Readers' Choice: True Lies: Why Mathematics is an Illusion

If an existential entity, rather than mathematical abstract, must be defined by at least two different quaternions,( because it is -change- in quaternion spatio-energetic position that gives existence to every entity), this will solve Zeno of Elea's arrow paradox.

The arrow never is at rest in a (subjectively experienced) instant of time. The arrow is defined by and only exists because of its change in position. Rather than ever having a static position.

Georgina

arrow move in space only and not in time. There is no paradox here. Paradox arises because one think arrov moves in time.

yours amrit

FQXi might be the best place to ask for basics of mathematics that are more appropriate for physics, not at all tedious as compared with Lawrence's set on the ass theory. In physics, continuity is an issue. Its definition by Peirce "something every part of which has parts" contradicts to Euclid's definition of a point: "something that does not have parts".

What is wrong for instance with a Dedekind cut? Already §2 of Stetigkeit und Irrationale Zahlen: "Vergleichung der rationalen Zahlen mit den Punkten einer geraden Linie" (Interpretation of rational numbers as points of a straight line).

Actually, it does nor matter what we count. We always start with one basic measure, for instance a unit length. Basic measures are assumed positive of course and exactly given without any doubt. The integer numbers of properties along a street start with number one and are actually finite while potentially infinite (Archimedes axiom). Nobody imagines property 1 as a point. It extends from the beginning of 1 to its border to 2. So the integer number n primarily represents an interval and not the belonging endpoint of it. Counting needs intervals. If a natural number is missing, the the line is discontinuous.

A piece of an interval can relate to unity in either a countable or an uncountable manner. Ever a countable one can be as small as we like. The same piece that is not a countable part with respect to one can be countable with respect to a basis that is not rationally connected to the measure one.

Nonlinear tunctions could be understood in terms of "real intervalls", which should be called irreal intervals because they are of size zero. It makes no sense to declare irreal intervals open or closed because they are naked without any size that could be added or removed.

Mathematics would perhaps no longer need a lot of boring courses in real analysis and other futile trouble. Physics could loose illusions too.

If this suggestion of mine is correct, then sets of points seem to be inappropriate. I cannot imagine that this idea is new and would like to know how it was refuted.

Eckard

Georgina, unconscious observer experiences timeless space through inner time as "present moment". Conscious observer is aware of inner time. He experiences timeless space as "eternal ever lasting present moment". In cosmic space is always NOW, present. Arrov moves always in timeless space, means in present.

Paradox has arised with preposition that in present moment arrow is still, that arrow moves from the past to the future. This is pure illusion. Past and future belongs to the mind, in the universe there is only NOW - present. Wrong prepositio has created a mental paradox that does not exist in physical reality.

yours amrit

Amrit,

I agree that the arrow is not actually moving in time. It can be modelled as moving through quaternion energy-space. I am aware that you dislike the use of dimensions for description. However if all descriptive and measurement terms are removed, it is then not possible to describe or measure anything and science can not get very far at all. Using the quaternion spatio-energetic description, time is not a dimension and the spacial element can be regarded as the means to measure change rather than being fundamental change itself. So, if space is also removed from consideration all then that is left is the un-measured energy (equivalent to that spatial change of position that is being ignored).

The point I was making was that the arrow is the change in position. That change in position being the energy that is the arrow itself. According to this model, objects only exist because of their quaternion change in position which gives them mass energy.If the object is observed to be moving through 3D space, that change in position is a part of the physical identity of the object. An existential object, rather than mathematical abstract entity, must be defined by at least two quaternions. That definition includes the element of change within it. (Meaning the arrow is not a collection of mathematical points that must be considered stationary). This solves the paradox.

Although integers and points can be used for physical description it is my opinion that they are part of an abstract language that does not relate directly to the existential reality of physics. Therefore producing abstract outcomes rather than outcomes that relate more directly to that which is observed. That is not to say that non quaternion mathematics is not useful.

Amrit and Georgina,

Your positions remind me of Einstein's helpless admission concerning the NOW and also of mathematical evidence for existence, e.g. of god and the fundamental theorem of analysis.

Does the real projective line provide evidence for the existence of a point plus-minus infinity?

Amrit denies the existence of past and future. What does existence mean to him?

I prefer to rather consider two mutually excluding views: Backward and forward.

Any actual process unites an unlimited diversity of influences from its past. They are real in the sense they left traces and cannot be changed any more.

Any prediction, plan, or preparation is limited to the expected future and always uncertain to some extend with respect to its agreement with what will become reality. There is no measurable future. Even in bird's brain, future is a mental construct.

Abstraction from reality removes the restriction of processes to the past and of predictions to the future. Mathematics is not an illusion but a tool. There are a few very basic illusions in mathematics and scores of illusionary applications of mathematics in physics.

Eckard

Eckard,

You ask "Does the real projective line provide evidence for the existence of a point plus-minus infinity?" Why do you ask? I'm not sure if that is a rhetorical question or statement to make "a point" or an actual question. I am not a mathematician. Though tempted to answer I can see myself falling into an unforeseen well of abstract mathematical theory and reasoning. I don't want to go there.

I am in agreement that there are signs of those influences encountered during the continuous process of change, that can be observed in behaviour and or physical structure, although there is no existential past "out there". The past can however form a part of mathematical analysis. I also agree that the future does not exist but can be imagined. It too can form part of mathematical analysis.

These important differences between mathematics and existential physics need to be borne in mind, rather than assuming that that which exists in the mathematics is physically realistic.

Eckard we do not have any experimental data past or future exist as a physical reality.

Past and future belongs to the mind, energy change run in timeless space.

Universe is ageless. "Before" exist only in a sense of numerical order measured with clocks - natural as Earth rotation or made one.

Universe is NOW.

yours amrit

Eckard,

"NOW" is not problematic in the model I am proposing. It is an individual subjective experience that is different for each observer. Each experienced present moment is formed from a patchwork of input arriving at the sense organs and filtered by the type and threshold of those senses and individual brain processing. Which may include such factors as state of alertness, alcohol,drug or caffeine consumption, training to attend to particular stimuli, number of other competing stimuli to be dealt with etc. etc. Further filtering occurs so unimportant or non urgent stimuli are not passed to the conscious mind, although attended to by the sub conscious mind. Association between memory is incorporated so that the input can be comprehended in the light of previous experience and learning and the result is experienced by the conscious mind.

The input has various sources varying in spatial distance from the observer. Possibly varying from millimetres to light years. However it is all "stitched together" by the brain to give a present or now experience of the conscious mind. So there is no universal present, it is all personal subjective experience of input from sources that may be considered to be well spread over time, if using a space-time model.There is no existential past, present or future. The present is an experience, part of the biologically generated subjective reality. It is not an external physical absolute or a foundational element giving rise to objective reality.

There is energy change, producing those forms that we identify, which can be modelled for comprehension within a quaternion framework of 4 spatio-energetic dimensions, without time. Within that structure the processes of chaos and complexity can (and I anticipate will eventually) be modelled and shown to gives rise to the universe that we observe via self assembly. IMO.

Whether an individual wishes to relate to a scientific explanatory model as description of their god is a matter of personal choice. The model just is what it is. What people choose to do with it outside of physics or how they wish to relate to it is a matter for the disciplines of behavioural psychology, sociology and theology to explore not physics.

I think the main point was that physics interfaces with biology (at the sense organs). I have called this the Prime Reality Interface. We -experience- the universe from the biological side of that interface. Which includes the experience of time.

Issues of "epsilons and deltas" in mathematics pertain to the consistency of the mathematics, which might be employed in physics. I Don't tend to worry too much about whether a real line can be dissected in some manner, such as a Dekekind cut, when it comes to directly physical implications. Again these are matters which concern the consistency of the mathematics employed.

The mathematical world which pertains to geometry is pretty tied to point-set theory, which deeper down is tied to the ZF set theory. I don't think this is likely to change in the future. The issues involved were inspired by calculus and the nature of infinitesimals (what Newton called fluxions) and the exact meaning of the limit.

Cheers LC

A problem with geometry is that it is static. However it seems that change is a most fundamental feature of the universe and the particles and matter within it. That is not reflected by the static nature of geometry, which can at best only give a series of static snap shots of 3D space. A block universe does not appear to move or change. That does not mean that geometry should not be used but its artificial rigidity should be borne in mind when interpreting its meaning.

Change is incorporated into the mathematics of quaternions which can give a sequence of rotations used to build up 3D structure. Chirality or handedness is seen in some inorganic substances and biological molecules. I think that it is not unreasonable to hypothesise that the nature of the particular rotation could lead to this chirality of structure. Which may be due to the particular shape of a structure under construction, giving drag or balance factors, that leads to a particular orientation of rotation in quaternion space.

Georgina, you say:

"NOW" is not problematic in the model I am proposing. It is an individual subjective experience that is different for each observer.

I would no agree, NOW is not subjective in a sense of "personal", NOW is objective in a sense that observer experiences what senses perceive.

In all people on this planet and all beings in the universe observer is the same, identical: observer is consciousness itself.

yours amrit

PS, read my article on file attachedAttachment #1: 1_Bridging_Observer_and_Observed__amrit_sorli.pdf

Amrit,

We will have to disagree then. Your usage of the term objective is not the same as mine. What the senses perceive is a filtered sub set of the data available in the universe which is further filtered and modified by the brain. The subject experiencing the product of that filtering and processed data is not directly experiencing the universe but a biological simulation. I call that biological simulation subjective reality. Every individual biological entity will be experiencing its own subjective reality interpretation of the external universe.Which includes an individual perception of a present. You are not a part of my present and I am not a part of yours.

Philosophically it may be argued that each individual is a part of a single consciousness but unaware of that. It may be the interpretation of the right hemisphere in a meditative state, which tends not to reduce and classify but thinks holistically, bringing things together and comparing. That is not the experience of alert mind in a usual situation.

Amrit,

When I said "That is not the experience of alert mind in a usual situation." I meant that the usual experience is not to "feel" that all life has one consciousness.

In the alert usual frame of mind objects and individuals are considered separate in both substance and consciousness. This is the left brain functioning as it should to allow us to make sense of the array of sensory input that arrives at the brain as flows of electrical impulses. Differentiating it into different and distinct sources.

The left brain is not correct and the right brain incorrect or vice versa. Both are interpretations of the data performed differently. I do not think that the right hemisphere perspective is more real or correct. A model that is able to fit with the interpretation of both cerebral hemispheres is in my opinion better than one that only fits with the interpretation of one of the two hemispheres.

Lawrence,

Both the closed interval [0,a] and the open interval(0,a) are deemed to have the same Lebesgue (Lebeg) measure. Do we need non-measurable Vitali sets? Do we need all the confusion due to sets of points at all? I would be interested in letters by Baire, Borel, or Lebeg on Cantor's sets.

The boundary between the property of mine and the property of my neighbor does neither belong to me nor to him. Mathematics can nonetheless be consistent:

Why not oo+oo=oo and why not |sign(0)|=1? The probability to manage setting the position of Buridan's ass or Schoedinger's cat exactly at a given measure equals to the measure zero.

My primary intention was to ask for how IR+ joins IR-, and I am now absolutely sure that the measure ( or [ 0, a) does not need a neutral 0 as to be immediately adjacent to the corresponding negative measure because any single real measure is finite and therefore has the measure zero. In engineering, I often used the forbidden by mathematics operation f/0=oo with f=anything finite.

I would prefer a year in prison instead of being forced to learn real analysis or scientific ML (Mengenlehre, also Marxism-Leninism).

You questioned practical consequences. I found out that arbitrary definitions can be unnecessary and misleading. Cf. the example I gave in my M283. Integral tables offer values for the integral 0 to oo over the function sin(x)cos(ax)/x not just with |a| smaller than 0 and |a| larger than 0 but also with an arbitrarily introduced middle value |a|=0 of measure zero .

While the latter is claimed to be necessary foe mathematical reasons, it does not yield the correct result, which must be the original function in case of a transform back and forth.

You already mentioned trouble with the interpretation of Dirac impulse at zero. I am no mathematician, so you might correct my guess: It is not always possible to directly perform integrals from negative to positive values but one has to split them into two parts with positive and negative argument, respectively. Accordingly, a Dirac impulse in IR+ is reasonable.

Further trouble with the unilateral Laplace transform has been reported by Terhardt at MMK in Munich.

Dedekind was of course not the first one who imagined the real line consisting of points.

Already Proklos in ancient times uttered similar ideas, and Albert von Sachsen (1316-1390) imagined in his book "Questiones subtilissimae in libros de celo et mundi" a wooden bar consisting of points. One of those who reasonably to some extent dealt with the matter was the almost forgotten German mathematician P. du Bois-Raymond.

I agree that mathematics is much too proud and unable for giving up illusions as to abandon such unproven obviously futile nonsense as aleph_2.

Progress in mathematics was always stimulated by reasonable application. 3,000,000,000 € are not too expensive if one draws the correct conclusions from a failure to confirm theories on possibly wrong beliefs. I am curious.

Eckard

The point-set topological approach to mathematics is so far the most consistent approach taken. There have been alternatives proposed, but they run into other difficulties. As for integrating from -∞ to ∞, breaking this up would change the answer if there is a delta function at zero. If the integral is set up between (-∞, o^-) and ()^, ∞) that would ignore the delta function. There are theorems about this for general functions instead of distributions, and the result is in general there is no difference.

It is not hard to show there is a difference between countable infinity and uncountable infinity. The Cantor diagonalization "slash" method illustrates there exists sets which have an infinite cardinality which can't be mapped to a countably infinite set. This leads to the power set generalization or the continuum hypothesis אּ_1 = 2^{אּ_0}, which in turn leads to higher aleph values for transfinite numbers. The continuum hypothesis has been found to be consistent in ZF set theory by Bernays and Cohen, but not provable. This was a set theoretic approach to using Godel's theorem.

I don't know if any of that stuff has much use in physics. It is pretty abstract stuff which tell us nothing about physical quantities. As for real analysis, I took a graduate course in it. It is not exactly my cup of tea. I prefer group theory, algebra, differential geometry and topology, and am much more prepared to make intelligent comments on that. Yet the subject of real variables does get into general integration theory, and integration over function of L^p spaces. For p = 2 this includes Banach and Hilbert spaces.

As a general comment, mathematics as known is pretty solidly founded with lots of theorems which render these systems consistent. The point-set topological approach to these foundations is pretty much bedrock stuff. People have looked into alternatives, but nothing has worked out with the degree of consistency and power.

Cheers LC

Georgina you say: The subject experiencing the product of that filtering and processed data is not directly experiencing the universe but a biological simulation.

Myself I'm pragmatic, I use my rational mind as a tool when I need it.

In the direct experience of the universe there is Oneness.

yours amrit