Math Fun

Just do it.

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.

This problem is pretty tedious, I think I must be doing it wrong.
[tab]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.[/tab]
Yep, definitely did it wrong :stuck_out_tongue:

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.

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.

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.

And as with your approach to the Blue Eyes problem, you’ve yet to show your work.

Your continued evasion merely proves my point.

OK, found the a problem:
[tab]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.[/tab]

Carleas???
[tab]10 Squares Puzzle Solution.png.png[/tab]

A fun paradox for you:

[youtube]http://www.youtube.com/watch?v=mW-0bZwoGwQ[/youtube]

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

[tab]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.[/tab]

Yep. =D>

Now try to explain where the energy is coming from in this:
[youtube]http://www.youtube.com/watch?v=m8-Kek8Halc[/youtube]

And this:
[youtube]http://www.youtube.com/watch?v=_HV9YWmGf8g[/youtube]

First one
[tab]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… :blush:

:-k

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

Second one
[tab]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.[/tab]

I think that you missed on both counts:
[tab]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.[/tab]

[tab]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…[/tab]

[tab]Ooo! I’ve been had! Treachery!! Fool me a half dozen times, shame on me #-o

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. =D>[/tab]

[tab]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[/tab]

[youtube]http://www.youtube.com/watch?v=_HV9YWmGf8g[/youtube]
Spoiler:
[tab]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. :sunglasses:

Edited[/tab]

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.

[youtube]http://www.youtube.com/watch?v=nVSM__R1bqs[/youtube]
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.