1.0 Does a mathematician 'predict' architecture or behavior with an equation? The mathematicians claim to 'predict' the architecture of a physical body by simply looking at an equation or, in the alternative, to be able to synthesize architecture with a mathematical expression. For instance, one prominent mathematician of the establishment claims that he can understand nature by simply looking at an equation:
"When I was in high school my physics teacher wrote an equation on the blackboard and then performed a very simple experiment—rolling a ball down an inclined plane. He showed that what I saw there in front of my eyes was described by the mathematical equation he had written on the blackboard... It's not obvious from our everyday experience that mathematics has anything to do with nature. For me this was astounding because mathematics is some- thing we do in our heads. It's like a game of Dungeons and Dragons. It's a fantasy. But because mathematics must also adhere to logical precepts, it restricts our imagination. Why it is that mathematics is the only language that our species has found to describe nature is a mystery that will probably never be solved. But it is the way that we have found our deepest understanding of nature. For the theoretical physicist, mathematics is like an extra-sensory- perception organ that we use to see the universe." 
It is not clear from this excerpt whether Gates is referring to architecture or to behavior. Is he saying that he can 'see' what an apple looks like by staring at a few mathematical symbols or is he saying that he can 'see' how the apple rolls down the plane? Of course, when put in these terms, the mathematician will come to his senses and deny that he can 'predict' architecture. He will clarify that he was alluding to dynamic scenarios and that the expression tells him where the apple will be after so many seconds. He is not talking about visualizing a still image. He is talking about watching a movie. Unfortunately, this is too little too late. No. I'll take that back. I'm being too polite, and I detest being politically correct. I'll be blunt. It's a big fat lie! The mathematicians do in fact claim to infer the shape and dimensions (i.e., qualitative aspects) of physical bodies. Or more precisely, they casually insinuate that they can, and then thoroughly deny it at the end of the dissertation when the press starts asking the tough questions. When you go to their next presentation, they repeat the act all over again. The mathematicians do this over and over from dissertation to dissertation. Allow me to present some evidence in support of my assertion. 2.0 The evidence Today, the mathematicians of relativity and quantum 'know' without a shadow of a doubt that light is a particle and that an electron is a particle. The mathematician instantly denies it. He will argue that the particle nature of light and the electron are merely assumptions. The facts say something different. Every equation concocted by the mathematicians in the last 100 years uses the infamous particle as a model. Quantum and relativity would disintegrate overnight if light and the electron were not particles! That's how much is at stake! But let's concede for the sake of argument that the mathematician is right and the infamous, discrete particle is just an assumption. What alibi will the mathematician invent to explain their position with respect to space-time? Einstein and others 'predicted' that we live within a physical object that is four-dimensional:
" we live in a 4D world"  " We must accept that time is not completely separate from and independent of space, but is combined with it to form an object called space-time. (p. 23) 
The establishment takes this entity for granted, and certainly Einstein did not see space-time from afar. He 'predicted' this physical 'object' through equations. Therefore, the mathematicians do in fact claim that they derived the structural nature of the Universe from a set of equations.
" it follows from the equations of Einstein’s general relativity that this positively closed universe cannot continue to expand forever… The… zero curved universe… continues to expand forever." (p. 325) 
Likewise, relativists inferred the structure known as a black hole from a set of equations. Schwarzschild and others 'predicted' that a 3-D star converts into a magical 0-D object. Among its attributes, this magical object has the ability to swallow clocks, astronauts, and corpuscles of light. Certainly, if a black hole can slurp gases and generate x-rays, the mathematicians are not alluding to aconcept. Is a black hole an abstraction like beauty or justice, or is it more like the tunnel a gofer digs in the ground? The mathema-ticians are alluding to a physical object. They are not saying that a black hole is hypothetical. They are way beyond this stage alleging now that these objects have been confirmed. But my argument is that the mathematicians 'predicted' the existence of these objects from a set of equations long before they started looking for them. They were telling us what a black hole would look and behave like, and were illustrating these creatures before they even started looking for them with their telescopes. Therefore, my argument is confirmed. The mathematicians do in fact claim to predict the existence of physical objects from a set of equations.
Returning to particles now, you will never hear a theorist say that the Standard Model of Quantum Mechanics is speculative or that a particle is just an assumption. The Standard Model is a done deal! Annihilation is a done deal!
" the process that occurs when a subatomic particle collides with its respective antiparticle. 
Virtual particles are a done deal!
" a virtual particle is a particle which exists for a limited time and space... " 
Particles of every kind are done deals! There is nothing to argue:
" To date, almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions...The individual behaviour of the subatomic particles that make up all forms of matter - electrons, protons, neutrons, photons and so forth - can often only be satisfactorily described using quantum mechanics."  " The evidence for the description of light as waves was well established at the turn of the century when the photoelectric effect introduced firm evidence of a particle nature as well. On the other hand, the particle properties of electrons was well documented when the DeBroglie hypothesis and the subsequent experiments by Davisson and Germer esta- blished the wave nature of the electron."  " Quantum Mechanics: The laws of physics that apply on very small scales. The essential feature is that energy, momentum and angular momentum as well as charge come in discrete amounts called quanta."  " everything from galaxies to mountains to molecules is made from quarks and leptons.  The universe, which we know and love, exists because the fundamental particles interact... a force is the effect on a particle due to the presence of other particles"  " it is possible to generate and detect individual photons. Technologies making use of the special properties of single photons include quantum cryptography, for the secure distribution of cryptographic keys. In the future, it may be possible to process quantum information using single photons and linear optics. For either of these quantum techno- logies, a source capable of generating single photons is a desirable resource." 
You have nothing to argue! When Anderson was awarded the Quantum Nobel Prize for 'discovering' the 'particle' known today as a positron, he did not regard it as an assumption.
" the tracks shown in Fig. 1 were obtained, which seemed to be interpretable only on the basis of the existence in this case of a particle" 
His peers rubber stamped it as a fact:
" The existence of positrons was first postulated in 1928 by Paul Dirac as a consequence of the Dirac equation. In 1932, positrons were discovered by Carl D. Anderson, who gave the positron its name. The positron was the first evidence of antimatter and was discovered by passing cosmic rays through a gas chamber and a lead plate surrounded by a magnet to distinguish the particles by bending differently charged particles in different directions... Today, positrons are routinely produced in positron emission tomography (PET) scanners used in hospitals and in accelerator physics laboratories used in electron-positron collider experiments."  " they imaged gold atoms on a carbon substrate, observing single atoms and groups of atoms, both stationary and in motion."  " researchers showed it is possible for an atomic force microscope to make images of the wing-shaped paths of minuscule electrons as they orbit atoms" 
Batson doesn't believe that the atoms he managed to image is anything but a particle. And Liu is not speculating that electrons are tiny beads. They take these statements as a matter of fact. And Tonomura is not speculating that electrons are particles. He knows for sure!
" you can be confident that electrons are particles" 
When it comes to particles, there is nothing to argue! Certainly, the people working at SLAC and CERN don't believe that they are stretching bedsprings or ribbons from one end of the accelerator to the other. These folks don't even talk about or believe in waves. They are absolutely convinced that they accelerate corpuscles. If you still harbor doubts about my argument prove it to yourself. I challenge you to try to convince the establishment that particles are just convenient assumptions. Go to any Internet forum and tell the regulars that particles are just speculative, that a corpuscle is just a model used to make the equations come out right. Yet the only reason the mathematicians of the world continue believing that light, the electron, the atom are particles and that space-time, fields, and mass are made of particles is because they have modeled all their equations with this handy entity. The mathematicians haven't brainstormed anything besides particles and waves in the last 400 years! The particle hypothesis has been turned on its head. The uninspired mathematicians used the point particle (i.e., center of mass) to model all their equations so that they would not be distracted by architecture and because it was the simplest thing a mathematician could think of. The idiots of our generation have lost track of this and converted the point particle into a reality. Ask any stupid moron coming out of college what light or an electron are and he will tell you, 'Why, particles! Of course!'. The assumption has now been summarily promoted to proof!
The mathematician may want to deny that he can predict architecture when you put the sword to his neck, but this is a lie. He is grossly distorting the facts. A mathematician never has doubts when he speaks about the structural nature of space, about black holes, or about particles. He doesn't even hint that he is speculating. He tells you that you live within the space-time balloon and that the light that just hit your eye is a particle. He reinforces these claims with authority. He tells you that Mathematics has predicted and experiments have confirmed his versions. There is nothing to argue. You just need to take a high level course in Mathematics at Cambridge to come up to speed. The entire world believes in 4-D space-time, black holes, and particles. If you don't, it is because you are an ignorant fool and a crank. The mathema-tician does not assume that light is a particle. He knows it is a particle, for else all his equations are wrong. And they would be wrong simply because in the last 400 years the corpuscle is the only valid entity that the entire mathematical establishment has proposed for light! (Waves do not qualify as valid physical objects in Science. The word wave is a verb, what something does.) The corpuscle is what a mathematician works with on a day to day basis. This is his bread and butter. If light or the electron are not particles, all of Quantum Mechanics dies this very instant-- one hundred years of it! If light is not comprised of corpuscles, Eddington's alleged confirmation of General Relativity's warped space and Einstein's alleged explanation of the photoelectric effect are absolute bunk! The stakes are that high. So the mathematician resolutely denies that he can 'predict' what light looks like by looking at an equation, but it had better BE a particle if the last 100 years of Mathematical Physics are to make any sense. He will entertain no other hypothesis.
Therefore, I have no choice but to show the stupid morons of Mathematics that numbers, variables, equations, inference, measurement, and experiment do not give them any authority to tell us absolutely anything about architecture, structure, shape, or the number of dimensions of an invisible object. There is only one way to determine what an invisible entity is or looks like and that is to brainstorm architectures and eliminate those that cannot explain natural phenomena until there is only one left. The mathematicians are in no better position than you to discover the true nature of light, the atom, energy, mass, field, or the Universe. A mathematician just makes you believe that he has an advantage over you. A mathe-matician has no special insight or power, and this becomes absolutely apparent from the fact that they have no idea today what any of these entities look like. I need to resolve once and for all that the mathematicians cannot 'predict' architecture with anything coming out of their ridiculous discipline. That way, when an idiot of relativity or quantum or string theory tells you that:
•he knows that the Universe is a physical object, that it is 4-D, that it is flat,
and that it is also curved,
• a physics predicts the existence of black holes and that they have been
•a muon is a particle and that time dilation has been experimentally proven
...you can just refer him to these pages. You would be doing him (and the rest of humanity) a favor. You would be educating a mathematician in the basics of Physics. In another page I show that light in fact is not a particle. 3.0 The three methods The mathematicians use one of three methods to prove to you that they 'know' things such as that the Universe is simultaneously a flat and spherical physical object, or that a positron is a point particle, or that dark matter is comprised of particles: inference, integration, and measurement. Here I investigate these techniques and methods and show that all of them fail. In Science, we don't infer objects, much less through Mathematics. The only way to come up with a valid candidate is to brainstorm possible architectures and configurations. And the only way to definitely certify an object is by visualizing it from a bird's-eye perspective. Otherwise, the scientific method requires the presenter to make an assumption. Without physical objects, a theorist has no scientific theory.