View Full Version here: : For the mathematicians PI doesn't exist??

sjastro

18-11-2010, 09:01 AM

Here is an example of pure drivel.

http://milesmathis.com/pi3.html

I know of 3 rebuttals to this nonsense.

I'll leave as an exercise for any budding mathematicians to refute.

Regards

Steven

Bugger, gee you lost me Steven, I will just stick to what I was taught so many years ago, it worked for me then, and I expect it will still work for me now.

Leon

Nice fudge!

It is, of course, this statement that is incorrect ...

"If we take this process to its limit, we take our path to the path of the arc AC."

As the number of sub-triangles approaches infinity, it is the sum of the hypotenuses of each sub-triangle that approaches the length of the arc AC.

The hypotenuse of a right-triangle is always less than the sum of the other two sides. Therefore, taking the limit, the arc AC < AD + CD

or arc AC < r, the radius of the circle.

Regards, Rob.

sjastro

18-11-2010, 02:09 PM

Thanks for your comments Rob.

If you use Mathis' geometrical step construction you will in fact find the sum of the lengths of the hypotenuses of the sub triangles is a constant value irrespective of the number of sub triangles used. You will never approach the length of the arc as the number of subtriangles approaches infinity.

http://mathisdermaler.wordpress.com/2010/11/15/a-reply-to-%E2%80%9Cthe-extinction-of-pi-the-short-version%E2%80%9D/

The second disproof of Mathis' ideas is particularly elegant.

Regards

Steven

I didn't find any reference to this constancy, which is patently ridiculous as sqr(x1^2+y1^2)+sqr(x2^2+y2^2)<>sqr((x1+x2)^2+(y1+y2)^2). The fact is that the length of any curve can be obtained by integrating ds where ds^2=dx^2+dy^2.

dx and dy can be considered the horizontal and vertical components of an infinitesimally small right triangle drawn on the section of curve. His assumption that ds=dx+dy is a clear contradiction of Pythagoras' Theorem. As I mentioned before ds<dx+dy for all right-triangles on the curve. His assumptions are unjustifiable.

Regards, Rob

CraigS

18-11-2010, 03:42 PM

Aha .. the violation of Pythagoras' Theorem !!

That was going to be my contribution, also !

But I don't think Miles cares about Pythagoras, either !!

:)

But how does he sneak this in ?? At the very beginning, he declares the angle to be 45 degrees and the sides DB and DC to be equal (this is pythagoras' theorem in action). Then he completely refutes it in:

"In other words, it is the hypotenuses of the little triangles that converges upon the curve, not the sums of the other legs of the triangles."

Its kind of like starting off with certain assumptions to prove something and then disprove the assumptions because of some other assumption !

Having made this point ...

Ahhh look, guys … Miles is right !! .. he's a genius and Newton … and everyone since … was just plain wrong !

:P:)

Cheers

PS: (As he carefully avoids the maths required to disprove Miles) !! :)

sjastro

18-11-2010, 04:09 PM

The flaw with Mathis is that he is calculating the length of the chord AC, not the arc AC.

This is clear from his geometrical construction.

For example the chord AC= (AD^2+DC^2)^0.5 is for the triangle ADC.

The chord AC is an approximation of the arc length using a single triangle.

For simplicity lets subdivide into equal subtriangles.

A subtriangle can be constructed with sides AD/n, DC/n where n is the number of subtriangles used. In this case 1/n is a scale factor.

The hypotenuse for a subtriangle is y= ((AD/n)^2 + (DC/n)^2)^0.5.

The total length is the sum of the hypotenuses = n*[((AD/n)^2 + (DC/n)^2)^0.5].

But n*[((AD/n)^2 + (DC/n)^2)^0.5] = (AD^2+DC^2)^0.5 which is the length of the chord AC not the length of the arc AC.

Hence for any value n the result is the same.

Mathis doesn't know his chords from his arcs.:)

Regards

Steven

sjastro

18-11-2010, 04:20 PM

Maybe we should have a "spot the number of errors" competition.

Regards

Steven

adman

18-11-2010, 04:33 PM

the equation he derives that relates the circumference to the radius of the circle is C = 8r....

bugger the mathematics - you could refute that with a piece of string!

CraigS

18-11-2010, 05:10 PM

Not that we're finished with this guy Mathis, yet but here's another beauty

Bill Gaede's Double Slit debunk (http://www.youtube.com/watch?v=v-MAW9YmN9s).

This one's actually a good laugh
mainly cause of Bill's performance (and of course .. the sheer attention to detail in setting up his experiment) !

Bill was a real life Cold War industrial spy who stole semiconductor industry secrets whilst working for Intel and sold 'em to the Cuban Govt. A wonderful character reference ! His main hobby is Physics
I think he got into it whilst he was in prison.

Still, one of our beloved members, publically recommends his Double Slit refutation !

To be perfectly honest, I think you'd need a Quantum Mechanical background to refute Bill's debunk of it all (??).

Have fun & get a bowl of popcorn for this one (it runs for about 10 mins - sorry, Steven).

:)

Cheers

Steven, I agree with your last statement. He doesn't know his chords from his arcs.

However, no matter what way you look at it, the sum of the minor hypotenuses (or chords) will still not equal the larger hypotenuse AC. The triangles are just not similar. You cannot divide AD equally into n parts and result in each sub-triangle having a height of CD/n.

Rob

Jarvamundo

18-11-2010, 07:40 PM

Steve, might be better if you start with his papers on orbital dynamics prior to moving into this one... then also go for the 'long' version of the paper.

2-dim pi is the circular ratio of circumference to diameter, C/D = 3.1415926...

3-dim pi is the spherical ratio of surface area to cross-sectional area, 4(pi)R2/(pi)R2 = 4

Strongly recommend reading his other papers... i started with this one first, it threw me off for a while. Having now read his book (but i still struggle with some parts of it), it leads you through the *ideas* in more depth before you hit this stuff, then you understand the domains for applying the *math*.

But yes, quite correct in 2dim pi = 3.14etc.... acknowledged by Mathis.... you need to switch to kinematics.

He's got a fascinating, confronting and challenging book, seems to be getting a bit of traction call the "Un-unified field", gets pretty big wrap from some at NASA, not that that should weigh your own mind examining the material, i'm sure this will be debated for a while yet. I'd love to have your take on it, if you ever find the time.

By the way, turns out associated hydroxyls are expected... still getting some more info on the chemistry, but thanks for the query and IR stuff, it helped my understanding... will write it up in a post when i have the detail in full, or near enough.

Unfortunately, I didn't have any popcorn but Bill's performance was rather humorous. Electromagnetic ropes - sounds like a stronger version of some string theory ... ropes and strings. ;)

Instantaneous action at a distance. Smacks a little of our holographic theory again - everything is connected to everything else.

Regards, Rob

CraigS

18-11-2010, 08:00 PM

Rob;

Yes .. loved the bit with the cork and the pin !

Sounds a bit like quantum entanglement to me !

Putting all the humour aside though, it did make me think about it all.

Cheers

CraigS

18-11-2010, 08:10 PM

Man Alex;

Beats me how you do it mate !!

It takes me ages before I can synch up with this bizarre world to the extent where I can understand where these guys are coming from .. let alone snoop out all the holes in their logic !!

Mind you, I've been thinking a bit about you & all this stuff lately ..

I think I'm prepared to make a concession ..

I really do think that unless you go looking for a specific phenomenon in the Universe, it is arguably, not probable that you'll stumble across it.

This much I do concede.

Such as intergalactic magnetic & electric fields (of notable magnitudes), or significant amounts of predominately non-ionised plasma.

This is not to say that mainstream does not go looking for them. They clearly do.

Just thought I'd say that.

Cheers

The_Cat

18-11-2010, 10:22 PM

Pure drivel ? Yes! definitely.

Quote from the article (above link):

" The tangent is a component of the arc ... "

and

" ... arc is composed of the tangent. ... "

I know the moderator will kill this sentence, but before one publishes statements like the ones above one really needs to establish the relative positions of the elbow and backside.

Jerry.

Jarvamundo

19-11-2010, 10:14 AM

Instead of dismissing, just apply some sincere attention to the material in full, or simply why even bother in the first place?

The guys preface was written by a current NASA Astrophysicist, whilst not an indication of correctness, it just illustrates there are some, well schooled, who might turn more than one page. It becomes fairly obvious, when studied, Mathis' has a very deep understanding of Newton's & Columb's original works, from original sources. His logic is always presented from first principles.

PS: I'm glad Gaede makes you think.... now try (add) this... http://milesmathis.com/double.html Miles work is very mechanical in nature, and so it uses the simplest of math, it is the ideas that are challenging for those with entrenched schooling, I am still working through and challenged by some of it.... other parts of it have resolved many paradoxes for me. Again i'm more than interested to discuss with anyone who studies the material, especially if some of the brighter sparks around here do so! There are many benefits in challenging ones ideas, if it's done with sincerity.

PPS: I suggest the book Isac Watts - improvement of the mind... written in 1830's it's what sparked Faradays endeavors. Tesla was not a savant obsessively dividing everything he saw by 3, because he was a nutter.... he was performing mind sharpening exercises, it seems modern man is not usually capable of bothering beyond the lazy quick-fire "does it match my textbook" effort, that these giants saw as necessary.

sjastro

19-11-2010, 02:44 PM

Alex,

Take Kepler's Third Law. The third law relates the period of a planet's orbit, T, to the length of its semimajor axis, a. It states that the square of the period of the orbit (T2) is proportional to the cube of the semimajor axis (a3), and further that the constant of proportionality is independent of the individual planets; in other words, each and every planet has the same constant of proportionality.

Guess what the constant of proportionality contains? It contains π=3.1416... , and yes this is a "kinematic" example. The law is based on empirical data.

It is absolutely ludricious to consider a static π and a kinematic π, let alone they should have different values. It reflects Mathis' nonsensical mathematics in this case.

Regards

Steven

Jarvamundo

19-11-2010, 03:26 PM

Yup, this is what's covered.... and why it's best familiarize yourself with all of the celestial mechanics papers.

Or yes get the book, it's easier this way since Miles has ordered the thesis in a more digestible manner. I wish i'd done this earlier.

I could back n fro here on IIS, but it'll just be pointless. The ideas need to be layed out from first principles, i do not have time to do this, and Miles has already done so.

Tickle your interest: http://milesmathis.com/cm.html http://milesmathis.com/ellip.html

I'll loan you my book when i'm done with it, or yeah i think it's 9 bucks for the e-copy.

CraigS

19-11-2010, 03:42 PM

So let me get this straight, Alex;

Although you haven't stated it outright, I suspect that you don't necessarily accept Miles Mathis' 'Proofs' as being correct, am I right ?

What you're pointing to is that his stuff gets one thinking and causes you to go back to when you first learnt this stuff in High School Physics ?

In my case, I simply can't remember all the ins and outs of Keplarian physics, first principles of geometry and then calculus. I simply accepted it, (perhaps naively at the time) but, as what I learnt all those years ago turns out to be scientifically and mathematically still valid, I don't have to revise some guy's incorrect version of it.

So, the real benefit of this rather painful exercise for me, has been to simply reinforce what I accepted all those years ago … is this any real benefit at all ?

Has it furthered my knowledge of anything ?

Sometimes relying on foundation concepts actually does lead to progress. In my case, I have made a career out of moving forwards in this way. (What we learn at school is not all myth !!)

It seems that Miles' 'proofs' are certainly not good foundations and thus can be safely discarded, now.

Please let me know your thoughts as I'm finding your support of this guy very difficult to fathom.

Cheers

PS: The same goes for Gaede's work … right ??

Jarvamundo

19-11-2010, 05:44 PM

Do what ever makes you comfortable Craig.

Regarding my views on Mathis' work, go back an read my posts.

Maybe I could accept a proof of a very minor inaccuracy in the calculation of the value of pi, unlikely as this would seem. But to say that C= 8r as compared to the slightly more accepted version of C = 2.pi.r or C = (approx) 6.28r, well, that just seems like a major error that has gone unnoticed for many centuries.

As for suggesting that the length AB is equal to the length of the arc AC; I think it was Steffen who suggested the use of a piece of string to prove/disprove. So I got a piece of string (as if my own eyes could not clearly tell me that this equation was blatantly incorrect) and, what do you know?

AB is significantly longer than arc AC.

So therefore it has to be quite apparent that any further calculations from that point must be incorrect.

It appear that Mr Mathis has his mathis wrong and that he has fulfilled at least one of the IIS criteria for pseudoscience; that of I am right and everyone else is wrong.

Cheers

Stuart

CraigS

20-11-2010, 08:07 AM

G'Day Stuart !

Amazing isn't it ?

I snooped around a bit to try and understand where this guy Mathis is coming from. Apparently, he's an artist (not too bad a one, either). His qualifications (yes .. he does have some) are mainly BAs from US universities. I think he's into philosophy as well (I guess that also explains his interest in mathematics/physics).

I also notice he's published a few books (as Alex has pointed out). I suppose he could publish cross word puzzles or something, to entertain the masses (as an alternative to entertaining pseudoscience).

Publishing books seems a good way to improve one's income beyond that generated by just selling artworks !

The problem is, that I think he may actually believe he is a player in the field of mathematics !! (If he does seriously think this, then he's lost the plot as well, eh ?)

:screwy: :)

Cheers & Rgds

And furthermore!

If you take his diagram and repeat it you end up with a square containing the largest circle that it is possible to fit within that square. Even a cursory naked eye examination will reveal that the perimeter of the square is obviously greater than the perimeter of the circle. But that's not very scientific, so, for those who, like myself, last studied maths in high school in the year nineteen quifty quar (apologies for the Goon Show reference, but it kinda seems appropriate here :) ), we once more take the piece of string and run it around the perimeter of the square and then around that of the circle and, guess what, the perimeter of the square is greater than that of the circle.

Since the perimeter of the square does actually equal 8x radius of the circle, and since I as a non recent student of high school maths have very simply shown 8 x r > circumference of the circle, it would seem that Mr Mathis' equations are incorrect. And that proven without the use of elegant mathematical formulae that someone like Mr Mathis can use to confound people into believing his new maths.

Cheers

Stuart

sjastro

20-11-2010, 09:15 AM

Since Mathis agrees Kepler's equations are correct and that Kepler uses pi=3.1416.... then clearly pi <> 4 as Mathis suggests for a "kinematic" event.

Now for the refutation of Mathis' ideas on orbital ellipses.

Mathis needs to introduce an E/M repulsive force in order to get an elliptical orbit to "work" is more a reflection in gaps in his own knowledge and understanding of the dynamics of an elliptical orbit than any issues with Newtionian physics.

The reality is that Newtonian theory for orbits is simple and straighforward and doesn't require a repulsive force.

This will be made abundantly clear.

This is only partially true. The gravitational field doesn't act perpendicular on an object. Where as gravity is an external force, a force acting along the tangent doesn't have to be external as Mathis suggests.

For example the occupants in a car will experience a centrifugal force when the car goes around a bend. The centrifugal force is a reaction force to the inward acting centripetal force. The centripetal force is not external but is created as a result of the non straight line motion of the car.

In an elliptical orbit a tangent force exists due to the angular velocity being variable. If the angular velocity became constant, the tangent force vanishes and the orbit becomes circular.

This is not correct. The tangential velocity of a planet at perihelion is greater than that at aphelion.

Tangential velocity = Radius X Angular velocity.

If the angular velocity was constant, the tangential velocity at perhelion would in fact be less than the tangential velocity at aphelion as the radius has a minimum value at perihelion. What happens is that the angular velocity increases at a faster rate as perihelion is approached.

The relationship between angular velocity and radius is given by the equation (Radius)^2 X Angular velocity = Constant.

If you half the radius, the angular velocity will increase 4-fold.

The tangential velocity reaches a maximum value at perihelion.

Mathis describes orbital velocity as the vector sum of tangential velocity and centripetal acceleration. This is total nonsense as you cannot add velocity and acceleration as their dimensional units are different.

The tangential acceleration is mathematically derived as a consequence of a non constant angular velocity. The tangential force follows from this.

This eliminates the need of introducing external contrived factors such as a repulsive E/M force.

Regards

Steven

CraigS

20-11-2010, 11:13 AM

So, I'm desperately trying to get something of some value out of Mathis' work, (assuming his objective is to create an alternative set of principles), but
.

.. Steven
from your previous post, it seems that he violates his own principle foundations in his subsequent statements. That is, his own alternative version of all this is, in itself, not even internally consistent.

Throughout his work, he refers to his other 'proofs' to build upon his previous work, so I can only explain his work as some kind of attempt at rebuilding dynamic classical physics from the ground up. To do this, I would've thought you have to be, at the very least, consistent and honest to yourself, or the foundations you lay out to start with ..??

I'm desperately searching for something of value in Mathis' work apart from being kind of like a poorly made physics test
that can even be disproven using string !!

Does anyone have any suggestions .??
just so I can restore some of my, (perhaps), misplaced trust in human beings ?

It seems that even Alex has abandoned me in my 'quest' to get where this guy is coming from ...

:shrug:

Cheers

sjastro

20-11-2010, 11:38 AM

His motives are highly questionable.

Did you read the splurge at the bottom of the article.

Good grief am I engaging in a conspiracy theory?

A perfect example of pseudoscience being logically inconsistant or perhaps in this case a scam.

Regards

Steven

Rick Petrie

21-11-2010, 09:34 AM

Strange theory on how straight lines can equate to circular measurements?

How to make the impossible possible!:shrug: Interesting assumptions though.:)

The_Cat

21-11-2010, 10:09 AM

Does anyone have any suggestions .??

Yes:

The first thing that Mathis should do is learn some maths, some Euclidean geometry would be nice for a start. Then some very elementary calculus then define the problem then write a mathematically consistent proof

That is all.

bojan

21-11-2010, 10:12 AM

Not quite...

The same suggestion should apply for his admirers as well.

CraigS

21-11-2010, 11:45 AM

And where might they be found ???

:shrug:

Cheers

Jarvamundo

30-11-2010, 10:16 AM

http://sagacityssentinel.wordpress.com/

Barrykgerdes

30-11-2010, 11:23 AM

Of course Pi does not exist. Except as a letter in the Greek alphabet. Mathmatitions and statisticians have been trying to find it for years. Some have even spent years trying to calculate it to umpteen million decimal places only to find it still needs umpteen more (ad infinitum).

We just need to accept what we are told and get on with using it as before. Forget about the egotists trying to make a name for themselves. It gives perfectly usable results;);):thumbsup::rofl::lol::sh rug:!

Barry

Geoff45

30-11-2010, 12:10 PM

Saying that pi does not exist because it requires an infinite decimal expansion is on a par with saying sqrt(2) doesn't exist because it requires an infinite decimal expansion. They just happen to be irrational numbers and as was long ago proved by Cantor, such numbers vastly outnumber:lol: the rational ones, ie those that have a finite decimal expansion. I realise some of these statements my appear a bit vague, but I'm trying to be brief. Have a look here (http://en.wikipedia.org/wiki/Cantor%27s_theorem) if you want the real version.

Geoff45

30-11-2010, 12:40 PM

Just for the fun of it, you might try using Mathis "logic" to prove that any straight line is longer than itself by an arbitrary large amount. Start with a straight line, make it the base of an isosceles triangle, flip the peak of the triangle about the halfway point to have two base-to-base triangles on the line, repeat with these etc etc. If you've followed the fallacy in Mathis' argument, you will quickly see where this is leading.

Geoff

Barrykgerdes

30-11-2010, 12:41 PM

Yes Geoff

The fact that these mathmatical functions are irrational is all I am refering to. We could not do very much maths or science without using these functions as they have been defined. This thread has been going on for some time because someone trying to make a name for himself has come up with a theory? that Pi does not exist. So to stir the pot I took the "doesn't exist side" with a tongue in the cheek reason.

Barry:lol::lol:

Geoff45

30-11-2010, 12:56 PM

Yes, I have also been known to do that.

Geoff

sjastro

30-11-2010, 02:36 PM

Alex,

I am going to throw this one right back at you.

Explain where Mathis came up with the orbital equation v=(2*PI*r)/t.

While it looks logical, try differentiating the equation with respect to time and provide a physical interpretation of the resulting acceleration.

How is it possible this acceleration leads to a stable circular orbit?

Regards

Steven

CraigS

30-11-2010, 02:47 PM

Yes .. I'm with Steven.

There are flaws in Mathis' logic everywhere.

There's reading effort needed to find them.

I'd rather spend time reading something (slightly) more reputable.

School teachers at least, get paid for correcting students' work.

Cheers

avandonk

30-11-2010, 03:21 PM

He is using a linear formula for speed and then thinks it represents circular motion. He most probably did not get past year 4 maths.

see

http://en.wikipedia.org/wiki/Circular_motion

You should always take the limit to the Planck Length never zero as that leads to absurdities like infinity.

my 2C

Bert

sjastro

30-11-2010, 05:37 PM

Exactly.

Regards

Steven

multiweb

30-11-2010, 06:54 PM

You guys got it all wrong. Pi is a piece of cake. Period. :whistle:

Barrykgerdes

30-11-2010, 07:48 PM

Yeah

and it also something to eat with peas or at the footy with sauce and can of beer.

Barry

The_Cat

30-11-2010, 08:57 PM

Can add much to the discussion but:

Talking about pi , most of us know about the school boy approximation of 22/7 (very poor accuracy) but what about this for accuracy pi ~ 355/113 . This is easy to remember:

take the first 3 odd numbers (1, 3 and 5) then double up (113355) then put the long division sign half way (113 | 355)

Jerry.

Geoff45

01-12-2010, 10:54 AM

Enough of analysing Mathis's argument. Simply by examining his conclusion you can see that it is wrong without having to waste time looking for the fallacy. He fails to do what any self respecting mathematician would do and that is to subject his results to a sanity check--that is, to ask "Is the result I have supposedly proved a reasonable one?" If you look at the attached diagram, you can see that Mathis (in effect) claims that the perimeter of a square has the same length as the circumference of the inscribed circle. Since this is clearly bollocks, we can state, without even bothering to look at his "proof", that his reasoning must be faulty.

Geoff45

01-12-2010, 11:01 AM

Quite good--accurate to better than 0.0000003

sjastro

01-12-2010, 11:35 AM

The bullocks factor is that Mathis isn't disputing the value of PI=3.1416... for static situations. It changes to PI=4 for a "kinematic" environment.

To show how absolutely ridiculous this idea is, consider a turnatable.

When the turnatable isn't turning pi=3.1416.... When the turntable is rotating PI=4.

So if the turnatable is of a fixed radius, the circumference of the turnatable is larger when it is rotating.:shrug:

Regards

Steven

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