Answering Imhotep (AI) Trisect the pyramid

STEPS

1. Extend the edges of the angle to some large length and inscribe a circle around the intersect with the compass.
2. Ruler: Secant line across top intersect with circle
3. Ruler: Secant line across bottom intersect
4. Compass: circle around left top, length of chord
5. Compass: circle around right top, length of chord
6. Ruler: line from left circle intersect down to ∞
7. Ruler: line from right circle intersect down to ∞
8. More things are possible, but this is one way

Here is a step wise trisect done legally according to the international rules of geometrics. It is quite odd as I discovered two new ways to trisect while playing with this. I suspect there are many ways. There are many solutions to the Pythagorean Theorem geometrically and I have devised one myself. From this point in this method there are many ways to continue, and they allow any integer or integer fraction of splitting. This is about as much time as I intend to spend on this topic as it is getting boring. I see no application and though it may be of some value to somebody, there are better things to do. It was fun doing it in Inkscape, then gimp and creating the animated gif, but the fun is gone and I won't return to this subject unless somebody pays me to be bored to tears.

I found more entertainment in this, I decided I could make an angle trisection machine. I doubt I will actually make one, but I can see the design in my head and it has a grooved circle with a scissors in the middle and the second scissor is connected to the lower chord and free at the top where it would ride along the extended top chord. It seems that the lower scissor would have a rotating section that was radius in length. I am fairly sure it would work, but things don't always work out like they are planned, but this has so few moving parts I would guess that it would work. I see that somebody got a lot of attention for a trisect origami.

Strange ways under space

Many new techniques are available for representing, managing and expressing relationships. The tikZ extension for \LaTeX is very interesting and new features of Inkscape are also useful. The combination of open source tools is advancing very rapidly. I have found them useful in expressing and understanding the complex interaction of space and energy. I have a fairly good idea of the nature of dark matter and where it originates and how it acts upon the universe. It is certainly one of those aspects for which there is no common tool or technique to measure and as such it would be virtually invisible and exists only by its disturbance of other measure. This implies the means to measure , even if only in some gross way. The coherence of information does imply some new relationships.

The understanding I now have of dark matter implies a "chemistry" which is more complex and convolved than the simple interaction of atomic bonding. Yet it does have pattern and perhaps can be placed in a type of periodic table.

Topology and reality

Topology stems from logical concepts and as such is disjoint in its origins to physicality. I have been looking at topology from its origin to its application and it suffers from the same problems that all logical concepts share. A mathematical system is founded in base principles and extended to be consistent. This does not mean it is consistent with reality, but only with its own rules. If I consider the Betti number of a graph it has a logical meaning in the number of cuts and holes, but where is the association to the physical world? Math is meant to model something and it can actually model nothing as a result. A system of scratches extended to a science suffers from the same problem that I always encounter. It assumes that there is something that exists that is ONE. The problem is that there is no such physical thing that exists in the universe. Everything is infinite in its effect.So, to separate some point as being object and effect it creates a paradoxical system.
It seems that topology has two intersects with the physical universe and each has different physical rules. If I were considering the nucleus of the atom, a black hole or field interaction it would be modeled one way, and if I am dealing with sets of particles or systems it operates another. The interaction of the infinities is different than the principles established. I personally do not see how everyone is enamored with a system that was created by a people who had no clue as to the nature and complexity of the universe. When the universe was considered a mixture of Air Earth Fire and Water, could you really assume that they have some perfect insight into a system that underlies all description of matter?
There is no doubt that mathematics has utility in its current form, but it is not the model that best fits the physical world.
I am taking topology apart, step by step and labeling those principles that relate to a purely logical operation and those that can be connected to physicality in some way. It is a very useful science and there are many things that remain true even in the physical world, so long as one realizes the limits of application. The numbers aren't magical and never have been. Euler was a very intelligent person by all accounts and there is no doubt that his skill with numbers was legendary. This does not mean it correlates to physical reality.
In the field of network topology there are many different methods that I use to graph, analyze, and understand its properties. This is another case where the rules do not always follow from one situation to another. The science of numbers is incomplete and perhaps it will always be that, but that is the sad fact about knowing, it is never complete.
In order to understand better it is necessary to make the problem more complex. I have set about reordering the rules of topology so that they can be consistent with the different applications and I hope I can devise rule sets that let me know which applications correlate to which rule sets. When it comes to the topology of higher spaces, that is where the greatest gain is achieved. The application of existing topology rules are not consistent enough to say for certain that X is the measure of Y and is then testable.
The entire system is more complex than the measure applied and that is obvious. In the lab when I am compounding some chemical, I can say at each step what I will have as a product and how that is determined. If I were to just mix chemicals at random and have no idea of which ensues then it would be similar to nuclear physics as it exists. It is as close to alchemy as one can get in the 21st century. The measure and characterization of the parts is obviously incomplete and as such it becomes a matter of adding 2 drams of animal tincture and hoping for the best. It doesn't have to be that way. The energy is there and the system is consistent. There universe never fails to calculate the proper direction that a planet will take in its orbit and that is the assumption, that the universe is a perfect calculator. Whether that is completely true in all circumstances is the subject of many opinions.
In the same way that chemistry required an under structure that was at least complete, nuclear physics requires that model that exists under the complexity. It requires that the methods be clean and appropriate to the system. As I said, topology is not a single coherent concept, but has more complex structure to model different aspects of the universe.
I don't think that science is anywhere near complete and consistent. It is no different than when Newton or Euler walked the Earth, each new understanding allows a closer approach to the complexity. It was not until the time of Rutherford in 1911 that the existence of the nucleus of the atom was measured in gross terms. That is less than 100 years ago. It is almost like a dark age in comparison, horse drawn carriages and telegraph. To assume that the present is the height of science is absurd. It has always been that way. In 1900 it was assumed that all secrets of science would be known in their lifetimes. In the 60's it was penicillin that would cure all disease, and now it is different projections and AI will exceed human intellect by 1980, oops, a little late, but maybe this year is the year of the AI desktop.
I discovered an interesting relationship between topology, matrices, calculus, and numbers. If this had been observed in ancient times, calculus would be several thousand years older. Oh well, it is cosmic soup and so I will add another dram of topology tincture and see if this cures my confusion.

Why sqrt 2 in the eigen

I am redoing some matrices that deal with interactive relationships and this can relate to anything, even Haar-like stuff, springs, heat flows, material stress, current or any linear process relationship. What I wanted to understand is why 2-sqrt(2), 2, and 2+(sqrt(2) [ 2-√2,2,2+√2] show up as terms in the eigen values. The trace or 2+2+2 = their sum and this is correct and the det(K) is properly computed. Perhaps I am looking too deep into this. I know there is a deeper relationship, but it has eluded me throughout the matrix analysis study and this is why I am going over it again with all the possible variations of its application. It has to do with dimensionality itself and perhaps I am just not able to grasp it as it is too complex for my mind. I had hoped that some really simple examples would make it easier to see.

I am glad that octave has A'=transpose(A) because that would be a real pain to type every time it was used. I almost thought that √2 was π and that has happened to me before and I thought I found some deep relationship to trigonometric relationships and it is just way too easy to (dyslexia)' 3.14 to 3.414 when I am thinking about something else.

Gravity methods

The gravity management would require too much energy to implement for space , however it does lead to gravidar, which I am assuming has no way to be shielded from or deflected. I do believe that radar was kept secret for quite some time as it was not known how it worked. I am guessing this is the case here. Since there is no coherent theory of gravity and no means to even detect the largest of effects, it will remain unknown for some time.

I installed sage from source to get the latest version and deal with some problems with differential equations. It is a 4 hour build, but worth it. It has improved since the last time I used it.

As far as gravity, it seems that it would be much much easier than any neutrino communication and could be implemented very simply. It would allow an entire new band of unregulated communication that is probably far less problematic than radio waves and would not be susceptible to interference by solar flares, EMP or other electronic effects.

I do not post comments that serve as links to companies. Just sayin'

It seems that there is a better method to deal with and identify eigenvectors of a system. It is an interesting aspect of vectors and has taken some time to appreciate the full value. Markov chains is another very useful method.

Mixing math methods

Further refinement of the idea of transporting equations to action, surfaces and demonstrations in blender.

Blender allows python scripts to be transported with the blend file and can produce movies with sound and animation. It is the perfect vehicle for carrying function with data.

The simplest space

The file is a k3d surface file and the image is with conditional boundaries spaces and with surface normals. The file extension is k3ds. I have been working at resolving the sqrt(-1) as it is extended into all mathematics. There is a different perspective to all this that is less contradictory, and allows an easy progression to higher space, but it is like learning math from the ground up in a new way. It doesn't bother me as I switch from language to language all the time in programming and on the net. Sadly, this is the simplest common denominator that I can create and even this is not the whole picture. I have started doing Python in blender to allow things that are only available in other packages like numpy and even gimp or inkscape. The image is of some related surfaces that also have connectivity between them and so this is another dimension and this is just the relationship of three dimensions. I can select surfaces in the 3D space and use them in blender to analyze and comprehend the complex functional space of a signal, gravity, or system.

Name:motey
/* 
Author: motey 
*/
F():(x/y)*(x+y)+
(y/x)*(x+y)+
(x+z)*(x/z)+
(z/x)*(x+z)+
(z/y)*(z+y)+
(y/z)*(y+z)-
15*(cos(x)+
cos(y)+
cos(z))

[x]: -pi , pi
[y]: -pi , pi
[z]: -pi , pi
Cnd: (x^2 + y^2 > 3.14) &
 ( x+y+z > -3.14)
;

When the matrices are included in this it becomes even more complex and this is the foundational relationship of numerical space or measured space and sets.

It is very complex and the rule sets are complex. I see no way to resolve it to anything less simple, in fact it must be 4 infinities more complex than this just to deal with common perception.

There is quite a bit of overlap in the packages, but it seems that Python is the common denominator which can integrate them all. Perl and CPAN is another, but Perl is a little trickier and somewhat obtuse. Python seems to be structured well enough to be understandable, though it lacks speed. This is where the libraries help.

I suppose I will use the blender template with python to integrate all of the math and graphics. It has 3space and time incorporated in the design and so is closer to the manipulation of S3 in S3 and T2 in T2, but that is as close as 3 infinities, but there seems no better way to deal with it or allow visualization.

G and c fall out as it is applied to charge space and so it gives a coherent expansion of the possibilities for matter from the lowest elements to the combinations of them.

An interesting correlation is the nature of information itself and that relationship to the DNA pair AT and also GC. I could say that a specific temperature that GC is boundary and AT is open and thus the combinations of ATⁿ are the information in the same way that 0s and 1s are the foundation of binary logic.

The TED talk by Michael Shermer is very entertaining and it is an interesting equation that deals with Type 1 and Type 2 errors when Type 2 is fatal. It is worth viewing. It does get to the heart of superstition. I would add that superstition and craziness can be a survival parameter in the same way that randomness can be applied to war games to get advantage. Just because some people are illogical and insane does not mean they are absolutely destined for a Darwin award, and in fact the crazy guy and his wife who hide in a cave could be the founder of a new race if there is a global calamity that makes them selected. It seems that there is an underlying survival mechanism that is explored in the "Mote in God's Eye" and that is the "Crazy Eddie" hypothesis. And the moties is the origin of the pseudonym motey that I often use.

This bodes well

A hole in a black hole, that does happen. As I said before, if two black holes collide, at the intersect tangent is a very odd effect where the "event horizon" is dissolved. As a result the inside becomes the outside for some period of time. This is true of any externally applied distortion. In the tangent space of the event horizon is another state that would exist for some time. So I am talking about time in time and so what is (m·L²/t²)·(t=time)²? The event horizon of a black hole would hardly be static and I suppose ( possibly incorrectly ) that the events at the horizon would be mirrored in its effect and are thus measurable in x-ray, and light. It seems there should be a transform that I could apply to x-ray data from the Milky Way galaxy x-ray survey to view half of the boundary. This is why data is so important and conclusions on data are merely an obfuscation.

 
set terminal svg enhanced size 875 1250 fname "Times" fsize 25 
set terminal postscript enhanced portrait dashed lw 1 "Helvetica" 14 
set output "bode.ps" 

G(w,n) = 0 * w * n + 100000 # 1 / (sqrt(1 + w**(2*n))) 
dB(x) = 0 + x + 100000 # 20 * log10(abs(x)) 
P(w) = w * 0 + 200 # -atan(w)*180/pi 

set grid 

set logscale x 10 
set logscale y 10 

set nokey #0.1,-25 

set style line 1 lt 1 lw 2 

set style line 3 lt 3 lw 1 
set style arrow 3 nohead ls 3 

set style line 4 lt 4 lw 1 

set style arrow 4 head filled size screen 0.02,15,45 ls 4 

set style line 2 lt 2 lw 1 
set style arrow 2 nohead ls 2 
set multiplot 

set size 1,0.5 
set origin 0,0.5 

set xrange [0.001:1000] 
set yrange [0.001:100] #set yrange [-50:150] 

set xtics 10 
set ytics 10 

set mxtics 10 
set mytics 10 

set ylabel "Gain" 
plot dB(G(x,1)) ls 1 title "1st-order response" 

set size 0.967,0.45 
set origin 0.033,0.05 
unset logscale y 

set yrange [-285:105] 

set ytics 45 
set mytics 3 

set xlabel "Frequency" 
plot P(x) ls 1 title "Phase response" 
unset multiplot

It works generally, but I think I have something wrong here.[SOLVED], decided to use matplotlib, scipy, numpy, numarray with python, which is often easier to apply.

octave math

It certainly is an extension to thought and expression. In the 1960's I used a slide rule and graph paper, created punch cards and ran a deck of cards against a computer as big as a house to model a spring. In microseconds seconds I can do that with GNU octave. I can do more in one day with my software, network of computers, and its link to the Internet than I could have done in 10 years. It is like being stupid at the speed of light.

It seems that it is possible to make something that extends that advantage again. I designed computer systems in the 1970's and wrote software to use them. It seems to me that from this vantage point it should be possible to multiply that 10,000:1 advantage. Parallelism and other methods of fabrication or scale is not the answer. It requires a turn in a new dimension and on to the nearest infinity. I can solve an equation that would have made a career and a book in the 1600's in a few nanoseconds. v-e+f=2 I use blender to convert and display millions of vertices, edges, and faces using matrix transforms done in a DRI interface to hardware. I have access to practically every library in the world. I wonder how Newton or Leibniz would have coped with that complexity.

octave:5> diary matrices.octave

octave:6> A=[1,2,8;2,1,3]
A =
   1   2   8
   2   1   3

octave:7> rref(A)
ans =
   1.00000   0.00000  -0.66667
   0.00000   1.00000   4.33333

octave:7> plot(A)

"dict anachronism"

  Anachronism \An*ach"ro*nism\, n. [Gr. 'anachronismo`s, fr.
     'anachroni`zein to refer to a wrong time, to confound times;
     'ana` + chro`nos time: cf. F. anachronisme.]                
     A misplacing or error in the order of time; an error in     
     chronology by which events are misplaced in regard to each  
     other, esp. one by which an event is placed too early;      
     falsification of chronological relation.                    
     [1913 Webster]                                              

It seems to me that if a structured interface were designed that emulated open source development , that it would be possible to establish a system that created that next leap. I am able to do many things and others are better than me and have a better grasp of their field of expertise. I spend a lot of time learning what many already know. It should be possible to establish an interface that allows me to apply my talent without duplication. I am sure that there are a few million people who understand matrix transforms and why would it be necessary to try and implement all in one. The Internet seems a chaotic implementation of that principle and what may be needed is simply a description of a framework and tools that integrates skill and need to a dimensional array of ability in such a way that it is self sustaining and extensible. That seems to be the correct approach at first glance. Looks like a design plan to me. I hope Skynet doesn't figure it out first.

I never read "The Moon is a Harsh Mistress", but there are some very interesting concepts there. I read the synopsis at Wikipedia and the premise is a reasonable enough scenario. Somehow between 1966 and now, the message has been lost. That was 44 years ago.

Eigenvectors infinite recursion

I was using the file below and I thought I would name it appropriately as "plot.m". At first glance that would seem to be okay. Internal to octave is the ability to run files as functions if they have the ".m" extension. Perhaps you see where this is headed. Since I have created a file named "plot.m" then I run the command :

octave plot.m

In the program is the command "plot". Apparently the ".m" files take precedence over built-in functions and as a result, BOOM! ( or Bohm ), infinite recursion until all file handles are consumed. Circular dependency. So I renamed it "aplot.m" and all is right with the world. It was certainly a WTF moment. I was doing this as a stage to plot some eigenvector relationships, and I was doing it in stages as this always happens. If I write a 300 page program and then debug it, it is like fighting a fire hose.

clear
x = linspace(0,10*pi,100);
y = sin(x);
clf;
plot(x,y);
pause;
plot(x,y,'ro');
pause;

And finally a very confusing graph of some Eigen sub-space.

When we see the particle detectors flash or hear the click of a Geiger counter then Everett's theory interprets this as our wavefunction responding to changes in the detector's wavefunction, which is responding in turn to the passage of another wavefunction (which we think of as a "particle", but is actually just another wave-packet). No particle (in the Bohm sense of having a defined position and velocity) exists, according to that theory. For this reason Everett sometimes referred to his approach as the "pure wave theory".

The above quote is about an interpretation of particles and waves. I have said there is no such thing as a photon, and each thing is infinite. Essentially, Bohm is stating exactly the same thing in a different way. It goes beyond that as there is a deeper understanding to be had. It is my way to add complexity to a problem to make it simpler. If all the variables are not present then it is necessary to expand the NULL space to accommodate the complexity and then fill in that space with the possible solutions.

I already found that underlying relationship and so it is very simple to constrict the matrix to model these sub sets. I can even see why it is so confusing to others. It is dependent on variables that are not in the equation. Some of these are physically hidden effects and some are purely logical.

New open math tool

This is very neat as this is exactly what I wanted. I wanted to mix and calculate with the imaginary and it requires the representation of variables in parts.

Something generated with blender.

The snap is a 2x2 matrix and solved with a vector and so Ax=b. An odd thing that I ran into is that Gauss or somebody of that stature wrote a manuscript complaining that x should not be used as the symbol for multiplication as it overloads x as the unknown and creates confusion. At least I am in good company when I moan about symbol overloading and the confusion it can create.

I was testing this program ( extcalc in the debian ) and it has lots of promise. I wanted to make my own calculator that implemented matrix generation and analysis for the sake of graphs and circuit analysis and whatever.

It is a useful base tool but has some SIGSEGV issues in the corner cases. It is BETA. I will get the source and see if it can be made to integrate with Python, Blender and my other utilities. I specifically wanted to examine n-dimensional matrices of graphs like Kirchoff circuits and determine some principles for compressible space or systems. The idea that a node has in=out implies a lack of compressibility, which is not true in real systems. There is always something going on and the generalized formulas can lead to situations that are unexpected. A capacitor stores e^- and so is compressible in a sense. I wanted to integrate some functions as elements of matrices in time and state. By using a series of matrices like a Markov matrix which describes the equal distribution of charge by voltage, I would hope to get some insight into higher dimensional flux and what it might represent.

I was looking at the pigeon hole principle and the extensions to infinite sets and I think I see why it seems paradoxical to me, because it is and that is known. Infinity is not a real thing and so it could never be tested. The analysis of relative infinities is done within the scope of a specific aspect and so it seems that it can be characterized in relative terms in many ways.

motey-$ concalc "bin0001|bin1101"
13
motey-$ concalc "sin(pi/4)"
0.707106781186547524
motey-$ concalc "(1+1/1000)^1000"
2.71692393223589258

And some examples of the shell utilities that are available with concalc. This will be useful in shell scripts. Below is an octave example of a Wheatstone bridge done with a matrix. I have done these in my head usually. Notice that the matrix operator is \.

octave:1> A=[300,100,150;100,650,-300;-150,300,-450]
A =                                                 
   300   100   150
   100   650  -300
  -150   300  -450

octave:2> b=[0;0;-10]
b =
    0
    0
  -10

octave:3> x=A\b
x =
  -0.039080
   0.032184
   0.056705

octave:4> AU=triu(A)
AU =
   300   100   150
     0   650  -300
     0     0  -450

octave:5> AL=tril(A)
AL =
   300     0     0
   100   650     0
  -150   300  -450

SO... that is the Ax=b of that matrix. It is like having the mind of Gauss in software.

Hidden secrets in plain sight

I like to wander the net in new ways and explore some of the corner cases. A good example of that is Wikipedia. I was looking at examples of the product and chain rule in Calculus and I decided to take a left into the unknown. I had assumed without foundation that the French, German, Arabic, .... pages were just translations of English. I should have known better as some of the names that are encountered in science are like Pasteur, Gauss, Heisenberg, Cherenkov, Fermat, Da Vinci, Bernoulli , .... and so does the world revolve around England? I was pleasantly surprised that some of the best and most elegant examples and descriptions were yet to be found. The image above is part of the German interpretation and is quite informative.

The tour of the world left me a bit humbled.

2 times the Grand Faloon

I was reading some very old manuscripts that recently became available on the internet and I discovered a new formula. It was something well out of the time that it should have been known. The strange thing is that I had read that before and translated it. The reason it became obvious is that I knew what they were talking about because I had discovered it myself. What it means is that without the knowledge and understanding of the subject, you can translate to your hearts desire and never see what is said. There are many things hidden in the cracks of history.

Ut pendet continuum flexile, sic stabit contiguum rigidum inversum

I have been following some interesting lectures at Gresham College in England and they have many good historical accounts of mathematical foundations. The best historical account of the origin of e^i*π I have seen yet. Stanford has the best open courseware on the application of it and its relationship to Fourier and use in quantum mechanics.

e^x-\bigg( \lim_{n \to \dot \infty} \big [ \big (1+\frac{1}{n}\big )^n\big ]^x \bigg )

So I get it. And this is the problem. I have spoken about the number -0 before in he context of using the upper bit of a word as sign. What happens is that when that number is 0 and you change the sign, you have a new number which is -0. It is undefined in operation and subtracts like 0 or adds like 0. The problem with math in general is the human tendency to enjoy mysticism, whether in the form of organized religion, state, or science. People are far more interested in something that comes from a magical incantation or seems to have no origin, than that which is complete and as a result very dull. To me the math is very dull and is simply something that describes things in the same way as language.

The problem originates in one dimension and gets twisted into n-dimensional space by process. I saw an example of this magical science thinking the other day. A wave in water is characterized by a sine wave. This is not how I think of it or for that matter current either. There is never any negative water or negative electrons. When I say there is a negative current of electrons, what do I mean? I am removing electrons from something. There have to be electrons present for me to remove them. The negative is a logical negative. Anyway, someone suggested that you could use interfering gravity waves to create anti-gravity. Good luck with that. It reminds me of the fact that two waves interacting at right angles have a wave front that travels at √2 v and if that is c then it travels faster than c. This is something that Tesla thought about later in life when he was not in top form. The effect does travel faster than c, but it is another of those logical illusions that are so easy to become involved with, if you have a tendency to magic. Shadows can move at c+ also, but there is a difference between logical and real.

I suppose that I could go into the limit of -(α/α) as α approached zero, but I will stop now. The structure and use of calculus is its own worst enemy. In order for it to progress the code has to be rewritten as there have been too many hands playing in the source and it has some memory leaks. Some code is well structured and easily extensible, math is not. It can't be extended until the SIGSEGVs are removed.

Mystery of the ages

Using only an unmarked straightedge and a compass, Greek mathematicians found means to divide a line into an arbitrary set of equal segments, to draw parallel lines, to bisect angles, to construct many polygons, and to construct squares of equal or twice the area of a given polygon.

Three problems proved elusive, specifically:

***** Trisecting the angle,
    * Doubling the cube, and
    * Squaring the circle

I just did this a couple posts ago and it is a no brainer. It is all done with a single straight edge. Wiki says that it has been elusive for 2,000 years. I must really be missing something. I wouldn't try squaring a circle as π is transcendental and known to be so. I thought I had seen trisecting an angle was difficult in passing somewhere. I am reasonably sure I have a way to untangle sqrt(-1) now and I understand why it arises and what it implies.

Imaginary things i*j =-1 unless it is j-hat

I thought I was the only one who had a problem with using this. It seems to me to be a way to introduce a 4 value function into calculation and nothing more. I have been watching some new ideas about sets and numbers and how they are applied. It doesn't seem to me that I have to be bound by techniques that were defined before all the facts were in.

Anyway Sixty Symbols looks interesting, as does Hanny's Voorwerp. And more analysis of the voorwerp.

Trisecta

I don't know if I am missing something, but things like trisecting a line or any number division of a line with a straight edge is simple. I assume the same is true of angles or affine space. I just don't feel that it is like magic or even requires some advanced skill.

The only thing that fills me with wonder is that somebody must think it is something difficult to figure out. I surely must be missing some fact about the process.

The line is extended ( parallel ( 2 above ) ,( 1 below ) ) ( bisect lower ) and then diagonal lines are drawn. Enclosed in the circle is the original line.

I read some of the gobbledy goop of alchemists and though they can make astute observations, the problem is too complex to be characterized by a simple relationship and it just sounds like a child explaining nuclear fusion. Plato, Socrates and existentialism is also a load of dung. A person first needs to understand the universe before they can consider their relationship to it.

The image was created with Inkscape using snap to grid with Bézier curves. Elapsed time 1 minute. There are some new options to Inkscape.

I will have to investigate the math a bit to see if this holds on transformation and rotation.

I would think so at first glance, at least in Euclidian space. UNSW Linear Algebra.

Tribute to Archimedes creativity

Archimedes was said to have solved the weight and composition of a crown by the water it displaced. Here I have a way to create graphs with various programs and then perform integration by counting the filled area color using the histogram function. It is a method to perform a definite integral Σf(x)δx a→b of any function without any mathematical skills whatsoever. It also allows me to get the length of the curve without any calculus whatsoever. It is also possible to select by color to perform surface integrals.

It seems a kind of solution that Archimedes would have appreciated. It may not be rocket surgery, but I find it interesting.

This is what I would expect from a gamma ray burst initiated by FTL. It would produce a halo of red shift that expanded outward and would have a red shift that varied with the distance from the point of GRB. It would be unique in the fact that it would produce a transient red shift in emitted light along the direction of acceleration proportional to the z of the GRB. If this is true there should be an opposite effect at the terminal end which is the opposite polarity. It could be determined by drawing lines between the vectors what paths were taken. This would give the extent of travel. Since the ring would be a plane in the direction of travel it would not be a TSP problem to connect the dots. At this point it is pure speculation, but I will continue to look for the specific signature that I have calculated to exist. I know that FTL is possible even if it would be beyond the technology. It seems reasonable to consider that if it is possible and the universe is large, the natural progression of technology would lead to this. I would doubt that a space faring race would bear any resemblance to us. Advances in DNA and cybernetics are already being implemented and I would guess that being human in the future would be quite different. I saw a TED talk on new interfaces and I think they have it wrong as the natural progression of computational interface is direct to the DNA.

I also doubt they would be willing to augment humans, any more than we would build squirrels with human brains and equip them with cyber enhancements. There must be some purpose for moving about the universe, other than conquest. It seems this is just another level and beyond that is something that I suspect exists and would like to confirm, if I can make a good model. I do not think black holes are homogeneous and that inside them is something strange. There is more mass inside a tiny space than is in an entire galaxy. I have no idea how one would peer into a black hole, but perhaps it is possible to look inside.

I assume that the majority of GRB are simply collapses of stars just because of the uniformity, but the energy output seems to be all wrong. I would make a wild guess that it is a black hole eating a smaller black hole. I had modeled this before and it would have some odd consequences depending on the size of the two objects.

i is imaginary, u is not

The title is proper grammar. The letter i represents the imaginary number and creates complex numbers.

I have a problem with paradox and sqrt(-1) and a few other things that I ( not imaginary ) cannot accept as elements of a rational mathematical system. The picture resolves the difference between how I view multiplication. Imaginary numbers arose in the solutions of a equations. They are applied in electronics and physics. I understand the numbers differently. There are numbers that apply to quantity and those that apply to dimensional space. In quantities, I can have 10 fewer of some object and that is not illogical. It is the presumption that a number system is consistent in its rules across many applications. In some cases x·y is not the same as x×y or y·x

You might think that I reject things like e^iπ as bad math. That is not the case. It is the fact that mathematics has failed to be flexible enough to correct its own structure. Numbers were once considered to have mystical powers. I see the computations in a very straight forward and consistent way and this i is a symptom of the vision of Alice Through the Looking Glass. A mixed metaphor of calculation. It unnecessarily complicates the application and understanding of physical systems. Math is method. It is the same as programming in almost all aspects. In this case there are procedures that depend on the order of their execution and it is not explicit in the design of the number system.

When someone is contemplating i², they are contemplating the resolution of a paradox created in the specification of the system of calculus itself.

It is quite clear that dimensionality and order are applied in vectors like <i,j,k> and the methods which act upon them are correct, however, the whole of the system of mathematical modelling is inconsistent in its association of methods to objects. In object oriented programming the same method is used for like objects. When a method is applied to an object of different properties an anomaly occurs and though the anomaly may be resolved in the application, it still is improperly implemented. If one procedure adds 1 to all letters and they are displayed by subtracting 1 when they originate from an improper method, then the result is the same, but the process is unnecessarily convolute and becomes difficult to express and teach. It is like a box with negative width, depth, and height. The traverse of negative space is very much different. I consider that multiplication is not commutative in some cases. I also presume that -1 × -1 sometimes implies the addition of an operator which is -|- . It was a long time before zero was admitted into the lexicon and method of calculus. It can be 0⁰ ( zero to the zeroth power = 1, or one) messy problem when the system of logic itself is inconsistent.

I thought about this -1 times and I am sure it is correct.

Alien Intellect (AI)

The Nature of Dimensionality
And so on...
points 0 Space	lines 1 dim	triangles 2 dim	pyramids 3 dim	4DStruct 4 dim
	"Triangle Numbers"
1	0	0	0	0
2	1	0	0	0
3	3	1	0	0
4	6	4	1	0
5	10	10	5	1
6	15	20	15	6
7	21	35	35	21
8	28	56	70	56
9	36	84	126	126

I was browsing through the history of math and I happened on the idea of "triangle numbers" at Wikipedia, in the context of Fermat polygonal number theory. I had to say: "WTF is that!" When I realised what it was, I had an ephiphany . I had done this work long ago in trying to understand dimensionality itself. Those numbers show up in a table I created about 15 years ago to deal with n-Space and the nature of dimensionality and sets.

At that time I resolved some relationships with numbers that involve things like (1+1/n)^n and a host of other things that have to do with integers. This gets back to that number I hate and it is sqrt(-1). I know that everybody else accepts this as part of normal math, but I do not. To me it is the place between two numbers that does not exist. Well, in any case I am dealing with e^iπ+1. It seems to me that even though this very useful and I can apply it and use it in context as well as anybody, I don't like the derivation and application. There is much more to this and the way i is defined gives rise to something that I use that is equivalent.

That is why I named the post "Alien Intellect" as the way I deal with science is truly alien. I don't mean that I am an alien, just that I devised methods that are more effective by not accepting that which was given. The math and physics is incomplete, this I always knew.

This table also has something to do with Fibonacci and life and genetics. There is a deeper something in all this that is perhaps in the realm of metaphysical.

I discovered another odd thing when doing an implementation of flock emergence with my n-Body math. I have to complete the code and test it, but I will post some results and videos.

1
1	1
1	2	1
1	3	3	1
1	4	6	4	1
1	5	10	10	5	1
1	6	15	20	15	6	1
1	7	21	35	35	21	7	1
1	8	28	56	70	56	28	8	1

It does relate to Pascal's triangle also. I had my own version of that also. There are many of these things that are completely new to me. Dimensionality and topology is one of the oddest and though there is no evidence of dimensions beyond 4, it does not mean they could not exist. It occurs to me on occasion that what we experience is just the shadow of something very strange. It does have something to do with e^iπ.

Reimann Robots

1. Blender flock
2. elsamuko flocks (boids)

I am modifying this for red and black ants and super ants as they exist with multiple queens. I also have a test I wanted to try using Reimann integrals in n-Space. Boids and the blender animation are interesting. The implementation of boids by elsamuko is easy to modify and well programmed. There is an interesting intersect between genotype to phenotype and Reimann as well as swarm behaviour.

Interesting thought, is the internet starting to swarm, and is that what scares the governments so much? I saw some interesting things on emergent government and it seems that it would create a new informal structure. The parametrics are more complex than this, but I can see for myself that people with similar interest are likely to act in the same way, independent of any actual association.