The limits of mathematics

Marcel,

Given a salesman offers 50% off and an additional 40 % reduction. Does this mean you have to pay just 10%? Why do you feel entitled to simply add probabilities?

You may add velocities but you have to multiply reductions of price as well as probabilities. Ergo, probability can neither get smaller than zero nor larger than one. You were muddling probability with velocity.

What about the question whether or not the positive plus negative numbers together are more than only the positive ones, Cantor found it correctly out but he admitted to Dedekind: I cannot believe it. Take his doubt as an other example for a typical fallacy due to superficial thinking.

Forget unnecessary musing about even, odd, and prime numbers. You should rather ask yourself why on cannot put zero and infinity in these drawers. The original structure of numbers, as already be found in Euclid's definitions, was carelessly abandoned in the 19th century mathematics.

Eckard

Eckard,

"Given a salesman offers 50% off and an additional 40 % reduction. Does this mean you have to pay just 10%? Why do you feel entitled to simply add probabilities?"

--- In dealing with the probability of position of a particle... the sum must be one; the particle exists somewhere. But, it is more of an image. Gravity is often portrayed as a dip in a sheet, an attractor for balls rolling in the vicinity. Consider now a bump in the same sheet. Place a ball on the bump and it will leave in whatever direction... this bump is my negative probability.

"You may add velocities but you have to multiply reductions of price as well as probabilities. Ergo, probability can neither get smaller than zero nor larger than one. You were muddling probability with velocity."

--- I know I am muddling something in my explanation, but it is not what you say.

"What about the question whether or not the positive plus negative numbers together are more than only the positive ones, Cantor found it correctly out but he admitted to Dedekind: I cannot believe it. Take his doubt as an other example for a typical fallacy due to superficial thinking."

--- Superficial reading: Since the early Greek philosophers, we have understood the distinction between two important concepts: the underlying reality and our perceptual experience. Over the centuries, we have always mixed the two concepts at the same time and amounted to nothing. Around the time of Newton, Descartes and others, the empirical method was born. We would forget for now/for now about the underlying reality and would consider the universe as a black box. We would concentrate our study on our experience of the black box, i.e. the empirical concept and approach and find the laws that best described our experiences. But no matter how successful the empirical concept is in this year 2010, the other concept (underlying reality) is still sitting on the back burner where we left it 300 years ago. Because we do not know what the universe is made of (what is the substance) and what makes it work by itself (the cause), all of our best science remains an educated guess on outcomes. And, that is the limit of physics. Your superficial reading of my essay did not reveal this to you. Unless one understands this state of affair, he cannot ask the question and the answer to this question certainly means nothing to him. The future of physics lies with metaphysics.

"Forget unnecessary musing about even, odd, and prime numbers. You should rather ask yourself why on cannot put zero and infinity in these drawers. The original structure of numbers, as already be found in Euclid's definitions, was carelessly abandoned in the 19th century mathematics. "

----- My monistic description of the universe suggests that there is a natural and logical structure under the even odd and prime numbers... and maybe not... not loosing too much sleep over that one.

Marcel,

Spanner?..just where does infinity begin?..somewhere between 0 1?

Infinity cannot possibly start from Zero, so it has to be One. The fractional reduction from 1 to 0 cannot produce the same "infinity" as the continueous whole number "infinity"? There can never be a total discrete zero, a very finite part "fraction" will exist for all Zero's.

In the opposite continuum, there can never be a viable "total" infinity, a continuum of whole consecutive numbers. One can class the Prime number process, when a new number is reached infinity is falsefied, but as infinity is a function of "time", you will eventually come across a prime number that will take a certain time to discover, or check, tou will need the collective time of at least TWO Universe's!

It is not where Infinity ends that is important, it is where one defines its source?

Ian your succint discrete point_infinity does not equal your total continuous infinity by fact of functioning time constraints?

Best p.v

Hi Ian,

Thank you for your reply.

"...To be clear, I take the non-absolute nature of time to be an empirical result so, to me, it's not using relativity to support relativity. ..."

I assumed that was the case. It is the answer adopted by theoretical physicsts. I am not one, however, this is the way I see it:

Yes clocks will measure different intervals due to distance from mass. They are not intervals of time; they are intervals in time. Everything occurs durring time. This is not evidence that time controls everything. It is evidence that the cause of a particular activity is changing. Is time is a cause of activity and does time control the rate of activity? To prove either of those possibilities we need to perform experiments on time? Experiments on clock's of any type is no more informative that experiments on any other activity in the vicinity of the measurements. GPS adds only more additional information about how physical activity varies with respect to distance from mass. Unless time is established as the cause of all of this activity, then time is not the subject of the measurements.

The time dilation equation is actually the t dilation equation. The t in physics equations is a measure in time (some duration of some physical activity) and not of time (as in a testable property in itself). All activity is measured with respect to a standard of activity. That standard can be chosen by virtue of its exhibiting as stable as practical cyclic activity. For example, if one wished to measure the rate of cyclic activity A, one would compare it to the standard for cyclic activity. Both of these cyclic activities are material in nature and are therefore subject to effects brought upon them by other material objects. In other words, they both are variable.

We use the name seconds for the unit of measurement in physics equations: however, in the most fundamental sense, the units of t should be referred to as cycles of the standard chosen. So, by measuring cyclic activity A against the standard cyclic activity B, The true fundamental form of the units for both of them is (#cyclesA)/(cycleB). The property of time is not shown to be affected by this action. All activity requires time to occur. The time taken is a duration in time simply because time is passing during the activity. Time itself is not a physical property that can be sliced up, contained, or molded into a new form.

"...But I am of the opinion that we have to rely on empirical results to at least some extent because we built technology out of this stuff and it's all got to work and be consistent. ..."

I think it is crucial to remain dependent upon empirical results as closely as possible and to use theory only when necessary to risk moving forward in analyses in the face of the unknown. That is why I first refer back to photons as our source of information. They tell us that particles of matter changed their velocities. If there is no change of velocity, then we receive no information. There has never been an experiment that included a change of velocity for either time or space. They just are not available for us to trap and experiment upon.

"...Regarding your fundamental quantities, I might agree with space and time, but I definitely don't agree with force, at least how it is presently defined. I might be inclined to agree if we found a "broader" definition that took into account non-interaction-related correlations. ..."

I use the word force in a generic form, meaning that anything that causes change of velocity is a force. Gravity is a force. If a change in position of one object causes a change in position of another object, regardless of whether or not it is faster or slower than the speed of light, then I think that indicates a force exists. I see no fundamental problem with allowing for this possibility. I see it as analogous to saying that the speed of light is a constant in free space. Any coordinated behavior acrossed the universe is evidence that something is controlled by a means that exists outside the limitations of the speed of light.

"...As for things like black holes, even Newton predicted them. But my point is that the empirical evidence of their existence seems irrefutable. See, I personally believe that theory works best when it is based on empirical results since, for better or for worse, that's the window through which we view the world. ..."

Newton's black hole and Eistein's black hole are very different. Einstein's relies upon the existence of spacetime. There is no evidence that either space or time are affected by the activities of matter. There is evidence that matter affects other matter and that matter and light both affect each other.

I guess this might be getting tedious for you. I appreciate your time. I will let you have the last word. You are the expert.

James

Marcel,

You wrote: "In dealing with the probability of position of a particle... the sum must be one; the particle exists somewhere. ... Gravity is often portrayed as a dip in a sheet, an attractor for balls rolling in the vicinity. ... Place a ball on the bump and it will leave in whatever direction... this bump is my negative probability."

-- I understand dip and bump as attractive or repulsive force, respectively, which are factors that influence an otherwise random motion. Addition is only allowed as a linear approximation for small values.

I am not familiar with monism. I merely know that it relates to Ostwald, Haeckel, Parmenides, and Zeno. My old dictionary calls it a naive kind of materialism. Admittedly, I did not yet read your essay at all. I just used the search option for negative probability as to clarify whether there is any reasonable use of negative probability.

Yes, around 1650, the time between Descartes (1596-1650) and Newton (1642-1727), Guericke contributed to the experimental method. His intention was to understand the forces that rule the motion of planets, and eventually this gave rise to steam engine and electricity. Guericke did not like mere speculation. You wrote: "The universe as a black box". Did you not understand that we are living within this box and have no possibility to look at it from outside? The very notion universe is in this sense a prison we cannot escape. This is however no relevant limit to physics if we accept that within the notion universe there is enough to investigate. It is perhaps possible to find almost any causes of something tangible but definitely impossible and therefore useless to deal with "the" primary cause. Causality and time are nearly synonymous in that they structure all events that already happened (probability one), to be seen from the chosen point of view (probability of correct observation smaller than one). Future causality and future time are not yet observable and more or less uncertain. Do you object?

Eckard

Eckard,

What I understand is that we dropped the ball some 300 years ago and I picked it up. My essay is my answer to the best of my abilities. So, it is possible/possible to ask and answer the question. What I need are people who can wrap their mind around this concept and back engineer it into our present knowledge to make it complete.

(Complete knowledge = physical description logical understanding.)

"..mere speculation.... have no possibility... of something tangible... definitely impossible and therefore useless.."

These words tell me that you are not one of those people. (Maybe I'm not in the right forum ..)

All the bests,

Thanks,

Marcel,

Marcel,

Yesterday LHC has been switched on again. I will appreciate a negative outcome that could possibly give rise for taking R more seriously and use mathematics no longer without knowing what is really behind it.

I will quote you because you are still considering yourself a monist:

"Understanding is about knowing the logic behind the existence and evolution of the universe."

--- Logic behind the existence of the universe? As it is meant, this sounds unrealistic to me, because I understand the universe as something unlimited and ergo comprehensive but incomprehensible.

I rather see the logic behind the existence of the notion universe.

"The metaphysical and logical understanding of the universe is accessible, understandable and necessary for us to progress beyond the limits of physics. It is certain that this metaphysics still has to be engineered back into physics in order to produce something new and practical in our reality.

--- Understandable understanding. Hm.

"The universe has existed and evolved by itself for about 14 billion years."

--- Isn't this a hypothesis that is based on results from the experimental method?

--- Doesn't it contradict to Monist Parmenides: "The universe consists of only one object, it exists timelessly and changelessly." "There is no motion, since motion implies the existence of more than one thing, namely, a finishing place and a starting place."

Zeno tried to demonstrate something I do not deny: "True existence evades measurement."

--- No further comment,

all the best for you and respect for your effort,

Eckard

Let's have you Marcel LeBel the last word: The box contains everything physicists ever wanted to know about the universe. The content of the box is the only thing that will allow us to make sense of all the theories and equations (unification). But they can't get it with the empirical approach. The empirical approach is about finding things by experience, trial and error. It is a choice we made long ago between knowing and doing. The empirical test is not just the proof of a theory. It is before all a practical demonstration of control over some segment of the universe and this control provides the illusion that we understand what we are doing. We don't

James,

You wrote:"The t in physics equations is a measure in time (some duration of some physical activity) and not of time (as in a testable property in itself)."

Zeh also dealt with the question of "direction in time" (A) or "direction of time" (B). He called his book "The physical Basis of the Direction *of* time.

I feel forced to almost agree with your statement because you refer to the common assumption of an a priori given coordinate time (A) for using "t in equations" (C).

Nonetheless I would like to object that this use (C) refers to an abstract notion t that cannot be measured at all. Let me call it even unrealistic in so far as future is predictable to some extent but it definitely evades measurement in advance.

Any clock primarily performs a measurement *of* currently elapsed time, not *in* elapsed time. You have to synchronize it before it shows a moment in commonly agreed time. Notice, I changed the point of view. The usual notion of time needs an arbitrarily agreed point of reference. Positive elapsed real time counts "backward" from t=0. The same holds for anticipated elapsed time.

Why do you consider a timespan a measure in an a priori given time between minus infinity and plus infinity when there is no future timespan available? Do you also allow for negative distances in space?

Eckard

I blamed Dirichlet and Dedekind wrong. Let me start explaining. There are several problems concerning definitions that were made for R if we try to follow physical restriction to R+, cf. e.g. criticism by Terhardt of integration for unilateral Laplace transform from a small negative value to +oo or by Aseltine §3-6. Likewise, the usual illustration of Dirac impulses fails with restriction to R+. Common sense tells us that each single rational number must be countable in the sense it is different from any other one by a non vanishing value while genuine continuity as defined by Peirce demands that real numbers behave differently.

Dirichlet ignored this different properties when he gave the well known example of a function f(x) that is 0 for rational x and 1 for irrational x. While it has been called nowhere dense, I would rather see this the other way round.

Furthermore, Dirichlet attributed the mean value [f(x-0)+f(x+0)]/2 to discontinuous functions. Using pertaining integral tables I found out that the mean value is misleading. It does not make sense to exclude or include a "single" real number from the continuum of reals. It does not matter whether or not zero, infinity or any rational number exist within the continuum. There are infinitely many possible substitutes that cannot be distinguished from it. Accordingly I consider |sign(0)|=1 justified and a separate treatment for the very point zero between R+ and R- pointless.

Dedekind continued the strictly speaking inadmissible while pragmatic neglect of the fundamental difference between rational numbers and the uncountable manifold of potential points of continuum. He caused additional confusion when he referred to numbers as to points instead of measured that relate to a common unity.

Cantor caused a tempest in a teapot and ongoing trouble when added some useless speculations and the analogy based notion of cardinality. Isn't it sufficient to distinguish between in principle countable, discrete, rational numbers on one side and fictitious real numbers of continuum on the other side? I never heard of any application for aleph_2. Of course, I distinguish between let's say the number five as a rational number and an equivalent real number five.

Eckard

Ian, there can never be totally isolated physical objects outside of mathematics?..for instance an absolute nothing, will have a discrete part of it as a finite of "something"?..and thus likewise a total everything something(infinity)..will have a "zero" assigned part to it?

The Riemman Zeta Function for zero distribution is really natures mathematical devise that orders zero's to this effect?..at least this is my understanding!

In this sense mathematics itself has to adhere to the same fact?

best p.v

Eckard,

I think you raise good challenges, and I am glad you are actively participating here. I will not be answering quickly, because, I have had a busy week that led to my undergoing an out-patient surgery today. I am back at home, doing fine and it is not real serious. However, I think I will wait until I am off pain medication before responding. I just wanted you to know that the delay is not due to lack of interest.

James

Dear Eckard,

How do we get back to knowing, rather than doing.

Pankaj,

You wrote: "How do we get back to knowing, rather than doing."

-- As someone whose mother tongue is not English, I have to admit being not sure I understood what you meant in your rather cryptic question without question mark.

Some experts argue not just the future but also the past is unknown to us. I do not think so. Well, it is imaginable that somebody lost his memory while he can be told what will most likely happen. My reasoning refers to physical reality which is exclusively determined by influences that originate in the past. So it is reality that does not know the future.

Does this answer your question?

Eckard