Taking Down Determinism

[The Man]

Your analysis baffles me.

To elaborate:

If you can't dazzle them with brilliance, baffle them with BS.

Would that be "non-deterministic information” BS? If so, it only seems to be baffling you.

Oh, like you understand that hodgepodge that you just posted.

Indeed I do.

Idea: Pi has a value that is not determined by any physical state of the universe.

Really, so if the universe (or even just geometry) were entirely random or entirely non-deterministic would the ratio of a circles circumference to its diameter be constant?

How about if our abstract concept(s) of geometry were to at least some extent deterministic while the “physical state of the universe” were not? Then our abstract concept(s) of geometry would not be very applicable to physical aspect of that universe. It is in fact quite the contrary, our abstract concept(s) of geometry are specifically based on their applicability to the physical aspects of our universe that we can perceive.

You can select a circumference for a circle or you can select a diameter and it does not matter which you consider to be the initial condition, but you can’t independently select both as one is determined by the other.

This determinism is also reflected physically by Pi, because if you change the diameter of the wheels on your car, your speedometer and odometer will no longer provide accurate data.

Idea: Someone may base an action on the value of Pi.

So what, you’ve already asserted that even if you consider Pi to be your "non-deterministic information”, actions resulting from it can still be deterministic.

That you find these ideas ridiculous says a lot more about your ability to reason and comprehend than it does about the proof.

Actually it was your “proof” that I said was ridiculous and it remains so, as your “Ideas” don’t demonstrate or even require any non-deterministic result from your “non-deterministic information”. This says the same “about your ability to reason and comprehend” and your “Ideas” as it does about your ridiculous “proof”. Once again the deterministic aspects of the universe are required for the ratio of a circles circumference to its diameter to be constant. That consistency is a demonstration that to at least some extent the physical universe is deterministic.

 

[epix]

Idea: Pi has a value that is not determined by any physical state of the universe.

Any idea is neat as long as it doesn't function as a premise that supports a certain conclusion. Stephen Hawking calculated and calculated in order to see how the universe will end -- if ever. If the universe ends, then it must change its physical state and the major role in this process will be the particle decay leading to the conclusion that Hawking arrived at: nothing will be left -- all mater gone. But the particle decay is not a random process; it can be described by

(2π)⁴ —— |M|² dΦ_n = dΓ_n
2M

where Pi is the part of the numerator.

So your idea doesn't exactly match the reality, coz you can rearrange the equation to isolate Pi.

 

[Bill Thompson 75]

I find it interesting that you can say they are no different in principle and in the next sentence imply the opposite.

If you do mean it is no different in principle, to me that means you agree that accepting that Socrates is a man, and accepting that all men are mortal causes us to conclude that Socrates is mortal.
In the same way, accepting that space-time is flat, and that things like limits, series and calculus are logically sound, we are caused to find a certain value for pi.

Neither space-time nor logic nor mathematics cause the value of geometric values, such as Pi.

Yes they do determine it. That's exactly my point. The very axioms you begin with immediately imply a value of pi, regardless of the number of logical steps you need to make. Pi is a necessary theorem as soon as you have your axioms. You just have to find the steps to get there.
If you use different axioms, a different value for pi may come out, and if that happens to be so, it was already necessarily implied by the new axioms.

We discover the shape that is called a circle and then we form definitions and axioms to standardize our understanding of what constitutes a circle. The value of Pi is intrinsic to the shape, it is not caused by the shape, and it precedes our definitions and axioms. Our definitions and axioms do not cause the shape of a circle nor the properties of a circle, including the value of Pi.

 

[Bill Thompson 75]

Maybe the right adjective is "absurd." The value of Pi couldn't be determined when the universe was 10 million years old, coz it was way too hot and disorderly to develop life. The universe had to change its physical state for Pi to exist in the form of awareness as a product of the mind. The universe, as defined by the cosmologists, doesn't have a mind, which is the only source of the particular awarness of various relationships including number Pi, even though some scientists may come to think otherwise:
http://www.bbc.co.uk/news/science-environment-11391434

How do we get out of this funky tunnel?

I think we go that way.

So, you think that until mental awareness existed nothing in the universe could be circular. And that that is not "absurd".

 

[Bill Thompson 75]

Would that be "non-deterministic information” BS? If so, it only seems to be baffling you.

Indeed I do.

Really, so if the universe (or even just geometry) were entirely random or entirely non-deterministic would the ratio of a circles circumference to its diameter be constant?

How about if our abstract concept(s) of geometry were to at least some extent deterministic while the “physical state of the universe” were not? Then our abstract concept(s) of geometry would not be very applicable to physical aspect of that universe. It is in fact quite the contrary, our abstract concept(s) of geometry are specifically based on their applicability to the physical aspects of our universe that we can perceive.

You can select a circumference for a circle or you can select a diameter and it does not matter which you consider to be the initial condition, but you can’t independently select both as one is determined by the other.

This determinism is also reflected physically by Pi, because if you change the diameter of the wheels on your car, your speedometer and odometer will no longer provide accurate data.

If you don't present arguments that exist within the universe of reason I cannot be expected to rebut them.
It is just too much effort to interpret the declarations that come from your mind and untwist whatever it is that you call thought.

So what, you’ve already asserted that even if you consider Pi to be your "non-deterministic information”, actions resulting from it can still be deterministic.

Actions that are not determined by a prior state of the universe are not determined by a prior state of the universe and therefore are not deterministic.

Actually it was your “proof” that I said was ridiculous and it remains so, as your “Ideas” don’t demonstrate or even require any non-deterministic result from your “non-deterministic information”. This says the same “about your ability to reason and comprehend” and your “Ideas” as it does about your ridiculous “proof”. Once again the deterministic aspects of the universe are required for the ratio of a circles circumference to its diameter to be constant. That consistency is a demonstration that to at least some extent the physical universe is deterministic.

Amazing.

 

[Bill Thompson 75]

Any idea is neat as long as it doesn't function as a premise that supports a certain conclusion. Stephen Hawking calculated and calculated in order to see how the universe will end -- if ever. If the universe ends, then it must change its physical state and the major role in this process will be the particle decay leading to the conclusion that Hawking arrived at: nothing will be left -- all mater gone. But the particle decay is not a random process; it can be described by

(2π)⁴ —— |M|² dΦ_n = dΓ_n
2M

where Pi is the part of the numerator.

So your idea doesn't exactly match the reality, coz you can rearrange the equation to isolate Pi.

Wikipedia, "Pi",

"Although not a physical constant, Pi appears routinely in equations describing fundamental principles of the Universe, due in no small part to its relationship to the nature of the circle and, correspondingly, spherical coordinate systems. Using units such as Planck units can sometimes eliminate Pi from formulae."

 

[H'ethetheth]

Neither space-time nor logic nor mathematics cause the value of geometric values, such as Pi.

Yet, you give no evidence for it. In fact, I've given evidence to the contrary, namely that if one starts from different axioms, one arrives at a different value for pi. You're not addressing this at all.

We discover the shape that is called a circle and then we form definitions and axioms to standardize our understanding of what constitutes a circle.

No, that's not how that works. People had an informal understanding of circles in a universe that is not very curved at all. Euclid formalized it, yet understood that he needed certain axioms for that; certain axioms we're not even quite sure are true in our real universe.

The value of Pi is intrinsic to the shape, it is not caused by the shape, and it precedes our definitions and axioms.

No, I'm sorry, but it really doesn't. Change your axioms, and you change the value of pi.

Our definitions and axioms do not cause the shape of a circle nor the properties of a circle, including the value of Pi.

Yes they do. That is exactly what they do.

 

[The Man]

If you don't present arguments that exist within the universe of reason I cannot be expected to rebut them.

That is probably why you don’t seem to expect that people will rebut and have rebutted your arguments that obviously don’t “exist within the universe of reason”.

Even though your arguments do not “exist within the universe of reason” I would certainly still expect you to rebut them yourself, unfortunately you just don’t seem so inclined.

It is just too much effort to interpret the declarations that come from your mind and untwist whatever it is that you call thought.

Well, don’t strain your brain.

Actions that are not determined by a prior state of the universe are not determined by a prior state of the universe and therefore are not deterministic.

Once again you’re simply presuming non-deterministic aspect of the universe. Please tell us how one performs some action based on Pi if it is not part of some “prior state of the universe”? The fact that one is performing some action based on Pi necessitates one having at least some knowledge of it prior to that action.

Amazing.

Not nearly as amazing as you thinking that your “poof” proves anything other than simply your presumption.


ETA:

We discover the shape that is called a circle and then we form definitions and axioms to standardize our understanding of what constitutes a circle.

Really? How does one “discover” a shape “not determined by a prior state of the universe”?

 

[Bill Thompson 75]

Yet, you give no evidence for it. In fact, I've given evidence to the contrary, namely that if one starts from different axioms, one arrives at a different value for pi. You're not addressing this at all.

No, that's not how that works. People had an informal understanding of circles in a universe that is not very curved at all. Euclid formalized it, yet understood that he needed certain axioms for that; certain axioms we're not even quite sure are true in our real universe.

You followed "No, that's not how that works." with a paraphrase of my argument. That is not a rational approach to rebuttal.

No, I'm sorry, but it really doesn't. Change your axioms, and you change the value of pi.

Yes they do. That is exactly what they do.

It doesn't matter what your axioms are.

If you can describe the set of points in a plane such that they are all equidistant from another given point in the plane but which is not in the set, then the distance required to traverse the set of points divided by the maximum distance between two of the points in the set is a constant value, regardless of the distance between any single point in the set and the point not in the set.

Call that ratio whatever you want.

 

[Bill Thompson 75]

That is probably why you don’t seem to expect that people will rebut and have rebutted your arguments that obviously don’t “exist within the universe of reason”.

Even though your arguments do not “exist within the universe of reason” I would certainly still expect you to rebut them yourself, unfortunately you just don’t seem so inclined.

Well, don’t strain your brain.

Once again you’re simply presuming non-deterministic aspect of the universe. Please tell us how one performs some action based on Pi if it is not part of some “prior state of the universe”? The fact that one is performing some action based on Pi necessitates one having at least some knowledge of it prior to that action.

Okay, see if you can handle this. Pi can enter a state of the universe and once it does it invalidates the deterministic nature of the universe since the state that Pi entered is not fully determined by the prior state.

Not nearly as amazing as you thinking that your “poof” proves anything other than simply your presumption.

ETA:

Really? How does one “discover” a shape “not determined by a prior state of the universe”?

Maybe this will help you understand the proof:

My claim is that the value of Pi is not determined by a prior state of the universe. Once you lose sight of the argument I made in the opening post, which is an obvious certainty, you will remain lost.

 

[H'ethetheth]

You followed "No, that's not how that works." with a paraphrase of my argument. That is not a rational approach to rebuttal.

I intended to highlight the difference between "axioms to standardize what people know constitutes" a circle" and "axioms that we're not sure are true in our universe". But yes, you're right, I could have worded this more clearly.

It doesn't matter what your axioms are.

I'll say this one last time: It matters precisely what your axioms are. That's what axioms do. They form the basis of a logical structure, the conclusions of which are dependent only on the axioms and the rules for generating conclusions.

If you can describe the set of points in a plane such that they are all equidistant from another given point in the plane but which is not in the set, then the distance required to traverse the set of points divided by the maximum distance between two of the points in the set is a constant value, regardless of the distance between any single point in the set and the point not in the set.

Call that ratio whatever you want.

I'll call it pi, like everyone else.
Now here's where you're wrong: If we create such a set of points in a space where euclid's parallel postulate doesn't hold, the value of this ratio will not be 3.14159...

 

[Bill Thompson 75]

I intended to highlight the difference between "axioms to standardize what people know constitutes" a circle" and "axioms that we're not sure are true in our universe". But yes, you're right, I could have worded this more clearly.

I'll say this one last time: It matters precisely what your axioms are. That's what axioms do. They form the basis of a logical structure, the conclusions of which are dependent only on the axioms and the rules for generating conclusions.

A circle does not need a logical structure, unless you are saying that circular structures cannot exist in the physical universe.

I'll call it pi, like everyone else.
Now here's where you're wrong: If we create such a set of points in a space where euclid's parallel postulate doesn't hold, the value of this ratio will not be 3.14159...

How can Euclid's parallel postulate not hold in plane geometry?

 

[westprog]

A circle does not need a logical structure, unless you are saying that circular structures cannot exist in the physical universe.

Circular structures almost certainly can't exist in the physical universe. Approximations to circular structures might exist, but then they aren't described by pi, just an approximation to pi.

 

[H'ethetheth]

A circle does not need a logical structure, unless you are saying that circular structures cannot exist in the physical universe.

First of all, I guess I am saying that. If you disagree, then please indicate one physical structure in the universe that is exactly circular. That is, something that is not a conception in your brain, made using euclidean axioms and logic.

Secondly: Of course a circle needs a logical structure. For instance, the existence of euclidean circles requires the assumptions that space-time is continuous and flat, and that there is such a thing as a point or a line.
The euclidean circle is an abstraction, a model, that follows from these assumptions, yet we know that gravity deforms space-time and there is a theory of quantum gravity that explores the idea that space-time might be discrete.
The former makes minced meat out of the parallel postulate, the latter makes it impossible to even define a circle in euclidean terms.

In short, Euclid's axioms are a very ingenious abstraction of spatial phenomena on the human scale, but they're no more or less than that.

How can Euclid's parallel postulate not hold in plane geometry?

I'm not talking about euclidean plane geometry. That's the point: Euclid's axioms are one arbitrary set of axioms among a host of alternative sets of axioms.
Pi is not inherent in the universe, it's inherent in one specific approximate mathematical model of certain aspects of the universe.

 

[Bill Thompson 75]

Circular structures almost certainly can't exist in the physical universe. Approximations to circular structures might exist, but then they aren't described by pi, just an approximation to pi.

Sure they can. A circle exists such that its center is at the center of gravity of the sun and the points on the circumference of the circle are the points' centers of gravity which are 1 kilometer from the sun's center of gravity.

The value of an approximation of Pi is not determined by the physical nature of the universe...either.

 

[nimzov]

Sure they can. A circle exists such that its center is at the center of gravity of the sun and the points on the circumference of the circle are the points' centers of gravity which are 1 kilometer from the sun's center of gravity..

Then the head of Donald Duck also exist around the sun, if you take the points corresponding to the drawing of the head.

 

[Bill Thompson 75]

First of all, I guess I am saying that. If you disagree, then please indicate one physical structure in the universe that is exactly circular. That is, something that is not a conception in your brain, made using euclidean axioms and logic.

A circle exists such that its center is at the center of gravity of the sun and the points on the circumference of the circle are the points' centers of gravity which are 1 kilometer from the sun's center of gravity.

Secondly: Of course a circle needs a logical structure. For instance, the existence of euclidean circles requires the assumptions that space-time is continuous and flat, and that there is such a thing as a point or a line.
The euclidean circle is an abstraction, a model, that follows from these assumptions, yet we know that gravity deforms space-time and there is a theory of quantum gravity that explores the idea that space-time might be discrete.
The former makes minced meat out of the parallel postulate, the latter makes it impossible to even define a circle in euclidean terms.

In short, Euclid's axioms are a very ingenious abstraction of spatial phenomena on the human scale, but they're no more or less than that.

Refutation of your entire previous argument: Circles existed before Euclid was born.

Also, you are arguing that the physical universe defines the existence of abstract objects.

That is wrong about a dozen different ways.

I'm not talking about euclidean plane geometry. That's the point: Euclid's axioms are one arbitrary set of axioms among a host of alternative sets of axioms.
Pi is not inherent in the universe, it's inherent in one specific approximate mathematical model of certain aspects of the universe.

The ratio of a circle's circumference to its diameter predated any mathematical model in history.

 

[The Man]

Okay, see if you can handle this. Pi can enter a state of the universe and once it does it invalidates the deterministic nature of the universe since the state that Pi entered is not fully determined by the prior state.

That was handled the first time you suggested it, the “deterministic nature of the universe” can only be ‘invalidated’ by such a “deterministic” ascription not being valid in the first place. To reiterate what I have said before, a totally deterministic universe has no mechanism by which your “non-deterministic” information can enter. So again your assertion of what you refer to as “non-deterministic” information ‘entering’ some universe already presumes that universe not to be entirely deterministic.

There are plenty of valid augments as to why our universe may not be entirely deterministic, the uncertainty principle, the big bang (or perhaps big bounce) singularity (a causal singularity), quantum fluctuations and virtual particles (where everything that can happen does happen) and even the problem of the decoherence of quantum states in superposition resulting in some particular outcome state. However, your simple presumption of non-deterministic aspects of the universe (by you simply labeling some information in the universe as “non-deterministic”) again only proves that you are just presuming some non-deterministic aspects of the universe.

As others have noted before, the total determinism of Laplace and 19th century science, died about a hundred years ago (for the above stated reasons). The meaning of determinism has shifted to the predictability of some future outcome based on current information (including Pi), basically asserting that the outcome is not random. As you don’t seem to be arguing that actions ‘based on Pi’ have inherently unpredictable or random outcomes based on that initial information (even just in theory) you are just arguing with yourself over an outdated interpretation of determinism that you just seem to hold yourself.

Maybe this will help you understand the proof:

My claim is that the value of Pi is not determined by a prior state of the universe. Once you lose sight of the argument I made in the opening post, which is an obvious certainty, you will remain lost.

Maybe this will help you understand invalidity of your “proof”:

Your claim is demonstrably false, "the value of Pi" (as others have noted) is completely determined by our abstract concept(s) of geometry and you seem to be the only one who has lost sight of that (if you have ever bothered to acctualy look it).

You seem to be fixated on some information that you simply label as “non-deterministic” ‘entering’ the universe (specifically a universe that you consider, at least up to that ‘entry’ to be entirely deterministic) and resulting in some 'action' that you also simply label as “non-deterministic”. However, even in the limited physical sense where (again as others have noted) the value of Pi is just an approximation of that abstract determined value. Actions based on Pi are still deterministic, meaning not random. Unless you actually have some evidence that such actions have unpredictable or random results?

To try to put that abstract concept of Pi in some physical 'action' sense, my steering wheel is a ring. As I apply some constant force tangential to the circumference of that ring through one rotation. My car turns in a direction determined by the direction of rotation from that force vector. The energy that I have applied to the steering wheel (E_s), through that 1 rotation, results in an applied torque on the steering column through one rotation (T_s) turning the steering mechanism. Would you like to guess what the proportion of that applied energy of that 1 rotation to the applied torque through one rotation is on the steering column?

E_s/T_s = 2Pi

Are you claiming that steering your car is “non-deterministic” as it is an action based on Pi?

 

[Bill Thompson 75]

That was handled the first time you suggested it, the “deterministic nature of the universe” can only be ‘invalidated’ by such a “deterministic” ascription not being valid in the first place.

Why do think this is so?

To reiterate what I have said before, a totally deterministic universe has no mechanism by which your “non-deterministic” information can enter.

There does not need to be a mechanism because there is no barrier? It can enter through calculations, reading, etc.

So again your assertion of what you refer to as “non-deterministic” information ‘entering’ some universe already presumes that universe not to be entirely deterministic.

The properties of the universe which contribute to its deterministic nature are not immutable. The universe can change from deterministic to non-deterministic. A presumption is not needed.

There are plenty of valid augments as to why our universe may not be entirely deterministic, the uncertainty principle, the big bang (or perhaps big bounce) singularity (a causal singularity), quantum fluctuations and virtual particles (where everything that can happen does happen) and even the problem of the decoherence of quantum states in superposition resulting in some particular outcome state. However, your simple presumption of non-deterministic aspects of the universe (by you simply labeling some information in the universe as “non-deterministic”) again only proves that you are just presuming some non-deterministic aspects of the universe.

The fact that you label all arguments and reasoning as "simply labeling" indicates that you do not have ability to analyze or comprehend rational debate.

As others have noted before, the total determinism of Laplace and 19th century science, died about a hundred years ago (for the above stated reasons). The meaning of determinism has shifted to the predictability of some future outcome based on current information (including Pi), basically asserting that the outcome is not random. As you don’t seem to be arguing that actions ‘based on Pi’ have inherently unpredictable or random outcomes based on that initial information (even just in theory) you are just arguing with yourself over an outdated interpretation of determinism that you just seem to hold yourself.

1. If you think that philosophical arguments that were popular hundreds or thousands of years ago are no longer being debated you are very poorly read and naive.

2. If you think that the form of determinism I presented in the opening post is no longer a held belief you are very poorly read and naive.

Maybe this will help you understand invalidity of your “proof”:

Your claim is demonstrably false, "the value of Pi" (as others have noted) is completely determined by our abstract concept(s) of geometry and you seem to be the only one who has lost sight of that (if you have ever bothered to acctualy look it).

Fact 1: You claim a demonstration and provide none.
Fact 2: Circles existed before geometry.
Fact 3: You are incompetent in presentation and ignorant of history.

You seem to be fixated on some information that you simply label as “non-deterministic” ‘entering’ the universe (specifically a universe that you consider, at least up to that ‘entry’ to be entirely deterministic) and resulting in some 'action' that you also simply label as “non-deterministic”. However, even in the limited physical sense where (again as others have noted) the value of Pi is just an approximation of that abstract determined value. Actions based on Pi are still deterministic, meaning not random. Unless you actually have some evidence that such actions have unpredictable or random results?

You have now revealed your complete ignorance of the topic at hand.
Determinism does not mean "not random" and non-determinism does not mean unpredictable. My opening post explicitly presented a definition and if you have been arguing from inapplicable definitions then it is no wonder you have appeared to be completely inept.

To try to put that abstract concept of Pi in some physical 'action' sense, my steering wheel is a ring. As I apply some constant force tangential to the circumference of that ring through one rotation. My car turns in a direction determined by the direction of rotation from that force vector. The energy that I have applied to the steering wheel (E_s), through that 1 rotation, results in an applied torque on the steering column through one rotation (T_s) turning the steering mechanism. Would you like to guess what the proportion of that applied energy of that 1 rotation to the applied torque through one rotation is on the steering column?

E_s/T_s = 2Pi

Are you claiming that steering your car is “non-deterministic” as it is an action based on Pi?

Do you really think anyone bases a decision on how far to turn a steering wheel upon an evaluation of that equation? You have no idea what this whole post is about.

 

[The Man]

Why do think this is so?

Could you please be more specific about the question you are asking?

There does not need to be a mechanism because there is no barrier? It can enter through calculations, reading, etc.

“no barrier?” An entirely deterministic universe precludes any non-determinism. “calculations, reading, etc” would be, well, mechanisms you cite for said ‘entry’ of your “information“. If they aren’t entirely deterministic than the universe was already not entirely deterministic.

The properties of the universe which contribute to its deterministic nature are not immutable. The universe can change from deterministic to non-deterministic. A presumption is not needed.

What, “not immutable?” If the universe has and/or can go from entirely deterministic to non-deterministic (in at lest some extent) then they are, well, entirely mutable, by your own assertion.

The fact that you label all arguments and reasoning as "simply labeling" indicates that you do not have ability to analyze or comprehend rational debate.

Really? Where did I claim the following “arguments and reasoning” …

There are plenty of valid augments as to why our universe may not be entirely deterministic, the uncertainty principle, the big bang (or perhaps big bounce) singularity (a causal singularity), quantum fluctuations and virtual particles (where everything that can happen does happen) and even the problem of the decoherence of quantum states in superposition resulting in some particular outcome state.

…as “"simply labeling"“?

Everyone here, but you, seems more than willing to have a rational debate about the current status of determinism. When you finally catch up to current interpretations inherent in that debate, please let us know.

1. If you think that philosophical arguments that were popular hundreds or thousands of years ago are no longer being debated you are very poorly read and naive.

If your think that such debate over “hundreds or thousands of years” hasn’t changed the arguments, assertions, assumptions, definitions, and interpretations, then your are just naive and poor, like poor Laplace.

2. If you think that the form of determinism I presented in the opening post is no longer a held belief you are very poorly read and naive.

As I’ve already said explicitly before you evidently hold that belief, so I guess your also just a poor reader.

Fact 1: You claim a demonstration and provide none.

It has been provided to you many times, you do understand that "the value of Pi" is both an irrational and transcendental number, don’t you?

Fact 2: Circles existed before geometry.

"the value of Pi" as an abstract concept of geometry did not, only approximations of that value did. That has already been pointed out to you.

Are you now claiming that "the value of Pi" was determined by some prior state of the universe before geometry?

Fact 3: You are incompetent in presentation and ignorant of history.

You’re just incompetent “in presentation” of any argument about the current state of the debate about the determinism of the universe and evidently simply ignorant, apparently deliberately so, even of your own assertions.

You have now revealed your complete ignorance of the topic at hand.

Nope, evidently that is just you.

Determinism does not mean "not random" and non-determinism does not mean unpredictable.

Try actually studying the history of those debates over those “hundreds or thousands of years” and the current state of that debate. You evidently just what to take the debate back 100 years.

My opening post explicitly presented a definition and if you have been arguing from inapplicable definitions then it is no wonder you have appeared to be completely inept.

Again your “definition” was demonstrated to be “inept” about a hundred years ago. Please tell us how you have a prior state of universe that began a finite time ago.

Do you really think anyone bases a decision on how far to turn a steering wheel upon an evaluation of that equation? You have no idea what this whole post is about.

No they base that decision on the outcome being deterministic. That determinism is based on the cited deterministic relations. Were this not the case some force you apply to the steering wheel could result in a torque of the opposite direction on the steering column, or none at all. You apparently have no idea what the debate on determinism is currently about.

In physics such rotational (or even radial) actions are determined by a subtended angle, measured in radians. Giving them applicability to all circles. Would you like to guess what is the proportion of a rotation (Cycle) to a radian (Rad)?

Cycle/Rad = 2Pi

Oh, and before you inquire, much of the actions that you take everyday and expect some deterministic result (even though you may not realize it, though fortunately someone else did) are based on that deterministic proportion. A simple consequence of our modern technological society.