On the myth that probability depends on knowledge

[Studiot]

There is a difference between testing a human and testing the assertion that a particular bridge will collapse with 75% probability when a particular truck crosses it at a particular time. The latter is impossible and proves that the statement has no scientific content.

Actually that is where you are wrong.

You introduced the example of radioative decay, which is exactly parallel.

I take particular exception to the notion that my statements 'have no scientific content'.

That is a highly coloured value judgement sir!

 

[A. Neumaier]

Actually that is where you are wrong.

You haven't proven me wrong. You haven't provided a way to test the statement, thus making it amenable to the scientific method.

You introduced the example of radioative decay, which is exactly parallel.

No, it isn't. Radioactive decay is a mass phenomenon and the probability for decay applies (as I had explicitly argued) _only_ to the ensemble of all isotopes of a particular kind, and not to any single decay. The latter is completely unpredictable and a probability statement about it is - like any statement assigning a probability dofferent from 0 or 1 to a single event - completely uncheckable.

Thus applying the probability for the decay of an anonymous atom to a particular atom has as much scientific content as claiming that a ghost has appeared on my desk.

I take particular exception to the notion that my statements 'have no scientific content'.

The statement that I called devoid of scientific content, namely ''that a particular bridge will collapse with 75% probability when a particular truck crosses it at a particular time'' was mine, not yours.

 

[A. Neumaier]

I take particular exception to the notion that my statements 'have no scientific content'.

The statement that I called devoid of scientific content, namely ''that a particular bridge will collapse with 75% probability when a particular truck crosses it at a particular time'' was mine, not yours.

Whereas the statement that you actually made in this context, namely

You test your assessment by driving over the bridge.

is plain wrong.

How can a nontestable statement have scientific content?

 

[Studiot]

No, it isn't. Radioactive decay is a mass phenomenon and the probability for decay applies (as I had explicitly argued) _only_ to the ensemble of all isotopes of a particular kind, and not to any single decay. The latter is completely unpredictable and a probability statement about it is - like any statement assigning a probability dofferent from 0 or 1 to a single event - completely uncheckable.

I grow weary of this verbal fencing - it achieves nothing.

Instead of constantly flatly refuting everyone else's comments you might gain something if you asked for more information about why such and such statement was made.

Radioactive decay, for instance, is actually a function of time, not mass.
The objective measure is the fraction ( a pure number) decaying within a certain time period.

So it is with lorry journeys and bridges.

Again I repeat this is a quantum mechanics forum.

In QM there are at least two ways of interpreting probability, since there are at least two independent variables.

So it is with lorry journeys and bridges.

 

[Dale]

Of course, the model reflects knowledge, prejudice, assumptions, the authorities trusted, assessment errors, and all that, but that's the same as in _all_ modeling. Hence it is not a special characteristics of probability.

If the model depends on knowledge and the result of the model is a probability then how can you claim that probability does not depend on knowledge? And I agree that it is not peculiar to probability.

I think you are confusing your concept of "subjective" with knowledge. With a specified family of priors and an algorithm for determining the hyper parameters from the available knowledge then the probability depends on the knowledge objectively. I believe that you are really just saying that scientists shouldn't just use subjective "gut feeling" priors.

 

[SpectraCat]

There is a difference between testing a human and testing the assertion that a particular bridge will collapse with 75% probability when a particular truck crosses it at a particular time. The latter is impossible and proves that the statement has no scientific content.

Ok .. let's work this through:

There is a bridge, trucks drive over it. Each time a truck drives over it, one of two things will happen .. it will collapse or it won't. Objectively, for each trial (i.e. truck journey) there is no way to say with certainty which outcome will be obtained until either the truck crosses safely, or the bridge collapses. Ok so far?

Now consider two bridges, a wooden bridge designed for pedestrian traffic, and a steel bridge designed for truck traffic. You are the truck driver ... which bridge do you take? I guess that is what you are calling a subjective probability judgment? It seems to me that there is a higher objective probability that the wooden bridge will collapse when the truck is driven across it. Do you agree with that? If you do agree, then can you explain how you measure the difference between the cases? Or is the difference unmeasurable?

Note the exactly the same analogy can be drawn for radioactive decay lifetimes of different isotopes: given two atoms of different isotopes, one with a half-life of 5 seconds, the other with a half-life of 5 years, which is more likely to decay in a given time interval? It seems that there is a clear, objective difference between the probabilities of the two events. What is wrong with that analysis?

 

[Studiot]

Well SC you seem to have caught the essence of it.

The bridge assessment question is faced by some bridge engineers every working day of their lives.

You may have heard of AILs - Abnormal Indivisible Loads.

When a load larger than the legally allowable the max gross weight needs to be transported the transport company approaches the bridge authority for any bridge they propose to pass over to ask under what conditions they can cross the bridge.

A real world example might be a train company transporting a 250 tonne locomotive to another location along roads and across bridges where the max gross weight is 38 tonnes.

 

[lalbatros]

There is a difference between testing a human and testing the assertion that a particular bridge will collapse with 75% probability when a particular truck crosses it at a particular time. The latter is impossible and proves that the statement has no scientific content.

Is that not a bad news for engineers, specially in the nuclear safety field?
Reliability theory and practice is completely build on the assumption that probabilities (even very small) have a meaning even though they often cannot be measured.

The book "The Black Swan" by Taleb illustrated very well the risk of blindly using probabilities.

This discussion is interresting.
Jaynes has clearly shown that the concept of probability needs to be analysed more deeply.
I have no doubt that probabilities are -in way- subjective and that this explains conceptual difficulties in physics, specially quantum mechanics.

The "frequentist" interpretation is conveniently used to hide difficulties in quantum mechanics, but these difficulties remain even if they are hidden.

 

[Studiot]

Reliability theory and practice is completely build on the assumption that probabilities (even very small) have a meaning even though they often cannot be measured.

The engineering answer to a quantity that cannot be calculated or measured exactly is to bracket it between upper and lower bounds to prove that is lies within acceptable limits.

The whole idea of limit state is that the probability of failure is quantifiable in this way and acceptably low.

 

[lalbatros]

The engineering answer to a quantity that cannot be calculated or measured exactly is to bracket it between upper and lower bounds to prove that is lies within acceptable limits.

The whole idea of limit state is that the probability of failure is quantifiable in this way and acceptably low.

I agree, but the evaluations cannot be tested ... and humans often do mistakes!
The black swarn approach would be to ban Nuclear Power plants: never trust Gaussian assumptions if your life is at stake.
Or in extended form: never trust any assumption if your life is at stake.

 

[Studiot]

Mistakes can usually be caught and corrected if proper procedures are followed.
That is what the independent check is all about for instance.

Deliberate mis-evaluation is more difficult to cope with.

 

[A. Neumaier]

Instead of constantly flatly refuting everyone else's comments.

I only refute what doesn't hold water.

Radioactive decay, for instance, is actually a function of time, not mass.
The objective measure is the fraction ( a pure number) decaying within a certain time period.

a ''mass phenomenon'' does not refer to masses measured in kg, but to masses measured in large numbers. I could have written as well ''ensemble phenomenon''.

So it is with lorry journeys and bridges.

Again I repeat this is a quantum mechanics forum.

I don't see the connection of lorries and bridges with quantum mechanics.

 

[A. Neumaier]

There is a bridge, trucks drive over it. Each time a truck drives over it, one of two things will happen .. it will collapse or it won't. Objectively, for each trial (i.e. truck journey) there is no way to say with certainty which outcome will be obtained until either the truck crosses safely, or the bridge collapses. Ok so far?

Yes, and since you say ''each'' time, you acknowledge that it is a matter of ensembles, not of driving across this bridge now. The single instance is not a matter of probability, but what happens each time someone does something is. That's the whole point.

Note the exactly the same analogy can be drawn for radioactive decay lifetimes of different isotopes: given two atoms of different isotopes, one with a half-life of 5 seconds, the other with a half-life of 5 years, which is more likely to decay in a given time interval? It seems that there is a clear, objective difference between the probabilities of the two events. What is wrong with that analysis?

That you equate objective probabilities for ''each time'' with subjective probabilities for
a single instance. Applying the probability is admissible only if you regard the single instance as member of the observed ensemble, and then it refers to the ensemble and not to the single instance. This becomes obvious if you ask for the reason why the subjectve probability was assigned. invariably there will be an explanation involving
''each time''.

Suppose a second person would assign different probabilities based on ignorance, and a third person would assign different probabilities based on better knowledge unknown to the driver. Since all are subjective probabilities, all are as valid as any other. Now the driver picks one of the roads and drives - with or without success. Who of the three were correct or wrong? Being subjective probabilities, all were right. Thus the scientific method is impotent to distinguish between these probability assignments - although they would be mutually conflicting if they were saying something about the bridge rather than the subject defining them. This clearly shows that subjective probabilities are properties of the subject and not properties of the bridge.

 

[A. Neumaier]

When a load larger than the legally allowable the max gross weight needs to be transported the transport company approaches the bridge authority for any bridge they propose to pass over to ask under what conditions they can cross the bridge.

But this is a matter of law, not of science.

 

[Studiot]

But this is a matter of law, not of science.

Are you seriously suggesting that the weight carrying capacity (ie whether it is physically possible to support a statd weight) of a structure is a matter of human legislature, not of science?

''mass phenomenon'' does not refer to masses measured in kg, but to masses measured in large numbers

Are you suggesting that the probability of atomic decay (chain reactions apart) is a function of the number of atoms present.
And I always thought that the measure was the probability that a certain % would decay in a specific time, regardless of quantity.

 

[A. Neumaier]

Are you seriously suggesting that the weight carrying capacity (ie whether it is physically possible to support a statd weight) of a structure is a matter of human legislature, not of science?

Don't exaggerate my statements so that they look foolish!

I am seriously suggesting that the probability of failure of a particular structure at a particular time (unless it virtually equals 0 or 1) is not a matter of science, since there is no way to check the agreement of the assignment with what actually happens.

What is a matter of science is the calibration of an ensemble model for bridges of a certain kind that allows one to assign failure probabilities to arbitrary bridges in the ensemble.

Such a model can be used by legislation to place limits on the weights of specific bridges in dependence on their characteristic parameters, in such a way that the failure probability in the ensemble under the legally allowed operation conditions remains below a level tolerated by the legislating body.

This is how limit state analysis is applied in real life.

Are you suggesting that the probability of atomic decay (chain reactions apart) is a function of the number of atoms present.
And I always thought that the measure was the probability that a certain % would decay in a specific time, regardless of quantity.

No. I was suggesting that verifying decay probabilities is done by measuring how many atoms from a huge ensemble decay in a a certain time interval large enough that so many decays actually happen that the probabilistic estimate has some statistical accuracy.

Nobody is able to check a statement about decay probabilities by looking at a single particle for a single half-life, to see whether it decays with 50% probability.

 

[Studiot]

I think your analysis of atomic decay is flawed.

You claim

''mass phenomenon'' does not refer to masses measured in kg, but to masses measured in large numbers

Whether we are talking about kg or numbers of atoms they are essentially the same, since one is directly proportional to the other.

Where in the SI (or any other) system are masses measured not in kilograms but in 'large numbers'?

Your presentation of statistics is also flawed.

It should yield the same result whether you
Take one single atom and observe the decay for a specific time period and repeat the observation 10 million times, combining the results into a probability.
Or whether you take 10 million atoms and observe them all for one single specific time period together, again combining the results into a % probability.

Let us now say that in 100 hundred hours of observation of the 10 million atoms taken together, 50 million have decayed.

Are you saying that you disagree that if you had observed 10 million atoms separately for 100 hours each some other number than 50 million (near enough) would have decayed?

I maintain that the probability anyone of these particular atoms decaying in 100 hours is 50%, regardless of whether it is surrounded by zero or trillions of similar atoms.

Do you not agree?

 

[A. Neumaier]

I think your analysis of atomic decay is flawed.

You claim
Whether we are talking about kg or numbers of atoms they are essentially the same, since one is directly proportional to the other.

Where in the SI (or any other) system are masses measured not in kilograms but in 'large numbers'?

Why should this create a flaw in my analysis? You mentioned ''not mass but time'', and I replied that you has misinterpreted my usage of the word ''mass''. For the statistical analysis only the number of instances matter, not any equivalent description in other units.

Your presentation of statistics is also flawed.

It should yield the same result whether you
Take one single atom and observe the decay for a specific time period and repeat the observation 10 million times, combining the results into a probability.

Or whether you take 10 million atoms and observe them all for one single specific time period together, again combining the results into a % probability.

No. _Your_ argument is flawed. Suppose I observe a single particle in 10 million consecutive periods whose length is one half-life. I observe exactly one decay, say in period 2. Or in period 8. Or in period 50. In a very unlucky case perhaps in period 2345. In neither case can I conclude anything about the true decay probability in that period.

If there were anything to be combined into a probability, the decay probability per period would appear to be 10^{-7} in each case, which is nonsense since the 10 million observations are not independent.

On the other hand, if I observe 10 million atoms for a half-life and find 50.2% decayed, I have a good confirmation of my theoretical model.

Thus there is a world of differences between the two scenarios you described.

 

[Studiot]

Suppose I observe a single particle in 10 million consecutive periods whose length is one half-life. I observe exactly one decay, say in period 2. Or in period 8. Or in period 50. In a very unlucky case perhaps in period 2345. In neither case can I conclude anything about the true decay probability in that period.

That is a different experiment from the one I proposed and I one have not commented on.

It is quite invalid to use it to provide any commentary whatsoever on the experiment I proposed, although I agree with your observation that since you have only observed 1 decay you have not gained much information.

So I repeat my question

Do you agree with my conclusions from the experiments as I posted them or not?

 

[A. Neumaier]

I agree with your observation that since you have only observed 1 decay you have not gained much information.

Thus you should agree that applied to only one particle, one can't check any probabilistic statement about it. Therefore assigning probabilities to single events is scientifically meaningless.

So I repeat my question

Do you agree with my conclusions from the experiments as I posted them or not?

Once one can repeat experiments on multiple particles, one an ensemble, and
if the size of the ensemble is large enough, it is meaningful to talk about probabilities.

Thus your experiments do not contradict my statement that assigning probabilities to single events is scientifically meaningless.

 

[Studiot]

Thus you should agree that applied to only one particle, one can't check any probabilistic statement about it. Therefore assigning probabilities to single events is scientifically meaningless.

No the second statement does not follow from the former.

And yes, one can check some probabilistic statements about even one single atom.

Throughout most of your high handed, sometimes rude, responses to my comments I have mainly been trying to point out that you have make sweeping, all embracing statements by the use of these small words like 'any'. You are just courting refutation by using them.

For instance I can check the statement:

The probability that one atom will decay within 30 years is 1 (or zero).

It may be a far fetched scenario but it is checkable.

Edit - I realize that zero probability is strictly not checkable in this case so should be struck out.

 

[A. Neumaier]

No the second statement does not follow from the former.

And yes, one can check some probabilistic statements about even one single atom.

Throughout most of your high handed, sometimes rude, responses to my comments I have mainly been trying to point out that you have make sweeping, all embracing statements by the use of these small words like 'any'. You are just courting refutation by using them.

For instance I can check the statement:

The probability that one atom will decay within 30 years is 1 (or zero).

It may be a far fetched scenario but it is checkable.

Edit - I realize that zero probability is strictly not checkable in this case so should be struck out.

Of course. Usyally I qualified my statements of this kind by saying ''probability different from zero and 1'', and thish was also meant in the present case.

Thus the conclusion of our long dispute is that applied to a single instance of a system, one can't check any statement about it of the form ''The probability that the statement
S applies to this system is p'', where 0<p<1. Therefore assigning probabilities different
from 0 or 1 to single events is scientifically meaningless.

 

[Studiot]

Thus the conclusion of our long dispute is that applied to a single instance of a system, one can't check any statement about it of the form ''The probability that the statement
S applies to this system is p'', where 0<p<1. Therefore assigning probabilities different
from 0 or 1 to single events is scientifically meaningless.

Again no I don't agree.

If you had stuck to decaying atoms that would have been fine but you again chose to generalise.

This brings us back to structural engineering.

The bridge assessment example I gave is a real world example from my professional experience.
Admittedly extreme examples like that only occurred 2 or 3 times a year - the overload was normally much less severe.

But it did occur and had to be coped with in a scientific (=rational) manner.

And yes I got the load across safely.

As regards to limit state, you presumabably realize that there are many limit states and that the controlling limit state is usually not the limit state of collapse but the limit state of serviceability.

Since this last state is a non destructive state it can be checked, even in a single instance.

 

[Fra]

Thus you should agree that applied to only one particle, one can't check any probabilistic statement about it. Therefore assigning probabilities to single events is scientifically meaningless.
...
Once one can repeat experiments on multiple particles, one an ensemble, and
if the size of the ensemble is large enough, it is meaningful to talk about probabilities.

I see your point of view, but my main objection is this:

As far as I can tell, your concept of probability is useless in decision making, simply because the decision generally has to be made before the confidence in the odds are well defined enough.

This is the basic challange of reasoning upon incomplete information in the first place. Not only do we now konw, we do not even konw (in your objective sense) the odds, so we need to place our bets based upon EXPECTATIONS of the odds. Yes, at some point these expectations are subjective.

But the question is then: What do you do? The point is that, either you make a decision or you don't. But reality will not halt the game, "no decision" is in fact also a decision, it's the decision that "we do not have sufficient scientifc basis for a decision".

You describe a strict descriptive view, and you pretty much say that when the descriptive view fails then so does science, right? If we accept that, I can understand your perspective. There is a kind of rationality in your reasoning. This again brings us to the root issue, what is the basic problem here?

I think you see it as a descriptive problem?
I see it as a decision problem.

Actually, if we for the sake of argument accept the descriptive view, I agree with a lot of what you have said.

/Fredrik

 

[Studiot]

The probability that one atom will decay within 30 years is 1

There is an absolutely wonderful short story by Ray Bradbury on this subject, about two ornaments on a mantleshelf.

 

[A. Neumaier]

The bridge assessment example I gave is a real world example from my professional experience.
Admittedly extreme examples like that only occurred 2 or 3 times a year - the overload was normally much less severe.

But it did occur and had to be coped with in a scientific (=rational) manner.

And yes I got the load across safely.

As regards to limit state, you presumably realize that there are many limit states and that the controlling limit state is usually not the limit state of collapse but the limit state of serviceability.

Since this last state is a non destructive state it can be checked, even in a single instance.

Ah. But now you changed the assertion.

You no longer discuss a probabilistic statement of the form ''the probability for crossing the bridge safely in this particular instance is 99.99%'', which is uncheckable and hence unscientific.

Instead, you discuss a definite statement ''the bridge can be crossed safely'' (because of an underlying probabilistic analysis)!

I agree that the latter is a scientific statement. based on a probabilistic analysis that refers to the ensemble of all bridges taking into consideration for constructing the model on which the analysis is based.

 

[Dale]

Are you avoiding my previous: https://www.physicsforums.com/showpost.php?p=3284903&postcount=110

This whole debate is purely semantic. If you require probabilities to be defined only over an ensemble then the probabilities do not depend on knowledge (for Bayesians the posterior is not a function of the prior given an infinite amount of data). If you allow probabilities to be defined over individual trials or small samples then the posterior is a function of the prior so the probabilities do depend on knowledge.

That dependence on knowledge may be objective if you have a well-defined rule for generating a prior based on the knowledge, or it may be subjective if you have a "gut feeling" prior.

 

[A. Neumaier]

Are you avoiding my previous: https://www.physicsforums.com/showpost.php?p=3284903&postcount=110

No. It was an oversight.

If the model depends on knowledge and the result of the model is a probability then how can you claim that probability does not depend on knowledge? And I agree that it is not peculiar to probability.

Because this sort of dependence of knowledge is universal to every discussion, hence adds no information to the discussion. It is like emphasizing in a discussion of a computer program ''programs depend on knowledge'' - true but not relevant for the substance of what a computer program is.

Knowledge needs no mention in discussing deterministic models, so it creates an undue and misleading emphasis if mentioned for probabilities. The usual usage there suggests that the dependence of probability on knowledge somehow explains its peculiar nature, while in fact it acts as a smoke screen hiding the real issues.

I think you are confusing your concept of "subjective" with knowledge. With a specified family of priors and an algorithm for determining the hyper parameters from the available knowledge then the probability depends on the knowledge objectively. I believe that you are really just saying that scientists shouldn't just use subjective "gut feeling" priors.

I am saying more:

With a specified family of priors and an algorithm for determining the hyper parameters from a set of data then the probability depends on the data objectively. Independently of whether the data arise from knowledge, simulation from a hypothetical source, prejudice, fraud, divination, or anything else.

That it depends on knowledge if the data depend on knowledge is true but irrelevant.

The model is only as good as the data, that's the only relevant point here.

This whole debate is purely semantic.

Of course. It is a matter of precise usage of the concepts. Semantics is important in interpretation issues.

If you require probabilities to be defined only over an ensemble then the probabilities do not depend on knowledge (for Bayesians the posterior is not a function of the prior given an infinite amount of data).

But one is never given that much data.

If you allow probabilities to be defined over individual trials or small samples then the posterior is a function of the prior so the probabilities do depend on knowledge.

No. it depends on the sample, which could come from a computer simulation rather than from real data. It depends on knowledge only if the sample represents the knowledge someone has about the intended application; so mentioning knowledge is less accurate and makes more unspoken assumptions.

What if nobody has ever seen the data but the computer program processing it? Does the program then know? Or does the human who started the program know? Knowledge is a philosophically difficult concept prone to misunderstanding.

That dependence on knowledge may be objective if you have a well-defined rule for generating a prior based on the knowledge, or it may be subjective if you have a "gut feeling" prior.

If you substitute ''knowledge'' by ''data'' I'd agree. The latter is a much more descriptive word.

Why substitute it with an unspecific word that assumes that there is someone having the knowledge and invites associations with states of the mind of experimenters?

 

[ndung200790]

It seem to me that the thought of God controls all the quantum processes,and the thought of God continuosly work all time ,but the human can not understand the thought of God.Then before the eye of people,the objective probability nature of quantum physics appears.

 

[A. Neumaier]

It seem to me that the thought of God controls all the quantum processes,and the thought of God continuosly work all time ,but the human can not understand the thought of God.Then before the eye of people,the objective probability nature of quantum physics appears.

Note that, with the definition I gave here, objective probability is not restricted to the quantum domain.

 

[ndung200790]

Please teach me what is your definition of objective probability.Because in classical physics,probability depends on the knowledge of the human,but we would definitely guess the happening even if we were supplyed enough the information.

 

[ndung200790]

I think that the definitely happening of events in classical physics do not affect the ''law'' of large number events.The large number of ''definitely happening'' events regulates the probability of single event if we have not enough the information about this single concrete event.

 

[A. Neumaier]

Please teach me what is your definition of objective probability.Because in classical physics,probability depends on the knowledge of the human,but we would definitely guess the happening even if we were supplyed enough the information.

It is amply discussed if you follow the thread; you should read it all and post questions to a particular posting if you don't understand something there.

 

[SpectraCat]

Yes, and since you say ''each'' time, you acknowledge that it is a matter of ensembles, not of driving across this bridge now. The single instance is not a matter of probability, but what happens each time someone does something is. That's the whole point.

That you equate objective probabilities for ''each time'' with subjective probabilities for
a single instance. Applying the probability is admissible only if you regard the single instance as member of the observed ensemble, and then it refers to the ensemble and not to the single instance. This becomes obvious if you ask for the reason why the subjectve probability was assigned. invariably there will be an explanation involving
''each time''.

Suppose a second person would assign different probabilities based on ignorance, and a third person would assign different probabilities based on better knowledge unknown to the driver. Since all are subjective probabilities, all are as valid as any other. Now the driver picks one of the roads and drives - with or without success. Who of the three were correct or wrong? Being subjective probabilities, all were right. Thus the scientific method is impotent to distinguish between these probability assignments - although they would be mutually conflicting if they were saying something about the bridge rather than the subject defining them. This clearly shows that subjective probabilities are properties of the subject and not properties of the bridge.

Maybe I don't completely understand, but it seems like you didn't really answer my question .. since this is a quantum forum, let us stick to the question of atomic decay. Consider my example from before: Atom A is of an isotope with a half-life of 5 seconds, atom B is from an isotope with a half-life of 5 years. I agree that the half-lives are characteristics of ensembles, which I think you agree can be stated objectively.

So we have two objective statements:

1) Atoms A & B come from different ensembles.

2) The half-lives of the two ensembles are 5 sec & 5 years for A & B, respectively.

Can you please answer the following questions?

In your view, is it possible to make an objective statement about the *relative* probability of decay of A vs. B for some time interval?

If so, how should it be phrased? Is there a way of obtaining a quantitative measure of the relative probability?

If it is not possible to make an objective statement about the relative decay probabilities, then please explain why? Is it because we are relying on the knowledge about the ensemble statistics for A & B in order to make such a statement? Does that automatically make it a subjective statement in your view? Or is there something else that makes any such judgment subjective?

 

[A. Neumaier]

Consider my example from before: Atom A is of an isotope with a half-life of 5 seconds, atom B is from an isotope with a half-life of 5 years. I agree that the half-lives are characteristics of ensembles, which I think you agree can be stated objectively.

So we have two objective statements:

1) Atoms A & B come from different ensembles.

2) The half-lives of the two ensembles are 5 sec & 5 years for A & B, respectively.

Can you please answer the following questions?

In your view, is it possible to make an objective statement about the *relative* probability of decay of A vs. B for some time interval?

It depends (a) on your definition of relative probability (I don't know this concept), and
(b) on whether A,B are anonymous atoms from a large ensemble (where the answer is likely yes) or particular selected atoms (where the answer is no if the statement of interest still contains a probability).

If so, how should it be phrased? Is there a way of obtaining a quantitative measure of the relative probability?

Since you invented the concept, you are responsible for giving it an appropriate meaning, before we can discuss it.

If it is not possible to make an objective statement about the relative decay probabilities, then please explain why?

At the moment I can't say anything since I don't understand what you mean.

So let me guess: One possible intended interpretation might be:

A, B are specific atoms (defined by their position under an atom microscope say), and the statement is that
in the next ten minute, atom A will decay N times as likely as atom B, where N is the number of seconds in a year, the statement is untestable and hence subjective.