Wednesday, January 2, 2013

Turning the crank

Years ago - I was perhaps 14 - my Dad went on a business trip to check out an inventor who was trying to sell some of his ideas. He took me along. The main gizmo that my Dad was dispatched to look at was something that was similar to a Wankel engine. I won't bother with the details of the design here, since everyone already has a working knowledge of how this engine works [1].

Turning the crank on the Ramelli water pump

Perpetual motion machines

The talk of the engine went over my head, but I was intrigued by the inventor's perpetual motion machine.

Perpetual motion machines I understood. At the tender young age of 8, I had responded to a "sell us your inventions" ad in the back of a comic book with a perpetual motion machine of my own. I had the brilliant idea to connect a generator up to a wheel that was running on a motor that was run by the generator. If only I had had the foresight to apply for a provisional patent before I sent off my idea! How was I to know that that those unscrupulous folks would sell my idea to Toyota. The intellectual property that I so naively gave away was to become the cornerstone for their regenerative braking system. [2]

"This invention is a pendulum structure that operates as near as possible 
as a perpetual motion machine to provide activity and entertainment to one using same."
US Patent 4,422,530

So, let me describe the perpetual motion machine that I saw at this inventor's shop. It was a large brass disk, about 18 inches in diameter and a few inches thick. It was mounted on a shaft so it was free to rotate. Magnets were embedded  along the circumference of this disk.

On the outside of the disk, there were magnets mounted on a mechanism of gears, springs, and levers. By virtue of this beautiful collection of parts, the magnets were brought almost into contact with the magnets in the brass disk, north pole to north pole, as the disk spun. Each near contact would give the disk a little push and momentum would carry the disk on to the next magnetic propulsion station.

The ingenious inventor gave the mechanism a little spin and it whirred away for ten seconds before coming to a stop. "I just need to make a little adjustment here." I wanted to stay and what him tweak the incredible machine into perpetual life [3]. I was not very happy with my Dad when he whisked us away. "The guy's a crank. You can't build a perpetual motion machine." "Are you going to buy his other invention?" "Absolutely not. He has proven himself to be a fool."

"But Dad, the momentum will always carry it up to the point where the magnets can push it again. How can it ever stop?"

Dad was so dismissive.

A tale of another crank

Just recently, I had an interchange with a crank [4]. I had posted information that he disagreed with. Fair enough. I make mistakes. Maybe I made an incorrect assumption or faulty argument. I provided him with a detailed proof and asked for him to help me find the error. He replied with a lengthy post that I couldn't comprehend. I asked him once again to find the error in my proof. I copied the proof again, this time with line numbers, making it completely clear that I wanted to know exactly which line was in error, and what the error was. 
John the Math Guy, puzzling over his proof

This was a long an frustrating discussion. Over the course of it, I requested no less than five times for him to provide me with the location of the step in my proof that was wrong. I never did get an answer.

I started asking myself... is there something important I am missing? Something I don't understand? Or is this a hopeless task? Is my proof just complete and utter gibberish? Do I have any bananas in the cupboard?  

The fellow had a rather uncommon name, so it wasn't hard for Google to find him. I found eight forum discussions that answered all my questions. Except for the question about bananas.

This gentleman has been referred to by the following epithets: persistent cretin, stupidity, complete nutcase,  trolls and/or insane, ignoramus, monumental ignoramus, delusions of grandeur, crackpot (twice), pseudoscientific, crank,  "are you still in high school?", and "stupid or dishonest". His posts have been refered to as patented cretinisms, masterpieces of idiocy, tortuous, horribly wrong, and utter stupidity.

Wow. I thought I had played to some tough audiences.

My own experience with him - him avoiding direct questions with inane rambling - was common. Here are some quotes from various people who were expressing frustration at this fellow in various discussions:

"I would love to follow what you are saying but for me you are not precise enough in your description. You use too many words."

"I have given up trying to follow [name elided] and your huge posts."

"I hope that there is some relevance to your tortuous conversations."

"I can never understand the point that you are trying to make. You make 10 half points and I don't understand any of them."

"In the Space that you spent going around the question without actually bothering to answer it , you could instead have answered it." 

"I am afraid that I cannot read your dialogue. You are not succinct enough."

"I've read through your response a few times and I have no real idea what you are saying."

"No matter how long-winded your explanations get, please bear in mind that you cannot defeat the fact that ..."

"I realize that English may not be your native language. But I can't respond to something that is not only incoherent..."

"You have simply written a very complicated paper (which appears to have errors) to state the obvious and draw an incorrect conclusion from it."

Two people had interchanges similar to mine. They tried to get the crank to answer a direct question. Here are the repeated requests from one frustrated person. The crank responded either off topic or incoherently in between each request. 

"Longer posts aren't going to do it for you [name elided]. Respond to what I said."

"Your refusal to respond to the questions in my post shows that you are avoiding the issue."

"I asked questions you're unable or unwilling to answer. Why is that?"

"I agree that further "discussion" is probably fruitless because you're not discussing the issue. I asked a couple of simple questions here to try to have you look at my point of view. You have refused to do that. I can only conclude that you see that you are wrong and are simply avoiding the issue."

Resistance is futile

Here are the frustrated requests from another person.

"Just post the scalar function for which you think the curl of its gradient in not zero. You don't need an article just to write down a function."

"Just post the function. If it exists and you know what it is, then nothing prevents you from posting it, especially given the fact that you would be quite happy to rub my nose in being wrong..."

"Just post the function. I'm not going to read nine pages of a convoluted argument about the curl of a gradient not being zero when you can post the function for which you claim that relation doesn't hold in a single line."

"I conclude that despite a lot of motivation to post such a function, you haven't done so because you know that if I take the curl of the gradient of that function."

"Either post the function or get lost…  If you had a real result, you wouldn't hesitate to post 1 function rather than post a lot of crap to cover for not having a function."

"Post it and I'll see it."

When the crank said that he had already posted the function, this was the frustrated reply:

"Where? You have spent this entire thread making excuses for not providing it."

Yet another crank case

As if this wasn't enough fun, another crank turned up on LinkedIn during the same week. This one claimed to be able to trisect an arbitrary angle [5], and claimed to have a "correct" value of pi (3.1547...). Naturally  there was a firestorm of explanations and proofs that he was mistaken. 

Pi to the World,
twenty two over (eight minus one),
Irrational though it be.
Let every round thing
Now fit the expounding
With each and every degree,
With each and every degree,
With each, with each, and every degree.
(from John the Math Guy's Math Carols, 1974 [6])

Here are some ridiculous (as in, worth of ridicule) links to websites, each with their own true value for pi:

      pi = 3.146264   (Just send $14 for their 12 page pamphlet!)

      pi = 4   (Of course, this is only true for kinematic situations.)

      pi = 3.125

My own favorite true value for pi is based on the golden ratio, phi. You will no doubt recall that phi = (sqrt (5) + 1) / 2. If you square this number (or add 1 to it, same thing!), and then multiply by 6 / 5, you get 3.14164...   [7] I'm gonna start my own campaign to get this number into textbooks as the correct value.

The wonderful thing about pi is that there are so many values to choose from!

And more...

Here is a quote from a recent post on LinkedIn:  "Reality and Fact are that we are NOW in the transition period of the Magnetic Pole shift."  The poles are going to shift - north becomes south and vice-versa.


I feel the need to add a conclusion to this. I wish I had one. I don't understand what is going on in these crank's heads. I understand the excitement of finding something that no one else has found. The potential glory of going down in history as the person who corrected longstanding misconceptions... I don't understand how people who are clearly intelligent can delude themselves into not seeing the glaring mistakes in their proofs, especially when others are kind enough to point them out.

[1] I really honestly don't want to bore anyone with the inner workings of the Wankel engine. Really, seriously. My lack of explanation has nothing to do with me having no knowledge whatsoever about what a Wankel engine is. Abject ignorance has never been an impediment for my pontification. 

[2] After this and a few unfortunate incidents with xray specs and Charles Atlas abs, I learned not to trust these comic book ads.

[3] The motion of the machine was almost perpetual! As an aside, I once used the phrase "almost infinite" in a group of math-savvy people and got the little titter that it deserved. Then I started noticing the phrase being used seriously. Sigh. As a further aside, here is how a mathematician responds to a funny joke. "Oh yes. That is really quite humorous. I will have to share that one with my wife." This is to be spoken without the barest hint of inflection.

[4] Wikipedia defines crank as follows: "Crank" is a pejorative term used for a person who holds an unshakable belief that most of his or her contemporaries consider to be false. A crank belief is so wildly at variance with those commonly held as to be ludicrous. Cranks characteristically dismiss all evidence or arguments which contradict their own unconventional beliefs, making rational debate a futile task, and rendering them impervious to facts, evidence, and rational inference.

[5] Trisection means to cut the angle into three equal pieces, using only a compass and straightedge. Everyone knows that this can't be done. My dog Truffle was eight weeks old when he came up with his first proof of this.

[6] Also included in the Math Carol songbook are such favorites as "Arcs the mighty compasses bring", "We wish you a semi-circle", and "I'm proving the Pythagorean Theorem", and "Oh Sum, all ye Mathful". Classics, every one of them. I wrote these in high school, and honest to god, my math class walked through the halls singing these one day before Christmas.

[7] A simpler form of this computation, which does not use phi as a stepping stone, is (3 / 5) (3 + sqrt (5)). This is the answer to the riddle: "3  5  3  5" - add plus, minus, multiply, divide, and square root signs to this series of digits to make an approximation to pi that is accurate to four decimal places. I asked this riddle of Mike, and he cleverly came up with "3 + (5 / 35)", which is only accurate to two places.

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