, and this is what the experiment in the video demonstrates: when you're moving around a circle, it takes the same amount of time to travel 3.14 meters (or whatever unit of measurement) as it does to travel to 4 meters in a straight line.

So if you and someone else set off in a car maintaining a constant speed at 100kph, say, then one of you takes a turn on a circular track, by the time the other person who went straight had traveled 4km, you would have only travelled 3.14km. Miles argues that it's because the distance is actually longer in a curve in such situations. Another way to say this is that anything moving in the circular path will necessarily take 4 times as a long as a linear motion across 1 diameter. The same basic logic applies to any curve.

What it means is that it will take more time to travel the same length in a curve as it would to travel that length in a straight line, assuming an equal speed. So if the computer is using Pi=3.14 to calculate your arrival time, it should underestimate your arrival time, because the computer should be using 4 instead.

And yes, we would expect to see this on running tracks, but Miles argues that it is less noticeable because runners on the curve also get a 'gravity assist.' Or something like that. That's from a previous paper on the running track.

Anyway, I really wouldn't get too bogged down in the this Pi=4 paper. It's really irrelevant to about 99% of his work.
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Re: Discussing Miles W. Mathis

Unread postby Flabbergasted on Fri Sep 30, 2016 12:34 pm

daddie_o wrote:And yes, we would expect to see this on running tracks, but Miles argues that it is less noticeable because runners on the curve also get a 'gravity assist.' Or something like that. That's from a previous paper on the running track.

Oh, good. A dummy variable to make the argument work.

daddie_o wrote:Anyway, I really wouldn't get too bogged down in the this Pi=4 paper. It's really irrelevant to about 99% of his work.

To me it is very relevant.
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Re: Discussing Miles W. Mathis

Unread postby VexMan on Fri Sep 30, 2016 2:11 pm

Flabbergasted » September 30th, 2016, 1:19 pm wrote:
VexMan » September 29th, 2016, 12:27 pm wrote:I can count a few examples of kinematic circular motion in real life : an archer shooting his arrow, playing a ball/badminton game with my children, jumping into the sea for a swim, catching a friends lighter thrown at me, trying to save a glass from smashing while falling from my desk,....
I claim that in all named cases, trying to mathematically prove trajectory would bring wrong results by 21% if Pi=3,14... is used to calculate their location (as opposed to where you'd actually find them).

Perhaps I am being thick, but you seem to imply that the science of ballistics gets every prediction wrong by 21%, and so far nobody in the arms industry has bothered to correct the problem. Or are you saying that Pi=3.14 is not employed in ballistics?


Yes, that would be exactly what I meant with my statement - if we'd go and measure the distance of a projectile, it would be 21% farther than we've calculated using Pi=3.14... How much distance it actually covered is NOT equal to distance measured on the ground for the same movement. I wouldn't say that nobody bothered to correct the problem, the problem can be easily solved with "trial & error" method, in which we'd create a chart i.e. that would list values of degrees aiming at vs. expected distance. (like 10deg=300m, 20deg=450m, etc). It's a tickling point made with this Pi=4 revelation, I really suggest taking some time looking at this gif animation : http://www.f.waseda.jp/takezawa/mathenglish/geometry/cyclo/gifcyclo.htm . What it implies is : following the red point on the boundary of a circle -> the distance a point traveled in its actual trajectory is larger by 21% than the distance a point traveled measured on the "ground". It is 8*R vs 2*Pi*R .

Lets not forget about the forces of drag and gravity, friction due to spin, etc, which in ballistics do have a significant impact to calculation of distance. What they teach at ballistic classes is for surely not saying anything about this possibility of Pi=4 or that we may have been looking at the wrong kind of formula to calculate real life measurements. SO maybe they just add some new fudge into the existing formula, like Psi=0,21 and mystery is solved, what can be easier than that? :) If otherwise was true, I believe we would be learning about it in college physics for sure, but I bet it is the other way around. What is your thought about it?
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Re: Discussing Miles W. Mathis

Unread postby VexMan on Fri Sep 30, 2016 2:26 pm

Flabbergasted » September 30th, 2016, 1:34 pm wrote:
daddie_o wrote:And yes, we would expect to see this on running tracks, but Miles argues that it is less noticeable because runners on the curve also get a 'gravity assist.' Or something like that. That's from a previous paper on the running track.

Oh, good. A dummy variable to make the argument work.

daddie_o wrote:Anyway, I really wouldn't get too bogged down in the this Pi=4 paper. It's really irrelevant to about 99% of his work.

To me it is very relevant.


This gravity assist is actually due to the fact that a runner does put slightly larger force on his outer leg while in the curve in order to maintain his course. In Mathis words, I quote:
No doubt many will answer me, “The surveyor's wheel doesn't fail, since what a surveyor is interested in is a simple length, not some mystical kinematic distance like you are inventing here.” But that is false as well. Let us say a surveyor is measuring a running track for the Olympics. Well, he has to measure both the straight legs of the track and the curves. And what he wants to know is how far the runners have run, right? Well, running is kinematic. It is like a little orbit. It requires real bodies to move through the curves. It is not just curves sitting on the ground, it is curves being run in real time. Therefore, to calculate the correct distances through the curves, the surveyor must integrate all the motions involved. Treating the curves as equivalent to the straights will fail to do that. And yes, I am telling you the inside lane of the standard track is longer than 400 meters. Or, the runners are running considerably farther than 400 meters. This should be easy to prove by timing groups of top athletes through straights and curves. I predict it will be found that the athletes appear to move through the curves much slower than can be accounted for by stress on the inside leg, etc. But if you use pi=4 to measure the length of the curve, this discrepancy will vanish.

In fact, I find that some tests have been run, confirming this. At this link to Brigham Young University [p. 25], http://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=3347&context=etd, we find that “Depending upon the track, athletes may spend up to 60% of the race on the turn (P. R. Greene & Monheit, 1990).” Holy Cow! 60%? And no one ever thought that was strange? Using pi=4, we would predict 56% of the time to be spent in the curves [4/7.14]. The other 4% would then be given to tighter curves requiring more leg adjustments. Using running dynamics, you would never predict a slowdown that great [60/40] in the turns. That's a slowdown of 33%. But if we give most of that slowdown to a mismeasurement of the curve using pi [a “slowdown” of 21%], it makes more sense.]

full link: http://milesmathis.com/pi2.html

I wish it could be explained with less words ....

To be honest, daddie_o, to me this is also very relevant. Big time relevant.
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Re: Discussing Miles W. Mathis

Unread postby Seneca on Fri Sep 30, 2016 3:08 pm

SacredCowSlayer » 30 Sep 2016, 13:59 wrote:
Seneca » September 30th, 2016, 2:26 am wrote:Vexman, thanks for finding that in Wikipedia. It is not exactly what Mathis wrote but it goes in the same direction. But for all I know Werner Von Braun could be just an actor in a movie.
That is why I asked if there are no examples to be found in other fields, that we can actually verify. I meant examples were the use of pi when motion is involved gives wrong results and this is noticed by real scientists or real people.

Mathis and his followers had 8 years to find these examples and the only ones I have seen mentioned are the ones I quoted in my earlier post.
If I understand correctly the effect should be noticed in athletics. Running the same length on a circular/oval track should take longer than running in a straight line at the same speed.
It should also be noticed in the use of route planners. Trajectories with lots of curves should take longer than is calculated when this is not taken into consideration. Actually in my experience, the time travelled in reality is often indeed longer than the time calculated by route planners like Google maps.

Edit: corrected some spelling mistakes and weird sentences


Seneca,

I'm not trying to be deliberately obtuse here, rest assured. But could you spell out what you're saying for those of us unfamiliar with this particular PI "issue"?

For example, "[r]unninf the same length on a circular or oval track should take longer. . ." and "[t]rajectories with lots of curves should take longer. . .".

Should take longer when what? When traditional PI calculations are used? Or with the Mathis version?
And your experience with google maps. I've had a couple of head scratching experiences as well with this. But could you explain what you mean as far as how it relates to pI?

You have to complete these thoughts for the likes of people like me. My apologies if it should be clear enough. A short answer will do fine I think. I'm interested enough to at least ask for your clarification on this point.

I'm not super interested in Mathis or what his Math(Is), but I'm trying to at least follow this thread. And I'm trying to at least keep an open mind about him.

But since I just made that statement right there, I'll just simply say that I'm admittedly suspicious of him (assuming he's an authentic individual person) if for no other reason than his volume of output and the whole Infowars thing. But I'm NOT interested in any shouting matches about him-not that you would take it that way. I don't know him or anything about him other than what's been posted on the webs.

Thanks and cheers,
SCS


SacredCowSlayer, thanks for letting me know I should be more clear. I was indeed writing under the presumption that what we see in in the experiment is real, just as Miles Mathis is arguing for years. I was always very sceptical of this idea until I saw the experiment. It made me more open to the possibility that it is real and made me do more effort to understand what Miles Mathis was saying. But I am still sceptical about Miles Mathis himself, as some of my questions show.
Maybe somebody could start a new topic about this interesting pi=4 topic so we can somewhat separate it from the main subject of this topic, which is Miles Mathis.

I hope Vexman and daddie_o were able to answer your other questions, if not please let me know. However, I disagree with Vexman's answer on your ballistics question. I don't think pi is used in ballistic calculations and there should not be any errors. But I could be wrong, I don't have any experience other than calculations in school.

Thanks for the example of the running track, Vexman. I thought I had made this up today but now I see I had probably read it in the paper (at a time when I didn't understand it.)
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Re: Discussing Miles W. Mathis

Unread postby VexMan on Fri Sep 30, 2016 7:58 pm

Seneca, this is the official formula to calculate range in ballistic science:
Image

and this is the equation to find a required angle for required range:
Image

It all goes beyond my comprehension of physics trying to prove this equations, I truly hope that Mathis will one day chew into this "subfield" of ballistic science. What is obvious to me knowing that: "The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y-component divided by the x-component)." (from wikiland on trigonometric functions)." My logic reasoning is as follows : with above equations we're looking at the static circle, and circular functions are functions of an angle. Yet we are observing the wrong curvature with it...while at motion the object follows the cycloid curvature and that one is the only relevant to its traveled distance. So, I may be 100% wrong on this, however for me Pi=4 implies what I just said regarding ballistics.
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Re: Discussing Miles W. Mathis

Unread postby Seneca on Fri Sep 30, 2016 10:27 pm

I think if you took your time, you would have not much trouble proving these equations. From what I remember it is simple math. The motion of the object being simulated is split into its horizontal and vertical component and each is analysed independently. I think the problems that Mathis is talking about don't arise if you split the motion that way. They are not trying to calculate the distance that the object travels on its curved path. They are only interested in the range, which is the length it travels in the horizontal direction. This only depends on the horizontal component of the speed and the time it is moving. The time it is moving can be calculated by looking only at the vertical component of the movement, because once it reaches the ground it has completed its vertical motion and also its horizontal motion.
If they would try to calculate the distance that the object travels on its curved path or try to calculate its speed, (except for its starting speed), they would probably get into trouble, but why would you want do do that?

VexMan » 30 Sep 2016, 21:58 wrote:My logic reasoning is as follows : with above equations we're looking at the static circle, and circular functions are functions of an angle. Yet we are observing the wrong curvature with it...while at motion the object follows the cycloid curvature and that one is the only relevant to its traveled distance. So, I may be 100% wrong on this, however for me Pi=4 implies what I just said regarding ballistics.

I don't understand what you mean exactly. As you wrote, the trigonometric functions are used to separate the motion in its x-(horizontal) and y-(vertical) component. But it is not because you can draw these in a circle that they have to do anything with circular motion.
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Re: Discussing Miles W. Mathis

Unread postby VexMan on Sat Oct 01, 2016 5:45 am

Well, this is just us talking about it, I guess we'd need someone capable of breaking down those trigonometric functions even further. Just to put into perspective what I was trying to get at with my last sentence in my previous post : I believe all circular functions get affected once you introduce movement to them in the exactly same manner as it happens in case of the Pi, since they were all "developed" on static model of reasoning and with 1/2 of the perspective in mind (Pi vs cycloid path). That is only the consequence from Pi=4 implication and that makes sense to me (up to a point of my comprehension). I think as well, that at this particular point, conversation should turn to equations and proving with mathematical procedures how to calculate it properly (with the correct angle being observed in the picture being analysed). Only then could we discuss it further, it looks as at this point we're stuck with two different thesis, that are diametrically intuitive. In another words, one of us has to be 100% wrong about it.
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Re: Discussing Miles W. Mathis

Unread postby Seneca on Sat Oct 01, 2016 7:02 am

At the moment I prefer to look at the real world. If in certain fields the outcomes are different than the predictions, the math behind them should be reviewed.
I am not going to make the assumption that most people are making "if there was something wrong with the predictions, people would already have figured this out."
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Re: Discussing Miles W. Mathis

Unread postby Flabbergasted on Sat Oct 01, 2016 1:45 pm

Seneca » October 1st, 2016, 4:02 am wrote:At the moment I prefer to look at the real world. If in certain fields the outcomes are different than the predictions, the math behind them should be reviewed.
I am not going to make the assumption that most people are making "if there was something wrong with the predictions, people would already have figured this out."

If you prefer to look at the real world, as you say, then surely you must acknowledge that such a vast discrepancy (21%) between prediction and outcome would be of interest to any private enterprise with millions of dollars invested in, say, weapons sales. I am not talking about Werner von Braun´s rockets that "simply weren't where they were supposed to be" (how true!), but about real terrestrial business, something the elites do not take lightly. One would also expect endless controversy over the assignment of lanes to sprinters for whom one tenth of a second means everything.
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Re: Discussing Miles W. Mathis

Unread postby Seneca on Sun Oct 02, 2016 8:03 am

Actually, I don't feel I have to acknowledge that assumption. By the way, I already argued that if there is an discrepancy between prediction and reality, it isn't in ballistics.

For those people that are like me still struggling to understand, here is an analogy that could be useful. I am not sure it is exactly what Mathis is saying, but at least it is similar.

Just backtrack and forget everything you know about measuring circles. What if everybody is making a wrong assumption about measuring circles and curves? We are assuming that we can use a measurement instrument for straight lines (a ruler) to measure curves and still get correct measurements. But that is only an assumption. An analogy is the assumption that we could use a measuring scale to weigh a gas*. We can use tricks like using a flexible ruler or using a piece of rope and measuring that. Or we can roll a wheel over a table, take a point on the wheel, mark where it touches the table in each revolution, and measure the distance on the table. But we still have to prove these tricks give the actual length of the perimeter. Possibly the ruler or the piece of rope contract when we bend it. What we calculate as pi (3.14..) could be really the effect of bending the ruler or rolling a circle over a straight line.

What Miles Mathis and his supporters have done and the video shows can be considered as the first tool to measure the length of a curve. They get different results than we predict, suggesting that our assumptions have been wrong.According to Mathis and possibly proven by the experiment, the circumference of a circle is 8r (r being the radius) instead of 2pi.

What I still have to explain is why it is that when we calculate the surface, the old pi is making it back in the formula. Because I assume/hope that (old) pi x r² is still the correct way to calculate the surface. (I depend on this formula often daily to calculate the volume of wood in the trees I measure).

The appearance of the same pi in both formulas suggests that when we calculate the area of a circle something is happening that is similar to bending the ruler or rolling the circle.

Please let me now if this is clear enough and if it is making sense. (I can't make the last sentence much clearer because of my own lack of understanding.) Again it shows that Miles' use of the same letter pi is confusing.

*It is not a very good analogy but if you would try to weigh a gas in a similar way you use to measure a solid or liquid you would get a wrong result. Even if your scale is very precise and you find a way to prevent the gas from floating away. Because you also have to take into account that the gas is now taking the space of the air that it is replacing. Which you probably weren't doing for the heavier solids and liquids.
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Re: Discussing Miles W. Mathis

Unread postby Flabbergasted on Sun Oct 02, 2016 12:58 pm

Seneca » October 2nd, 2016, 5:03 am wrote:What Miles Mathis and his supporters have done and the video shows can be considered as the first tool to measure the length of a curve.

The "length of a curve" and other straight and sinuous courses may be quantified with measuring wheels. The handheld precision instrument on the right is used by architects.

The experiment performed by Steve Oostdijk uses a fixed trajectory (circumference) and a moving object (ball). But the experiment could be done the other way around by using a fixed object (the ground) and a moving circumference (wheel). I believe both scenarios illustrate "circular motion".

Image

As the argument goes, if the circumference of the rotating measuring wheel is not 2r x 3.14, but 2r x 4 (simply because it is rotating), such measuring devices would be useless in engineering and construction.
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Re: Discussing Miles W. Mathis

Unread postby VexMan on Sun Oct 02, 2016 1:50 pm

Well, the length of curve can be measured by measuring wheel, that is a legitimate option - however such measuring wheel should be made and calibrated considering that while in motion, a point on the boundary of such measuring wheel travels 8 times its radius while in spin for 1 full rotation. That would be actual lenght covered by that particular point (and a men walking it afterwards).As well, that would be cca 21% (21.46018% more precisely) MORE distance as opposed to the 2*R*Pi calculation. And this is a fundamental part of understanding circular functions in kinematic situations. Using the measuring wheel as the one in the Flabbergasted's picture would "measure" it wrongly, to be precise, it would measure alleged 100% of the supposed lenght, while actually it would be 121,46% of real length. (I needed quite a long time observing the animation of what I just said, to actually comprehend its implication, I'd suggest the same to all having difficulties with it).

Oostdijk's experiment is done with fixed trajectory, indeed, and I think as well that it would be the same if we "moved the ground" and measure it all accordingly. The principle remains unchanged. The biggest point in Oostdijk's setup is to notice time needed for the ball in a curved (circular) path to finish 1 full circle -> it needs exactly the same amount of time as the equal ball in the straight path covering 4R of length (where R represents actual Radius of the circle that is being used as track with the second ball) .

Flabbergasted, you say such devices as in the pictures, would be useless in engineering and construction - not totally though if all in one project is measured with the same wheel. Then proportions would be the same as if measured in different ratio (21.46% less) and it would remain unnoticed. I just wonder how is it possible that we all put so mz
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