Dear Sir,

Your paper was quite thought provoking. You have rightly described Shannon's "relative information" as "correlation" or as you say "downright crude physical correlation". In a previous contest here in our paper "INFORMATION HIDES IN THE GLARE OF REALITY", we had written "Information Theory is based on the concept of writing instructions that will make the computer follow and run a program based on those instructions or matching perceptions of the transmitter with the receiver. Perception is the processing of the result of measurements of different but related fields of something with some stored data to convey a combined form 'it is like that', where 'it' refers to an object (constituted of bits) and 'that' refers to a concept signified by the object (self-contained representation)". Your examples and definition at the end conform to this view. But we fail to understand why you distinguish it from "meaningful information"?

All information is meaningful to the receiver. Otherwise it will be data only. Firstly, Darwin dealt with biological evolution. Part of biology can be related to physics, but "intentionality" (we presume it is the same as freewill) is not a part of it. It can be dealt with cognitive sciences, and partially in psychology and linguistics. Secondly, the same information can have multiple meanings for multiple systems or persons. To that extent, it is relative. But each such information is correlated to something in the system and person, to make it meaningful. The "intentionality" is an outcome of that information - making it meaningful.

Darwinian evolution is still a postulate and there are many contra views to contest his concept of selection. You have rightly pointed out that "A dead organism decays rapidly to thermal equilibrium, while an organism which is alive does not". But this does not flow from Darwinian evolution. Also we fail to understand how "we can legitimately reverse the causal relation between the existence of the mechanism and its function"? Can a chicken be converted back to an egg? It is true that the mechanism exhibits a purpose. But is mechanism independent of the system, within which it functions? Why is the digestive system different in different species? Are our digestive system made for us or are we what we are because of our digestive system? Certainly our digestive system regulates our food habit. But we are not the product of our food habit.

The Darwinian concept of "life on Earth may be the result of random happening of structures, all of which perish except those that happen to survive, and these are the living organisms" cannot explain why the uni/multi cellular organisms are still the same as they were at the beginning millions of years ego? Why the monkeys are still there? The role of variability and selection in the evolution of structures are different. While there is no dispute over variability to explain divergences, the role of selection is questionable.

It is true that "surviving mechanisms survive by using correlations" and "mechanisms that lead to survival and reproduction are adapted by evolution to a certain environment". In fact only in that way they become "meaningful", as your example with bacteria shows. But here we land into a sort of chicken and egg problem. We find similar species with slight variations in different geo-climatic locations. Did the geo-climatic conditions varied the species or the species varied the geo-climate? Obviously the answer is geo-climatic conditions varied the species. A snake anywhere cannot move in a straight line and the only way to escape from a rampaging elephant is to run zig-zag. Here physics of biological structures gets precedence over earthly terrain. But this cannot explain the differences between a tropic goat and a mountain goat. The meaningfulness comes from geo-climatic adaptation.

There is nothing as "accidental correlations that are ubiquitous in nature" and there is nothing that "have no effect on living beings, no role in semantic, no use, and correlations that contribute to survival". Nature is highly ordered and economical. We fail to understand its elegance. True, "today's newspaper is not likely to directly enhance mine or my gene's survival probability", but newspaper is not a creation of Nature. And we avoid many problems due to the information we get from today's newspaper.

Truth and meaningful are related concepts. If something motivates us in a certain way or induces a reaction that remains invariant in all similar perceptions/encounters, the commonality arising from such perception is truth. In such cases, our reaction is meaningful.

Regards,

basudeba

Hi Carlo,

I greatly enjoyed this essay. I think that incorporating survival potential as a measure of fitness yields a good approximation of how useful or meaningful the information conveyed really is. I liked very much that you could adapt Wolpert's formulation to treat the essay question, and I agree that having a concrete definition for meaningful information could serve as a basis for future advances applying information theory to cognition.

Kudos for readability and making the technical concepts understandable. I think you communicated the meaning better than the last contest essay, and you show an increasing command of the English language. As with George's comment above; I am on the fence as to whether your formulation flies - but it certainly offers some valuable food for thought. I hope you fare well, this time around.

All the Best,

Jonathan

Dear Dr. Rovelli,

Thank you so much for your well-written and insightful essay. My own essay on complexity will be published soon and I suggest many of the same points that you do, although admittedly, not in such a polished and professional way. It's actually quite astounding to me, that the ideas about information and meaning that you touch upon are not common knowledge, i.e. their elegance and simplicity seems so apparent. My only suggestion for your work is to keep going. That is, I believe that there are lower levels of complexity/information that you might describe with equal eloquence. I wish you luck in the competition and would appreciate any comments you might share about my own essay.

Yours,

Kigen William Ekeson

Quite impressive, Carlo. You say "the structure could be generated precisely by the structure of the very "meaningful information" we have been concerned with here." Wolpert and Kolchinsky speak of a correlation between the state of the organism and its environment and it's this information that helps the organism stay out of equilibrium. What if the information breaks down in your equation: Meaning and Intentionality = info evolution. The organic source of information, DNA, has errors over time and the renewal process yields flawed copies, especially after organisms and a flawed environment interact. What does this do to your equation?

Jim Hoover

    Dear Carlo Rovelli,

    The essay correctly identifies the difference between probabilistic correlation with an information, and the semantic value (meaning) of the information, and that it is the correlation with the specifics of information that is central. It also brings out the distinction that dealing with the quantity of information as per Shannon, is not the same as description of the semantics of the information. While, it correctly places bounds on the domain of information, yet it does not go all the way to specify or quantify the semantics of the same information. I do agree with the importance of information as a link between different structures in science, but the first level task is to lay down a general method of expressing the semantics of universally all possible expressions that convey information.

    With respect to a DNA encoding the information on the structure of the organism, I suppose, at best, DNA can be said to encode the function and processes in highly specific contexts. It is entirely possible that in a different environment, different structure and phenotype may emerge. That is, the code is just one of the necessary elements for a specific structure to emerge.

    I restate that the path Carlo Rovelli identifies to describe the meaning of information is in the right direction.

    Rajiv

    5 days later

    This is an interesting essay that introduces a way of quantifying the notion of meaningful information. It is not clear to us that quantifying the notion of striving for survival in terms of comparisons of entropies will help with the problem of how organisms endowed with intentionality arise.

      I have two questions:

      Your essay describes a connection between mathematics and certain characteristics of agency (purpose and meaningful function). The mathematics is intended to parallel our knowledge that biochemical mechanisms facilitate, through their function, a meaningful and informational relation to or "about" the environment. The complexity of this relation inevitably increases over generations at the behest of survival pressures.

      Q1. Are you not tempted, therefore, to suggest further that over generations biochemical mechanisms become increasingly inclined to delineate environmental particulars in qualitative terms? In other words, if there is a value to be place on environmental particulars--expressed in the functions of an organism's physiology--are you not tempted to propose that the merit of any delineation towards environmental particulars will lead to physiologies that express a range of qualitative attributions towards those particulars (attributions that are qualified by their survival relevance); that such attributions might evince a 'qualitative feel' in the organism towards particular environmental characteristics as qualified by their comparative merits and relevance?

      Q2. If one then factors into an affirmative answer to Q1. the idea that such qualitative mechanisms might be assimilated, evaluated and prioritized through the operations of neural networks, can your mathematics serve to provide the foundations to solving Chalmers' (1995 - Facing up to the Problem of Consciousness) Hard Problem?

      If this sounds reasonable to you, I can provide you with the model which will successfully guide the application of your mathematical foundations to this end.

      Stefan,

      I think you make an important point here.

      What I would say in response is that the individual organism does not, itself, discriminate when interacting with the environment. Rather, the discrimination occurs over a generational timeline as the replicating lineage presents its templates (i.e., its individual organisms) to the environment. To explain... the consequences of survival pressures on the survival of a lineage's individuals make each individual, effectively, an interactive mechanism that serves to measure the merits of that individual's functional template in respect to the survival of the lineage. The discrimination is a generational process instituted by replication over a generational timeline. The consequences are physiological adaptations in which the lineage evolves increasingly complex discriminatory mechanistic individuals.

      Of course, Carlo did not say this, but I am suggesting a solution to this issue.

      Conscious agency in individuals is a feature of more complex interactive mechanisms which the mathematics does not address but I do believe that the mathematics can be extrapolated to do so.

      My essay comparing the dimensions of meaning in physics, biology and human communication is now available here.

      Congratulations, this is an excellent essay, truly original. I have 2 questions:

      - would it be right to formulate darwinian evolution as: Species evolve by modifying p(x|y) in such a way as to guide the joint distribution p(x, y) in the direction of increasing M? This makes sense to me, at least, when considering a single species evolving in a static environment. When many species are coupled, and the environment of each species is defined by the state of all the others, recursiveness may abolish the existence of a global landscape to maximize. For example, it could happen that by adjusting p(x|y) in the direction of increasing M, a species may end up changing y, and producing a catastrophic effect on itself.

      - P and P-tilde have been defined in terms of the probability of not surviving (S > Sthr), which makes the theory adequate to describe natural selection in living organisms. But could it be extended to more broad-directed behavior, encompassing all systems (not necessarily biological) that decrease their entropy as time goes by? Could the condition inside the integrals of Eqs. 7 and 8 be (Sinitial - Sfinal)? It seems to me that the meaningful information would in this case measure the degree up to which correlations contribute to a generalized goal, not necessarily survival. Or am I missing something?

      Carlo,

      Hope you check out my essay and provide your own comments.

      Jim

      carlo, hi,

      i was pleased to see that you explore the importance of evolution - the ability of a bacteria to increase its chances of survival (and thus propagation) through awareness of its external environment. i would love to have seen this explored further in connection with the essay's goal. in what way could your essay be an answer to the main question (or a variant of the same), "how can mathematical laws give rise to aims and intentions?".

      apologies if i have missed how your essay already answers that question.

      Dear Colleague,

      This was a very interesting essay, even though I was hoping that you could have found a connection between the concept of relative information and your relational interpretation of quantum mechanics.

      Jarmo Makela

      Carlo,

      Your good paper was thought provoking, in particular your distinction between meaningful information and directly meaningful information. This covers the stimulus-response relationship well. I was hoping to read how this relates to aims and intentions which encompass a not-yet achieved future state and encompass a strategy to achieve that desired future.

      William Goodwin

      Dear Carlo,

      one of the (many) merits of you essay is, I believe, to draw attention to a concept - meaning, or meaningful information - that was left a bit in the shadow in the Context Guidelines (the keywords there being long-term goals, intentions, agency etc.), and to convincingly argue that this concept could indeed represent a first crucial step in the path from physical to mental, which is of course much relevant to the contest objectives.

      Once the entropy-based notion of useful correlation between internal and external variables is given, it is easy to see how the human brain, enjoying memory and the ability to model the external world, can take advantage of these correlations even in a conscious manner, e.g. by playing simulations internally before triggering external actions.

      But I would be much interested in the opposite extreme: how far down can your idea be pushed?

      In a world conceived as a bunch of atoms of spacetime, or a causal set, rather than a network of cells or animals, when and how could I start spotting meaningful mutual information at work?

      Prerequisites include the emergence of sufficiently persistent regions (X, Y...) with an inside and an outside, and macro-variables (x, y, ...) on top of the available micro-levels, which enable entropy notions. Talking about correlations between variables x and y also requires many instances of their value pairs in 'time' and/or in 'space' (thus, persistent or multiple copies of X and Y).

      I am much attracted by the search for the most elementary formal systems -- possibly intended as models of a (young) universe -- that support your definition of meaningful mutual information, and its fruitful operation in evolutionary sense. I would be grateful if you could share your opinion on this issue.

      Thanks!

      Tommaso

      Hi Carlo,

      "We can easily imagine an alternative version of life where the meaning of two letters is swapped in the genetic code." Carlo Rovelli, 2017

      This doesn't quite work because it is the chemical structure of the mRNA that is the template for protein construction. A change in the code is a mutation that would give a different product that may or may not be functional. There might however be alien life that operates with a different genetic code building alien life proteins. Synthetic life with extra base pairs has been developed in the lab, with the idea of building novel chemical structures. And there is the remote possibility of undiscovered Earth life that has a different cipher from all currently known Earth life.

      The DNA can be regarded as a causal actor in eventual protein assembly. Looking back, the sequence of the DNA is an important underlying cause of the sequence of the protein. (It can't cause it alone though, as the cell apparatus and raw materials and energy supply are also needed). Does it add anything saying the DNA had this (protein sequence) meaning? Likewise, a signal carried by the optic nerve may cause a particular activation of the visual cortex. Does it add anything to say the signal had that meaning rather than it was cause of that activation?

        A signal is a physical event that conveys meaning. A ring of my phone, for instance, is a signal that means that somebody is calling. When I hear it, I understand its meaning and I may reach the phone and answer. Carlo Rovelli 2017

        Does it covey meaning or is meaning produced from the sound signal on arrival? There is no labelled attached to the sound waves that has its meaning. The information is only what it is. That could be, as examples, a pattern, a structure or a simple physical characteristic such as a frequency of light or frequency of sound. Only if the means to produce the meaning exist is that, which is transmitted, meaningful. That red means stop must be learned before it has that meaning. Stop is not transmitted but the red frequency light is. Likewise, DNA is just a chemical. The protein product is the meaning, that doesn't exist until it is produced. It would probably be better if we stopped saying meaning is transmitted or conveyed and say instead meaning is translated, extracted or produced, only the carrier of the information is transmitted.

        What distinguishes its being a signal, from its being a simple link in a physical causation chain? Carlo Rovelli 2017

        I think that is a good question. I also think that is a person/people deciding to classify it as a signal because there is clearly transmission happening and specific (receipt)-response correlation. There are very many specific chemicals in biology that are considered to be signals; that bind with specific receptors causing recognized effects. Which works against your next point that the carrier could be different. While in some situations that is true, any buzzer or bell could call an assistant, and in other situations such as 'finely tuned' biochemistry it is not.

        Thanks for a thought provoking, well written presentation.

        I wrote "meaning is translated, extracted or produced," extracted is definitely not the right word there . I should have said translated, inferred or produced, as i am saying meaning is not carried.