Impact of Gödel's incompleteness theorems on a TOE

[Hurkyl]

Hurkyl, I'm not following you. I'm not interested in convenience. I've already said there are limitations in what can be done in Tarksi's system. Your posts seemed to be arguing the contrary, but now it seems they are not.

I'm stating that Tarski's system is not as limited as you make it out to be. There are clear limitations -- e.g. that the theory of integer arithmetic cannot be expressed in it -- but it is not as limited as you claim -- e.g. it is able to discuss lines.

The objection you had against lines was that you were rejecting the syntactic tools of first-order logic. Constructing the type of Euclidean Lines from the type of Euclidean Points, for example, is pure first-order logic -- you are not creating a new theory by doing so.

 

[Chalnoth]

If you believe in that information is bounded and that any observer process and hold only finite info, there is a limit of the amount of confidence any information processing agent/observer can accumulate. At some point there is a saturation and you can't inflate the theory by adding the gödel scentences as another axiom, where the progression ends, and all the TOE means is an effective basis for further actions. Also there is not guarantee that there is any convergence to a unique TOE, it may be that it just keeps evolving by destruction of axioms and generation of new ones.

Yes, this is pretty obvious.

Basically our only hope of finding the TOE is if it turns out that mathematical consistency severely limits the possible TOE's so that the correct one can be experimentally distinguished from the others. There is obviously no guarantee that this is the case. And there is certainly no guarantee that we will be able to genuinely demonstrate that there aren't any TOE's that are also consistent but experimentally indistinguishable.

The more common idea that laws of physics are eternal, correspond as I see it to the "infinite confidence" limits in the progression mentioned. But this limit may not exists, for two reasons (unknow non-uniqueness/convergence) and the lack of information capacity to encode this limit/confidence (if at hand).

Well, you can make any laws of physics eternal simply by having the laws of physics describe any changes that occur. But in any event, obviously infinite confidence isn't possible, and I wasn't attempting to imply it was.

 

[bcrowell]

I thought we'd discussed this, and I explained that I thought that Tarski's system did not capture everything that is meant by first order geometry. This could come down to semantics - if by first order geometry you just mean Tarksi's theory, fine. But if you modify Hilbert's original theory, replacing the second order axioms with first order schemas, then I believe you have a system in which you can get arithmetic.

I'm willing to admit this could be wrong, but post 38 alone doesn't show it.

Like Hurkyl, I'm not convinced by your assertion, and I haven't seen you offer any evidence for it. My #38 does offer evidence for my assertion, in the form of a reference to Tarski's paper "A decision method for elementary algebra and geometry." Anyway, I don't know if any of this even matters for the purposes of this thread. It seems that we all agree that there are weaker and stronger formulations of geometry, that the weaker ones don't give enough arithmetic for Godel to apply, and that the stronger ones do.

 

[bcrowell]

I don't think decidability is a necessary or even particularly desirable property for a TOE.

I agree disagree only because IMO this is putting it too mildly. I don't think there is even any clearly defined notion of what it would mean for a physical theory to be decidable.

This thread is really just a quibble over what exactly constitutes a TOE.

And again I disagree only because IMO this is putting it too mildly. I think it's even less than a quibble over what constitutes a TOE. If we get a TOE, we'll know it's a TOE because it will unite the four forces, reconcile GR with quantum mechanics, and make testable predictions that are verified by experiment. That's how we'd know what constituted a TOE. We can't use decidability to define what a TOE would be, because the notion of decidability is fundamentally inappropriate for talking about physical theories.

 

[Lievo]

Nice job of quote mining, Lievo. You omitted the very next sentence.

Which states that the tape is unbounded, and that's not the same, technically speaking, as infinite.

the TM tape is still infinite from the perspective of the mathematical formalism.

This is just making no sense! Ok two ways to see it:
-the tape of any TM that halts is bound by the busy beaver function. It's large, it's unbounded, and it's finite. If the TM doesn't halt, you don't need any tape at all, because you'll never get the result of the TM -which is define as what remains when the TM stops. Of course you can't, in general, know if your TM belong to one or the other class. Doesn't change the tape you need is finite.
-if you think it's infinite, then precise what infinite you're talking about. Is it aleph 0? No, or you'd enter hypercomputation. Is it more? No, that's worse! Is it less than aleph 0? Well, if you believe there is such a thing as an infinite less than aleph 0, go and publish!

Sorry, I'm beginning to be fed up of stating the obvious. Last time I comment this.

 

[D H]

Which states that the tape is unbounded, and that's not the same, technically speaking, as infinite.

Technically speaking, saying that the length is unbounded exactly the same as saying it is infinite.

 

[Chalnoth]

-the tape of any TM that halts is bound by the busy beaver function. It's large, it's unbounded, and it's finite. If the TM doesn't halt, you don't need any tape at all, because you'll never get the result of the TM -which is define as what remains when the TM stops. Of course you can't, in general, know if your TM belong to one or the other class. Doesn't change the tape you need is finite.

If you don't know whether or not the program halts, then you don't know beforehand how much tape is required, which means you need infinite-length tape or risk your computer crashing.

 

[Lievo]

Chalnoth, as you previously teach me some stuff I should not refuse to answer you.

If you don't know whether or not the program halts, then you don't know beforehand how much tape is required, which means you need infinite-length tape or risk your computer crashing.

What you need, mathematically speaking, is at most the busy beaver corresponding to the number of non blank in the initial state. Nothing more, and that's finite. Pratically speaking, be sure your computer will crash before reaching it.

 

[D H]

Baloney. Busy beavers halt. Halting is not a requirement of a Turing machine program. An algorithm to compute the decimal representation of an irrational computable numbers such as the square root of 2 will not stop. The decimal representation of course requires an infinitely-long tape.

 

[Coin]

We are getting a little off topic. But.

What you need, mathematically speaking, is at most the busy beaver corresponding to the number of non blank in the initial state. Nothing more, and that's finite. Pratically speaking, be sure your computer will crash before reaching it.

I think some of this disagreement might be avoidable if we speak precisely.

1. A turing machine must have access to an unlimited amount of tape in order to capture the full power of the turing machine formalism.

2. Any given turing machine, when run on an input for which it terminates, will only use a finite amount of that tape.

The lack of a limitation on space can't be waved away by saying "but that's only for terminating programs", because a significant portion of the power of turing machines in the first place comes from the fact that turing machines have the option of never terminating. The decidable languages are a smaller set than the recognizable languages. If there is a known bound on either runtime or space used, then all programs are "decidable" and you have something weaker than a turing machine.

You are correct that the busy beaver function does define an upper bound on space usage for halting programs. However this statement is not useful to know, because BB(n) is noncomputable. (In other words, BB(n) is a bound, but it is an unknown and unknowable bound). In fact your statement here is basically tautological, because BB(n) is defined as the maximum number of tape squares used up by an eventually-terminating program of a given complexity. So what you are saying is that the number of squares used by a terminating program will be equal to or less than the number of squares it uses.

Do you disagree?

 

[friend]

I think it's even less than a quibble over what constitutes a TOE. If we get a TOE, we'll know it's a TOE because it will unite the four forces, reconcile GR with quantum mechanics, and make testable predictions that are verified by experiment. That's how we'd know what constituted a TOE. We can't use decidability to define what a TOE would be, because the notion of decidability is fundamentally inappropriate for talking about physical theories.

A Theory of everything would at least explain why there are particles, fields, and even spacetime to begin with. Are we going to be fully satisfied if we predict and/or discover smaller, higher energy particles? No, we'll wonder where those came from, and so on, etc, etc. I think we will not be satisfied until we have explained everything in terms of the principles of reason. Once you derive physics from logic alone, then what is there left to question? There would be nothing left except to maybe question your sanity. But to predict the properties of things does not explain where they came from.

I think a theory of quantum gravity would probably be a TOE, because it would unit QM with GR, particles and fields with spacetime. And to unite spacetime and particles fields would probably require a theory from reason alone. For physically, there is nothing more fundamental than spacetime and particles/fields. And to explain something more fundamental than what is physical would have to rely on complete, abstract, generality about anything true; it would have to rely on principle alone.

So here we are discussing whether physics can be reduced to a complete axiomatic system. The question is not even relevant unless we can derive physics from a system of reasoning. I don't think it will reduce to the axioms of geometry because we would still have to explain why there is geometry, or spacetime, to begin with. It would have to reduce to reason, or we would still have questions and it would not be complete. (am I using "complete" equivocally here?)

 

[Chalnoth]

A Theory of everything would at least explain why there are particles, fields, and even spacetime to begin with. Are we going to be fully satisfied if we predict and/or discover smaller, higher energy particles? No, we'll wonder where those came from, and so on, etc, etc. I think we will not be satisfied until we have explained everything in terms of the principles of reason. Once you derive physics from logic alone, then what is there left to question? There would be nothing left except to maybe question your sanity. But to predict the properties of things does not explain where they came from.

I think a theory of quantum gravity would probably be a TOE, because it would unit QM with GR, particles and fields with spacetime. And to unite spacetime and particles fields would probably require a theory from reason alone. For physically, there is nothing more fundamental than spacetime and particles/fields. And to explain something more fundamental than what is physical would have to rely on complete, abstract, generality about anything true; it would have to rely on principle alone.

So here we are discussing whether physics can be reduced to a complete axiomatic system. The question is not even relevant unless we can derive physics from a system of reasoning. I don't think it will reduce to the axioms of geometry because we would still have to explain why there is geometry, or spacetime, to begin with. It would have to reduce to reason, or we would still have questions and it would not be complete. (am I using "complete" equivocally here?)

The difficulty is that there is no guarantee that there exists only one unique TOE. There may be a great many potential ones. Even after discovering a potential TOE, we would still need to determine whether or not it applies to our reality. Pure rational deduction can never ever tell us whether or not a TOE applies to our reality.

 

[D H]

It would have to reduce to reason, or we would still have questions and it would not be complete. (am I using "complete" equivocally here?)

You are using complete incorrectly here. This is a thread on Godel's incompleteness theorems, and whether they have any relevance to a TOE.

 

[Lievo]

I should not refuse to answer you.

I should not refuse to answer anyone. My apologies for this misbehavior.

An algorithm to compute the decimal representation of an irrational computable numbers such as the square root of 2 will not stop. The decimal representation of course requires an infinitely-long tape.

In case you care, please notice there is no such thing. Precisely because you can't compute something that need an infinitely-long tape. You may wish to read http://en.wikipedia.org/wiki/Computable_number" on this.

the computable numbers (...) are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm.

...I hope this is not quote mining too much.

In fact your statement here is basically tautological (..) Do you disagree?

Well said (...) No, except for some details: decidable and recognizable that'shttp://xw2k.nist.gov/dads/html/decidableLanguage.html" , I think it's usefull to know that BB(n) is the bound because basically, this is what separate computing from hypercomputing, and finally the fact that the bound is uncomputable doesn't make it an infinite. But I begin to desesperate here.

 

[yossell]

I'm stating that Tarski's system is not as limited as you make it out to be. There are clear limitations -- e.g. that the theory of integer arithmetic cannot be expressed in it -- but it is not as limited as you claim -- e.g. it is able to discuss lines.

The objection you had against lines was that you were rejecting the syntactic tools of first-order logic. Constructing the type of Euclidean Lines from the type of Euclidean Points, for example, is pure first-order logic -- you are not creating a new theory by doing so.

Don't know what you've got in mind when you talk about the `construction of types'. The existence of lines is not a first order consequence of the existence of points. The existence of first order definable regions is not a consequence of a theory that only talks about points. I Can see what you might have in mind if you've got first order set-theory in the background. But that is to add something to Tarksi's theory.

 

[friend]

Originally Posted by friend
It would have to reduce to reason, or we would still have questions and it would not be complete. (am I using "complete" equivocally here?)

You are using complete incorrectly here. This is a thread on Godel's incompleteness theorems, and whether they have any relevance to a TOE.

I'm not so sure. "reduce to reason" is a reference to logic which is relevant to Godel's Theorems. "still have questions" asks about how the subject in question is proven, which goes to Godel's incompleteness theorem. So it might be my use of the word "complete" is on topic.

 

[friend]

The difficulty is that there is no guarantee that there exists only one unique TOE. There may be a great many potential ones.

As I understand it, if two systems of complete and consistent sets of axioms agree at any point, then they are equivalent. If reality is completely logical and rational in every detail, then it can be reduced to logic.

Even after discovering a potential TOE, we would still need to determine whether or not it applies to our reality. Pure rational deduction can never ever tell us whether or not a TOE applies to our reality.

Are you suggesting that reality is somewhere, somehow not completely logical? I think you'd have a hard time actually proving that.

 

[Lievo]

Are you suggesting that reality is somewhere, somehow not completely logical?

In my view he's just suggesting that pure logic is not powerfull enough to find the TOE. There have been some https://www.amazon.com/dp/0521657296/?tag=pfamazon01-20about this.

 

[yossell]

Like Hurkyl, I'm not convinced by your assertion, and I haven't seen you offer any evidence for it.

So my citation of papers doesn't count? Ok - what would you like?

My #38 does offer evidence for my assertion, in the form of a reference to Tarski's paper "A decision method for elementary algebra and geometry."

But I've acknowledged the existence of this paper, and everything you say about it. I've not denied this. What I questioned is that every first order theory of geometry reduces to Tarski's formulation. I've even given the theory that I have in mind: the first order weakening of Hilbert's theory in his Foundations of Geometry. #38 just doesn't speak to this.

I'll sketch the idea, but it's going from memory so, as ever, I could be wrong.

If you like, think of Hilbert's second order axioms as being replaced with schemas, plus axioms asserting the existence of first order definable regions to give us the points to give us the lines, planes and regions of the theory (I disagree with Hurkyl that these regions exist as a matter of first order logic from the theory of points). Then one can define a region R which consists of an infinite sequence of points p1, p2, p3..., such that all points lie on the same line, p1p2 Cong p2p3, p2p3Congp3p4..., there is no point p on R such that p1 lies between p2 and p...

Basically, we can define the existence of a region using the points of an arbitrarily, infinite spaced region with one endpoint, and these then behave like the natural numbers. Certain geometric constructions allow us, within this theory, to define addition and multiplication on this points of this region, and then we have enough material to do the Godel construction.

 

[friend]

In my view he's just suggesting that pure logic is not powerfull enough to find the TOE.

The other criticism is that logic is too powerful and applies to more than just physical situations. But the fact that logic can apply to fiction as well as to fact means nothing. For all physical laws apply to fictional situations as well as to factual situations. Every problem in a physics textbook does not refer to any actual facts in nature, but they refer to fictional situations invented in the imagination of the author.

Your response still sounds to me like you're suggesting that reality is not completely logical. I don't think that is the view of science. I think that we go off in search of answers because we think things are rational. I don't think that any credible scientist is trying to prove that reality is illogical.

 

[tom.stoer]

Basically one can derive from Gödel's theorem(s) that given X is the ToE
- one can neither derive X nor can one show that X is consistent;
- one cannot derive all results of X

 

[Fra]

Calnoth, I think your post was reasonable also to me, but I mainly used your post as a handle to connect my input to a context, rather that picking specifically on you.

Well, you can make any laws of physics eternal simply by having the laws of physics describe any changes that occur.

Actually I disagre strongly here. This is IMHO at least, exactly what you can not do, because to do this, you need even more information capacity. To even encode the evolution of one theory, you need to at least partially be able to encode a history of such theories and that takes much more capacity.

If you think about, how to go about to acquire CONFIDENCE in how a given theory, does evolve is should be quite clear that you need a BIGGER theory. My conjecture based on information bounds is that such bigger theory simply won't fit and can't be encoded.

This is why I arrive at tha plausible conclusion that all information evolves, and the difference between STATES and LAWS are that the most fundamental laws evolve in a undecidable way, while that STATE evolve in a decidable way (relative to laws).

This connects to the Smolin/Unger discussion about evolving law: then isn't there again a law that governs the evolution of law? My *opinion* to that idea is no. That LAW isn't even decidable, and it's due to incompleteness forced by the information bound, *and* also sometimes because the law changes to fast that information process never gets around to reach maximum confidence before input again has changed.

/Fredrik

 

[tom.stoer]

This is IMHO at least, exactly what you can not do, because to do this, you need even more information capacity. To even encode the evolution of one theory, you need to at least partially be able to encode a history of such theories and that takes much more capacity.

Fredrik, perhaps I missed something, but this need not be the case. A universal Turing machine is a very simple counter example. It acts on an infinite strip and it can store both data and program code on that strip. Essentially it does not distinguish between reading data and reading code. Therefore it does not distinguish between writing data and writing code, either. It can modify its input (it will read later). Therefore one can interpret this (from a different perspective) is changing the algorithm.

Of course the example is not perfect b/c it is a Turing machine and may therefore be not powerful enough to describe (or be) a ToE, and b/c there remains a fixed part of the algorithm which is not stored on the strip and can therefore not be modified.

 

[bcrowell]

Basically one can derive from Gödel's theorem(s) that given X is the ToE
- one can neither derive X nor can one show that X is consistent;
- one cannot derive all results of X

No, because Godel's theorems only apply to formal axiomatic systems, and physical theories aren't formal axiomatic systems.

 

[Fra]

Tom, it's hard to tell if we are focusing on different details but if we remove the information capacity constraint, the the story is different but...

It acts on an infinite strip and it can store both data and program code on that strip.

My point is that the abstractions that considers infinite (or even unbounded) tapes, simply doesn't correspond to a physical system. My perspective is that any given observing system, encoding a theory and processing information about it's environment has a given finite information capacity. This can grow and shrink, presumable related to the process that is responsible for the origin of inertia and mass, but it doesn't charge arbitrarily.

So IMO, what we have here is a "natural truncation". This truncation is also what limits decidability.

If we consider a larger theory, they it's possible, I agree, but then this also corresponds to a different (more complex) observer. This is IMO somewhat analgous to the gödel expansion. But this expansion is IMO a physical process and is constrained by inertia. That's why we have saturation and overflow of data. I think all these things have interesting connections to physical interactions, radiation etc. But now we get into more speculaton. I mainly wanted to add "my line of association" to Gödel theorem. I do not find that abstractions of information, and computability that makes use of unbounded tapes, or infinite computational times to be physically useful.

As I see it, expectations are produced analogous to computations, and what's interesting IMO is that the computation is completed/halted at a rate that is on par with the rate of new input. This suggest that the constrainst of information capacity and computing power, determine what is the optimum algorithm. As a simple mind, needs simple rules. A complex mind will use more complex rules.

As I see it there is a highly dynamical interaction here that involes evolution of algorithms, and there is from the point of view of a given observer a limit as to what's decidable. And this can ideally be exploited by a larger observer, to predct how two smaller systems interact, by revealing "their logic".

But any given observer has a decidability limit, and this IMHO at least, is very likely to show up (as observable effects) in the ACTION of this observer, as this is effect a natural cutoff, that is systme dependent.

/Fredrik

 

[D H]

An algorithm to compute the decimal representation of an irrational computable numbers such as the square root of 2 will not stop. The decimal representation of course requires an infinitely-long tape.

In case you care, please notice there is no such thing. Precisely because you can't compute something that need an infinitely-long tape. You may wish to read http://en.wikipedia.org/wiki/Computable_number" on this.

the computable numbers (...) are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm.

...I hope this is not quote mining too much.

It is apparently a complete misunderstanding on your part regarding the concept of a Turing machine and computability. About Turing machines: You are right that there is no such thing as an infinitely-long tape. However, there also is no such thing as a "real" (i.e. physical) Turing machine. It is an idealization of computing invented well before the first digital computer. About computable numbers: The square root of 2 most certainly is a computable number, as are pi and e. Here is an algorithm for computing e: $e=\sum_{n=0}^{\infty}1/n!$

 

[Fra]

I personally see that this discussion also closely connects to the use of real numbers in physics.

The issues is not just information capacity and memory, it's also about time.

As I see it, one of the type-problems that are interesting in relation to physics is this:

How to rationally compute/infer - given available resources - the optimal next move/action. In a real situation decisions need to be made, based not only upon incomplete information, but also equally important - based on incomplete processing time. Fitness will select such information processing agents for a compromise, that is compromising with halting performance and responsiveness.

I think in physical interactions as well as any decision making process, the "optimum" action - ie. the one chosen by nature an evoluton is a balance between optimality and responsiveness, as BOTH traits are important but to increase the level of optimality make reduce responsiveness, and vice versa. This along introduces randomness and variation around expectations in interactions as it takes a certain amount of time, to reach a certain level of confidence even if the memory isnt' limiting. At least if you define the arrow of time in terms of this computational flow.

/Fredrik

 

[Hurkyl]

Don't know what you've got in mind when you talk about the `construction of types'. The existence of lines is not a first order consequence of the existence of points. The existence of first order definable regions is not a consequence of a theory that only talks about points. I Can see what you might have in mind if you've got first order set-theory in the background. But that is to add something to Tarksi's theory.

There is a class Preline which is a subclass of Point x Point of elements satisfying:

Preline(x,y) = x != y​

and the class Line is the quotient of Preline by the relation:

If (x,y) and (u,v) are in the class Preline, $(x,y) =_{Line} (u,v)$ iff Collinear(x,y,u) and Collinear(x,y,v)​

and the incidence relation "lies on" on Point x Line given by

If (x,y) is in the class Line and z is in the class Point, z lies on (x,y) iff Collinear(x,y,z)​

(and this is a well-defined relation, because it respects =_Line)

No set theory involved, just abstraction.

 

[tom.stoer]

No, because Godel's theorems only apply to formal axiomatic systems, and physical theories aren't formal axiomatic systems.

Why not?

They haven't been reformulated as sets of axioms, but that does not mean that this is not possible in principle (I agree that it is not usefull in order to make progress in physics). Up to now physical theories are a collection of rules instead of sound axioms; physical theories are mathematically ill-defined partially , but nevertheless what you are describing is the current status, not necessarily the future one.

 

[genneth]

I think people are getting far too caught up in the specifics of Gödel's theorems without realising that it is merely the tip of a very large iceberg. Gödel's theorems apply to systems of arithmetic, and as many people have noted, the embedding of arithmetic into other systems is a tricky prospect; that's even ignoring the issues of whether physics is an axiomisable system in the first place.

However, I would argue that the take-away message of Gödel is that systems which can refer to themselves are *interesting*. Compare with Turing's Halting Problem and also Hilbert's Decision Problem. Experts will tell us that there are fundamental differences between these things, and precise embeddings are often controversial. Nevertheless, thy clearly share a common nugget.

Where does self-reference occur in physics? The clearest example I can think of is in quantum measurement --- to measure is to entangle oneself with the system under observation, then inside the observer there has to be a self-referential copy to indicate that measurement has occurred, etc. I've often thought that half of quantum mechanics is really about formalisation of this fundamental inability to represent faithfully one's own physical state (i.e. non-compression of quantum information --- we can store a classical approximation, but no quantum copy is going to be strictly embeddable).

 

[Lievo]

Your response still sounds to me like you're suggesting that reality is not completely logical.

As I didn't toke position, it sounds to me that's what you want to believe.

It is apparently a complete misunderstanding on your part regarding the concept of a Turing machine and computability. About Turing machines: You are right that there is no such thing as an infinitely-long tape.

I guess this is your spicy way to say I didn't know, thank you.

Does any doubts remains (to you) that TM does not use infinite-length tape?

 

[D H]

I guess this is your spicy way to say I didn't know, thank you.

Does any doubts remains (to you) that TM does not use infinite-length tape?

I do know, thanks. The problem is that you do not. Do you have any doubts that pi is a computable number or that a Turing machine can compute all the digits of pi? That the calculation will take an infinite number of steps and an infinite amount of tape (memory) is irrelevant to the concept of Turing machines. That the algorithm used to do the computation is finite is all that matters.

 

[Lievo]

Do you have any doubts that pi is a computable number or that a Turing machine can compute all the digits of pi?

Pi is computable, but no there is no single Turing machine that can compute all the digits.

That the calculation will take an infinite number of steps and an infinite amount of tape (memory) is irrelevant to the concept of Turing machines.

The result of a computation is defined as what remains on the tape when the TM halts. If it doesn't halt, there is no result. So yes, of course it's relevant.

 

[D H]

Pi is computable, but no there is no single Turing machine that can compute all the digits.

Baloney.

The result of a computation is defined as what remains on the tape when the TM halts. If it doesn't halt, there is no result. So yes, of course it's relevant.

More baloney.

Read posts #68 and #80 by Coin. Read some more on what a Turing machine is and is not. And finally, stop posting your misunderstands as fact. You are derailing this thread, and given that this thread is already on a pretty thin set of rails, further attempts at derailing are not good, not good at all.

 

[Lievo]

Read some more on what a Turing machine is and is not. And finally, stop posting your misunderstands as fact. You are derailing this thread, and given that this thread is already on a pretty thin set of rails, further attempts at derailing are not good, not good at all.

Is there anything I can do so that you understand that this, in fact, does apply to your posts, not mine? Would you accept a bet for example?