Robinhood46 wrote:That gives me another idea Agor.
The one weight falling a quarter and the leepfrogging of the weights (or whatever it was leepfrogging).
John believes the number 5 to be very important too.
How about 5 weights or multiples thereof, with one weight leepfrogging the other 4 and causing them to lift on the way? Each taking it turns to do the leepfrogging.
I also thought
"jumping" = "leap frogging" - perhaps hinting at 'snakes and ladders' of sorts.
I am most certain however than the significance of the number 5 is that 'five quarters' equals 125% of unity.
Three quarters, OTOH - per the 'AP wheel' - represent 75%; on the one hand, a loss, but also the efficiency of each individual 'quarter' (they're momentum yields, basically).
One such momentum yield is 25% efficient, wasting 75% of input energy.
Two in succession (again, each losing 75%) gives
50% net efficiency, dissipating the other half.
Three consecutive helpings of these individually-75% lossy momentum gains brings us to a net efficiency of 75%.. so, a nice symmetry exists here..
A fourth serving brings us to unity. That is, four successive 75%-inefficient accelerate-and-collide cycles produces
mechanical unity, where system KE = input PE. This however ignores the dissipated losses, by which we're now comfortably OU..
Still, a
fifth, identical, 75% inefficient asymmetric inertial interaction brings us up to 125% of mechanical unity.
So where the AP wheel represents an interesting (if perhaps slightly ominous) nexus of
key,
functional, loss ratios, the five cycles of asymmetric CW / CCW torques displayed on the Toys page directly mathematically accumulate to an I/O efficiency of 125%.
So these 'quarters' fall out of a mathematically-idealised system; effectively, 'elements' of a minimally-complex system: a
reductive symbolism, as employed by Carl Sagan in designing the Pioneer plaque - the key issue being how to communicate in a trans-cultural, universal syntax? Bessler resigned his IP, along with any chance of eventual exoneration, truly,
to posterity.. evidently having little faith in the prospects for those in his own timeline, or even their cultural descendants.. looking ahead to
anyone, of
any tongue, of
discerning mind only.. Sagan's 'elements' were things like hydrogen's wavelength, C, and binary, from which he constructed basic 3D maps and scales showing Sol's position and human forms etc., while Bessler's were,
inevitably, these fixed-price momentum yields, that effectively decoupled the PE:KE cost / benefit ratio.
Again, because a single reactionless acceleration at
any ambient speed could instantly swing up a nice GPE gain, yet Bessler is instead plainly framing an interaction that is
optimally and
elementarily-efficient
only when involving either 1:1 or 3:1 inertia ratios and inevitably, collisions between mutual accelerations (ie. 'closed-loop inertial interactions', asymmetric or otherwise), we can safely assume he wasn't able to crack asymmetric accelerations either, and instead, is painting this interaction involving discrete accelerations, collisions, and a 25% per-cycle efficiency accumulator on the KE value of the rising angular momentum relative to its cost of production, a la 'quarters'.
It's one big jigsaw, but the pieces are beginning to fit..
Here's another swerve-ball for yuz:
• what if the initial "one pound" is
also one of the "four" that jump four quarters?
IOW it performs an action that acts upon itself, in concert with another
three masses..
Note he only explicitly tells us about
four masses - never expressly intimating that the initial 'one' is actually
a fifth.. merely an assumption we project..?
Because, then, you know, we'd be looking at an inertial interaction in a 3:1 ratio..
..and you all know how the maths pan out by now - you just add the inertia ratio, so, 3 + 1 = 4, to get the 'unity threshold' - the no. of elapsed cycles at which the KE = PE, provided no one's counting losses, in which case we
technically have mechanical unity but with free heat from nowhere, tho we can only guess if Bessler was aware of this.. Point is tho that a 3:1 inertia ratio would indeed furnish the 25% p-c efficiency accumulator,
matching the Toys page interaction cycle..
If a 'cross piece' is one complete minimal mechanism, comprising four masses, and one of these undergoes a normal, reactive, acceleration, which is then arrested with an
asymmetric deceleration against the combined inertia of the other three in an inelastic collision, then we waste 75% of input PE in the collision, and retain the other 25% as KE. That's the first rung on the Toys page ladder.. do the maths, you get 50% on the 2nd cycle, then 75% on the 3rd, unity at the 4th, 125% at the fifth, 150% at the 6th, 175% @ the 7th, 200% @ the 8th etc. etc.
So, maybe there's only four pounds / masses
in total - the 'four'
including the 'one', rather than the
ostensible 'four
plus one'.
It's a
physics problem, as much as a semantics game..
