Cognition Systems and the Model 'F2'

This page under construction.  

Part I: Conceiving the Spiral Wave

Here is some of the work that went into the construction of the 'F2'. The first thing to do was to understand how life exists on this planet. Considering it in hierarchal form:

There is a designation, although arbitrary, of the high, low and elemental minds. Assuming without prejudice that all life has some form of cognition, I was able to generate the above figure. Having a concept of life systems, I was ready to review Tesla's patents and try to duplicate his work in a succinct format.

First off, here are the patents I used to understand the genius of Tesla's designs:

Here is patent #723188 of 1903. It is an extension of #645576 of 1897.

From reading Tesla's writing within the patents and work with the Model 'F', I came to realize the propagation of the wave and its ability to transmit energy was directly dependent upon the container in which the wave was to be utilized, and not a function of the windings. How was the energy to be utilized? Using the I-Cybie constraints, I had already designed a card:

In terms of the Tesla patent, my system would appear:

At the bottom of the figure is the deployment of the card within the I-Cybie container.

There had to be a way to use components I had already constructed in the new model. I had to devise a methodology, or a characteristic equation template, to describe and predict the effects of using the card in the composite transmission system. The first step is to look at the container in which the card is to be inserted. Since, for the purposes of this early analysis, the value of integers in the equation is irrelevant—I am merely trying to generate the equation and proper values can be inserted later. If the space within i-Cybie is 4cm x 2cm x 3cm, I can devise a simple equation to describe the geometry:

(1.1)

Where:

Solving this equation the value is 24cm3. We need to calculate the number of non-redundant slices in the container. For this we use the following formula:

(1.2)

Solving (1.2):

There are 98 non-redundant two-dimensional surfaces in the structure. The next step is to alter (1.1) and multiply the solution by the potential in the following form:

(1.3)

Where rho is measured in volts and psi is the dimensional value cm2 which for the purposes here, is 1. When solving the equation with rho = 6V and inserting the proper values of Xs, Ys, and Zs, it is discovered that the answer is:

How did we come to the solution? The waves contacting the surface interact with the container in two-dimensional planes. The first step is to understand the container, which is a cube, as a series of slices of the cube in two dimensions. The next figure is a composite drawing of the container surface:

(Fig 1)

Each of the cubes represents 1cm3. Each of the hued surfaces, or slices, represents 1cm2.

The issue in this analysis is to discern how the slices interact within the composite system; that is, as a function of the incoming transmission planes along each corresponding axis x, y, and z. Conceptually, the best way to visualize this composite system is to see the waves in the following fashion:

(Fig 2)

Figure 2 is a conceptual picture of the planar wave in the wireless power system. The left side of the figure shows the incoming transmission waves, the right side shows the components of the plane. In physical electrical wave terms, the magnitude width represents the M vector, the direction length, the E vector, and the amplitude width represents the H vector. However, I will only be discussing the magnitude width and the direction length. At the present time, while delineating the receiving system container (Fig 1), for purposes of simplicity and understanding what types of equations are necessary, two dimensions will be considered. Amplitude width will be covered later.

The next step is to consider how the planar waves would interact with the container structure. In order to accomplish this, we must break down the container structure into a series of slices:

(Fig 3)

Each of the slices in Fig 3 is organized by their orientation to the planar axes. For example, slices oriented along the x axis would absorb energy from the planar wave traveling along the x-direction. The slices are from the top, middle, and bottom of the cubic structure. Slices oriented along the y and z axes would absorb energy from the planar wave traveling along the y and z-directions. The slices are shown accordingly.

The solved quantity in 1.3 is only valid on a fixed point. A dynamic representation is required to explore how it functions within the active transmission environment. It should appear as 1.4:

(1.4)

The next step is to think of the slices as matrix quantities to understand how each functions individually and to construct a proper computer model. We want to consider:

Where each of the matrix quantities—1,0;0,1—are normalization values for the purpose of constructing the equations. Actual values will be interpolated later.

Part II: Understanding the Spiral Wave

In the first section, I covered the conceptual framework for perceiving a spiral wave. It is best when initially thinking of these types of waves to see them as planes. In terms of the actual wave, they travel in planes but their geometry is quite different. Let's begin this discussion by breaking Equation 1.4 into parts and integrating each individually:

We use indefinite integral since the range only provides a finite value within it. We are more interested in the behavior of the integrals. Notice also, we have removed the multiplicative quantity rho/psi, it will be of relevance once the new equation has been generated and the plots understood. Using Maple, we want to see what form the integrands take. For a, b, and c:

As expected, each is a parabola. Since we have parabolas, we can try to visualize the system of equations on a polar grid. Beginning in two-dimensions, the equation is written in Maple notation:

> plot([18*x^2,16*x^2,x=0..2*Pi],-100..100,-100..100, coords=polar);

Which generates the plot:

Which is a spiral not unlike the windings of the transmitting array. This indicates that the equations might be on the right track to properly defining the physical system. We want to reassemble the split equation and add the integrals. Next we can expand the plot into three-dimensions. For the function called “implicitplot”, we employ the new integrands with the solution found in (1.4) and using a stimulus value, rho/phi, of 6 volts. Using the following Maple code:

> implicitplot3d(18*x^2+16*y^2+15*z^2=588,x=-10..10,y=-10..10,z=-10..10,coords=cylindrical);

we can generate the following plot:

The above figure is a good picture of how the composite waveform will appear. Inputting different stimulus quantities at the different values in the next figure show the behavior of the wave and demonstrate the amplitude of the general form. The figure compares the values at the lower, mid and upper limit:

Part III: Applying the Spiral Wave

The goal of this paper is to utilize the hypothesis explored and to present a method where it can be exported into a usable technology, specifically, powering a mobile robot. I have decided to use an off-the-shelf robot toy called i-Cybie made by SilverLit Electronics. The advantage of using this is 1) availability of cheap parts, 2) ease of disassembly and refitting, and 3) access to a large open-source group who write software and hardware upgrades regularly. I have personally worked with this robot for two years and am quite familiar with its programming and limitations. It has lent itself well to modification and retrofitting of previous wireless power experiments namely, the Model 'F'.

Computations presented in this paper so far have been in the pursuit of this goal. To this point, I have written the equations with in mind studying their behavior. At a later point, I was to return to the hypothesis and apply real values. The first thing to consider is the amount of potential the on-board i-Cybie system requires for its operation. The original robot comes with a 800mAh Ni-Cd battery pack mounted in the belly of the robot. At a potential of 14.438 volts at 210mA, the device consumes 3.032W of power.

The system is constrained by the size of the compartment. To use the wireless system to power the device, it must fit into the compartment, else the robot will not be able to function unobstructed. The dimensions of the inner compartment, standard battery pack, and Model 'F' receiver card are:

Compartment (A): 10.20cm x 6.80cm x 1.80cm
Battery Pack (B): 9.80cm x 7.10cm x 1.70cm
'F' Receiver Card (C): 10.10cm x 6.80cm x 1.70cm

The total area of each are: A—124.848cm3, B—118.286cm3, C—116.756cm3. The number of most value to continue calculations is A, since we are interested in the container space and not necessarily with the components that occupy it. In order to calculate the number of slices, we first generate a graphic of what the structure looks like (in rounded cm for ease of modeling—l=10cm x h=7cm x w=2cm). From experience, rounding the shape doesn't effect the general equation greatly, but altering the scale to mm for accuracy reveals more of the quantum effects of the model which doesn't much help the task at hand—to understand the dynamics of the system and construct a physical model.

(Fig 4)

Consider this problem in terms of the first model, create a chart delineating each of the traveling planes:

(1.7)

With the visual from Figure 4, we can generate the values to calculate the container. Solving (1.7):

(1.8)

There are a total of 524cm2 slices in the container. Deploying (1.4) and the solved quantities:

Since in (1.4) phi is always 1, we can change the variable to show the potential of the stimulus signal rho(v) in volts. We need to construct a polynomial to plot the different solutions. First, showing the relationship:

Inserting the quantities from (1.8):

Reduces the equation into the polynomial:

(1.9)

We are most interested in the real case when the potential rho(v) is 15 volts, the polynomial takes the form:

This is the characteristic equation. Plotting with the following Maple code:

> implicitplot3d(80*x^2+105*y^2+77*z^2=7680,x=-10..10,y=-10..10,z=-10..10,coords=cylindrical);

the plot is generated as:

Which is identical to the model we constructed.

Part IV: The Function of the Limit

In the previous section, I successfully demonstrated the mathematics behind the Model 'F' Wireless Power Transmitter. This section will discuss the function of the limit in the characteristic equation. In the last plot, the composite form of power transmission can be seen in its geometric form. Notice though, how the shape is altered by a change in limit. First, the lower limit:

Next, the upper limit:

The limit is the range in the characteristic equation (1.9) in each direction x, y, and z, it is that which provides the computational values to transform each into a vector. The general form has the limit inscribed between -10 and 10. By dividing the limit between -10 and 0, 0 and 10, we can see the symmetry of the form. One of the conceptions I have devised to describe the spiral wave, during the Model 'F' tests, was to think of the traveling wave in two parts—one half generated by the spiral windings of Tx the other half by the spiral windings of Rx. Here are two plots that have been rotated to show the tuned halves. To the left is the upper limit; to the right, the lower limit:

Each half was a piece of a tuned pair which created a conduit whereby power could travel through it and information could be transported on the carrier surface. The value of changing the limit is to understand the convergence point of the waveform, that it is a product of two tuned spiral halves which construct an epicenter and generate the composite form in the container structure accordingly. Experiments with the Maple code show that the form only tangibly exists within the -10 to 10 range. Expanding the lower limit to -15 shows the same form, but it is still constrained in the defined range.

This shows that the shape is quasi-linear possessing properties linear enough to make the concept valid to generate consumable power for the mobile robot. This also suggests that the waves travel in packets of quantized energy which in the future will provide interesting quantum insights.

What the form is still remains a mystery. There is a thought that there is an opposing force present in the core, something that has the same properties of the normal form, that allows the outer shell to be manifest. The property of mass is the same but charge or spin differ. This suggests that there might be positrons present in the system. From experiments in August 1999 and April 2004, I discovered large discrepancies when comparing input power to output power. It seemed the behavior of the wave packets are stronger as an output form than the sum of their inputs when thinking in conventional electrical terms. Perhaps these packets are stable in their spin when they are first transmitted, but after an indeterminate time the spin starts to decay and the positrons react with electrons present in the environment causing the release of energy. One major question I had was how can a small-scale 5 volt pulsed input into a coil no larger than 4cm cause large-scale severe weather phenomenon over a distance of 40km? For a long time, I believed my equations were in error but seeing I can repeat the scenario as much as I desire, it maybe lend credence to these thoughts.

One of the more interesting thoughts is that this form is somehow alive, or the spark to make something alive in the cognitive sense of the word. I suspect that when this form is introduced into the Boagaphish Compiler, it will give the software the dynamics to make it function.

All materials copyright and remain the intellectual property of C.A. Tucker 2011