The limits of mathematics

Ian,

You are right. And the future possibility is unrevealed today because mathematics in inexhaustible. Thinking outside the box about emergence, I believe no where but in humor we see this in its extreme form. Humor is very contextual and extremely sensitive to the natural selection rules of the sociological "landscape" (to paraphrase Susskind). For example, to people 100 years ago, a Seinfeld episode would looked completely strange. We laugh at different things because we constantly find new patterns in our daily life. And those patterns are just new emergent mathematical axioms. But this is maybe all too fuzzy. We can pick another area: morality and law. We can understand morality as an ever evolving landscape of fuzzy heuristic possibilities and the new laws as quasi-formalized axiomatic systems that passed at least some form of consistency check.

Florin

Ian,

When I mention the idea of a single fundamental cause, I am not referring to boundary conditions or an initial act such as the big bang. I am thinking in terms of a single, ongoing, always present cause for all activity at all times. That is why I pointed, in an earlier meassage, toward the importance of properly interpreting even as simple an equation as f=ma. If it was properly interpreted, then the cause for all activity would reveal itself even in that equation.

It cannot happen under current circumstances, because, the equation was very quickly made subservient to unempirical ideas such as mass being an indefinable property. Once that decision took hold, the equation became incapable of revealing any information that could help us identify a single cause for the accelerations of all matter under all conditions.

Instead what happens is that theoretical physics introduces additional indefinable properties that lead to different mathematical identities for f. In other words, force cannot reveal information about a single cause because force is theoretically separated into gravity, electric force, weak force, strong force, etc.

Each indefinable idea such as mass, electric charge, temperature, other than distance and time subjects the equations of empirical physics to artifical restrictions without empirical justification. In other words, the added on ideas of theoretical physics distort and restrict the usefulness of the equations. The empirical form of the equations, before the theoretical ideas weigh them down, are the most useful form for the equations to exist in. It is in their empirical form that they can be inspected and contemplated and reveal real knowledge, with real empirical support, about the underlying cause for activity in the universe.

I recognize the incredible mathematical skills, vast theoretical knowledge, and empirical knowledge of theoretical physicsts. I do not wish to appear to disrespect their high level of education and intelligence. However, I am pointing to fundamental theoretical decisions that remain, in my opinion, unsubstantiated and unexplained to this day. I would argue that higher level theory, built upon a foundation of unexplained theoretical ideas, can be no more correct than are those fundamental ideas. The errors are likely compounded as theory becomes more and more complex.

Here is a different example of an unexplained fundamental property. I have raised this issue before in earlier messages in other forums here: What is thermodynamic entropy? I am not asking for an explanation that skips past a direct immediate answer and moves instead immediately to Boltzmann's interpretation and others that followed from it to the present day understanding of available microstates. Thermodynamic entropy is successfully used for important work in different fields. It is something real and yet we cannot explain what it was that Clausius discovered. He gave a very precise definition with its ideal conditions. Those conditions must be met or the calculation of thermodynamic entropy will be incorrect.

These conditions do not apply to the alternative definitions of entropy. In other words, thermodynamic entropy is not represented by those other definitions. What is thermodynamic entropy? Furthermore, its definition includes temperature. Temperature is another indefinable property. What is temperature? I am not asking what it can be related to in so far as related changes occuring to other properties such as energy. Temperature is not energy. I do not think that kind of answer explains what temperature is. How can these questions go unanswered to this day? Why were they skipped over? What problems has this caused for higher level theoretical analyses? Are they fundamental evidence that the mathematical equations of 'theoretical' physics, not empirical physics, became separated from reality right from the start?

James

Ian,

I decided I should make it clear that I am not myself searching for these answers. I have answers. I am asking for answers from theoretical physicists. I am avoiding filling this forum with my ideas, yet, I think it is important to raise these questions and establish whether or not they have been answered or can be answered by theoretical physicists. I say they definitely have not been answered directly or explained as being clear separate properties in their own right.

James

James,

You wrote: "Theoretical physics has been speculative right from its start" and "I am not referring to boundary conditions or an initial act such as the big bang. I am thinking in terms of a single, ongoing, always present cause for all activity at all times".

Given, there is no understanding of a ubiquitous cause available, why should science reject sometimes using speculative heuristic elements in addition to predominantly success-controlled methods? Let me return to what Ian solicited, discrepancies between speculative mathematical physics and what is reasonably considered the real world. Can you contribute anything but sterile skepticism?

I am not sure whether I already uttered my opinion both understandably and acceptably enough: We should search for overlooked cases of non sequitur. Why did you simply ignore my arguments instead of trying to refute them? I wonder why we seem to agree so much with respect to speculations like Big Bang and boundary conditions.

Eckard

Eckard

I have a strong evolutionary standpoint on mathematics. I consider mathematics to be nothing more than a communication product of the evolution of human brains, which means that understanding mathematics first boils down to understanding human brains.

I speculate that brains started with the macroscopic multicellular organism's need to move around its environment to reach better living conditions. To this mean, it developed a motor nervous system to innervate muscles for contraction. It then developed a variety of sensory systems, feedback mechanisms that, once appropriately engineered and linked to the motor component, enabled movement adaptability to the changing surrounding environments.

I'd argue that ever since the sensorimotor system has been developed, the brain's evolutionary challenge has been to determine what is the sensorimotor algorithm that provides the best chances of survival (say, for a given species in a given environment). We started with nervous arc reflexes (motor and sensory neurons); we then developed more sophisticated neural computations that required more and more interneurons to process the computing steps between the motor and sensory neurons.

As our brains evolved in an environment to which they were sensitive, they were exposed to recurring sensory patterns of "physical phenomena" and their evolution was shaped by conserving the neural organizations that most accurately predicted these "physical phenomena" for the largest number of contextual sensory inputs. These neural organizations were the rudiments of logical reasoning.

This means that human logical reasoning has been shaped based on the "physical laws" that seem to permeate our external world. This explains why a Cro-Magnon individual could mentally calculate the angle and force that would throw his spear to hit its target: its brain had internalized the physical laws of ballistics to which it had been repeatedly exposed to. This was way before mathematics was developed. Then, one day, some individuals started transcribing on paper these principles of logical reasoning in their best possible accuracy, and this was the birth of mathematics.

Mathematics is thus not an invented science nor a discovered science. It is a means of communication of logical arguments between individuals. It is the human logical reasoning system externalized into a universal language.

From then on, things started speeding up. Logical reasoning segments could be communicated with great speed and efficacy between individuals, and soon a whole community could work on the same logical reasoning problems that in the past, individuals had been trying to solve alone. This increase in total computing resources enabled human beings to solve more and more complex logical reasoning problems, which, because the logical system was tailored to reflect the macroscopical physical world that had surrounded our brains throughout their evolution, were proved to be very useful in the macroscopic world. Protocols of conduct were elaborated on the basis of this successful reasoning system, one of which was the scientific method, which has led us to the kind of science we know today.

As said earlier, mathematics has proven to be very useful at understanding macroscopical physical problems (e.g. problems in Newtonian mechanics), which also seem intuitive to "understand" to the human brain. However, we must keep in mind that mathematics is actually a reflection of our logical system, which was designed to work in a macroscopical physical environment. When we try to use mathematics to describe the physical world at different levels, i.e. at the microscopic scale, the nanoscale, or the cosmologic scale, things get tougher and we find ourselves with logical conclusions that seem more and more unintuitive and even far-fetched. I think this is because our logical system is not adequate to describe the external world on such scales.

Therefore, I think that, like any other evolutionary tool, mathematics may very well have use limitations, especially when used to describe physics in the non-macroscopic scales. Things in mathematics that are not physically conceivable, such as the concepts of a point or of infinity, are not a problem for me, as I see these as simply some of the basic concepts that our logical system uses to base its operations on.

The question is, will this logical reasoning system be sufficient to enable us to describe, within this system, the physical phenomena on all possible scales? It may or may not be, but I think that the most likely scenario will be that living beings will eventually use a superimposition of many evolutionary tools (some of which may not yet be developed) at once to solve complex problems of description such as the ones we currently encounter in quantum physics and cosmology.

I haven't specified why I put some words in quotes, nor have I touched on other topics, esp. truth (I think there is no absolute, Platonic truth, and that our tendency to relentlessly search for one truth is part of our pre-programmed logical reasoning system), but if you are interested I would be glad to share these thoughts too. I would be very curious to hear about your opinions on my evolutionary pure speculation!

Eckard,

I apologize. These last two weeks were uncomfortable for me to sit at my computer. I am right now printing off messages and I will reread them. I may have missed reading or did not read carefully enough some of the messages. I will look back over the messages of these last two weeks and prepare a response.

James

Florin,

You wrote: "the future possibility is unrevealed today because mathematics in inexhaustible."

You are definitely the son of exactly one mother and one father. Maybe, you already have children and possibly even grandchildren. This is not revealed to me. However, I doubt that their grandchildren already exist in the sense they are merely not yet revealed because mathematics is inexhaustible.

Can we really just not see in advance future events like a clairvoyant or did they simply not yet happen? I imagine the moment of consideration like a border of integration for all influences from reality. Some influences may be calculable others are more or less likely, some are seemingly marginal, unseen, or erratic; but the origins for all of them belongs to the past while seen from moment under consideration the future integration is as ramified as is the causal tree of the past. I do not deny that there are reasonable heuristic rules, e.g. trees do not grow too high or mors certa.

Is something wrong in this consideration?

Eckard

Eckard,

The point I was trying to make was not that future exists because math is infinite, but that an interesting and novel future exists because of that. Over time, many people proclaimed "the end of history", or equivalently that everything is already discovered. The inexhaustibility of math is what keeps things interesting for future generations, otherwise we would be conceptually no different that a hamster going round and round in its wheel.

Florin

Genevieve,

I have a simple question/challenge for your evolutionary standpoint on mathematics. Was 1+1=2 true before humans (or any other intelligent beings) realized it?

On the other hand, you are right about the different logics operating in different domains. In quantum mechanics, the Boolean logic of set theory does not apply, but the logic of subspaces (where de distributive property is replaced by the modularity property for lattices). Still, there are so many different logics possible, and yet Nature seems to favor only one. Why is that?

Florin

Florin,

To be precise, we may expect not just indefinitely many future events but uncountably much. The distinction is quite simple: discrete combinations would grow on the common basis one with 2^n and therefore be countably infinite. However, nature combines continuous integrals to an uncountably growing and simultaneously also dying diversity.

Nonetheless, at least to my understanding future events cannot be revealed or discovered because they do not yet exist. Perhaps we agree on the hamster Ben Akiba and likewise nonsensical closed world lines.

I would not call natural relationships mathematics but mathematics a tool to describe them. Nonetheless I also disagree with those who are denying objective relationships that are independent of how we perceive and more or less collectively understand them.

Eckard

I think there is a logical evolution to repetetive_events, that would instigate repetative solution? Think of how the humans grasped shaping the end of a blunt piece of wood. I can imagine our far distant ancestors throwing objects at other intruding wild species, say a prairie pack of wolves trying to snatch a tribes stored food supply.

Blunt objects would have maybe scattered one or two wild animals, but eventually all the objects thrown would have contained an accidental "sharp" object, which would have injured animal to a degree of killing it. Then the ratio of blunt to sharp objects being thrown would have evolved in favour of only "sharpened" objects being thrown? Once tribes had taken this repetative action of choosing sharp objects, shaping "weapons" would be the next action? the tribes would have honed their skill of repetative throwing and hitting objects as "practice", what we would today deem as field sports events?

Once the brain has experienced a certain amount of repetative actions, I think there is a process that kicks in, and the activity is logically accepted. Mathematics is the process of "honing" repetative events,as a post_logic activity ?

mathematics therfore, I think are a construct of Human evolution.

best p.v

Eckard,

I do not bother to give answers to my own questions because the answers have no value if the reader sees no value in the questions. I consider the practice of guessing to be an unacceptable and unscientific part of theory. I think it is the need for guessing, due to lack of real empirical knowledge, that creates the need for theory. I expect that any theory formulated by competent professionals to be useful. However, usefulness is due to the practice of fitting the equations of a theory to the patterns observed in empirical evidence. Those patterns are always found in information about changes of distance with respect to time. If the theorist interjects ideas about properties that cannot be expressed in terms of distance and time then the theorist is inventing properties that have no empirical basis.

There is no point that I can see for my mentioning what I believe is the single ongoing cause for all effects. If the reader is not interested in revisiting the decisions made during the development of the fundamentals of theoretical physics, then what is the point of doing anything more than raising the questions. If the questions are considered correctly answered, then who will care about other possible answers. If you think that f=ma has been properly interpreted, then there is nothing to be gained by my discussing anything additional about it. I questioned the validity of the interpretation of mass in f=ma because I think guesses should be challenged. I questioned it because I think it is the most important question that theoretical physicists should be asking themselves. I questioned it because I think correcting the theoretical interpretation of mass is the key to removing that guess and additional guesses from theory and bringing theory much closer to empirical knowledge. If fact, it may be possible to eliminate the need for theory. In other words, I think it is possible for facts to replace guesses.

"Given, there is no understanding of a ubiquitous cause available, why should science reject sometimes using speculative heuristic elements in addition to predominantly success-controlled methods? ..."

There is no chance for understanding if important fundamental questions remain unanswered. I think your statement does express the attitude that has given rise to the practice of theoretical physics. You refer to 'speculation' where I would use the word 'guesses'. I take a firm position against the practice of guessing just so that the theorist can move on with formulating their theory.

"...Let me return to what Ian solicited, discrepancies between speculative mathematical physics and what is reasonably considered the real world. Can you contribute anything but sterile skepticism?"

I assume you wish to return the discussion back to the point where you think the discrepancies exist. I have done the same. We disagree on where that point is. I say it begins with the speculative interpretation of f=ma. You describe this as 'sterile skepticism'. I presume that you reject any need for reviewing the original theoretical interpretation of mass. I think the use of the word 'sterile' indicates that you believe in most of theoretical physics. I assume you see no need to challenge that which you believe has repeatedly been proven to be correct. If this is the case, I reject the belief that any of the guesses forced into theoretical physics have been proven to be correct interpretations of real empirical properties.

With regard to time, I think that Einstein's theory of relativity is clearly wrong. I choose the words 'in time' to remove the property of time from any possible control by us or anything event that occurs in the universe. I do not see why that word implies anything more than that. For any event to be recorded as having occurred, it must be referenced to changes of distance with respect to a duration of time. We cannot work with the idea of an instantaneous time that does not have duration. You speak about influences of the past. I suggest that there can be no such influences unless we allow for duration. It is the use of duration that provides the information necessary to explain both the past and predict the future.

My voice is only that of an individual. I think you probably have important points to make. I enjoy reading your challenges and the responses by others. There may be much to be gained by you from discussions with physicists and mathematicians. They are the qualified experts who's opinions matter.

I have waited to see if Ian would respond to my last message to him. He has not. I think that my approach to this discussion has run its course. I will return to continuing to advance my own work. In my own work I answer all questions that I raise. I think the questions deserve real answers.

James

Eckard,

"...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. ..."

The 't' in physics equations can be measured. It cannot be measured into the future, but it can be quite accurate in forcasting future 't'. In no case does any of this apply directly to real time. Real time cannot be measured because we use only physical means to attempt to measure it. Real time does not extend into the past anymore than it extends into the future. Real time is a major part of what keeps the operation of the universe orderly. The 't' of theoretical physics can't even keep theoretical physics orderly.

"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."

Any clock performs a measurement of its own rate of action that takes place during time. I simply prefer the word 'in' instead of 'during'. I have to use the word that I think best represents the act of separating real time from the theoretical 't'.

"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?"

I think it is reasonable to speak about plus and minus time so long as we are speaking within the realm of theoretical physics. Theoretical phyhsics does not deal with real time or with other real properties. If the properties are proven to be real, then they are empirical properties. Theory is necessary only for filling in gaps of knowledge about what is real. With regard to real time, there is neither the future nor the past available to us for the purpose of study. There is only our record of activities that occurred previous to now. All information we use is information that is not occurring now. It is always information about the past separate from any instantaneous now. We function according to information about the past. We never know what it is that is occurring now.

I do not allow for negative space. Lengths or distances can be referred to as either plus or minus depending upon their usefulness in equations. That kind of use for either time or distance is not attacking the concepts of space and time as themselves being negative and positive. This practice is simply a mathematical convenience suitable to help us communicate our ideas. If our ideas work better by choosing a reference point either in the past or in the future, or plus or minus, I see no problem with doing that so long as we do not believe that our theoretical ideas are true.

Both space and time are communicated to us as ideas. They have equal standing as ideas. It is our ideas formed from information about distance and time that we use to form our impressions and interpretations about the form and nature of the universe. We never experience anything other than information that our minds become aware of only within ourselves.

James

James,

You wrote: "I expect that any theory formulated by competent professionals to be useful."

What about aleph_2? Nobody managed to use it. Not just Ebbinghaus mentioned "an obvious mistake".

--- What about SUSY, Higgs boson, string theory, white holes, hairs of black holes, anti-worlds, etc. I do not exclude that at least a few of them are unrealistic, useless, or not even testable. Why do you consider "competent" professionals always correct? I was a university teacher for 40 years. Do you consider someone like me not competent enough as to have revealed foundational errors? Admittedly, I am not familiar with SUSY, etc. However, I maintain my argument that future does not yet exist before the moment of concern.

You wrote: "I think correcting the theoretical interpretation of mass is the key to removing that guess and additional guesses from theory and bringing theory much closer to empirical knowledge. If fact, it may be possible to eliminate the need for theory. In other words, I think it is possible for facts to replace guesses."

--- Uncle Al tried to substantiate his doubt by referring to facts. Do you support him?

I wrote:""Given, there is no understanding of a ubiquitous cause available..." and you replied: "There is no chance for understanding if important fundamental questions remain unanswered."

--- Those who are believing in a religion will agree in that science hat its limits. Except for such questions like the beginning/end/size, etc. of the world, there are almost unlimited possibilities of understanding. I am sure: You cannot explain how answering of your question would contribute to any understanding. Let me say it quite pronounced: I see your question for a primary cause pointless.

I wrote: ²Let me return to what Ian solicited, discrepancies between speculative mathematical physics and what is reasonably considered the real world.

You replied: "We disagree on where that point is. I say it begins with the speculative interpretation of f=ma." and "... original theoretical interpretation of mass".

--- Could you please specify to whom you refer who gave an original theoretical interpretation of mass and to whom who speculatively interpreted it. While I am not at all interested in any interpretation of mass, I would like to understand you.

You wrote:"I choose the words 'in time' to remove the property of time from any possible control by us."

--- Well, I am ready to accept expressions like 'in elapsed time' or even "in the time to come". We should agree in that any travel in time is only possible on the level of imagination. I do not accept the ideas that the future already exists in advance, and the very moment does not matter in physics.

You wrote: "You speak about influences of the past. I suggest that there can be no such influences unless we allow for duration."

--- Yes, duration is a sum (integral) of time-increments. My point of view is merely uncommon. The traditional notion of an integral leans on the traditional notion of time with an arbitrarily chosen point zero. Alternatively we may consider the steadily growing duration from a fixed event in the past to the steadily changing instant zero. This way integration and differentiation both at zero would no longer be different from each other: Traditionally we have two borders of integration and an integration constant but d/dx refers just to the slope at a single x. Mathematicians will be worried.

Eckard

Eckard,

Part One:

'James wrote: "I expect that any theory formulated by competent professionals to be useful."'

Eckard: "What about aleph_2? Nobody managed to use it. Not just Ebbinghaus mentioned "an obvious mistake".

James: What about the theory of relativity? What about quantum mechanics? Even Lorentz's theory was useful in his time. I am not vouching for the competnece of all professional's. I am referring to theories that have won common acceptance. In other words, competent professionals use them to achieve results that are usefully close to empirical results.

'Eckard:--- What about SUSY, Higgs boson, string theory, white holes, hairs of black holes, anti-worlds, etc. I do not exclude that at least a few of them are unrealistic, useless, or not even testable. Why do you consider "competent" professionals always correct?'

James: I did not say that competent professionals were always correct. I have gone so far as to say that Einstein was incorrect. However, his theory has been very useful. What I do say is that I think all theory that has been developed upon the bases of guesses is at high risk to be wrong. Furthermore, it is my opinion that all theory that uses the current interpretation of mass is wrong. I think that the subjects you mention above are silly ideas put forward by theorists who are more interested in scorring points at a chalk board than they are at proving their theories first with empirical evidence.

Eckard: "I was a university teacher for 40 years. Do you consider someone like me not competent enough as to have revealed foundational errors? Admittedly, I am not familiar with SUSY, etc.

James: I think you certainly are competent enough to have revealed foundational errors. I think you are more capable of doing this service than are a great many theoretical physicists who proceed on the basis that that which has preceded them is deemed to be correct.

Eckard: "However, I maintain my argument that future does not yet exist before the moment of concern."

James: The future never exists. However, we do not know anything beyond what the past is telling us. We do not know what is happening now. Photons take time to reach us from any source. I am not saying that the past persists. I am saying that the knowledge of the past persists and that is what we receive in the form of information. I am also saying that that information is understood by us to be changes of distance with respect to a duration of time. The duration itself may not exist. I would expect that the passage of time is instantaneous. However, we do not receive information about instantaneous changes. The information we receive is always about lengths of distance and durations of time. This information tells us about how some effect has changed during a past experience. It is from that past experience that we are made knowledgeable enough to predict the future.

Eckard: 'You wrote: "I think correcting the theoretical interpretation of mass is the key to removing that guess and additional guesses from theory and bringing theory much closer to empirical knowledge. If fact, it may be possible to eliminate the need for theory. In other words, I think it is possible for facts to replace guesses." ...

...--- Uncle Al tried to substantiate his doubt by referring to facts. Do you support him?"

James: Uncle Al has no bearing on this matter in so far as I am concerned. I have seen the real Uncle Al at work in other forums. I prefer to think differently and be different from him. I will have nothing more to say about him.

James

Eckard,

Part Two:

Eckard: 'I wrote:""Given, there is no understanding of a ubiquitous cause available..." and you replied: "There is no chance for understanding if important fundamental questions remain unanswered."...

...--- Those who are believing in a religion will agree in that science hat its limits. Except for such questions like the beginning/end/size, etc. of the world, there are almost unlimited possibilities of understanding. I am sure: You cannot explain how answering of your question would contribute to any understanding. Let me say it quite pronounced: I see your question for a primary cause pointless."

James: I think I understand. You disdain religion. You think that your disdain for religion gives you a better scientific viewpoint. I do not have a religion. I said that there is one primary cause because that is what true unity requires. The piecemeal approach of developing disunified theory and later trying to force unity upon it is what leads to silly theories such as string theory. Extraordinary measures are required to cover up a long list of questionable theoretical guesses. If error is not corrected then it must be covered up by piling on more guesses.

Eckard: 'I wrote: ²Let me return to what Ian solicited, discrepancies between speculative mathematical physics and what is reasonably considered the real world. ...

...You replied: "We disagree on where that point is. I say it begins with the speculative interpretation of f=ma." and "... original theoretical interpretation of mass". ...

...--- Could you please specify to whom you refer who gave an original theoretical interpretation of mass and to whom who speculatively interpreted it. While I am not at all interested in any interpretation of mass, I would like to understand you. ..."

James: I introduced my concerns about mass by pointing out that it was arbitrarily assigned an indefinable nature and was assigned indefinable units of measurement. I think I have been quite clear and consistent on this point. No one could have known that that was an empirically justified act. I take the position that not only was it as guess, but that it was a wrong guess. The evidence for a correct guess is that any property mentioned should be reducible to empirical properties. The empirical properties upon which all of our knowledge is based include only distance and time. In other words, mass can have made up units such as kilograms, but it must be possible for the theorist to demonstrate that kilograms are based solely upon units of distance and time and it should be shown how this is done.

Eckard: 'You wrote: "I choose the words 'in time' to remove the property of time from any possible control by us." ...

...--- Well, I am ready to accept expressions like 'in elapsed time' or even "in the time to come". We should agree in that any travel in time is only possible on the level of imagination. I do not accept the ideas that the future already exists in advance, and the very moment does not matter in physics. ..."

James: What I wish to convey about time is that regardless of what words we use, Einstein's relative time is not the time that I speak of nor is it the time represented in any current phyhsics equation as 't'. It is my position that neither space nor time are properties to which we have access to for the purposes of either experimentation or control.

Eckard: 'You wrote: "You speak about influences of the past. I suggest that there can be no such influences unless we allow for duration." ...

...--- Yes, duration is a sum (integral) of time-increments. My point of view is merely uncommon. The traditional notion of an integral leans on the traditional notion of time with an arbitrarily chosen point zero. Alternatively we may consider the steadily growing duration from a fixed event in the past to the steadily changing instant zero. This way integration and differentiation both at zero would no longer be different from each other: Traditionally we have two borders of integration and an integration constant but d/dx refers just to the slope at a single x. Mathematicians will be worried."

James: I applaud your efforts.

James

James,

I do not appreciate you considering Einstein's theory of relativity wrong without revealing to what extent and for what reason. I do not share a basic assumption that was taken for granted not just by him: the a priori existence of time.

Dealing with Kant, I found: "Space is not an empirical notion ...(but) ... a necessary imagination, a priori, ... . ... a priori determined. ... a priori, i.e. prior to any perception...".

Perhaps, Ritz was not entirely wrong. The old Einstein admitted being seriously worried and "a matter of painful but inevitable resignation" (Zeh, 4th ed., p 198).

Eckard