There are many ways in which science could be different. Had we done something different in the past, we would now have a different science, perhaps a better one. Were we to do something today, we would change the science to come. Or wouldn't we? What does this really mean? As far as we know, the world line of our universe is a single-trial experiment. What does it mean to contemplate different alternatives? Although we are continuously exerting counterfactual reasoning, and although social sciences are based on counterfactual logic, the hard sciences have not yet provided a context in which the meaning of counterfactual reasoning is clear. This essay is an attempt to go towards a science that provides a scientific framework in which questions as “How could science be different” are clearly framed. To that end, I discuss the way in which the geometry of the world lines describing the evolution of the universe have to change when coarse-graining the description, in order for causal (that is, directed and manipulable) relations between events to emerge from an a-causal physics.
The geometry of counterfactual science.
Dear CinnabarMink,
I like your essay since it examines counterfactual reasoning. I also like your humour very much – and therefore I did NOT prevent the sun to raise at home – I did it some time ago in a save environment (in Norway :-)))). Hope you also like my humour. I also like your lovingly scribbled pictures to illustrate the points you want to make clear in your essay.
However, I did not fully understand the term “noise” and want to ask you. Is that “noise” to be understood as a completely undecipherable hidden variable, one that is nonetheless considered as non-random (especially when interacting with a certain environment), but merely unknowable for scientists – or has it to be considered as genuinly a-causal in the sense that there exists nothing that determines how much it will interact (if at all) with its environment?
Hi AquamarineTapir, thanks for reading and commenting! I the essay, I have taken “noise” to be a product of describing only the classical variables, and ignoring the heat variables, with no ultimate fundamental randomness. It is the impredictabilty that stems from not keeping track of all the degrees of freedom. The perspective I have taken is valid for classical physics, and also for quantum-mechanical descriptions in which the low-level state is the wave function of the whole universe, and the higher-level ones are density matrices in which the non-interferring branches are the ones resulting from tracing away the heat degrees of freedom. The perspective, however, has to be changed if we want to describe the world as one observer experiences it. The observer is, by definition, inside one of the branches, and they have no way of predicting in which branch they will land. This noise is intrinsic, and appears from taking the density matrix description, and conditioning on the branch the observer is travelling through. I admit I have not thought how to include this description into the perspective of the essay. I have taken the bird's point of view, sometimes also called God's point of view, you are asking a perfectly valid question: how does this change when we take the worm's point of view? In the end, we are inside the branches, as a worm is inside the earth. So let me do this: I will give it a though in the next few days, and come back to you. •‿•
In the meanwhile, I may run into your essay, since I am exploring the forum, lots of nice things to read!
Hi CinnabarMink, thank you for your friendly and honest reply! For me, exploring the forum and the essays is really an adventure, since there are so many creative ideas out there to ponder about. I for myself have also thought a lot about counterfactual reasoning in the past and how one may handle it for being able to eventually come to some safer conclusions. It seems that we humans cannot totally abstain from that kind of reasoning, especially when it comes to fundamental questions.
I am happy that you want to take a look at what I myself wrote for this contest. A little warning may perhaps be appropriate, because I include the notion of God in my essay, but hopefully not in a bigotry manner. If nonetheless, please let me know, maybe I am not aware of that manner.
Anyways, the bird's view I am advocating for as a “new” framework is my kind of way of taking a bird eye's view of the world, without the intention to form a complete picture of what God is. I consider it “new” in the sense that maybe it would be helpful for one or the other reader to re-discover that “old-fashioned” worldview from within a fresh perspective. It is not ment to “evangelise” the whole scientific community (and surely isn't able to do so). After having read my essay I would be happy to read your thoughts about it! Anyways, have an entertaining time with reading and digesting in the forum!
Ines Samengo
Dear Cinnabar Mink,
thanks a lot for this refreshing essay on counterfactual reasoning, I follow the Tapir and also like your sense of humour and the way you explained causal connections in dynamical systems with these really great sketches.
One question that came to my mind after reading: what about the Duhem Quine thesis here? You didn't mention it explicitly when trying to argue why the sun is causing the many different impacts on the world when rising and it's not the rooster's cry. So how does the entire "package of additional underlying assumptions" that leads us to assume that the sun causes flowers to open up in the morning enter your picture that counterfactual reasoning does not play a big role in our world if cast in a certain physical framework? I could imagine that DQT could actually open up a little space to allow for more pondering about alternatives...
Best wishes,
Beige Bandicoot.
Hi, Beige Bandicoot, thanks for reading and commenting! I agree that it is impossible to falsify a hypothesis with certainty. In particular, it is impossible to determine the direction of causality with full confidence. That is why I like probabilistic descriptions within a Bayesian framework. If we want to choose between “sun drives rooster”, or “rooster drives sun”, we can evaluate the ratio Prob(sun drives rooster | data) / Prob(rooster drives sun | data). According to Bayes’ rule, and assuming equal priors (which, admittedly, can be questioned), this ratio is equal to Prob(data | sun drives rooster) / Prob(data | rooster drives sun). These two probability distributions are not delta-like, since both hypothesis have some probability to produce the data that we actually observe. But the data turn out to be overwhelmingly more easily linked with “sun drives rooster” than with “rooster drives sun”. In more technical terms:
Hypothesis 1 is: “The rooster wakes up the world”
If then we observe that the world is not following the rooster’s crow (because it does not), we may conclude that (a) Hypothesis 1 is false, or (b) a very large number of exotic phenomena A1, A2, …, Ak required for the world to look as it does even if H1 is true must have happened. Since (b) is kind of unlikely (because there are a huge number of degrees of freedom involved in “the world waking up”), we take P(data | rooster drives sun) to be small.
Hypothesis 2 is: “The sun wakes up the world”
If then we observe that the world does follow the sun (because everything indicates it does), we may conclude that (a) Hypothesis 2 is true, or (b) a very large number of exotic phenomena B1, B2, …, Bk required for the world to look as it does even if H2 is false must have happened. Since (b) is unlikely, we take P(data | sun drives rooster) to be large.
Ultimately, this is a counting argument. How many unobserved facts do we have to assume to be true for H1 to hold given the data, as compared to H2 to hold given the data? The requirement for the system to be dissipative is imposed for there be many degrees of freedom involved, so that these two numbers be very different. In the original system, before the degrees of freedom are separated into thermal and classical, these numbers are not different.
Let me know if your question was in this direction, I am not sure whether I am answering your question, or just rambling. And yes, there are good many ideas that I have not cited. I just submitted the essay in the last minute. I have now looked at my reference list and it looks kind of a weird selection. But well, there was no time to improve it, I could either submit it as it was, or not submit at all ¯_(ツ)_/¯
Thanks again!
if clasical mechanics is a a subsistem of quantum
Therefore, there is no way to identify which events in the past
should have been different for the present to be different.
than, maybe for example take two present moment let say i put a bottle of water on the table i wait five minutes and look at the table , and there ; the bottle sits on the table , me moving the bottle is the event and the present after the five minutes is the observation . observation made. than i select an other present moment in witch the bottle is not placed on the table after five minutes i could say that for certain i have identified an event that make my present experience different
Ines Samengo
Hi Cinnabar Mink,
thanks a lot for the further explanations. I totally agree that one can never tackle everything there is to say on 9 pages. Concerning the package of assumptions that can never be falsified, I understand what you are aiming at. My question was to one part about the things you sketch and to another, if we look for some "hidden" additional assumptions to support a certain hypothesis, how far would we be willing to go until we deem the additional assumptions to be implausible? As a very clear example we would say is rubbish: let's assume that the rooster has a telekinetic ability to make the sun rise, the problem is just that he cannot do this every day in exactly the same way because it is so tiring and he's not yet very good at it... a less clear example yet of similar kind: we miss some mass in galaxies to explain the way stars move in that gravitational potential. Do we propose to modify our laws of gravitation or do we assume there is some matter that we cannot see in there? How far do we go both of these paths even though neither of them seems to provide a fully satisfying picture on its own?
This is a topic for another entirely new essay, I am just curious, as you like Bayesian statistics, what do you think is the role of physical plausibility compared to mere mathematical arguments when trying to rank models? Occam's razor only makes statements about simplicity and elegance but not about ontologically realistic options.
Bests,
Beige Bandicoot.
Hi Cinnabar Mink,
from your reply I conclude that your base framework may be the Everettian formulation of QM. I pondered a lot about it in the past and out of sheer curiosity I would like to ask some questions about how to properly understand that framework ontologically. So first let me recapitulate:
The assumption that the ontology of all-there-is is identical with a universal wave function results in the world view that everything is some kind of data processing. The results are not genuinly random, but only subjectively random. Since that overall data processing is not defined in space, I have to conclude that on a fundamental level, the assumption of the existence of such a universal wave function inclusively all its existing branches must be considered as immaterial, meta-material – since in the Many-Worlds framework, the frog's view perspective merely confuses the circumstances about the evolution of its world with the real world, the latter being the universal wave function, a highly abstract fundamental ontology made out of a evolving network of compatible and incompatible relationships in a realm that may be timelike, but simply is not space-like.
Now, since the evolution of all-there-is could – theoretically – be described by that universal wave function, the latter is an interesting piece of mathematics. My question now is what the appropritate ontological status of all the rest of mathematics should be within the framework of Many-Worlds? Do all logically possible mathematical relationships reside in that timelike, but not space-like realm where also the universal wave function is assumed to reside? I would be happy about an answer, since my own essay deals with the quest of the ontological status of mathematics.
Jenny Wagner Hi, Beige Bandicoot, thanks again! I actually think Occam's razor can be taken beyond a mere ranking of models due to their simplicity. There is a beautiful paper by David MacKay that shows that Bayesian methods can actually determine which level of simplicity is the adequate one for the data at hand. You can read it here: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwi198qx3f_-AhWdqJUCHS-zCH4QFnoECBYQAQ&url=https%3A%2F%2Fauthors.library.caltech.edu%2F13792%2F1%2FMACnc92a.pdf&usg=AOvVaw2NAZ-jgP3S_m0CwDRbYgN0 (Note to the organizers: This is not a paper of mine, nor linked to me in any way). There MacKay shows that when trying to infer the parameters of a model that best explain the data, Bayesian methods are not too different from others, they only add priors. But when trying to infer the model itself, kind of a second level of inference, they provide a precise framework to decide up to which degree Occam's razor should be taken seriously. This is the approach I would take to determine how many ad-hoc explanations I would be willing to accept in order to decide whether the rooster drives the sun, or the sun drives the rooster. Basically, if the family of explanations that I am considering can explain the data I have, and not much more nor much less, I accept them. But if that same family could be used to fit, not only what I observe, but also many other unobserved phenomena (with a convenient choice of parameters) then the family is rejected. Here by "family" I mean "level of ad-hoc-icity" or "number of parameters" or "complexity of the model". MacKay had a huge impact on my Bayesianity ㋛
Stefan Weckbach Hi, Aquamarine Tapir - I still owe you a response! I did not have the time to round up my ideas about it. But I can respond to this new comment even before I tackle the older one. Yes, I do adhere to the Many Worlds interpretation (MWI), mainly because it is the only one I have found where "Observers" are nothing special: Observing a system does not require for us to add special rules, like the Bohr-like wave function collapse, nor to abandon locality, as in the Pilot Wave, etc. It only implies getting entangled with some degrees of freedom of the so-called "environment", that is, degrees of freedom that we do not keep track of. I am not sure, however, whether I fully agree with you in that the MWI implies that all the non-visited branches of the wave function have only a mathematical ontology. I still have the hope (though I am not an expert in the field) that it should be possible to produce a small enough entanglement in a given measurement, for the result of the measurement to be observable, or "recorded" somewhere, without the different alternatives to separate from each other for ever. To put it in another way, I'd love to see the Schrödinger cat alive, and then to have both me and the cat interfer with another branch of the wavefunction where I have seen the cat dead. I know this may be too much to ask (perhaps it destroys me, or my memory, but hopefully it might not destroy another observer observing both me and the cat) but I still hope for somebody to figure out whether something like this experiment is possible. I have often tried to determine whether the delayed choice quantum eraser experiments are not a version of this.
With respect to your question, I do not have a finished opinion. But perhaps I dare to say that I am quite sympathetic to David Lewis' conception that all possible worlds are equally real, and Max Tegmark's view that there is no clear division between the "real" world, full of "stuff", and a mathematical world, filled with only ideal objects and manipulation rules. If our consciousness is, as I believe it to be, an emergent property of the evolution of quarks and fields, then it should also emerge if the ultimate substrate is just a simulation, or an "empty" mathematical model with initial conditions. And in that view, yes, all formal systems (no matter which manipulation rules you choose) are equally real (or unreal). Only thing, some are more fruitful than others. Some contain whole universes, others are just boring. I guess I give the same ontological status for all that is, and all that could be. But I reserve myself the choice of what I want to focus on, and what is useful to me. I am typically interested with the set of universes and rules that are compatible with what I have around myself.
Please forgive me if all this sounds very crude - it is crude. I have not a finished opinion about these matters. But I still want to respond to you, because you seem interested, because this is a most important topic to be interested in, and because even if I cannot articulate things clearly, I can at least be a data point in your sampling statistics of "what other people think".
More soon!
Ines Samengo
Re “Yes, I do adhere to the Many Worlds interpretation…”:
Isn’t this the exact problem with physics? The problem is that people are willing to believe that we live in a type of structure in which there exists many worlds, in some of which worlds Vladimir Putin never invaded Ukraine?
Physics could be different, science could be different, if physics wasn’t chock-a-block full of people unable to face up to the real world.
Hi CinnabarMink,
thanks a lot for your reply. You need not apologize for your answers, I just wanted to know how the Everettian world view handles the ontological status of mathematics and you gave an honest answer, what I appreciate very much.
By the way, in my previous post I concluded that also our own branch, since it would be part of the universal wave function, must then be seen as mathematical in ontology. This surely would “confirm” what Max Tegmark expresses with his MUH. In my own essay, I argue against that MUH, or in other words, I try to critically scrutinize it. I would like to know your opinion about my lines of reasoning there and whether or not they could be considered as logically sound. So I will wait and hope that you find the time to take a closer look.
I also added a comment in my comment section to give a rough hypothesis about how the mind-body problem could be faced – for the case that observers are indeed special. Since that assumption is not your “cup of tea”, I guess you are not interested in that comment, but I would also be happy if you could comment on that. In any case, I thank you for having taken your time to answer me!!!! :-)
Cinnabar Mink concluded: ”Counterfactual reasoning makes sense when there is a hierarchy of dissipative relations between the coordinates used to describe the system, hidden in the geometry of worldlines, and in the way variables are chosen. Science could be different if these relations were better understood.”
Marty used counterfactual reasoning to better understand antimatter. The pay-off was enormous, a new preon theory!
Congrats on an entertaining and well written essay on an extremely important topic.
- Edited
wordscloud: anterograde amnesia, laplace demon, earliest childhood memory,
would a person with a memory condition experience a different physical reality ?
Beware, however, that in this description, the present is as dependent on the past as the past is on the present. This classical universe is as a-causal as the full one, the only difference is that now, the relevant variables are familiar to us.
the past present future time of time of time of time..
Therefore, there is no way to identify which events in the past
should have been different for the present to be different.
than, another for example take two present moment let say someone in park place a bottle of water on the table i wait five minutes and look at the table , and there ; the bottle sits on the table , the person moving the bottle is the event and the present after the five minutes is the observation . observation made. than i select an other present moment in witch the bottle is not placed on the table after five minutes i could say that for certain i have identified an event that make my present experience different
here the cause of the action is external
the first present moment , is in the past of the second present moment, it should not be considered the real present because is not a real present , it is a memory of previous present