Incompleteness, Undecidability, and Uncertainty

[J_B_]

I made an offhand comment here, but now it's going to bug me. I might as well get it out of my system.

It seems to me that if science were necessarily tied to mathematics in an existential way, a scientific incompleteness theorem would simply be an extension of the mathematical one (i.e. Godel). However, that seems impossible to establish.

Maybe something based on measurement, as in physics' uncertainty principle, would be a more realistic possibility. That is, maybe some measurement in biology (etc.) would imply a biology uncertainty principle.

What do you think? Is there, maybe, an incompleteness, undecidability, or uncertainty principle for sciences other than physics?

 

[Speedwell]

It depends on what you are looking for wiggle room for.

 

[J_B_]

It depends on what you are looking for wiggle room for.

Maybe I don't understand you, but I don't see how. It either is or it isn't. My gut says an incompleteness/uncertainty principle applies to all the sciences, but as I said in the other thread, I have no idea how it would work. Godel & Heisenberg were smarter than I'll ever be.

 

[Speedwell]

Maybe I don't understand you, but I don't see how. It either is or it isn't. My gut says an incompleteness/uncertainty principle applies to all the sciences, but as I said in the other thread, I have no idea how it would work. Godel & Heisenberg were smarter than I'll ever be.

Godel's incompleteness theorems apply to axiomatic formal systems--which science is not.

 

[J_B_]

Godel's incompleteness theorems apply to axiomatic formal systems--which science is not.

Noted.

 

[Ophiolite]

What do you think? Is there, maybe, an incompleteness, undecidability, or uncertainty principle for sciences other than physics?

What would be the function, or benefit, or application of such a principle?

 

[J_B_]

What would be the function, or benefit, or application of such a principle?

The same as Godel is for math or Heisenberg is for QM.

 

[Ophiolite]

The same as Godel is for math or Heisenberg is for QM.

Heisenberg's principle, as I understand it, is description or interpretation of observations within QM theory. I am unclear as to how you see this in some ways different from other observations/interpretations within the field. Consequently I cannot yet see the relvance to an analagous "thing" in other sciences.

 

[J_B_]

Heisenberg's principle, as I understand it, is description or interpretation of observations within QM theory. I am unclear as to how you see this in some ways different from other observations/interpretations within the field. Consequently I cannot yet see the relvance to an analagous "thing" in other sciences.

Google is a wonderful thing. I had no idea this existed.

Uncertainty principle of genetic information in a living cell | Theoretical Biology and Medical Modelling | Full Text

The date was 2005, so I'm gonna check the followup.

 

[J_B_]

Google is a wonderful thing. I had no idea this existed.

Uncertainty principle of genetic information in a living cell | Theoretical Biology and Medical Modelling | Full Text

The date was 2005, so I'm gonna check the followup.

Apologies for the frenetic pace, but in checking publications that referenced the above paper, I found this:

Unsolvable Problems of Biology: It Is Impossible to Create Two Identical Organisms, to Defeat Cancer, or to Map Organisms onto Their Genomes

I think it's fascinating that someone is claiming unsolvable problems in biology. How widely the idea is known or accepted is a different matter.

 

[Ophiolite]

Useful. The abstract alone has given me two things:

• A clear(er) picture of what you were driving at
• An explanation for why I was having some difficulty in getting your drift: I consider absolute certainty to be a silly idea and in geology (my field of expertise) issues are so 'macro' that the uncertainty you are interested in doesn't arise (in any meaningful way [thus far{to the extent of my knowledge}])

 

[J_B_]

Useful. The abstract alone has given me two things:

• A clear(er) picture of what you were driving at
• An explanation for why I was having some difficulty in getting your drift: I consider absolute certainty to be a silly idea and in geology (my field of expertise) issues are so 'macro' that the uncertainty you are interested in doesn't arise (in any meaningful way [thus far{to the extent of my knowledge}])

I'm glad it helped. You can tell me if this changes anything for you.

https://www.journals.uchicago.edu/doi/abs/10.1086/629321

 

[FrumiousBandersnatch]

Apologies for the frenetic pace, but in checking publications that referenced the above paper, I found this:

Unsolvable Problems of Biology: It Is Impossible to Create Two Identical Organisms, to Defeat Cancer, or to Map Organisms onto Their Genomes

I think it's fascinating that someone is claiming unsolvable problems in biology. How widely the idea is known or accepted is a different matter.

Why is this so notable? Living systems are dynamic, in continual flux, and that includes their genomes.

Heraclitus was aware of this principle around 500BC...

 

[J_B_]

Why is this so notable?

I love to explore and discover the world. It fills me with a sense of wonder. A facet of my sense of wonder is that I wish others would share it with me. Yet, when I mention such ideas, or ask questions about them, the response is much too often (as here), 'Meh.' That saddens me.

I've often wondered if my own field might be constrained by an uncertainty principle, but, as I said, had no idea how to approach it. These papers, recently found*, sparked a thought regarding the general approach that may be at play here. It was especially important to find both the biology and geology papers. Why? Because one question niggling at me was: What facet makes simple confidence levels (something long known in science) rise to the level of an uncertainty principle? Now I have an answer.

My first impression is that the case presented by the biology papers is a significant finding; the case presented by the geology paper, while worthy of publication, is just a small step in the understanding of uncertainty in geology.

Still, I would like to hear the opinion of @Ophiolite on that.

- - -

*Just as my recent discoveries of Kauffman, Longo, etc. opened up some fascinating new territory regarding the nature of first principles.

 

[Ophiolite]

My first impression is that the case presented by the biology papers is a significant finding; the case presented by the geology paper, while worthy of publication, is just a small step in the understanding of uncertainty in geology.

Still, I would like to hear the opinion of @Ophiolite on that.

Interesting. Since you are focused on a search for some Uncertainty Principle you see the geology paper as "a small step in the understanding of uncertainty in geology".

Since I'm focused on the development of our geological knowledge I see it as progress in the use of geothermometry and a review of some of the constraints on its reliability.

As the paper is behind a paywall I don't know if there is anything in it to justify the title. Based on the abstract alone, that title "The Granulite Uncertainty Principle: Limitations on Thermobarometry in Granulites", is either a tongue in cheek dig at physicists, or a desperate measure to get more readers. I don't think it speaks to your search.

There's fifty years of development in techniques since I studied them as an undergraduate. Vast improvements in analytical methods, extensive field work and detailed laboratory studies have led to more accurate, more precise and more revealing data, but at the boundaries we are making assumptions and testing them. That's what the paper is about.

 

[J_B_]

Since I'm focused on the development of our geological knowledge I see it as progress in the use of geothermometry and a review of some of the constraints on its reliability.

I defer to your expertise.

As the paper is behind a paywall I don't know if there is anything in it to justify the title.

Sorry. There was always the chance that you had access, given you work in the discipline. Regardless, thanks for taking a look.

Based on the abstract alone, that title "The Granulite Uncertainty Principle: Limitations on Thermobarometry in Granulites", is either a tongue in cheek dig at physicists, or a desperate measure to get more readers. I don't think it speaks to your search.

Maybe my wording didn't connect with you, but this is exactly what I was trying to say. Thanks for confirming.

 

[essentialsaltes]

Some star in some distant galaxy has the most planets around it. (There could be ties.) We will never know how many planets it has. There are all sorts of things we can never know. But this kind of incompleteness is not very interesting, I think.

 

[Ophiolite]

Sorry. There was always the chance that you had access, given you work in the discipline. Regardless, thanks for taking a look.

I'm retired and my work deviated from geology to engineering decades ago. I've revisted geology as a hobby over the last twenty five years, but I make do with text books and such papers as are accessible.
There is no need to apologise. The abstract gave me new information that will inform my future reading and literature searches.

 

[FrumiousBandersnatch]

I love to explore and discover the world. It fills me with a sense of wonder. A facet of my sense of wonder is that I wish others would share it with me. Yet, when I mention such ideas, or ask questions about them, the response is much too often (as here), 'Meh.' That saddens me.

We all have our own interests. I just found it odd that you would be captivated by the fact that biology is messy and uncertain - when those are its characteristic features...

It was especially important to find both the biology and geology papers. Why? Because one question niggling at me was: What facet makes simple confidence levels (something long known in science) rise to the level of an uncertainty principle? Now I have an answer.

It's not really an uncertainty principle like Heisenberg's Uncertainty Principle, which defines an important uncertainty relation, it's just the uncertainty of dynamic systems. I'm generally wary of taking the name of a specific concept and repurposing it for vaguely similar situations; I'm not having a pop at you, but at the people who want an eye-catching title for their article or paper.

My first impression is that the case presented by the biology papers is a significant finding;

I suppose it could be significant to geneticists, but I'd expect them to be well aware of the effect of mutations when comparing or duplicating sequences...

I'm probably getting cynical in my dotage

 

[Brightmoon]

That struck me as a little odd too! that they’d want to propose a type of ur-organism when even a biological concept such as species is blurry , Let alone individuals. Also the cells inside multicellular organisms doing different jobs means that some DNA is shut off