PaulCDaiber @pcDaiber

A singularity in physics is a reference to a division by zero in a mathematical model. To overcome the problem of division by zero, applied math needs to be improved to accept division by zero. In the same improvement, the continuum needs a more constructive definition than the Cauchy limit function provides. These changes are included in the book The 5th Dimension: Math for Physics Outside Our Universe by Paul C Daiber.

The recommendations for science books are mostly about physics and I have read many of these and they are quite good. Rovelli specifically in his explanation of how information one particle perceives about another are particularly good. My recommendation is to read my own which are Seeking Infinity: A Desperate Hunt for New Applied Math and also The 5th Dimension: Math for Physics Outside Our Universe by Paul C Daiber.

Octonions form the highest order self-consistent algebra per Hurwitz theorem. They get slightly altered in the SU(3) group that supposedly applies to quarks and gluons of the strong nuclear force. Because octonions are the highest order and because there appears to be no force beyond the strong force, perhaps octonions do underlie the universe. The implication is that our time-space universe is a subspace of an 8-d time-super-space. If this is of interest to you, read more in The 5th Dimension: Math for Physics Outside Our Universe by Paul C Daiber.

@Math_files Is there a similar integer reciprocal for the Padovan sequence? Or must it be the sum of two reciprocal integers!

True though it is that the Inquisition led by Saint Bellarmine prosecuted Galileo and a few years earlier burned Giordano Bruno alive (due to his astronomical idea of stars being suns with planets as one of his heresies), religion in general should not be blamed but rather blame the intrusion of politics into religion, so that thoughts get controlled as well as actions. Those two leaders in thought lived at a time of transition because the early 1600’s were a time of reform. For example the jubilee of 1650 was celebrated by planting flowers, which contrasts with 1600’s jubilee in which Giordano Bruno was so terribly killed. In support of Christianity as a religion separate from politics, note that in 1881 (shortly after the unification of Italy when the Vatican lost its lands and the people as political subjects) Pope Leo 13th opened the secret archives and stated “The Church should not fear the truth.” No political organization or other gangland empire would ever do that. Please do not condemn Christianity.

@Shaktidass18 @PhysInHistory Correct. The assumption process for the math-establishment’s countable and uncountable infinities is flawed.

If the language of physics is math, then the suggestion is that math must change before theoretical physics can change. There are several opportunities to improve math. First is to find the way to accept division by zero so that a continuum is a sequence of zero span intervals and removing the limit function from calculus. Second is to restate the continuum hypothesis to say there is no quantity between the largest number so far counted to in any count of place value digits away from the decimal point and, on the high side, 1/0, so that there is no countable or uncountable infinity. And third, dispose of the half-breed SU(3) and higher to stick to octonions and their 2x2 matrix isomorphs as the fundamental algebra, which is more restrictive. After these changes theoretical physics should follow from the math, I think.

My grandpa’s family near Breslau was placed in a camp by the Russians so that Poles could take the farm. The story is that the Poles were quite backward compared to Germans, so he had to repeatedly set up the tractor to need repairs so that he would be brought back to the farm. This was essential because there was no food in the camp and he had buried food on the farm. I am the eldest male heir and so would get the farm, or so I have been told, if the land gets returned. My cousin visited and the little church there is rotted. In all truth, wars are traditionally genocidal, and that was how the Germans were fighting, so there being any Germans left alive at all is enough to be thankful for.

There are two conclusions from the EPR experiment. First, the particle properties are created at the time of detection and not at the time of particle creation. Second, that the signal that correlates particle properties for the two widely separated entangled particles happens instantly.

To divide zero by zero, identify that a zero can be a different magnitude than another zero by giving at least one of them a subscript A. Per this nomenclature, 0_A/0=5 means 0_A=5*0. Think of points of zero interval extending from the origin. The first point can be 0 to the right or it can be 0_A to the right. Both are okay because the magnitude of zero is not correlated to nonzero finite numbers. This is the theory of Correlated Zeros. It gives a new perspective on integration and differentiation because the limit to infinity for integration and the limit to zero for the differential are not needed. If this is of interest to you, it is included in the book The 5th Dimension: Math for Physics Outside Our Universe by Paul C Daiber.

@trudat2020 @mkelek When I was a kid the Ontario Science Center was the best, most favorite place to go. We drove there from Buffalo quite often. It is very sad to hear the roof was not maintained so they had to shut it down. It seems there has been a culture shift over the decades.

Ebbinghaus’s work appears to be what our high school STEM chemistry/math/physics curriculum is based on. Year after year the same items are taught just in more detail as the students get older. At first I tried to push retention and recollection of details and exceptions, but those get forgotten. The important, general aspect is all that gets retained and the next year it gets reinforced and expanded upon. Slow building of young minds is really difficult on an industrial scale, but our county high schools seem to do pretty good.

Minkowski used the unit geometric vectors, the same that Heaviside applied to Maxwell’s Equations, but with the addition of a direction for time. The disagreeable new math was a use of hyperbolic radial coordinates. Good as Minkowski’s presentation of special relativity was, it had the problem that a dot product of two time directions equaled negative one, not positive one as with two same space directions. The problem comes with the cross product when time is multiplied by space because it suggests an i factor is needed, but there is no place for an imaginary space direction as the product. Tate, who was Hamilton’s successor in the promotion of quaternions could have found the answer but he held to Hamilton’s notion that the three quaternions replaced the complex number coefficient i and so could not combine them by having i for time and the three quaternions for space, these replacing Minkowski’s unit geometric vectors. This works with axial vectors having the quaternions as coefficients and polar vectors having quaternions divided by i. Well, now we know, and it was a long road of evolving ideas.

This story is appealing. But it is too much a reflection of contemporary values to be believed. If we were a hundred years ago before the digital age then the ones and zeros would be unexpected and intriguing and suggest, decades later, that it was a legitimate post-death vision. If today such a vision described a seven dimensional space of different dynamics, then it would be new and justify investigation. Or if it was in opposition to Christian morals that tell us to love everyone, and instead told us to emulate strong men who beat down others to raise a family in an over saturated population world as if we must return to our tribal roots, then we could feel some surprise. Even an advocacy for Calvinism would have raised an eyebrow. But no. We really need confirmation of the spiritual as opposed to atheist reductionism based on science, and we keep looking.

Cantor’s countable and uncountable infinities are conjecture because the bijection proofs only involve finite numbers. Probably it would be appropriate if every reference to Cantor’s infinities not only be limited to set size comparisons, as was properly done in the above tweet, but also should be given a disclaimer stating that Cantor’s infinities are only conjecture. They are mathematical baggage that has bogged-down innovations in math with respect to a more useful set of properties for infinity needed for applied mathematics.

There is a mathematical conundrum associated with setting rest mass of a photon equal to zero. Photons travel at the speed of light and that speed is represented by a hyperbolic angle equal to 1/0. Cosh and sinh of 1/0 is, perhaps, 1/0. Relativistic energy and momentum are calculated as rest mass times the cosh and sinh, respectively, and so for energy and momentum to be finite, rest mass must equal zero. But there is no theory of math in establishment math, applied or pure, that accepts 1/0 or 0/0. Because humans do not have the math, it is inappropriate to assign photon rest mass to zero. How do we fix this problem in our math?

To visualize the expansion, visualize the 3-d surface of a 4-d sphere. Draw two cubes separated far enough on the paper to draw a third cube between them. Inside the center cube draw a sphere with three circumferences that intersect at right angles. Draw a dot in the center of the outer two cubes. Draw three ellipses that touch the outer two points, one for each pair of intersections on the center 3-d sphere. These six circles and ellipses are six circumferences on the 3-d surface of a 4-d sphere. There is a radial direction from the center that extends through the 3-d surface. In this very simple model, the universe has a 4-d interior and 4-d exterior, and the center identifies the location of the Big Bang. The model conforms to Friedmannn’s balloon analogy but it supposes a reality to the interior and exterior which cannot be measured because only phenomena inside the 3-d surface can be measured. To push this model further, imagine the Big Bang was an explosion and the shockwave is our universe, and particles in our universe are analogous to phonons, and this analogy is supported by Gödel’s solution which requires a non-rotating universe to avoid time looping back to its beginning because shockwaves cannot rotate like a balloon can. This model is also supported by comoving distance in astronomy jargon.

Perhaps the simplest visualization of a gauge symmetry is to assume a scalar field P(x,y,z, t) exists universally and its 4-d gradient is added to the voltage. This P has no effect on the electromagnetic field because a curl of a gradient equals zero, even in 4-d. These gradient of P terms are then added to the voltage in the Dirac Equation, and the result is that a phase angle is added to the electron matter wave proportional to the value of P. In this way the phase angle is arbitrary. The calculation of particle properties uses a complex conjugate which divides away this phase angle. The math is quite simple. But the math is probably not as simple for the weak and strong force bosons.

In the book Special Algebra for Special Relativity by Paul C Daiber there is a sub chapter that calculates mass for an electric field parallel to motion and another calculation for perpendicular to motion and together they match relativistic mass of a moving electron using the classical radius approximation.

Cantor initially created two actual infinities, a countable infinity defined by matching one-to-one members of the set of natural numbers to another set such as the set of even integers, and an uncountable infinity for real numbers from zero (inclusive) to one (exclusive) matched to any other interval of real numbers. Only in the context of these bijection proofs are the infinities relevant. And each bijection proof starts the count as one, two, three, and the reader must extrapolate to infinity. Because of the incomplete proofs and the limited application of bijection comparisons, his two infinities appear to be conjecture, only conjecture. But great mathematicians like Cohen and Gödel have treated them like fact, and so by tradition no one is allowed to doubt they exist. Also, because there is no popular alternative, they are supposed to exist. But they are not directly useful in applied mathematics, and their indirect use in the Cauchy limit function in the formal definition of the derivative is questionable. If these two artificially inserted infinities are dropped as incorrect, then something has to replace them. If you read this tweet all to way to the end here, then you will enjoy the book that finds that replacement to Cantor’s infinities. Seeking Infinity: A Desperate Hunt for New Applied Math by Paul C Daiber.