## Math Fun

For discussing anything related to physics, biology, chemistry, mathematics, and their practical applications.

Moderator: Flannel Jesus

### Re: Math Fun

Arminius wrote:How big are the sides of each square at least, if they are all different in size and integer (thus: in whole numbers)?

I'm pretty sure this isn't what you mean, but it's true:
1, because that's the smallest (positive) integer.

Perhaps the question is better posed like this: ]
Suppose the smallest square is 1x1. How big is the largest square?

Is that the same problem?
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Carleas
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### Re: Math Fun

Carleas wrote:
Arminius wrote:How big are the sides of each square at least, if they are all different in size and integer (thus: in whole numbers)?

I'm pretty sure this isn't what you mean, but it's true:
1, because that's the smallest (positive) integer.

Perhaps the question is better posed like this: ]
Suppose the smallest square is 1x1. How big is the largest square?

Is that the same problem?

Be careful, because the following tab contains parts of the solution process:
Choosing the most qualified integer is alraedy part of the task. At first you have to derive equations from the diagram, then you must pay attention to some subtleties, then you have to solve the equations, and after that you should choose the most qualified integer ... and so on.

For reasons of simplification you should choose "1" as the most qualified integer for one variable.
Last edited by Arminius on Tue Sep 22, 2015 9:42 pm, edited 1 time in total.

Arminius
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### Re: Math Fun

For ease of reference:
rechteck_mit_zehn_quadraten.gif (4.04 KiB) Viewed 5146 times

No solution yet, but...
I did a bit of work on this before I realized that they are all different sizes, which means the whole shape is not a square (otherwise B = C).

So I have to start over, which I will do later. My basic plan of attack is to list out the equations (e.g. A + B = C + E + F, etc.), then let J = 1 and solve for each other variable, then multiply them all by whatever gets them all to be integers (I was wrong earlier, J can't be 1, because A - (B + H) < J, so if J = 1, either A, B, or H could not be a integer).
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Carleas
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### Re: Math Fun

Carleas wrote:No solution yet, but...

Carleas wrote:I did a bit of work on this before I realized that they are all different sizes, which means the whole shape is not a square (otherwise B = C).

So I have to start over, which I will do later. My basic plan of attack is to list out the equations (e.g. A + B = C + E + F, etc.), then let J = 1 and solve for each other variable, then multiply them all by whatever gets them all to be integers (I was wrong earlier, J can't be 1, because A - (B + H) < J, so if J = 1, either A, B, or H could not be a integer).

Just do it.

Arminius
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### Re: Math Fun

Carleas wrote:James, your thread is not about our conversation around the Blue Eye problem. You started a thread at best tangentially related to the discussion, and I'm not interested in that tangent (not least because it misrepresents my positions and our disagreement).

But, to repeat, and ask pointedly: do you agree that the following two propositions are true:
1) X does not follow from Y alone
2) my eye color does not follow as a logical consequence of your eye color alone

That is you - always just denying the other route and refusing to even discuss it while trying to press your own point again and again.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
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Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

James S Saint wrote:That is you - always just denying the other route and refusing to even discuss it while trying to press your own point again and again.

If you want to start a thread about the logic of the Blue Eye problem, I'm happy to engage. Instead, you started a thread about a "common mistake" in science and philosophy. And, rather than actually show that these mistakes are present in the canonical solution to the Blue Eye problem, rather than actually laying out your case, rather than quoting what I or anyone who's endorsed the canonical solution has actually said (instead of making up a quote that is trivially fallacious), you just state that it "dawned" on you and then explore an intro-level logical fallacy.

Whatever prompted you to have your dawning, that thread is not about the logic of the Blue Eye problem. So far, this is the only thread in which that problem has been directly addressed.

Arminius wrote:Just do it.

This problem is pretty tedious, I think I must be doing it wrong.
Here are some equations:

A = C+G
B = H+D
B = I+F
C = G+E
D = H+J
E = G+I
F = J+D
H = I+J
A+B = C+E+F
A+C = B+H+I+F
A+G = B+H+I

Should be enough. Let's try and solve for a variable in terms of J.

A+C = B+H+I+F
(C+G)+C = (I+F)+H+I+F
2(G+E)+G=2(I+F)+(I+J)
2(G+(G+I))+G = 3I+2F+J
5G+2I = 3I+2F+J

F = J+D
F = 2J+H
F = 3J+I

5G+2I = 3I+2(3J+I)+J
5G+2I = 5I+7J
5G = 3I+7J

A+G = B+H+I
G = (H+D)+H+I-(C+G)
2G = 2H+(H+J)+I-(G+E)
3G = 3H+J+I-(G+I)
4G = 3H+J
4G = 3(I+J)+J
4G = 3I+4J
G = (3I+4J)/4

5((3I+4J)/4) = 3I+7J
(15/4)I+5J = 3I+7J
(15/4)I-3I = 2J
(3/4)I = 2J

If J = 1 -> I = 1.5
-> H = 2.5
D = 3.5
B = 6
F = 4.5

A+C = 14.5
A+G = 10

C-G=4.5
E = 4.5
G = 3
C= 7.5
A = 7...

Shit.

Yep, definitely did it wrong :P
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Carleas
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### Re: Math Fun

Carleas wrote:
James S Saint wrote:That is you - always just denying the other route and refusing to even discuss it while trying to press your own point again and again.

If you want to start a thread about the logic of the Blue Eye problem, I'm happy to engage. Instead, you started a thread about a "common mistake" in science and philosophy. And, rather than actually show that these mistakes are present in the canonical solution to the Blue Eye problem, rather than actually laying out your case, rather than quoting what I or anyone who's endorsed the canonical solution has actually said (instead of making up a quote that is trivially fallacious), you just state that it "dawned" on you and then explore an intro-level logical fallacy.

Whatever prompted you to have your dawning, that thread is not about the logic of the Blue Eye problem. So far, this is the only thread in which that problem has been directly addressed.

Why don't you properly show your full and clear understanding of the problem that I am pointing out (on the right thread). And then you can clarify the distinction between it and your reasoning. Why do you always avoid doing that every time? We have already annoyed this thread to death with our differences about the Blued problem.

Carleas wrote:This problem is pretty tedious, I think I must be doing it wrong.
Here are some equations:

A = C+G
B = H+D
B = I+F
C = G+E
D = H+J
E = G+I
F = J+D
H = I+J
A+B = C+E+F
A+C = B+H+I+F
A+G = B+H+I

Should be enough. Let's try and solve for a variable in terms of J.

A+C = B+H+I+F
(C+G)+C = (I+F)+H+I+F
2(G+E)+G=2(I+F)+(I+J)
2(G+(G+I))+G = 3I+2F+J
5G+2I = 3I+2F+J

F = J+D
F = 2J+H
F = 3J+I

5G+2I = 3I+2(3J+I)+J
5G+2I = 5I+7J
5G = 3I+7J

A+G = B+H+I
G = (H+D)+H+I-(C+G)
2G = 2H+(H+J)+I-(G+E)
3G = 3H+J+I-(G+I)
4G = 3H+J
4G = 3(I+J)+J
4G = 3I+4J
G = (3I+4J)/4

5((3I+4J)/4) = 3I+7J
(15/4)I+5J = 3I+7J
(15/4)I-3I = 2J
(3/4)I = 2J

If J = 1 -> I = 1.5
-> H = 2.5
D = 3.5
B = 6
F = 4.5

A+C = 14.5
A+G = 10

C-G=4.5
E = 4.5
G = 3
C= 7.5
A = 7...

Shit.

Yep, definitely did it wrong

You and I so often seem to take the exact same approach. The difference seems to be that when I find that it isn't exactly true, I look at different means of tackling the problem. That relates to why your answers to the Blued problem and the Master's logician meeting puzzle are not valid .. you ignore the possibility of alternative methods while the puzzles forbid any.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

James S Saint wrote:...on the right thread...

No more appropriate thread exists. There are many, many threads discussing many, many fallacies that I'm not invoking in my solution to the Blue Eyes problem. I'm not going to go into any of them and explain how that particular logical fallacy doesn't apply to my solution to the Blue Eyes problem.

James S Saint wrote:The difference seems to be that when I find that it isn't exactly true, I look at different means of tackling the problem. That relates to why your answers to the Blued problem and the Master's logician meeting puzzle are not valid...

And as with your approach to the Blue Eyes problem, you've yet to show your work.
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Carleas
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### Re: Math Fun

Carleas wrote:
James S Saint wrote:...on the right thread...

No more appropriate thread exists. There are many, many threads discussing many, many fallacies that I'm not invoking in my solution to the Blue Eyes problem. I'm not going to go into any of them and explain how that particular logical fallacy doesn't apply to my solution to the Blue Eyes problem.

Your continued evasion merely proves my point.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

Carleas wrote:Yep, definitely did it wrong

OK, found the a problem:
A = C+G
B = H+D
B = I+F
C = G+E
D = H+J
E = G+I
F = J+D
H = I+J
A+B = C+E+F
A+C = B+H+I+F
A+C = B+H+J+F and/or
A+C = B+H+I+E
A+G = B+H+I

I'll have to power through solving for something in terms of J later.
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Carleas
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### Re: Math Fun

Arminius wrote:Here you can see a large rectangle, consisting of 10 squares:

10 Squares Puzzle.png (1.91 KiB) Viewed 4901 times

How big are the sides of each square at least, if they are all different in size and integer (thus: in whole numbers)?

Carleas???
10 Squares Puzzle Solution.png.png (3.79 KiB) Viewed 4901 times
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

Interesting, a little mind bending, and certainly difficult to express. Here is an attempt:

The circles are rotating at different speeds, and slower than the wheel. If there we more tick marks on the two circles and on the lines they are 'riding', it would be clear that the surface of the circle is moving slower than the string as they pass. That 'slippage' accounts for the difference in apparent circumference (the length of the string) and actual circumference.
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Carleas
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### Re: Math Fun

Carleas wrote:Interesting, a little mind bending, and certainly difficult to express. Here is an attempt:

The circles are rotating at different speeds, and slower than the wheel. If there we more tick marks on the two circles and on the lines they are 'riding', it would be clear that the surface of the circle is moving slower than the string as they pass. That 'slippage' accounts for the difference in apparent circumference (the length of the string) and actual circumference.

Yep.

Now try to explain where the energy is coming from in this:

And this:
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

First one
I think here the magnet acts as a fuel source, a source of stored energy and it will gradually lose effectiveness as the polarity of its atoms moves out alignment over time.
After writing that, I looked it up, and it is wrong...

OK, second guess: the potential energy from moving the ball away from the magnet is released as the ball moves towards the magnet.

Second one
Here, I'm pretty sure the initial twist of the spring is what's driving the spinning, and that that energy will gradually be lost as heat.
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Carleas
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Location: Washington DC, USA

### Re: Math Fun

Carleas wrote:First one
I think here the magnet acts as a fuel source, a source of stored energy and it will gradually lose effectiveness as the polarity of its atoms moves out alignment over time.
After writing that, I looked it up, and it is wrong...

OK, second guess: the potential energy from moving the ball away from the magnet is released as the ball moves towards the magnet.

Second one
Here, I'm pretty sure the initial twist of the spring is what's driving the spinning, and that that energy will gradually be lost as heat.

I think that you missed on both counts:
1) The ball doesn't move toward the magnet.
2) Note that for every turn of one end of the spring, the opposite end gets exactly one turn. The amount of twist in the spring must remain constant.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

In both, there is a subtle periodicity, i.e. they aren't in smooth motion, but are slightly jerky. In the spring example, that means that the torsion moves through the system like a wave, so that one part twists a bit, then the next, then the next, so that the twist is actually travelling around the system in a loop. It seems the wooden handles act something like a diode, making it so that the twist can only 'flow' in one direction.

In the magnet/ball example, the ball rocks back and forth, drawn toward the magnet, and then moves backwards by the spinning wheel. The motion is started when the magnet is pulled away from the ball, so that the magnetic force decreases slightly and the ball falls, starting the wheel spinning. The ball then rolls, which spins the wheel. The wheel itself speeds up and slows down; as it spins faster, the ball is moved farther from the magnet and the magnetic force on the ball decreases, slowing the wheel and increasing the force.

So the ball is moving towards the magnet -- and then away, and then towards, and then away...
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Carleas
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### Re: Math Fun

Carleas wrote:
In both, there is a subtle periodicity, i.e. they aren't in smooth motion, but are slightly jerky. In the spring example, that means that the torsion moves through the system like a wave, so that one part twists a bit, then the next, then the next, so that the twist is actually travelling around the system in a loop. It seems the wooden handles act something like a diode, making it so that the twist can only 'flow' in one direction.

Why do we care about the jerky motion?
a) The delay of propagation through the spring seems irrelevant to the issue.

b) The system isn't friction free

c) The system has two "null points" where the torsion advantage goes away. The null points could be removed simply by having two systems crossed over to each other and 90 degrees out of phase. The end result should be much smoother as each system forced the other passed its null points.

d) The direction is determined by the pre-twists in the spring. There is no need for a rectifier/diode.

The real issue would seem to be that regardless of how long it might take, for every turn of the primary torsion arm, the secondary torsion arm turns exactly once. That means that if the spring had 10 pre-twists in it at the beginning, a thousand turns later, there would still be 10 twists. 10 twists represents a torsion that is always present (not counting the time it might take to propagate the twists from one end to the other of the spring).

In the magnet/ball example, the ball rocks back and forth, drawn toward the magnet, and then moves backwards by the spinning wheel. The motion is started when the magnet is pulled away from the ball, so that the magnetic force decreases slightly and the ball falls, starting the wheel spinning. The ball then rolls, which spins the wheel. The wheel itself speeds up and slows down; as it spins faster, the ball is moved farther from the magnet and the magnetic force on the ball decreases, slowing the wheel and increasing the force.

So the ball is moving towards the magnet -- and then away, and then towards, and then away...

Again, that would appear to be no more than friction being un-smoothly overcome. In the long run, the ball doesn't get closer nor further from the magnet. So what is turning the wheel?

What impressed me about this video is that the wheel sped up faster and faster on its own. Why would it then slow down later?

I have been trying to find a video they had posted a while back that showed this same effect without using a magnet, but rather merely a well mounted ball. But I can't find that one. It was a little similar to this bike, except with only one wheel:

Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

Ooo! I've been had! Treachery!! Fool me a half dozen times, shame on me

Nice tricks though, clever setup. The one with the spring seems to have a motor in the frame, it looks like hits a switch with his right hand just as it starts spinning. I can't figure out the other one, but I'm thinking it has something to do with the silver block used to hold the magnet.

The magnet car was a bridge too far, I knew that one was no good.

Thanks for making me providing me the opportunity to look like an asshat, James.
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Carleas
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Location: Washington DC, USA

### Re: Math Fun

Nonono... you are selling yourself short. These are from VEProjects. They don't use tricks. They merely don't tell you everything so that you can figure it out. There are no hidden motors involved
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

Spoiler:
The question proposed in the video asks if the torque at the servo spindle (right side) is greater than it is at the generator spindle (left side). The equation for the torque at the servo is:

t{g} = F * cos((π/2 – A) * sin(g)) * √¯((cos(g) * R / sin(A))² + (R * sin(g))²)

wherein;
g is the rotation angle of the generator spindle from top position,
F is the force applied by the generator spindle,
R is the length of the generator spindle radial arm, and
A is the angle of the servo spindle from horizontal upward.

With that, you should be able to answer half of the puzzle question: "Where is the energy coming from?"
.. although always check my math .. it is just an estimate.

Edited
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

As it seems that no one is going to get this one:

The first spindle, A, has a torque advantage while it is positioned at the top and at the bottom of the spin circle. But at each side, the torque advantage becomes negative, a disadvantage. By integrating the proper formula for the torque advantage, one can see that the total advantage summed around the entire circle is zero = no advantage.

The question was, "from where does the energy come?" Obviously it has something to do with the twisted spring, but interestingly, the spring always has the same number of twists, implying that it isn't giving up the energy within the twists. No matter how many times the spindles rotate, there will always be the same number of twists in the spring.

The answer for this one is actually similar to that for a pendulum swing, except with a pendulum swing the arm never actually return to the same position it started. But the pendulum begins to swing because the initial position is one of higher potential energy. The pendulum must start at the top of the swing. Similarly, the spindles must start at the top of the rotation circle where spindle A has temporary advantage.

Because of the temporary advantage, Spindle A forces a rotation to begin and the length of the spring prevents the motion of spindle B from directly countering spindle A. For a brief moment, the B end of the coil spring is more tightly wound than the A end. And by the time that greater tightness catches up to the A end, spindle A is no longer at the top where it had advantage but rather at the first side (3 o'clock) being slowed down by its new disadvantage. So the extra boost from the B end of the spring as a momentary pulse helps spindle A to get around the negative arc. The initial advantage of A gets passed through the spring back for A to use during its disadvantage arc period. And at that point end B is back to the same amount of twist with which it began.

During the lower portion of the rotation, the same thing is occurring. Spindle A has an advantage which it uses to put extra twist back into the B end of the spring which propagates around to help A out during its next upcoming negative arc (at 9 o'clock). Do the math.

So does it continue forever? No. There is friction using up the initial potential energy and eventually the spindles stop turning during one of the negative arc periods (3 or 9 o'clock) even though there is still the same number of twists in the spring as in the beginning.

So the answer as to where the energy came from is that it is "momentum pulse energy" provided by the system beginning at a high potential energy state, just like a pendulum swing starting from the raised pendulum position. And the number of twists in the spring is analogous to the gravity field of the pendulum.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

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James S Saint
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### Re: Math Fun

This is the video that convinced me that these videos are clever tricks and can't be taken at face value.

Look in the upper left at the shadow changing, indicating some movement off camera. Then at 1:05, a wand of some kind comes into the top of the video above the spinning disk. That suggests that what's really going on is that someone is moving a wand above the disk to generate the motion, perhaps using a focused stream of air, or a fine thread attached to the disk.

After this, their credibility is shot. Looking at their other videos, none would be impossible to fake, and many have what look like tells in light of the skepticism this video engenders.
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Carleas
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### Re: Math Fun

Carleas wrote:
This is the video that convinced me that these videos are clever tricks and can't be taken at face value.

Look in the upper left at the shadow changing, indicating some movement off camera. Then at 1:05, a wand of some kind comes into the top of the video above the spinning disk. That suggests that what's really going on is that someone is moving a wand above the disk to generate the motion, perhaps using a focused stream of air, or a fine thread attached to the disk.

After this, their credibility is shot. Looking at their other videos, none would be impossible to fake, and many have what look like tells in light of the skepticism this video engenders.

Did you not understand my prior explanation?

This contraption is basically the same as the pendulum as well. He has to get the device in motion (the initial energy), in order for it to run. The mechanics are then balanced enough such as to allow that initial energy to keep flowing until the tiny bit of friction eventually uses it up.

It's no big deal, no trick. You are looking for the ghost in the machine, like the American Indians fearing the magic spirit pushing the rail train. The magic isn't there and they do not claim that it is. These are merely physical science puzzles made complicated by clever people trying to challenge perpetual motion .. and getting close. It is just fun physics games.

There are a great many "almost perpetual" mechanisms that rely on either getting the device in motion, leaving it with momentum to drive it for a while, or starting the device at a high energy potential point in a cycle such that it will start off gaining momentum until another part of the cycle. In this video, the cycle doesn't change from high potential to low or negative, so he has to push it in order to get it started.

Don't let your paranoia trick you into seeing ghosts or magicians that aren't there.

There is different i]category [/i]of mechanism that truly emulates perpetual motion because it absorbs energy from the surrounding air or fields. You are not seeing any of those kind from these people. But those are not breaking the conservation of energy laws either. They merely accentuate an inherent imbalance in potential energy. It is the "Second Law of Thermodynamics" that can be, and often is, broken. The "First Law of Thermodynamics", the conservation law, is never truly broken although it can be made to appear to be, and effectively be, broken.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

(Based on a true story)

Suppose you have an uninsulated hardwood floor that acts as a uniform heat sink for the room. You also have a blanket with an area $$A$$ equal to the area of the floor. Will you keep the room warmer by laying the blanket flat across the whole floor, or folding it to double thickness and putting it across half the floor?

I have an intuition, but I don't know the right answer; I'm more interested how people reason about this. Will post my thoughts when I have a minute tomorrow.
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Carleas
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Location: Washington DC, USA

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