Marc Séguin holds two master's degrees from Harvard University: one in Astronomy (under the supervision of David Layzer) and another in History of Science (under the supervision of Gerald Holton). He teaches physics and astrophysics at Collège de Maisonneuve, in Montréal, and is the author of several college-level textbooks in physics and astrophysics.
As a follow-up to the above post, on the issue of infinity, incompleteness and non-computability... I do not think that the Mathematical Universe Hypothesis runs into problems related to Gödel’s incompleteness theorem, because I believe that Gödel’s theorem only means that there exist true mathematical statements that can never be proven by a finite set of axioms manipulated by a finite mind. Non-infinitely intelligent mathematicians will never be able to fully capture the whole of mathematics within a consistent axiomatic system, but this would even be the case without Gödel’s incompleteness, because mathematics is infinite. Gödel’s incompleteness theorem only means that some mathematical truths will forever remain out of reach from any finite mathematician. So what? An infinite mathematical structure might seem incomplete from the point of view of a finite mathematician, but it doesn’t mean that it is not, in the proper infinite context, perfectly well defined --- so I think the Mathematical Universe Hypothesis (MUH) is well-defined even if it implies an infinite Maxiverse. I do not believe, like Tegmark does, that it is necessary to restrict the MUH to finite “computable” functions to make it work (what he calls the CUH, for Computable Universe Hypothesis). There is still the measure problem, of course… and I admit that until we get a better handle on the issue, we won't be able to determine if the regularity and relative simplicity of our universe is “likely” or “unlikely” within all the worlds of the Maxiverse.
Marc - So, if we find a non-provable statement at one level, we can add it as an axiom to build the next order - ad infinitum. But of course we could add it's negation instead - leading to a different mathematical universe. Euclidean and Reimannian geometry being good examples. This is analogous, perhaps, to the collapse of a quantum superposition. Very nice. But I am scratching my head over the no-axiom starting point - infinite degrees of freedom - no distinction - no structure. Sound like the Void. Of course, this is an interesting reflection of Absolute Infinity - but how does this spin the universe into being?
What seems to be missing (for me) is what I called intentionality - the willing of something from nothing. The first distinction - the first axiom - the first motion and light. Consciousness solves this problem, but then we have the bootstrap problem. For me, that is solved with the postulation of an infinite, eternal conscious entity, something that I, personally, cannot live without...
In his book "Theory of Nothing", Russell Standish talks about something similar to what you described as "quantum reincarnation". On page 185, he writes: "Dementia is also a very likely outcome as one ages. Some people have suggested that dementia will proceed to a point where one's experiences are indistinguishable from that of a newborn baby, in which case the principle of functionalism predicts that you begin life again as a newborn. Thus the idea of reincarnation receives support."
Thank you for the link to the Pusey, Barrett, and Rudolph paper. I did not read it in detail, but from what I understand, their conclusion seems to be that you have to accept that "each macroscopically different component [of the quantum state] has a direct counterpart in reality"... in other words, without saying it explicitly, they seem to indicate that the Many-Worlds Interpretation is the way to go, which just fits very well with Tegmark's ideas and mine. Do you interpret their conclusion differently?
P.S Here's a quote from their conclusion:
"Finally, what are the consequences if we simply accept both the assumptions and the conclusion of the theorem? If the quantum state is a physical property of a system then quantum collapse must correspond to a (problematic and poorly defined) physical process. If there is no collapse, on the other hand, then after a measurement takes place, the joint quantum state of the system and measuring apparatus is entangled and contains a component corresponding to each possible macroscopic measurement outcome. This would be unproblematic if the quantum state merely reflected a lack of information about which outcome occurred. But if the quantum state is a physical property of the system and apparatus, it is hard to avoid the conclusion that each macroscopically different component has a direct counterpart in reality."
My take away on Pusey, Barrett and Rudolf is not that MWI is wrong, but that it is uncertain. In fact this suggests that the wave function is outside of any philosophical category, whether epistemological, ontological, relative existential or … , and interpretations tend to be categorical impositions of this sort. All quantum interpretations have some element of truth to them, but they are also incomplete.
My essay proves a similar idea. However, my system shows that reality comes about from a particular mathematical structure and there is no way to get another design to produce a dynamic structure like our reality. But we are immortal because this structure exists regardless of our conscious feel of time passing. You can think of yourself as a circle of unit 1 ,2, 3 , 5 ...n finite as time passes, when you reach n you are finished. But this structure exists and another you at a different number and so on. There is no need to enumerate, it just exist. You don't need to say a circle exist now or later, or here or there, it just exists.
Unfortunately, my system involves programming(although very simple) and it is hard for people to spend the time to verify the results because it might be tedious and/or the claim sounds too good to be true(too grand). Moreover, the majority of the people are still hung up on math as a description tool. Although, it is puzzling to me since there are people who know programming here in the contest, but I feel they have not actually solved any standard quantum mechanics problem. Very disturbing since they are trying to discover the secret of reality.
Thank you for your comments. I will take a look at your essay. Good luck!
Alma Ionescu wrote on Mar. 17, 2015 @ 16:01 GMT
I found your essay to be a very interesting read. It shows a rather unique point of view. I like it that you choose to study mathematical definability and undefinability and to treat the consequences of incalculable or infinite probabilities; it's a complicated topic, intractable at the present moment. It's true that we all hold a narrow point of view that's very limited to our human perception. Actually I considered that limitation myself in my essay, but from the point of view of evolution in time.
While reading your paper, I had the feeling that your writing stems from a personal chain of thought. It's like there's an underlying unstated idea, possibly similar to many worlds, that makes all the details of this perspective come together.
There's one point that I'm not sure I understood properly. The Tegmarkverse and its insistence to rely on a specific kind of math has always looked to me like an attempt to keep some order in the chaos of a multiverse through conservation laws, whereas the Maxiverse hints at no conservation laws, or at least that's how I read an elephant’s trunk popping into existence. Do I understand it right? Would you elaborate a little on that please?
That being said, do share your opinion about my essay, if you have time to read it.
You are right: my essay stems from a long personal chain of thought, going back to 1986 when I was a graduate student in Astronomy at Harvard University. Rudy Rucker’s book “Infinity and the Mind” introduced me to ideas that became the core of the way I think about the world: (i) the fact that the largest possible kind of infinity, Absolute Infinity, contains no information beyond the mere fact that it exists (like Borges’ Library of Babel contains no information when taken as a whole), and (ii) the idea that our consciousness is the fundamental level of reality, and that ultimately (in a timeless, fundamental way) we all experience the same consciousness (when you strip it of all contingent, temporary details, your “I” is the same as my “I”). Over the next few years, I developed on my own many of the ideas that I put forward in my essay: Absolute Infinity, self-existing by necessity, generating an infinite multiverse where I exist simultaneously in an infinite number of different contexts, all these “I” being different yet the same. I soon found out (as Tegmark did --- see his book) that virtually all physicists see those ideas as unscientific, unwarranted and ultimately meaningless philosophical elucubrations. The indifference that I encountered at that time was certainly an important factor in my decision to leave academia (after finishing my master’s degree in Astronomy, and doing another master’s in History of science) and to go back to my home town of Montreal, where I teach introductory physics and astrophysics to 18- and 19-year-old students and pursue my personal cosmological and philosophical interests on my own time.
As the quotes in my essay testify, roboticist Hans Moravec had a huge influence on my worldview. It’s when I read an article about him in Wired magazine (“Superhumanism” by Charles Platt, October 1995) that I first got acquainted with the idea that simulated realities might outnumber “ordinary” ones (an idea that became the core of Nick Bostrom’s simulation argument), and the last chapter of Moravec’s 1999 book “Robot: From Mere Machine To Transcendent Mind”, available online on his website (“Simulation, Consciousness, Existence”), made all the pieces click together. Later, I was happy to see that Max Tegmark had become the champion of the mathematical universe hypothesis and its associated “mathematical democracy” argument: all mathematical structures (not just the one that corresponds to our universe) can equally give rise to physical universes.
If there’s an unstated idea in my article, it’s probably the fact that I think that the fundamental level of our reality is defined by our flow of consciousness (which is itself a mathematical structure): the regular and relatively simple physical universe that we find ourselves living in (itself a mathematical structure that embeds us) is the interface that allows our consciousness to witness each other and to communicate. As Moravec would say, “our existence is the product of self-interpretation in the space of all possible worlds”, and “a possible world is as real, and only as real, as conscious observers, especially inside the world, think it is!”
You mentioned that you had trouble with the idea that a Maxiverse without any limitation on the kind of admissible mathematical structures (in particular, no conservation laws) could be a viable hypothesis. This is, of course, the main weakness of any theory where “anything goes”: it seems plausible that if every possible universe exists, most universes that contain intelligences similar to our own will have some regularity (so life can be sustained), but not the rigid, universal, large scale regularity that we observe in our universe. As you expressed so eloquently in your own essay,
“We woke up in a place where so many things might have headed in a different direction, yet our universe is very well constrained. The constants are not changing and reality seems sturdy, like it will last forever. Everything insists to make perfect sense.”
My ideas on this issue are still in flux. Yesterday, I read Alexey and Lev Burov’s entry in this contest “Genesis of a Pythagorean Universe”, where they present an interesting, potentially fatal flaw of Tegmark’s Level IV universe (that applies even more to my own Maxiverse): according to them, the anthropic principle places limits on the stability of the laws of physics that are far looser that what we observe in our own universe. You should take a look at their essay if you have the chance. I am not convinced that they have an airtight case that condemns the Maxiverse hypothesis, but at least, contrary to what I wrote in my essay, I now believe that the Maxiverse hypothesis could potentially be proven false, which means that it is science after all! :)
I look forward to continuing this conversation here, and also in your forum after I comment on your essay.
You mentioned another essay which I just read at your suggestion. While I do rather fall on their side of the fence from the perspective of hoping our universe is not just made from meaningless coincidences, I can’t agree with the formulation of the argument. They say (pg 5, column 2 and a little in column 1) that the Tegmarkverse fails because we can measure our constants with high precision, a better precision than anthropic reasoning asks for. Aside from the fact that this mixes two separated ideas in a way that none of them was made for, that is wrong and wrong. The weak anthropic principle asks for regular worlds up to a certain threshold where they can maintain life, but without necessarily needing high measurement precision, but that doesn't forbid universes that manifest regularity up to 10100 decimal places or whatever they damn well please. The Tegmarkverse is democratic in the sense in which allows observers to exist in worlds that don’t have that regularity, but also doesn't forbid the nice smooth ones. Both a mathematical universe and the WAP allow for the existence of awesome universes like ours. Because a true A implies a true B (anthropic -> not necessarily too smooth), it doesn't mean that a false B implies a false A (very smooth -> not anthropic); it’s not an iff relation. Then they carry on with false dichotomy when they say (pg 5, column 6) that “since the laws… are not picked randomly, they can only be purposefully chosen”. Well. Why aren't they random? In an infinite number of universes, the chance for either single one of them to exist it’s exactly zero. Weird values are not predominant; they are equal to the number of fine-tuned values, because, just like you said, the probabilities can’t be calculated. And even if they aren’t random, that doesn’t exclude a third possibility, that there is just one recipe for making a universe, so there is no choice. So no, it’s not between random picking and purposeful picking, there are third options and maybe even more options that we didn’t consider so far. It’s not important if there are other options or not, since I already gave an example thus proving the dichotomy false. A lesser objection (because it’s a lesser part of their argument) is the cosmic observer hypothesis (pg 4, col 1) where they say that there’s a difference between cosmic observers and minimal observers, which is that the cosmic observers have theoretizable worlds. Well we don’t have an explanation for a lot of constants, do we? That rather places us in the untheoretizable pile. So this argument rather works against their line of thought than for it. We can’t argue that our universe has a special logical structure because some day we might have an explanation for it, because that’s selling the hide of the bear that’s still free in the forest. We will only be able to say that we are “cosmic observers” in the day when we will have a single TOE which proves the theoretizabiilty hypothesis, and would prove the random/purposeful dichotomy false. It’s a catch 22! I’m sorry to say these things, I respect the work of the authors and I respect them and their opinions and I reserve the right to change my opinion upon future extra input, but I can’t agree to these specific arguments because of the way they are built. Your Maxiverse is safe, and if it isn’t, it’s not because of the Pythagorean Universe. Actually in the reply I left for you on my page, I played a bit with weird conceivable parts of a multiverse, which in a certain sense says that those universes are theoretizable without necessarily being appropriate for life.
Very interesting take on the Pythagorean Universe essay. I like the way you state that our universe isn't that theorizable, since we don't have an explanation for the values of the universal constants. Yet, the values of these constants are very, very, very stable... if every possible universe exists, what are the odds? The damn measure problem again, so we don't have a clue... but still, I think the question of "by how much could the fundamental constants fluctuate without making our survival impossible" is an interesting one... I've read papers that talk about what would happen if the values of some constants were different, but I never saw an analysis of the effect of fluctuating constants on the stability of matter and the possibility of complex structures such as us... It would make for an interesting research topic!
I have read your reply on your forum and I will answer there soon.
Dear Jonhathan,
You raise an interesting question: "Are there self-contained structures, or only relational structures?" In the space of all possible (mathematical or abstract) structures, I think there are structures that refer only to themselves in a self-referential way, and can be considered as essentially self-contained. A causally connected physical universe that is not influenced by other universes might be one of these self-referential structures. It is less clear that a more limited structure like the one that represents a self-aware observer can be fully self-contained, since it "lives" within a larger structure that represents its universe. Yet, when I say in my essay that the substructures that corresponds to "me" exit within an infinite number of different larger structures, I imply that these identical substructures are precisely equivalent (because they are all equally "me"), so the fact that the larger structures they are embedded in are ultimately different is not really relevant -- so in this sense they are, essentially, self-contained. I think the notion of "self-contained" is relative --- from the limited point of view of looking only at each identical substructure (which encompasses all my experiences within a given time interval), they are all the same, but they are ultimately different from the point of view of an omniscient observer that can see the larger structures that they are embedded in... I don'k know if that's what you were getting at with your question, or if I addressed your question correctly... let me know!
Any issue concerning the definition of personal identity and the question of what constitutes personal identity through time is, of course, one of the thorniest in all of philosophy, and I agree there are many interesting parallels to be drawn to the views about self and non-self in the Buddhist tradition!
Jonathan Khanlian replied on Apr. 1, 2015 @ 19:05 GMT
"Digital Physics" has been submitted to the Fantasia Film Festival in Montréal, which takes place in July and August, so if you or the Collège de Maisonneuve have any connections there, please let them know of your interest in the film. Even if you don't know anyone connected to the festival, an email on behalf of your physics department might go a long way in terms of increasing its chances of being programmed:) Even though it is a fun movie, some of the ideas presented in it are challenging enough that it may be passed over for more traditional genre films. Sometimes movies that don't have a clearly defined genre can struggle. ("Pi" and "Computer Chess" are two movies that might fall in its genre.) The movie does have a little French spoken in it, so hopefully the festival programmers see that as as an additional reason to program it. I hope you have a chance to see it this summer at the Fantasia Film Festival, but if you don't, you may have to wait until it gets released online in late 2015 or early 2016.
Now on to the mathematics/physics:)...
Thanks for the explanation. I agree substructures can always be extended, with an unlimited number of possibilities, but I guess I am still curious as to what you think the substructure that represents you/self might be in this sense. When reading your paper, I first considered something like once you try to sever the observer from its environment, the notion of self might unravel, but maybe that was based on a misunderstanding of what substructure you really had in mind for a person/observer/entity. Do you imagine a substructure for "self" being something similar to the arrangement of atoms that make up your body or more akin to everything in your past light cone/observable universe?
I agree personal identity is probably one on the hardest problems to actually address, but it's fun to give it shot:)
Talk to you later,
Susan Plante wrote on Mar. 23, 2015 @ 02:04 GMT
Hello Marc,
Mind blown! Living with a single one of myself is already a challenge! And now your essay has me thinking about an infinite army of F-clones. How will I ever be able to sleep again? Me and my F-clones problem...not yours. Anyway, except for a couple of passages that this solitary mind found hard to grasp, I enjoyed the clarity of your arguments, the elegance of the equations and the humor. I would suggest that you make a video out of this, with maybe a catchy song that me and my f-clones could sing together in this "maxiverse" of yours.
Thank you for expanding my mind,
Dear Susan,
Thank you for your kind words. "The Maxiverse: The Musical" seems like a great idea indeed, and the best thing is that it is already playing in many multiverses near you!
Very nice essay, you explain well and convincingly the Mathematical Universe, and your arguments are well constructed. I share your disagreement "with Tegmark on this issue, because I do not think it’s possible to imagine an abstract structure which could not, in some way, be described by mathematics". Your argument against the testability of MUH or Maxiverse is solid, and the only way around it will be if there is a measure. I think that the measure problem can be solved, but the trade off is that we have to add a structure on top of it, and I have the feeling that this will affect the simplicity. I also agree with you that "According to Gödel’s incompleteness theorem, there exist true mathematical statements that can never be proven by a finite set of axioms manipulated by a finite mind, but I do not think it makes the MUH ill-defined, and I do not believe, like Tegmark does, that we have to restrict the MUH to finite 'computable' functions to make it work.)", and that Tegmark's limitation to finite structure is not justified, so what you name Maxiverse is a better choice. In fact, the argument from the last section of my essay is against Tegmark's strict notion of computable structures, as well as against his way of testing the (computable) MUH, even in the presence of a measure. I like the "same stretch of road" explanation for simultaneous self-location in infinitely many worlds. About the immortality argument, an apparent paradox occur: if in a world there is actually life after death, after you die in that world, you are a ghost or whatever. But in a world where there is no life after death, after you die, you continue to exist in the worlds where you didn't die, so this looks like a better immortality than for those in the worlds with afterlife :) Another remark: if you have a violent death, and you are aware of this, the worlds in which you can survive have to be those where you could survive that violent accident, so you will nod do very well. Similarly, if you survive cancer, you survive with cancer, one more second. So perhaps this sort of immortality is not desirable, because it is not eternal life, is eternal dying :) Leaving joke aside, I think that your argument of immortality either needs consciousness to be above the particular worlds (although the neural correlates are world-dependent), or it is merely an abstract equivalence class, which you can define about anything, and has no real relevance. Unrelated to your essay: you may like my older essay, in which I suggest that we get a Maxiverse out of the principle of explosion.
Excellent essay!
Regarding our F-clones having a beer together, cheers!
Thank you for your review of my essay. "Maxiverse" does have a nice ring to it, doesn't it? And, of course, any relation to Tegmark's first name is completely fortuitous! ;)
I have read with great interest all the essays you submitted to previous FQXi contests, and I was already familiar with your prize-winning essay from 2013, "The Tao of It from Bit". For my taste, your essays are always right on topic and at the perfect level to be challenging yet accessible, and you always manage to highlight thought-provoking examples (like the 0-1 line that contains every possible text in this year's essay). I find that I agree with most of what you are saying, probably more than any other regular contributor to the FQXi contests... In many ways, our thought processes are convergent! I will soon review your essay on your forum... I have some questions to ask about your take on free will...
I agree about your comment on the paradoxical nature of immortality within the context of a multi/maxiverse. The question you raise is interesting: is an afterlife where you "jump" to a different universe or become a "ghost" better or worse than just not dying because you always survive in an improbable yet fully real branch of your original universe? I think it depends on whether you have important/worthwhile things "left to do" in your original universe! When you're "older than old" and all your friends are dead, it is probably better to find out that it was all a simulation all along and find yourself uploaded (or back) into the "higher-level" universe where the simulation was run. Moreover, in some violent death cases (where your body is, say, pulverized to bits), the "regular physics" fluke that would allow yourself to survive in your original universe is so unlikely that you have to consider other scenarios as being more probable (your world turns out to be simulation, or your world turns out to be run by a benevolent or not-so-benevolent deity, etc.)
Your rightly point out that any discussion about immortality within the context of a multi/maxiverse seems to presuppose that "consciousness" is, in some sense, "above" the particular physical (ultimately mathematical) worlds. Some physicists/philosophers, like Bruno Marchal, have proposed that the fact that all mathematical structures exist "by themselves" leads to the existence of all possible thoughts, and that most of those thoughts require stable physical universes to make sense, so the ontological sequence is
math --> consciousness --> physics
On the other hand, maybe every level (math / consciousness / physics) is the fundamental one in its own "frame of reference", and different philosophers only seem to disagree when they say that "all is matter" or "all is mind" or "all is math"...
With that, my F-clone raises his glass to your F-clone!
I find yours a fabulous essay, one that rates with the best of works that live on the border of physics and philosophy, such as Rudy Rucker's *Infinity and the Mind.*
The depth of thought that it takes to answer the question of "what it means to be me" and the mathematical knowledge it takes to embed that question in the measurement problem, can only stem from the mind of one who has mastered both the philosophical and the technical issues that lie at the foundations of reality and consciousness.
There is a lot in common between my essay and yours -- though yours is far more eloquent. Where our arguments diverge, is on the limit of mathematics -- I agree with Tegmark's limit, that I define in a purely objective and local physical context. On the other hand, I also do not find it difficult to agree with your infinity of self aware and self consistent worlds.
Highest marks from me!
This "voting" scheme is the worst. No sooner do I vote an essay up, with reasoned comment, than some numbskull knocks it back down without comment -- and by implication, without reading. Unconscionable.
Dear Thomas,
Thank you for your comments on my essay. I have read your essay with great interest and will comment soon on your forum. I agree that the voting scheme is a bit bumpy... if I keep track correctly, I think I've gotten three 10 votes that were followed within a few hours with 1's or 2's... Maybe there are some voters who give a rating that will "adjust" the cumulative rating of any one essay to what they think it should be, instead of giving a fair grade to an essay irrespective of the rating it already has... Objectively, I think that very few of the essays that were submitted in this contest only deserve a 1 or a 2!
I am glad that the rules have been changed so that 10 out of 40 essays will make it to the final round at the discretion of the judges. It will make it less likely that some interesting essays will be purposefully eliminated from the finals by some unfair downgraders...
One more thing... In your comment above, your wrote "Where our arguments diverge, is on the limit of mathematics -- I agree with Tegmark's limit, that I define in a purely objective and local physical context." You are quite right about this divergence, but I think it is a consequence of the different ways we chose to interpret this year's FQXi's contest question. I have noticed that essays in this year's contest seem to divide in two camps: those who tackled the issue of the relationship between known (or potentially) known mathematics and the observable (or potentially observable) universe, and those (such as myself) who tackled the issue of the relationship between "All-of-Math" and "All-of-Existence", defined in a necessarily philosophical way (because these universal concepts are not observable).
That is a very interesting and insightful comment, Marc. It makes me realize that my love of limits probably reflects my love of analysis. :-)
I have agonized over this a lot and invite you to do same.
a) What is a world and does it have a size? That is, is a world an extended thing?
b) Can a world perish or is it eternally existing?
c) As your statement suggests, if your answer in 2) is Yes, what could prevent this from occurring again and again? Indeed, would the creation and perishing of worlds be the most fundamental event?
You can equate your Clones to my extended point, if your clone and worlds have a size of some very tiny limit. In my essay, I discuss the creation and perishing of extended geometric points. You may find it interesting.
Dear Akinbo,
You ask interesting and deep questions! Is space purely mathematical, or is there such a thing as a physical space (independent from the processes that take place within it) that emerges from the math? What is a world and does it have a size?
I think there are always many different ways to look at the same thing (that's why I believe that we live simultaneously in an infinite number of different larger contexts), and I think that space is one of those things that can be seen either as physically real (so that space can bend or stretch according to relativity and Big Bang cosmology), or as "merely" a convenient mathematical construct to make sense of the phenomena that we observe. The concept of world also depends on your point of view: from one perspective, your world is the sum of all your sense impressions, from another, your world is all that lies within the cosmic horizon of the observable universe, from another, it is even larger, being the totality of what could potentially causally connect with you.
You ask if a world can perish. Once again, it depends on your point of view. I believe that capital-E Existence ("All that exists") exists in an "atemporal and eternal" way: I don't think it makes sense to say that it can be different at different times, because it would mean that there is a "time-counter" outside of capital-E Existence to make sense of this change, and this is impossible because capital-E Existence is all there is! On the other hand, when you look at a subset of reality, at a "local" world, it is quite possible to define a time-counter outside this world, and relative to this time-counter, this world can be born, evolve and perish.
The fact that worlds are born and perish is certainly one of many properties that worlds can have, but I don't see it as fundamental. For instance, I have no problems with eternal physical worlds, and mathematical structures are, by themselves, "atemporal and eternal". Of course, it is possible to define a mathematical structure that is related to another structure that acts as a time-counter, and relative to that time-counter, the first structure can evolve, even appear and disappear, so I think it is possible to define a structure made of geometric points (or extended geometric objects) that, in some sense, can be "born" and "perish". (That's why I have no problem in believing that a physical universe that is born, evolves and ultimately perish can be thought as nothing more than a mathematical structure.)
I've read you essay and I know that "perishable geometry" is a crucial part of the theory you propose, and I will soon post my comments about your essay on your forum.
It is interesting to see that while you push the logical consequences of the MUH to the extreme, you still accept them, while I see them as a proof by absurdity against this hypothesis. Also I found it interesting that you have some common ideas with my view (see my essay): seeing consciousness as playing a fundamental role in giving mathematical universes a physical existence, and as you say "when we succeed at something in our universe (...), we do not change the Maxiverse in any way, we merely “visit” preexisting mathematical structures that have always been part of the Maxiverse." However we differ by the fact you consider consciousness as a particular mathematical structure, while I see it as non-mathematical.
Here are some remarks on the details:
You mentioned Occam’s razor, and that the MUH is basically unfalsifiable (though you mentioned changing your mind about the latter in your comments). I consider both concepts of Occam’s razor and falsifiability as different aspects of the more precise and general condition of quality for a scientific theory, as I mentioned in my essay: to give a probability law on observables which minimizes their entropy, i.e. presents the observed data in their most compressed form, where the size of the compression algorithm (or equivalently, the algorithm of probability law) is itself counted as added to the size of compressed data. Here, Occam's razor is about insisting on the need of simplicity of the algorithm.
The MUH is relatively unfalsifiable in the sense that it somehow gives a non-zero probability to every possibility, thus preventing the risk for an observation to contradict the theory : an observation which a theory excludes would mean the occurrence of a finite piece of data with infinite entropy as interpreted by the theory (theoretical probability 0 implies entropy = - ln 0 = infinity if it occurs). However, that a theory is prevented against infinite entropy, does not mean that it reaches a minimal entropy in comparison with other theories, which leaves the possibility to be relatively refuted by finding another theory doing a better job at explaining (compressing) the data, with a more precise and verified probability law. In any case, I consider that trying to avoid the issue of specifying probabilities by admitting the existence of all possibilities and qualifying the whole probability issue as a kind of mystery waiting for future elucidation, is not a very good theoretical job.
On this topic, you wrote "If you want to explain why one or only a few universes exist, you must specify the precise laws they obey and their initial conditions (at least). You must also specify and justify the rules which select these universes to be real while relegating all other possibilities to the dustbin of existence. Specifying the initial conditions alone might necessitate a mind boggling amount of information. On the other hand, to describe completely the Level IV multiverse, one short sentence is enough".
Later, you wrote: "Another argument against the Maxiverse hypothesis (in fact, against any theory which incorporates seriously the notion of a multiverse) is the belief that it critically undermines the future of theoretical physics.".
It seems to be the same character of the MUH that you first present as a quality (of satisfying Occam's razor) and then as a defect, isn't it ? I see the second view as quite amusing, as if, by principle, the Universe ought to have been well-designed for the purpose of giving jobs to physicists :) That reminds me the attitude of some climate-skeptics, which look as if the physical properties of the atmosphere had to be well-designed by God to ensure that free market structures will remain the best solution to all problems (the famous Invisible Hand) and thus for letting libertarians always remain the good guys in their defense of liberties.
In fact, a more detailed analysis of this question would let both alternatives roughly equivalent: given a piece of data that looks random as we could not find an explanation (compression), both hypothesis "It is really random" and "It only looks random but has a hidden pattern yet to be discovered" are as bad as each other at the job of actually compressing that piece of data. Chaitin's theorem ensures that the second hypothesis remains irrefutable even if it is false. However, the first hypothesis is falsifiable (by the act of finding an explanation), so that persisting failures to find any pattern (time passes without any discovery of explanation) progressively leans to the first hypothesis, while discoveries of patterns (traces of design, even if not well understood yet, as expressed in the essay of A&L.Burov) leans to the second hypothesis (if we find some patterns then there should be some metaphysical reasons for them).
You wrote : "I do not think it’s possible to imagine an abstract structure which could not, in some way, be described by mathematics" I think there is, that is called feelings or qualia, discussed by the famous hard problem of consciousness. For example, what is the sensation of the red color ? It is not expressible as a mathematical structure. The physical object of red light can be described by mathematics; the sensation of the red color can't.
"Moravec explains that we observe that our universe stays lawful and predictable, even if there are many scenarios where it doesn’t, because in these scenarios, our consciousness immediately ceases to exist". This reasoning is not applicable without probabilistic assumptions that beg for justifications. Namely, to imagine that just because a regular law was needed to reach some result, it will therefore continue to apply, means that just because some regularity happened, it will be more likely to happen again. But where does that law itself come from ? If I play heads and tails and happen to get 10 heads successively, will it make it more likely that I still get heads next times ? If I won at Lotto first, would it make it more likely that I will win again another time ? Is the Born rule of quantum probabilities, made more likely to be obeyed by future observations, by the fact it seemed to be obeyed in past observations ? And what other conclusion should we draw instead if it didn't seem so ?
"I expect to wake up in my bed and lead a more or less ordinary day, which must indicate that somehow (despite the measure problem), my F-clones which correspond to these ordinary scenarios greatly outnumber the other ones."
"Outnumber" : is it a matter of number ? It is well-known among specialists of the Many-worlds interpretation, such as David Wallace, that the Born rule cannot be justified as a measure of the ratio between numbers of distinct worlds with the different given states of a subsystem, because, first, there is no such a thing as a number of possibilities; second, even if there was, anyway such quantities do not fit.
Last autumn I wrote a description of the Many-worlds interpretation, with what I see as its necessary assumptions and consequences pushed to their extreme, which have a lot in common with your own description of the MUH. I do not subscribe to this interpretation but I think it is important to examine it, as part of the understanding of the one I support (mind makes collapse), because I include this many-world interpretation as part of the picture : it describes what happens in the absence conscious observation. And what remains of the physical universe when removing conscious observers, is precisely a purely mathematical world, which is ontologically equivalent to the MUH or Maxiverse (with the "small" difference that in the many-worlds interpretation of QM, the physical laws with the values of physical constants are fixed).
Thank you for your detailed analysis of my essay. It is very welcome!
I have read your essay, the more complete version on your website (“Specifications for a Mind Makes Collapse interpretation of quantum physics”, that you suggested to Tommaso Bolognesi) and your very interesting description of the Many-worlds interpretation that you suggested in your post above.
You certainly have many interesting and provocative ideas, and some of them do correspond to the way I (currently) see things. Like you, I think it makes a lot of sense to say that a mathematical structure becomes “physical” (whatever that means) when it is consciously observed. I really like the way you put in in your analysis of Laurence Hitterdale’s essay:
“But what do you think it might mean for a universe to "physically exist" when considered independently of the presence of consciousness? How would such an "independent existence" differ from purely mathematical existence? In my view, that is what it is: the physical aspects of the universe, insofar as we examine what "exists independently of minds", turn out to be mathematical because the mathematical nature is exactly what remains of the physical universe when the role of consciousness is removed.”
Where our views differ, is that your system is essentially dualistic, with consciousness existing in a separate realm, being NON-mathematical and NOT being subject to physical laws. I agree that our world does seem dualistic, with consciousness residing in a separate plane, but I believe that an Ultimate theory of Existence should reconcile all aspects of existence in a single category (so ultimately it would be monistic instead of dualistic). In keeping with the theme of this year’s FQXi essay, I argued in my essay that everything that exists (including consciousness) can be understood in terms of mathematical structures, but I think one could also make an interesting case that everything can be understood in terms of mental structures. So in my view, Existence is monistic, but this monism can be interpreted, from one point of view, as “all is math”, and from another point of view, as “all is mind”.
In your comment above, you make very interesting remarks about what gives “quality” to a theory: compressing the observed data, or, equivalently, minimizing the “entropy” of the explanation. You go on to say that the position I argue for in my essay, by avoiding “the issue of specifying probabilities by admitting the existence of all possibilities and qualifying the whole probability issue as a kind of mystery waiting for future elucidation”, does not constitute a “very good theoretical job”. I am fully aware of this, but what can I do? Suppose it is true that capital-E Existence (“All that exists”) does indeed follow from the most simple rule imaginable, “Everything Exists”, but that we are not advanced (or intelligent) enough to solve the riddle of the measure problem. Should we just refrain to make that hypothesis?
As an historical analogy, suppose a philosopher in the time of Kepler was skeptical of Kepler’s attempt to explain the fact there were 6 planets by linking the geometry of the solar system with the 5 regular solids, and said instead that the simplest possibility was that every possible solar system exists, but that the hypothesis was, of course, unverifiable with 17th century technology. If you had lived at that time, you would probably have said that the philosopher’s idea did not make a “very good theoretical job”. Yet, we now know that his idea was closer to reality than Kepler’s hopeless attempt to explain “from first principles” the contingent details of our solar system!
You claim that qualia (sensations and feelings) are an example of something that is not mathematical, and in your essay you also claim that the flow of time (the distinction that consciousness makes between past and future) cannot possibly be described by mathematics. But if mathematics is the general study of structures, that would mean that qualia and the flow of time are not structures. What are they then? I will address this issue when I review your essay on your forum (hopefully, within the next few days).
About the observed regularity of our universe… you criticize Moravec’s explanation (that our universe stays lawful and predictable, even if there are many scenarios where it doesn’t, because in these scenarios, our consciousness immediately ceases to exist) with the analogy of the lottery (“If I won at Lotto first, why would it make me more likely to win again another time?”). But suppose that the lottery’s prize is Existence itself. Then, you never become aware of the scenarios where you lose, and you always keep winning, against all odds. This is, of course, the main reasoning behind the “Maxiverse Immortality Hypothesis” that I describe in my essay.
As I said, I read your webpage on the Many-worlds interpretation, and I agree with you that there is no such thing as a number of possibilities, and that there are better ways to describe the thorny issue of the “amount of existence” of the different possibilities within a Many-worlds or Maxiverse model. I will try to be more precise next time when I discuss these issues! :) By the way, I really like the way you describe the Many-worlds worldview, especially when you deal with the issue of how the past evolutionary history of the universe, relative to a given individual, is largely undetermined (a view that is similar to how I view things, and that I have seldom seen so explicitely and clearly stated).
Sylvain Poirier replied on Apr. 3, 2015 @ 13:22 GMT
Indeed I might also describe my view as a monism, more precisely a mental one, since, as I wrote, consciousness can understand mathematics, but mathematics cannot describe consciousness. However, mathematics is then a remarkably stable part of this mental realm. And we (I mean, some people) have straightforward abilities to describe mathematical systems, that cannot be applied with such a success to non-mathematical ones.
"I am fully aware of this, but what can I do? Suppose it is true that capital-E Existence (“All that exists”) does indeed follow from the most simple rule imaginable, “Everything Exists”,"
What can be done: notice that science is no more in its infancy, and that we do already have some effective materials to consider. Namely : is existence described by a probability law or not ? We did find one important probability law, that is the Born rule. So we know that a probability law exists, and we can already describe it. Then, in case we feel lost in our speculations on the nature of existence, we should not forget that there is this thing we know, that needs to be taken into account, so that our ideas remain compatible with it. Now what I criticize about Moravec’s explanation, is its incoherent way of presenting arguments that are actually based on probabilistic assumptions (outside which no such arguments can make sense), while trying to deny having any clue on probabilities. My suggestion is to work on clarifying the structure of the probabilistic assumptions that these arguments are implicitly based on. Then, are such probabilistic assumptions compatible with the Born rule ? If you admit a non-probabilistic distribution of existence (i.e. not described by a measure), then in such a framework, how can any probabilistic law such as the Born rule make sense at all ?
About the flow of time, I wrote that we have an available analogy with the time of the foundations of mathematics, which I described in my site. So time has a sort of structure for which we have a mathematical analogy (better than the pure geometric view of linear order), yet it is only an analogy which does not suffice to describe the effective contents of consciousness and its time flow.
"qualia and the flow of time are not structures. What are they then?"
What sort of answer do you expect ? If a mathematical description was given, it would make these things mathematical. However it does not mean that it is a complete mystery, since, anyway they are things we somehow know by personal experience (unlike the concept of "nature" put forwards by materialists).
Dear Sir, I would have taken the time to read your entire essay, but after a page or so, I can see that it is simply preposterous and so a waste of time to continue reading. Sorry but the thesis is beyond absurd. It postulates the idea that mathematics is the universe and then postulates multiple universes because multiple mathematical structures are possible. While there is not a single concept in this essay that imposes any kind of common sense rules. So it is a waste of my time to continue reading. I think that this is an example of bad thinking and I hope that you are not teaching such nonsense to any empty headed students who might be beguiled into actually establishing a academic career based on promoting such an absurd approach to human thinking.
Dear Mr. Ricker,
I find your comment interesting, and I agree with you that the Mathematical Universe Hypothesis does not meshes easily with "common sense rules". In his 2007 article "The Mathematical Universe", Max Tegmark (who holds many of the views that I present in my essay) had this to say about the Mathematical Universe Hypothesis:
"[T]he MUH (...) forms a logical extreme in a broad spectrum of philosophical interpretations of physics. It is arguably extreme in the sense of being maximally offensive to human vanity."
By the distressed tone of your comment, I can only conclude that he is right.
If I were to deal with every (from my point of view) objectionable idea, it would simply take too long. Instead, I selected three sections from your essay that I think might be representative of our differences. After each quote, I have added my response to it.
After these three sections, I continue with a general discussion of the issue, and explain (necessarily without much detail) my own views of these things.
“Imagine there’s only math — physics is nothing more than mathematics, we are self-aware mathematical substructures, and our physical universe is nothing more than a mathematical structure “seen from the inside.””
But this starting assumption is just that – an assumption. I don’t deny that if you start with this assumption, then your conclusions (and likely a few more) can be said to follow.
“According to the MUH, physical reality is a web of relationships between entities that are themselves purely abstract: it’s “all structure, no stuff,” a view that Jim Holt [4] calls cosmic structuralism.”
Only “stuff” can have real-world structure. Abstract structures (represented by drawings, computer simulations, or mathematics) contain no “stuff,” and therefore cannot give rise to the (material) universe.
“But if you accept that a living being can be thought of as nothing more than a complex arrangement of atoms obeying the laws of physics, is it really that hard to accept that a physical universe can be thought of as nothing more than a complex mathematical structure?”
I think the implied equivalency is extremely weak.
We are free to define words like “existence” any way we like, but it is most useful to stick with accepted dictionary (usage) definitions. Ambiguity in philosophy or physics is not desirable, so I define “existence” as follows. Only those things that we can detect with our senses (even in principle) or those that we can detect with an enhancement of our senses (with instruments etc., again, even in principle) should be said to exist. If we included abstractions in “existence,” it would be mixing very different things. (Of course, without abstractions, we would be leading a very primitive life.) Mathematics, per se, does not exist under this definition (what you see on paper or a computer screen is just ink or “pixels,” the rest is happening inside your head).
Let me try a real world analogy. Consider an ordinary pocket calculator. It has a certain organization of atoms arranged so that when you press certain keys, you get a “desired” display as a consequence. We “say” that it has an internal logic, but what we actually did (in building it) is to utilize how the universe behaves on its own (in this case how silicon and electricity, etc. behave) and then used those behaviors to get the functioning we wanted. We are “exploiting” already built-in behaviors of the universe, but we think that we imputed logic into the calculator (and in an abstract way this is how we speak) while in fact we are only riding on the universe’s coattails (to borrow an idiom from another discipline). The calculator is not doing any “mathematics” (although we call it that, and it is useful) – it is simply streaming electricity along different paths, depending on the keys you press.
The MUH is essentially saying that the implicit rules guiding the various electron streams (we abstract those rules and call them “mathematics”) is the “cause” of the calculator itself (or better yet, is the calculator itself). The rules (which don’t have a physical existence) cannot create the calculator. And the calculator is not doing any more “math” than a bicycle chain interacting with the gear it is engaged in. The bicycle chain only needs to have the right dimensions to fit the gear, and the rest is done “via that very fact” (no calculations are performed as you ride the bicycle).
My view is diametrically opposed to the MUH. The universe does no calculations of any kind. It just behaves that way without any mathematics. To put it more colloquially: “the universe does not even know what mathematics is.” Mathematics just helps physics to describe (and economically codify) how the universe behaves. Of course, math has applications everywhere, and is not “subservient” to any other discipline.
Marc, I will give you a high rating on your essay. I like it. I don’t feel any need to convince anyone about my views, and I don’t think that a belief in what you said in your essay is in any way detrimental to science. I am sure you can think of many counterarguments to what I said, and after all, you could be right.
Dear "En Passant",
Thank you for your detailed comments. They are much appreciated!
Indeed, we all start with basic assumptions. Mine is that there is a "monist" way to understand the world, a fundamental level of reality that can account for all that exists and is self-existing and self-explanatory --- which I identify with "All of Mathematics", an infinite structure that globally does not contain any information (like the Library of Babel of Borges' short story). On the other hand, you start with the assumption that only those things that we can detect with our senses or with an enhancement of our senses should be said to exist. Then, as I said in my original message on your essay's page, your conclusions are very well argued and follow naturally. I really like the way you put it in the your post above, with the example of the pocket calculator. When I put on my "pragmatic physicist" hat (to borrow the expression from Sophia Magnusdottir's essay), I completely agree with you!
I hope your essay finds the audience it deserves and does well in the contest. All the best!
In fact, in writing my own essay, I initially intended to find out the proportion of the set of physical theories in the set of all mathematical theories, the latter corresponding probably to your Maxiverse. But it appears to me that this set is ill-defined, as set theory is a mathematical structure, and if applied to itself runs into logical problems. Do you avoid these problems by adding the qualifier "imaginable"? But who imagines? Is it some mathematical structure that imagines another (in which case the definition is cyclic and difficult to accept), or is it me or you? Then the whole thing becomes very anthropocentric and is difficult to accept as well.
More generally, I believe that mathematics as we know it is more of a human creation than we might want to believe - already judging from the fact that it uses Boolean logic in which logical variables have a well defined value 0 or 1, and at least the math established from finite axiomatic systems can be obtained from a classical computer program - as opposed to a quantum one. Will a new "quantum math" arise now that we are quite sure that not all observables have well defined value 0 or 1 at all times and that quantum computers will soon be on sale at Macy's? :-)
Of course you might argue that if so, this just extends the Maxiverse to so far unthought levels. But it makes me suspect that math has a human component to it - which would make the idea of the Maxiverse be too anthropocentric to be acceptable.
I would be happy to read your thoughts on this. In my own essay I finally settled down to the much more humble and down-to-Earth question what the "size" (cardinality, really) of the set of possible physical theories is, resting with the structure of those that we know. It is infinite as well. But which infinity? If you want to find out you will have to read it :-)
Thank you for your comments on my essay.
Your comments made me realize that I did use the expression "all imaginable [something]" quite a few times in my essay, which begs the question "who does the imagining", and can give the impression that my system is fundamentally subjective, or, as you say, "anthropomorphic". Perhaps I should have used "possible" (or "logically possible") instead of "imaginable" --- that's indeed what I meant to convey.
You ask a very interesting question about what I mean when I talk about mathematical structures that are different "clones" of myself. You define a mathematical structure as "a set of equations, inequalities, or of axioms, and possibly the full set of theorems that follow from them". What you describe I would rather call a "mathematical system", as I use the term "mathematical stucture" in a looser way. For instance, I would say that the digits of pi are a mathematical stucture, even if they are not in themselves a set of axioms that generates a system of theorems, so, for me, a "mathematical structure" is a generic term that can be used to describe any abstract structure. In my view, what makes up "me" at a given time (my sense impressions at that time, my thoughts at that time and my memories) is a mathematical "sub"-structure that can be embedded in different larger mathematical structures, or universes. In the space of all possible mathematical structures, there are related sub-structures that correspond to slightly "later" versions of me (having memories that correspond to my current direct sense impressions), and the set of all these sub-structures constitutes my F-clones. (This view of "timeless" structures that taken together give rise to a subjective flow of consciousness in time is described in Julian Barbour's book "The End of Time", and also in the sub-section "Living in the moment", on pages 284 to 289 of Max Tegmark's book "Our Mathematical Universe".)
Daniel Braun replied on Apr. 7, 2015 @ 22:04 GMT
thank you very much for your reply. I think I understand now better what you call an F-clone. Is it correct to say that if you define "me" as a collection of information, e.g. complete information (the full many-body quantum state really) about all my atoms at a given time, F-clones would be a possible time-evolved state?
If so, coming from quantum mechanics, one wonders how relevant such a "mathematical substructure" that only pertains to "me" can be: the vastly overwhelming majority of states of "me" and universe are entangled, and so one can almost never describe "me" as an independent mathematical substructure of a larger mathematical structure. In the end, there would be only one big mathematical structure, the big
and subsystems don't have an independent existence.
On the other hand, with this definition of F-clones, the set of F-clones of "me" would have cardinality
I suppose: a 1-parameter continuous manifold
The same would hold for the cardinality of the set of F-clones of the entire universe. Even for multi-dimensional time, it would still be
Your essay might be described as MUH + nothing else, but with your clear way of expressing these ideas you take it a lot further.
My own ideas about the MUH which I called the Theory of Theories was developed independently at the saem time as Tegmark. The unique ingredient in my version which goes further is the answer to the question "Why is our world so lawful and simple" The answer has to be that in the complex system of all mathematically logical possibilities there is a principle of universality that determines the underlying meta-laws of the universe. It is an emergent principle of self-organisation that is as important to the nature of mathematics as it is to the nature of physics. Anthropic principles only come into play when looking at the possible solutions to those meta-laws.
The latter parts of your essay follow thoughts that I have been through many times myself which lead towards ideas about conciousness. I hope a future FQXi contest will be brave enough to ask us about conciouness and free will so that I can write my own ideas about what we should learn from "F-clones" It was not something I had space for this time.
When I see how clearly you express the philosophical ideas that I agree with, I find myself surprised that there are so few of us who see it that way. I hope your exposition will generate a few more converts.
Dear Philip,
Thank you for your comments! About a week ago, following a reference at the end of Jonathan Dickau's essay, I came upon your almost twenty-year-old essay Theory of Theories, and I found your extension of the idea behind Feynman's path integral to the space of all possible theories absolutely fascinating. Quoting from that essay:
"We might well ask if the same can be applied to mathematical systems in general to reveal the laws of physics as a universal behavior which dominates the space of all possible theories and which transcends details of the construction of individual theories."
I then reread your entry in this year's contest, where you expand upon this idea, whose significance I had missed on first reading, and followed your reference to the recent paper by Seth Lloyd and Olaf Dreyer, The universal path integral.
If I were to rewrite my essay today, I would certainly mention these ideas. I totally agree with you that, if all possible mathematical/physical universes have potentially the same existence as ours, the anthropic principle is not enough by itself to explain why we find ourselves living in a universe that is so regular and relatively simple. Something like your Theory of Theories could "collapse" the chaotic ensemble of all mathematical possibilities, via something like a path integral, to a reduced set of relatively well behaved "coherent" scenarios, on which the anthropic principle would then act. The principle of stationary action has always been my favorite idea in all of physics, and to think that something similar would play a role in "regularizing" the "smorgasbord" of the Maxiverse is very appealing to me!
I agree with you that a future FQXi contest on the relationship between consciousness and physics would be absolutely fascinating! In this year's contest, we have splits between mathematical platonists and anti-platonists, as well as the usual split between the "let's evolve physics from the current accepted theories" crowd and the "bring back local realism and/or absolute space-time" crowd. Imagine if we add a split between "consciousness-first" and "matter-first" views, and between the "free-willers" and the "free will is an illusion" camp... Oh what a wonderful, delicious and mad cacophony this would be! :)
P.S. I will also post this on your essay's page, and come back with a proper review of your essay, hopefully within the next few days!
Marc, our thought processes are very closely aligned.
Although I would not be surprised to be labeled as a platonist I do accept some of the criticisms of the anti-platonists. I think if mathematics is seen as a realm that exists in a physical sense as platonists like to see it then the problem of existence has been pushed back rather than solved.
I now prefer to think of mathematics as a description of possibilities for existence rather than of things which exist in a platonic realm. This avoids the criticism. I like your explanation that physics is mathematics plus nothing else in the same way that biology is chemistry plus nothing else. There is no missing vital spark needed for life to emerge from chemistry or for reality to emerge from mathematics. This is a powerful analogy (except to those who still think there is a vital spark or soul required for life) It expresses exactly how I see the mystery of existence resolved.
I am glad I brought some references to your attention. You also had some good references that I was not aware of.
Philip,
Your comment above (in particular: “I now prefer to think of mathematics as a description of possibilities for existence rather than of things which exist in a platonic realm”) is eminently reasonable. But some of your “brethren” might consider you an apostate.
Btw, I observed your comments (giving wise advice to some of the more, shall we say, enthusiastic commenters) and, if you are willing to accept a compliment without thinking it is in some way patronizing, I would say that “you have got it together.”
Anonymous replied on Apr. 9, 2015 @ 20:15 GMT
En, thanks.
I dont think I have converted over to the other side. I still see mathematics as prior to physics. The naturalists see it the other way round. I am merely taking my definition of "reality" to not include mathematical abstractions. Perhaps the difference is just semantic, but it matches my understanding better.
Maybe we are all obscuring the issues by insisting to label as "mathematical" or "physical" (or even "mental") the fundamental structures that make up reality. Why not just start with the ensemble of all possible structures: those that have the right properties to be physical universes exist as physical universes --- no extra ingredient, selection principle or "living spark" needed. The practical end result is the same: Maxiverse! :)
Language plays a big role in our philosophical thinking. It can guide us or mislead us. Making up new words and phrases is a good thing to do because it avoids the baggage that is attached to old words. I avoided the word "multiverse" in my essay entirely for this reason. You have used it but have been careful to clarify which of the different multiverse ideas you are talking about. I like "maxiverse".
Words like "reality" and "existence" are particularly dangerous, but they are also tools we have to use. Our minds are programmed with an understanding of words like this that makes us want to apply them when we talk about topics beyond everyday experience. They make us think that there must be something there when there isn't. To gain understanding we need to recognise when things we expect to find are just not there. Einstein's biggest philosophical advance was to recognise that there is no ether. We also need to recognise that there is no magic ingredient that needs to be added to make life out of chemistry, reality out of mathematics, conciousness out of psychology etc. Instead we need to look at the process of emergence that brings these things about with nothing else needing to be added. I like the way you have tackled this in your essay.
I confess to being the anonymous above :-) hopefully this post will have my name on it
James Lee Hoover wrote on Apr. 7, 2015 @ 17:45 GMT
Yes my head is spinning in the vortex of my disbelief in the Maxiverse hypothesis, but due to your rather fetching argument, I find it impossible to dispute your argument with anything but humdrum arguments.Love your methodological reductionism argument at beginning and your devil's advocate approach.
I too have used the Hut argument that as a type 0 civilization we have too little understanding of math, physics and consciousness to perceive the concepts of a type 2 civilization, for example. That is my excuse as well.
My essay seems pedestrian in arguing the use of math to represent and model a physical world that has brought epiphanies regarding our universe in terms of quantum biology, DNA and our early universe.
Thank you for your comments! I will re-read your essay and come back to you, hopefully within a couple of days.
I appreciate your lighthearted and relatively even-handed presentation of the maxiverse hypothesis. Although it is very far beyond what I'd be prepared to believe, your essay was fun to read. The idea of cosmic structuralism reminds me of the von Neumann universe, or cumulative hierarchy of ZFC. Let me throw a couple challenges your way:
1. The contrast between our 'boring' universe and the more exciting one seems like a false dichotomy to me, in the sense that one would expect there to be a spectrum from 'boring' to 'exciting', and I am not sure that anthropic considerations are equipped to handle this: It does not seem all that difficult to imagine more exciting universes than ours which are equally compatible with our existence. If so, then for each copy or our world there are is a copy each of an infinite number of more exciting universes compatible with our existence. Why don't we live in one of those?
2. If the maxiverse includes absolutely every imaginable mathematical structure, it also contains every imaginable inconsistent one. But any inconsistency in a mathematical structure infects the entire structure, so is it not the case the maxiverse is inconsistent?
3. What kind of mathematical structures are feelings, perceptions of color, dreams (I do not mean the neural correlates, I mean the qualia themselves)?
I hope you enjoy these,
You are right: the Maxiverse has a lot in common with V, von Neumann’s hierarchy of all sets. My first acquaintance with V came in graduate school, when I read Rudy Ricker’s book “Infinity and the Mind”, which had an important influence on the way I see the world.
The three questions you ask are very interesting.
1. I agree with you that a major challenge to the Maxiverse hypothesis is to explain why we live in a universe which obeys laws that are so regular and relatively simple (what Moravec calls a “boring” world). In my conversation with Philip Gibbs (two threads above this one), I hint at a possible solution that has recently come to my attention. Could it be that all the universes that contain versions of ourselves that are more or less similar “interfere” with each other like the different paths in Feynman’s path integral formulation of Quantum Electrodynamics, “evening out” in the process to yield fairly regular and "boring" outcomes, in the same way that Fermat’s principle averages out the behavior of the wavefunction of a photon to yield a behavior consistent with the laws of classical optics? This seems to me an idea well worth pursuing!
3. I agree with you that qualia (perceptions, feelings) can seem awfully un-mathematical, but whatever they are, I believe they are “structures” of some kind... and if mathematics is the general study of structures, then they are ultimately mathematical, like everything else. But then again, I believe it is only because the structures that correspond to our universe are observed “from the inside” by self-aware substructures (us) that they acquire physical existence. (It would make no sense to say that a mathematical structure that doesn’t contain self-aware substructure exists physically, because there wouldn’t be anyone to “feel” its putative physicality.) Therefore, from a certain point of view, qualia could be said to make up the fundamental level of existence. So, depending on your point of view, “all is math” or “all is mind”...
Thank you for the questions... I hope you enjoyed the answers!
I will study your essay and post comments on your page, hopefully within a couple of days.
The previous post is truly mine, but this cannot be proven within the set of axioms that define the FQXi forum system, because of the well-known Spontaneous Log-Off theorem.
Thanks for the response. A quick comment:
"The way I see it, to be mathematical, a structure has to be consistent by definition..."
Then I take it you are not aware of paraconsistent logic and mathematics? The online Stanford Encyclopedia of philosophy has some good introductory articles on these, calling the latter "inconsistent mathematics". The last sentence of section 6 expresses my second challenge in more general terms. I believe this issue is separate from Goedel's theorem. I wonder whether Max Tegmark is aware of this? If not, somebody should point this out to him.
Incidentally, I appreciate your offer to study my paper. I look forward to your challenges, although due to the incompleteness of the framework, it is probably not so difficult to come up with some but every bit of constructive criticism helps.
Thank you for bringing the topic of paraconsistent logic to my attention. It's interesting to see that some mathematicians are attempting to make logical sense of "illogical" statements! Somewhat paradoxically, it makes me believe even more that the Maxiverse hypothesis is well defined: if human mathematicians can find ways to deal with paraconsistent logic, surely the Maxiverse can thrive even with some paraconsistency or Gödel indeterminacy within itself!
Armin Nikkhah Shirazi replied on Apr. 10, 2015 @ 23:38 GMT
I appreciate your honesty in admitting: "Somewhat paradoxically, it makes me believe even more that the Maxiverse hypothesis is well defined".
Yes, you seamlessly went from
"In my opinion, if incompleteness could “infect” the Maxiverse and make it inconsistent, then nothing would exist"
"if human mathematicians can find ways to deal with...
"if human mathematicians can find ways to deal with paraconsistent logic, surely the Maxiverse can thrive even with some paraconsistency or Gödel indeterminacy within itself!".
Moreover, you made this move even though the Maxiverse requires precisely the kind of conception of mathematics that those human mathematicians, who are otherwise comfortable with inconsistencies, pointed out as being problematic. To quote the last sentence of the inconsistent mathematics article (also referenced in my previous post):
"It is only if one takes as a starting point the primacy of the mathematical object as the truth-maker of theories, that one has to worry about how their objects manage to co-exist."
This is a good example of a psychological phenomenon known as the "backfire effect". If you would like to know more about it, an excellent article that discusses various facets of it can be found here.
My own experience in this contest has so far borne it out completely. I have challenged the beliefs of more than half a dozen participants in their ideas in this contest by presenting contradictory evidence, and not in a single case did it result in the modification of their beliefs.
Actually, in some cases it became apparent that they did change a belief; it was not a belief about their cherished ideas, but a belief about me. In one case, my efforts to explain to a relativity denier some fallacies in his reasoning and some misunderstandings about relativity resulted in him considering me as "possibly brainwashed" by the physics establishment, while in another my efforts to point out to a physicist with expertise in relativity that there is a straightforward interpretational difficulty at the foundations of special relativity about which the physics community is currently in denial resulted in him considering me to pursue a "crazy idea". If I were more distant from these experiences, I would find them amusing.
Your frank admission that your belief in your ideas got stronger when you were presented with contradictory evidence is the most honest response I have got so far, and probably the best I can hope for. Given that the subject of discussion is science and not, say, religion or politics, I wished I could hope for more.
Good luck with your theory and best wishes,
The link for the backfire effect above does not seem work, so here is the URL
As I just mentioned in a reply on your essay's page, I agree with you that it is very hard to make comments that really change the point of view of your interlocutor. It's even harder when your interlocutor has a set of basic assumptions about the fundamental nature of things and their relative importance that is completely different from yours --- and such a mismatch of basic assumptions and interests happens often in an eclectic environment such as a FQXi contest. For you (correct me if I'm wrong), the "real world" is the observable physical universe and mathematics is a way for us humans to represent it. For me, what is most important is to find a satisfying answer to the question "Why is there something?". It seems to me that the only answer that does not create more questions has to be something like "all abstract structures simply ARE, and one of these IS our observable universe". In this context, I use "mathematical" almost as a synonym for "abstract" and talk about "mathematical structures". You rightly mention that some subsets of mathematical structures, when analysed by a finite mathematician, exhibit "pathologies" such as indeterminacy and possibly "inconsistency". You conclude from this that it is impossible that mathematics can be the fundamental level of reality. For my part, the fact that subsets of the Maxiverse are indeterminate (from the point of view of a finite mathematician) or inconsistent does not mean that the Maxiverse can't exist, or that within it our universe can't exist in a more or less determinate and consistent way. Furthermore, it may well be that our physical universe is partly indeterminate and inconsistent... that would explain many things, wouldn't it? :)
Joking aside, thank you for the opportunity to have this discussion. Beyond ratings and prizes, it is the main reason why I participate in these FQXi contests!
Thank you for taking the time to check out my essay. Having read and rated so many essays, but sometimes waiting to do the latter, I return to check them. I find that I rated yours on 4/7. With a present score of 6 and a large number of ratings, mathematically speaking, my 9 didn't register much.
Another interesting idea is that math never implies causality but physics does. This is because the time element in physics. There is no place or treatment for time in math. What does that tell us about time? My guess is that time is the culprit of a lot of misunderstanding in physics. Time essentially is a psychology quality in living organisms. It’s not a physical entity at all. Is there is...
Another interesting idea is that math never implies causality but physics does. This is because the time element in physics. There is no place or treatment for time in math. What does that tell us about time? My guess is that time is the culprit of a lot of misunderstanding in physics. Time essentially is a psychology quality in living organisms. It’s not a physical entity at all. Is there is physics that exorcizes time vector?
We may consider the current world as a domain A and the world in the next moment as another domain B. Time is the operating mapping rule to map each element in A to B. But unfortunately there exists none reverse mapping, hence time travel is a meaningless phrase. In every domain there is no time element. Time itself is an illusion for organisms to incorporate the mapping operation into innate experience.
The physics law can be re-interpreted under this new paradigm. Instead treating time as a presumed independent physical variable, it is a function T. For every element (positions and masses) of domain A, we have a time function T(.) that operates on it.
2nd Thermal dynamic law:
T(a) = b, where a is the entropy of element a in domain A and b is the entropy b in domain B, and the rule is b>a;
Speed of light:
T(a) = b/c, where a and b are relative position coordinates in domain A and B, and c is a constant, i.e. speed of light.
Fundamentally we cannot measure time, and time is not an absolute variable like position. Making time-space a 4 dimension doesn't help, except more confusion. It caused crisis after crisis in physics because of the confusion of time. If time is treated as an operator things will be much clearer.
Here are three ideas which might be of some interest and relevance.
First, I think it would be helpful to clarify whether there are any non-mathematical possibilities. If there are not, then your Maxiverse might be the same thing as Tegmark’s Level IV multiverse. Tegmark believes some things are conceivable or imaginable, but not mathematical. Hence, according to Tegmark, these possibilities need not exist even in the most comprehensive mathematical universe. Tegmark would probably maintain that the non-mathematical “possibilities” do not and cannot exist, for existence in his view is wholly mathematical. This seems to imply that there are no non-mathematical possibilities; whatever we thought were such have turned out to be really incoherent impossibilities. If I correctly understand your view, you would say that many of the things people thought were possible but non-mathematical are actually mathematical structures after all. (Bottom of page 2 and top of page 3.) As you know, standard examples are the flow of time, conscious qualia and perhaps other aspects of consciousness, and cause and effect. The issue is not quite whether there are abstract “structures” that elude mathematical definition. Rather, the issue is whether there are abstract “possibilities” that do not possess mathematical structure or definition. We could say that there are no such possibilities. That might be true, but the question does not seem to be settled as yet.
Second, the lawfulness and simplicity of the local part of reality is probably more of a problem. (Pages 3 and 4). Suppose that all possible universes are actual. The question then is not whether we live in a universe which is typical among all actual universes. The thinking behind the anthropic principle already tells us that we do not. Our universe is atypical because it contains conscious cognitive creatures such as ourselves. As far as consciousness and knowing are concerned, most actual universes are empty. But the question is whether we live in a universe which is typical among all the actual universes which contain cognition and understanding. Unless we have reason to believe that our universe is special as compared to another cognition-containing universes, we should assume that it is typical of them. We do not have any reason to believe that our universe ought to be even more special within this restricted class of already very special universes. However, it seems that our universe is much more special, because it is simpler and more lawful than would be typical. The literature on this point includes many interesting topics, such as Boltzmann brains, simulated universes, and much more. Here is where the reasoning collides with the measure problem. If all possible universes are actual, then the actual universes are so various and so numerous that there is no fact of the matter about what is typical or atypical for them. So, if the measure problem is not only unsolved but genuinely insoluble, we cannot explain our universe by saying that it is probable compared to other instances within some class of actual universes. In this context, the concept of probability would be undefined. Some people would go so far as to say that the difficulties should make us hesitate to accept multiverse hypotheses, at least those hypotheses which postulate multiverses said to be infinite. Much more could be said about that.
Third, the puzzles about personal identity, free will, and related matters would arise even in large but finite multiverses. (Pages 4-7.) It seems that a person might well be lost in a scheme of thing which is far smaller than the Maxiverse or Tegmark’s Level IV multiverse. Suppose that in the fullness of all existence there are a billion exact copies of “you”, plus a hundred quadrillion more closely similar counterparts. Some, although perhaps only a few, of the hundred quadrillion lead extraordinarily wonderful and satisfying lives, while some others, perhaps also only a few, suffer dreadful fates. Perhaps most of the hundred quadrillion must be content with an indifferent mixture over a lifetime. A billion and a hundred quadrillion are big numbers, but they do not compare to infinity, and I think we could make the same point by using smaller numbers. It is interesting to speculate about multiple universes, but the speculations become much more interesting, and more complicated, when we realize that the hypotheses imply multiple selves in multiple universes. The moral value of thinking about multiple selves is to provide a human individual with a new perspective on what often appear to be the encompassing problems of the moment.
Steven P Sax wrote on Apr. 21, 2015 @ 22:23 GMT
Your essay is both fascinating and accessible; I like your determined and comprehensive approach in developing out the concepts of MUH, and how you extended this to the maxiverse concept. You're right we do touch on similar points about explaining properties of our universe. As you noticed in my essay, not only does this include an anthropic principle relating to consciousness/causality, but also a multiverse-thropic principle selecting those universes whose mathematical structures allow an infinite multiverse explanation. Your discussion on ordering within infinite ensembles is very illuminating, especially as you applied this to the anthropic principle, and our ideas support each other. Also your analogy of the shared highway stretch to explain simultaneous, indistinguishable contexts is illuminating. Finally, your discussion on infinite exact copies or clones is intriguing, and I appreciate your assertion that free will acquires more meaning within a maxiverse. Very interesting contribution that clearly addresses this forum topic, I rate it very highly.
PS I took a very pleasant trip to Quebec a couple years back and your reference reminded me of it, so thank you for that too.
KoGuan Leo wrote on Apr. 22, 2015 @ 07:27 GMT
Thank you giving me your kind comment and rated my essay highly. If I may differ with you a little but agree with you a lot in most fundamental way in which physics is math but this math is KQID Zeroth Law.
Physics = KQID Zeroth Law = math. This Zeroth Law is ☰00☷ = Ee^iτ = A+S= IΨ(CTE) = Ψ(iτLx,y,z, T) ⊆T=1. This is why we have an orderly universe that we have been observing as the privileged Anthropic Observers that create and distribute Anthropic principle. Thus we have many similarities but each is unique being. Each has infinite clones if physics = math. Furthermore, if physics = math, we will have so many bizarre realities which we have observed. I believe Existence must be "orderly" and "regular" infinite possibilities, Theregore, KQID Zeroth Law governed its evolution from its initial to its infinite potentialities. KQID has the bit paradigm that functions like our neocortex brain on top of the it paradigm that function like our mammalian brain. The bit rules over it whereas its manifested the bits in our realm.
I rated highly your essay and I wish you the best in this contest.
Member Tommaso Bolognesi wrote on Apr. 22, 2015 @ 08:37 GMT
at page 2 you mention the argument that it may be cheaper to specify all possible universes than only a few, or just one:
“On the other hand, to describe completely the Level IV multiverse, one short sentence is enough: the collection of every mathematical structure which has the correct properties to correspond to a physical reality.”
The idea that describing everything is cheaper than describing only something is reasonable and often mentioned (e.g. by Schmidhuber in connection with Turing-computable universes). But your specific formulation of it triggers an objection: how costly it is to specify “the correct properties” that a mathematical structure should have to correspond to a physical reality? Is it enough for the mathematical structure to be consistent? On do we require more? How costly it would be to specify this?
A related consideration. In a way, Priss (as you observed about my essay) regards mathematical structures from which self-conscious entities emerge as the only relevant physical realities. How costly it is to specify this restricted class of mathematical structures?
You also raise the issue of the (boring) order and predictability in our universe, and discuss the way this aspect can be dealt with under the Maxiverse hypothesis. Let me just note that the 'surprising' amount of order in our universe finds a rather natural explanation if we assume a computational engine at the root of everything (see Zenil's essay 'The World is Either Algorithmic or Mostly Random' ).
Overall I found your essay very enjoyable, although you are right in predicting some final head-spinning in the reader... Multiverses in general always give me some headache, and always remind me of a quote by composer Pierre Boulez: 'when everything is allowed, nothing is possible'. The only 'multiverse' I feel somewhat comfortable with is the darwinian one depicted by Smolin, with I find in its own way 'natural' and appealing. In conclusion, I can't but fully agree with Piet Hut's remarks about the current weakness of our understanding of the math/physics/consciousness triangle!
I hope you found the time to rate my essay, after your very recent and positive comments.
Thank you for your interesting comments. You raise an interesting question about the idea that the level IV multiverse is "cheaper to describe" than a single universe (or a limited collection of them). In my essay, I single out the parts of the multiverse/Maxiverse that have "the correct properties" to correspond to physical realities as being particularly interesting, but of course, if all mathematical structures simply exist, nothing has to actually specify which ones correspond to physical realities. Among the collection of all mathematical structures, some just happen to have the correct properties to be physical realities, and those who contain self-aware substructures are considered "physical" from the point of view of their "inhabitants". So Priss can be right (among all mathematical structures, only physical structures are relevant) without the need for a special mechanism that specifies the relevant mathematical structures.
Thank you for suggesting Hector Zenil's essay from the "Is reality digital or analog" FQXi contest. I had never read it, and I found it very interesting. The idea that simpler mathematical structures are easier to compute and therefore have a higher "measure" within the Maxiverse is, of course, one promising way to show that lawful and stable universes like ours are typical among all the realities within the Maxiverse that can support thinking beings like us.
I have rated your essay yesterday, and since then, like most of us, you've probably seen your rating go up and down, often without any comments. The FQXi community is harsh: I have read a sizable fraction of all the essays in the contest, and among the 30 essays or so that I enjoyed the most, almost half of them have currently a rating below 5.0.
At least, the judges have the option this time to pick 10 essays for the finals irrespective of rating, so the most important thing is to have fun "throwing some ideas in the wind" and learning from each other's ideas and (hopefully constructive!) comments.
The Gods of FQXi willing, see you in the finals!
Thanks for a fun essay to relieve heavy reading (though just as testing!). I was reminded a little of my hypothesis 2yrs ago (well supported) of a 'Law of the Reducing Middle' replacing the excluded middle and based on a very consistent cyclic cosmological model, where everything that CAN happen (an assumedly some that can't in the present cycle) eventually will. The multiverse is then temporal as well as, seperately, spatial (as each universe would have spatial limits a little like galaxies).
I also agree your conclusions (if not premise!) This 'ultimate case' scenario may be marginal but was certainly an important one to explore and air and you did it well. You also re-assured me that the 'left field' concepts I invoke are really not so at all. Everything's relative!!
Yafet Erasmo Sanchez Sanchez wrote on Apr. 23, 2015 @ 01:24 GMT
I like your essay a lot. The style is very fluid and the concepts are presented in a clear form. I am not really familiar with the Maxiverse idea, but your presentation make it very intriguing.
In your essay you say that there might be an infinite number of Universes. Is this infinite some specific cardinal or for the discussion this is not necessary. Would the discussion change if it is the case that it is not even a cardinal, not even an inaccessible cardinal?
I guess it will in the sense of the number of possibilities, even if they are infinite.
Yafet
Member Sylvia Wenmackers wrote on Jun. 11, 2015 @ 13:48 GMT
Sorry that I had not read your essay earlier, I really enjoyed doing so now! And I would like to respond to five elements in your piece.
* Regarding the "“gut feeling” that mathematical structures and physical structures cannot be equivalent":
- I agree that current science has shown that matter is not 'as material' as our daily experience would have it. I...
- I agree that current science has shown that matter is not 'as material' as our daily experience would have it. I recently attended a lecture by philosopher James Ladyman, who talked about why "particles are not particles", by which he means that the 'particle' in 'particle physics' does not correspond with the ancient particle concept (tiny pieces of 'stuff').
- On the other hand, the very notion of an equivalence relation in a logico-mathematical context (), involves systematically disregarding differences between elements (unless it is the special case of identity). So, even if there is some equivalence between mathematics and physics (in a broader sense), this does not prove that they are identical. It just shows that in some respects that we are interested in, in a particular context, ... there are systematic similarities. But that does not preclude that there may be systematic differences, too.
* Regarding multiverse hypotheses and "The idea that every possible universe is as real as our own has been proposed by several philosophers before Tegmark’s formulation of the MUH."
- As I also mentioned during the hangout, the observation that versions of this idea have popped up on multiple occasions has made me more skeptical of it. Similar ideas are used in fiction (e.g., Borges's "The garden of forking paths", the (Belgian! ;-) ) movie "Mr Nobody", maybe the movie "Lola rent", ...), logic (possible world semantics; Lewis; Kripke/Prior branching time structure), quantum mechanics (many worlds interpretation), ... and now in cosmology (Tegmark, MUH).
* Regarding the 'measure problem' (the problem with combining probability and infinity).
My approach involved assigning infinitesimals to singletons (in the sense of hyperreal numbers, i.e. Robinson's non-standard analysis; article here). After this, and together with mathematician Vieri Benci and philosopher Leon Horsten, we applied the same idea to sample spaces of arbitrary cardinality. We developed "non-Archimedean probability" (NAP) theory (article here). So, in principle, we can apply this to the Maxiverse! :-) (However, I suspect the Maxiverse may be so large as to constitute a proper class rather than a set. We did not develop NAP theory for classes.)
We did not solve the arbitrariness issue. If anything, infinitesimals (and the degrees of freedom in selecting a free ultrafilter) make this issue worse. ;) On the other hand, our theory may be of help if probability-zero events are at the root of some problems.
* Regarding your view of consciousness and F-clones:
- This made me wonder whether you are familiar with the work of philosopher Arnold Zuboff? He was the originator of the "Sleeping Beauty problem", which you may know since it combines issues of probability and anthropic reasoning (which you also write about). In any case, in his 1990 "One Self: The Logic of Experience" Zuboff advocates his view on personal identity, called "Universalism", which can be summarized as the view that "we are all the same person". I am certainly not an adherent of Universalism (and I think there are problems with Zuboff's statistical argument for it). Universalism clearly does not coincide to your view either, but I find it fascinating what led Zuboff to this view, since there may be a similarity to your position.
Zuboff reports reading the short science fiction story "The other tiger" by Arthur C. Clarke as an important source of inspiration. (If you don't know this story, please read it! e.g. here) This and other events made Zuboff wonder about copies, very similar to your F-clones. He wondered: As long as one copy of me still exist, I still exist? And eventually, this led him to token-freedom and Universalism (a further step that you clearly didn't take).
- My view is to resist even the first step (equating the consciousness of the F-clones). It is related to my earlier point about equivalence relations: sure, there are some clear similarities, but not identity (even if the differences may not be empirically accessible to the relevant subjects).
* Regarding the final part:
- I really liked your reference to Piet Hut. Of course, the same applies to mine and all other essays: we may simply be missing the relevant input to make sense of these matters. We should stay humble. But meanwhile we might as well enjoy some specultation. ;-)
So, although I don't agree with your premise, I do like the way you expose the topics, in a clear and accessible style. Your prize seems well deserved. Congratulations!
PS: I also watched your videos that won an earlier prize: great work! I plan to show them in a future course. :-)