Why pi isn't 4: short and simple version

Thanks for commenting. I don't understand your first question, so I can't answer it. Your second question is however a good one, because I think this is where most people will get stuck. Think about it this way: if Jim drinks 10% more coffee every day than Bob, how much more coffee will Jim drink in a week? 10%. A month? 10%. A year? 10%. The percentage difference doesn't change with any number of iterations. Now, if someone says that Jim and Bob drink the same amount of coffee every day, but also that Jim drinks 10% more coffee in a month, you would think that person is nuts, right? That is the contradiction. Jim either drinks more coffee than Bob or he doesn't. He can't drink the same as Bob every day but more than Bob in a month. The rule is enshrined in the distributive rule of multiplication over addition.

With that in mind, consider: if two balls travel near-identical paths with the same initial speed, but one path is SLIGHTLY curved and the other one isn't, how much will the transit times differ? Maybe a little, but not 27%. That is just impossible, right? Now repeat that process, say, 1000 times. One ball keeps going straight, while the other one eventually comes around and makes a circle. If the transit times don't differ by 27% over an individual segment, how can they differ by that much over the whole trip, which is just a chain of those segments? Remember, this is supposed to be a model of motion in general, including orbits, so we have to assume that the balls aren't slowing down or oscillating in speed. That means each trip through a segment is the same as the next, and we are just iterating the same process over and over.

All of this is a way of saying that any model of the real world, including motion, has to exhibit continuity between curves and lines. We have to be able to approximate one with the other, or measurements and calculations become absurd. I knew that from the beginning, of course, but I had to chew on it for a while before I realized how to prove it. Turns out it's just the distributive rule (d'oh!).

Calculus is of course a generalization of this idea, being based on the analysis of functions in terms of their linear approximations. I considered going through his calculus papers and pointing out the problems and absurdities there, but that really isn't worth my time.

I should say that it is a sign of respect that I am even bothering to dwell on this question. You won't see me refuting Flat Earthers, because I don't consider those people worth responding to, and I don't want to be in the position of defending the mainstream: rather, that is where they want me. This one is a kind of Flat Earth for high-IQ people, a test of whether you are really using your brain or are still being bluffed by specious arguments and imposing rhetoric. I have to admit his rhetorical game is strong, and he had me questioning my own sanity for a brief while. I needed to settle the question if only for my own peace of mind.

@ben Sorry that my question / ponderings are badly expressed. I really am not advanced enough to get to grips with expressing this stuff mathematically.

Let me try and clarify my question(s).

In the theory why does Pi = 4? Yes, of course I should know this

What is acting on the equation Pi = c/d to change either circumference or diameter? Is it the circumference relatively increasing, the diameter contracting or some other mechanism (though since there are only two elements in the equation I can't see what that could be). [Yes, of course I should read the paper, but I have read plenty papers to find that he doesn't actually cite or work through his evidence. As you say very strong rhetorician .[/em]

I am afraid I don't even know the distributive rule.

But on question 2. I assumed that the transit time did differ by the 27%, if it doesn't there is no theory. Hence my question, what is making the speed differ (which is, presumably, whatever is making Pi = 4)

Which did indeed come from watching the YouTube video that @daniel_Archer refers to

@daniel_Archer my objection to that video is that it took someone else to do it for Miles and once I researched it seemed to be the accusation that the theory had come from a Dutch guy in the first place. Sorry, I really can't remember his name.


I am just adding this www.askamathematician.com/2011/01/q-%CF%80-4/
Any thoughts?

Having just read as much as I could stomach of milesmathis.com/pi7.pdf it is so obvious that it is not any of the a, b, or c paths But a curved D path around the edge, that is why he is wrong. Any child with a piece of string can work that out. The distance around the circle is neither a lot of jaggered left and right angles, or diagonal increments. To go round a curve one follows a curve. I really don't understand how this got more complicated, maybe trying to prove it in maths is but in basic measures it isn't

Having said that I don't understand the YT video result by Steven Oostdjik (who is the Dutch guy I was referring to). Link to the YT video is in the paper.

And, I am not paying enough attention to figure out why Miles keeps saying 21% rather that 27% that @ben is using which makes sense as it is 4/3.142.

The objection is, it's too low-res by orders of magnitude. It is too small and moves too fast to properly assess what is happening. Several explanations for the result are possible, but pi being 4 is absolutely not one of them. You couldn't even make an animation that obeyed basic physical laws and showed pi = 4 at sufficient resolution. It is mathematically impossible. If you can't make it happen in an animation, how can it happen in real life? Again, basic logic.


It is the circumference increasing.

Hardly atypical. Most people go through, what, 13+ years of school and don't remember anything except what they learned in the first few years of grade school. It just shows what a ridiculous farce education is.

The author assumes the Euclidean definition of arc-length. Miles's argument is that you can redefine arc-length in terms of other metrics, such as the taxicab metric. My argument is that, while such a redefinition is mathematically valid, it cannot possibly apply to real moving bodies. Among other things, taxicab geometry implies that it takes as long to go along the sides of a square as along the diagonal, which is obviously not right. And even if you only apply it to circular motion, it implies that your speed oscillates as you orbit at constant angular velocity, which is utterly absurd.

Is it possible to define a metric under which pi is 4 while maintaining continuity between lines and curves, symmetry under rotation, and other properties we naturally expect? At first I thought it might be possible, but now, I am absolutely sure that it isn't. That's the point.

Sorry not sure how to quote individual parts like @ben can.

@daniel_Arhcer

Taking a straight line is 1 line

Taking a curve is 2 straight lines.



That is the basic difference we are talking about here.



As Miles referenced the PBS video, showing circular motion is exaxctly 2 straight line motions combined.

I still reckon taking a curve is taking a curve and I reckon you can work out Pi by dividing the circumference of a circle by its diameter. I honestly think it is as simple as that. I really can't conceptualise it any other way. Clearly I would need to give all of this a lot more thought if that is where my raison d'être lay. 

As for PBS, I don't suppose Miles is always as trusting of them as a source of truth, as he is when they support his argument.  

Is Steven still studying under Miles?

@ben
I don't want to be in the position of defending the mainstream: rather, that is where they want me.

I missed commenting on this, this is very interesting, it sounds like something Miles would say. You are saying it to a smaller audience, therefore it doesn't sound like it could be coming from a place of ego. Are you saying they want you in particular wasting your time, or does that apply to all of us? And does this they include Miles?

It is the circumference increasing.

Well,, at least that gets us away from steps or polygons. I assume the c/d ratio of an ellipse could be 4 but I don't suppose this is the point. I have never seen a car with elliptical wheels and surely tie to go round an ellipse is still a factor of distance / speed. Yes, symmetry under rotation, I was going to say  "a bumpy ride" but I think yours is more mathsy! Oh, if I had only had the brains, interest  or the discipline....

Don't get me started on the farce of education. I despair. 

To be quite honest, it sounds like he just happened on this nonstandard way of calculating pi, and then tied himself into intellectual knots trying to fashion it into a great discovery. Most bright kids have little "discoveries" like this, which we later look back on and have a laugh about. I guess he just can't bring himself to do that. It would mean he was just a bright kid and not the smartest guy in history.


Bingo, bongo. I think you have hit Miles squarely on his round head. I think if he had studied maths at degree level he would have realised this, same goes for his art - which is technically fine but that is as far as it goes and really humanity passed that point a few hundred years ago. I think it must be hard when the only thing bigger than your IQ is your ego and unwillingness to take feedback (or a joke). 

He does claim that he tried to prove these things to the mainstream but his way of writing and his lack of rigour really don't suggest to me that he would be taken seriously. He seems to me like a child wanting to get maximum reward for little effort. I suspect his life hasn't really gone the way he expected, but it has gone exactly the way that a relatively bright observer would expect it to. But I realise I have now strayed  completely into ad hominin, so I will stop. 

He calculated it incorrectly as 1-pi/4 rather than as 4/pi.

Oh, that isn't good. Especially for a proof of a theory that has been up for c 10 years and has numerous updates to it. Reassuring for me that I am not going completely mad - thanks for that!