A Project to Find the Fundamental Theory of Physics

by Stephen Wolfram

Released alongside the launch of the Wolfram Physics Project, this book provides a unique opportunity to learn about a historic initiative in science right as it is happening. The Wolfram Physics Project is a bold effort to use breakthrough new ideas and the latest in physics, mathematics and computation to find the fundamental theory of physics, often viewed as the ultimate goal in all of science. Written with Stephen Wolfram's characteristic expositional flair, the book includes both an accessible introduction to the project and its background, as well as core technical documents, and breathtaking visualizations that bring to life a dramatic new understanding of how our universe works.

Genres: Physics, Science, Nonfiction, Mathematics

770 pages, Hardcover

Published June 19, 2020

About the author

Stephen Wolfram is the founder & CEO of Wolfram Research, creator of Mathematica, Wolfram|Alpha & Wolfram Language, author of A New Kind of Science and other books, and the originator of Wolfram Physics Project.

Reviews

[Manny]

In his classic How to Cheat at Chess, Bill Hartston explains that it's easy to annotate chess games once you know the result. If a complicated sacrifice worked, praise it as "the logical conclusion to a well-played attack"; if it didn't, dismiss it as "desperation, but White was lost anyway." Hartston says that when you see a chess journalist intently studying the position in an ongoing tournament game, you can be sure that what they're doing is mentally composing those two parallel narratives, so that they'll be able to mail in the right one as soon as the game is finished.

Inspired by Hartston's remarks, I offer you the following two reviews of Stephen Wolfram's new book. I'm hopeful that at least one of them will turn out to be right.

Positive review

People who want to score big often need to do things their own way. Einstein, who changed the face of science for ever, spent his most productive years working as a patent clerk; it gave him time to develop his thoughts at leisure, away from the relentless pressure of the academic world. Wolfram has been no less original. Starting off as a science wunderkind - he got his PhD at 20 - he soon realised that what physics needed most was better computational tools. He started developing the software that eventually turned into the Mathematica package, and founded a successful company to market it.

The more he worked with computation, the more he began to suspect that this was the true substrate of reality. Investigating a huge range of computational systems, he found that even the very simplest ones - in particular, the remarkable 'Rule 30' - could display astonishingly complex behaviour. In his 2002 bestseller, A New Kind of Science, he presented his initial findings, but then returned to growing his company. Now, in this latest book, he completes the Odysseus-like journey that has led him back to the fundamental physics he started from, and shows new ways to address the problems that people have been stuck on since the 70s. Instead of increasingly recalcitrant mathematical frameworks, Wolfram uses a twenty-first century approach and shows how the power of modern computer technology can be harnessed to simulate artificial universes that are starting to reproducing the physical phenomena we see in our own world.

Wolfram's bold hypothesis is that the universe, at its deepest level, consists of a huge network, which is constantly evolving according to a single rule whose precise formulation is, literally, the ultimate answer. His intuition, honed on a lifetime of working with such systems, tells him that this rule is very simple - so simple, in fact, that it can be found by having machines systematically check through the possibilities. He has not yet found it, but he says he's close. Already, he has been able to demonstrate that a large class of these systems follow the equations that define Einstein's theory of general relativity. He has an incomplete but suggestive argument, developed with a student, to show that a slightly more restricted class of systems also display behaviour characteristic of the quantum mechanics we see in our own universe, and in particular reproduce the path integral formula developed by his one-time mentor Richard Feynman.

Wolfram takes a broad-brush approach, and freely admits that important details still need to be resolved. (In particular, it is still not quite clear how to resolve the difficulties posed by Bell's Inequalities). But he thinks his initial successes cannot possibly be accidental, and that we're now within sight of the answer. He is making all his findings and methods generally available, and encourages other people to join in. It's hard not to believe that there will be an enthusiastic response.

Exciting times!

Negative review

People who have screwed up big often feel an urge to justify themselves. Einstein, who wasted the second half of his life on a fruitless search for the Unified Field Theory, ignored horrified entreaties from his friends to stop throwing good money after bad after bad and move on. Similarly, Stephen Wolfram, despite all the evidence to the contrary, is unable to accept that his strategy for investigating the nature of reality might be totally mistaken. Having abandoned a promising career in fundamental physics to start a software company, he is determined to show that software engineering is going to reveal the secrets of the universe. He says himself that his physicist friends beg him in vain to do something else.

Discovering that simple rewriting systems like the overpublicised 'Rule 30' can sometimes create complex structure (a result already well-known, for example, from Conway's 'Game of Life' and the Mandelbrot set), Wolfram decided that the nature of reality had to be in some way related to this finding. In his 2002 self-published screed, A New Kind of Science, Wolfram outlined these ideas and was met with a resounding lack of interest from the scientific community. He went back to working on his company. But he has evidently not had the sense to leave well alone, and is now wheeling out the same old arguments again. He seems to have forgotten how to work with equations. Instead, he shows us interminable pages of output from his simulations, and tries to convince us that they are somehow better.

Wolfram's tired hypothesis, all too familiar from the earlier book, is that the universe, at its deepest level, is some kind of rewriting system. The novelty this time round is that it is, specifically, a certain type of graph rewriting system. A New Kind of Science already made the unsupported claim that systems of this kind can display behaviour describable using the formal apparatus of general relativity. Here, there are a few more details and a link to a recent arXiv paper by a student. There is some extremely handwavy speculation about how quantum mechanics fits into the picture. I do not understand the claimed derivation of the Feynman path integral, which relies on some legerdemain in which energies are related to angles in "multiway causal graph space" (where does the geometry of multiway causal graph space come from?) and the magic formula ∫ exp(iHt)dt emerges from what certainly looks like Wolfram's sleeve. He has still not found any actual rewriting system that displays the properties he keeps promising us must be there.

Bell's Inequalities come up momentarily in the final chapter and are then brushed under the rug, despite the fact that, as Wolfram says, they are the standard objection to hidden variables accounts of quantum mechanics. The best known book on this kind of framework, Nobel laureate Gerard 't Hooft's The Cellular Automaton Interpretation of Quantum Mechanics, is not even mentioned. For some reason, Wolfram thinks his work is interesting, and is making it all publicly available. Knowledgeable people seem less than blown away. You can see some typical comments here.

Depressing times.

[Rossdavidh · Rating 4 out of 5]

So, I was given a copy of this book in exchange for an honest review. I'm not sure if I'm smart enough to be reviewing this book, but they asked for it, so here goes.

First of all, let me say that physically, it is a very satisfying experience to read this book. That may sound odd, but a nicely bound book, hardcover, with multicolor images in copious amounts on high-quality paper, is just satisfying to read, at a tactile, almost subconscious level. Which is good, because at an intellectual, conscious level, this book is definitely demanding that you sit up straight and bring your "A" game, so it is nice to have an emotional reward for doing so.

The images are actually useful in an intellectual sense, also, because what Wolfram is talking about here is in one sense quite abstract, but it does relate to networks (sometimes quite large) of connections between nodes. If one were to attempt to read a book about that without the images to make it a little more clear what we're talking about, it would have been hopeless. There are pictures on every page, I think, or nearly so, and they are in many colors and many shapes. We see abstractions of abstractions, and one attempts to learn words like "foliations" and "multiway graph" and "branchial graph", and it is better to at least be able to look at one of these things and think, "huh, that kind of looks like those 'choose your own adventure' diagrams they would have at the end of the story". Which is actually a thought I had when I woke up in the middle of the night, apparently having been thinking or perhaps dreaming about the contents of Wolfram's newest magnum opus.

What he claims, here, is that he has the framework for a theory of everything, which will explain relativity, quantum physics, and everything. Not, as Einstein and Bohr and etc. did it, by postulating certain things as just given, but rather proving that they must work that way, by virtue of his theory of everything. In a few cases, I could kind of get what he was saying. It did look interesting. More plausible than, say, string theory.

This is not the same as saying that I think his theory is correct. It could be, for all I know, but I don't think I'm qualified to say, or really even to have a guess. It did look like it might be interesting to play with these kind of systems in simulation, but I don't know if I could tell whether or not it was true even if I had the time and supercomputing power available to do that. But it was fun to look at the diagrams.

This was a three star read until the last chapter or so, when he starts showing how to derive some of the fundamental facts of relativity and quantum physics from it. While I cannot say I'm quite a convert yet, that did look interesting enough to make me start to wonder. It could be that, ten years from now, this will be one in a long line of dead-end attempts to explain how and why the crazy physics of the 20th century (relativity and quantum physics) could be explained. But it also could just possibly be that it will be much more successful than, say, string theory, in going someplace.

But, let's be honest here, not if it requires me to be able to advance the field. It does have lots of nice pictures, though.

[David Wineberg · Rating 5 out of 5]

We are barely out of the period where we thought the Earth perched on the back of a turtle, was flat, was at the center of the universe and that we had discovered everything there was to discover without even knowing about atoms. Do we now suddenly know enough to be able to propose a unified theory of physics and therefore the universe? Do we now know every particle and its role?

Stephen Wolfram has a kind of workaround for those questions. Decades ago, he got waylaid by the potential of computers and the joys of discovery and invention in that field. Now, having just turned 60, he is coming back to his roots (He published his first physics paper at 15), throwing the doors wide open to tackle the holy grail – the underlying, fundamental theory of physics that dictates how the universe works, why it looks and works the way it does, and where it goes from here.

In his nearly 800 page announcement, called A Project To Find the Fundamental Theory of Physics, Wolfram expresses his delight to be able to do this now. He says had he tried decades ago, he would not have had the tools to launch or succeed in this effort. He created those tools himself, for other purposes. And along the way, he picked up a better understanding of what he faces: “We won’t be able to get even close to running those models for as long as the universe does. And at the outset it’s not clear that we’ll be able to tell enough from what we can do to see if it matches up with physics.”

He drops some important hints as to what has changed in his mind:
-“General relativity and quantum mechanics are basically the same thing.” This solves a huge conflict in modeling, and Wolfram “proves” it using simplified examples of causal invariance that by definition, end up branching back to the same state. This conveniently eliminates any potential conflicts.
-“I have an estimate that says that 10200 times more ‘activity’ in the hypergraph that represents our universe is going to ‘maintaining the structure of space’ than is going into maintaining all the matter we know exists in the universe.” So the universe is largely on maintenance.
Let those points guide your own theory attempts.

The book is about the fundamentals of modeling. He shows with great simplicity that a rule for a variable produces astoundingly complex images if repeated often enough. The book is festooned with an immense variety of results, from the basic rule to the first simple iterations, the point where before or after the very next step takes it into a new level, and then a 3D model of the result. If only for the graphics, the book is gorgeous. Wolfram makes great use of color to show what has changed from iteration to iteration, how structures differ, and to highlight what he talks about.

It is also an inspiration. If such simple rules (For every occurrence of AB, substitute BA) produce such sophisticated structures, there must be a way to structure a universe somewhere in there. In typical Wolfram fashion, he is opening up the treasure chest of tools and data to all comers. His meetings are livestreamed and recorded. He is making the collection of rules experiments, called notebooks, available to all, and allowing anyone to create their own using his tools. One way or another, Wolfram would love to see someone make a major breakthrough in the ultimate quest of physics. Starting with this book is a pleasant way to begin.

It could have been dauntingly technical, but Wolfram has made it appealing to all comers. Readers do not have to absorb the formulas or ponder the origins of the universe to enjoy it. The sections are color coded with tabs on the outer corners. It is actually a fast read. My only complaints are tiny type and graphics (This is the first book I have read with magnifying glass handy instead of a search engine), and paper so thin that images from the back side of the page are clearly interfering.

For this project to work, Wolfram simplifies by saying he thinks the universe is just a computer, carrying out formulas and rules. It’s all routine and predictable. He says the only thing special in the universe is ourselves.

David Wineberg

[David Jacobson · Rating 2 out of 5]

Stephen Wolfram is the world's expert on simple computer programs (simple like string-substitution simple). In the past—most famously in his A New Kind of Science—he has asked whether such simple programs, applied over and over, can give us new algorithms for solving problems or new ways of generating random, chaotic behavior. Now he is asking whether such simple programs can give us a unified description of physics.

If you take what he is doing as an exercise in building toy models, there is some value in it. He runs programs that progressively operate on hypergraphs (abstract networks connecting points) and is able to identify interpretations of the results that reproduce core ideas from many key areas of physics. The most convincing are his connections to special and general relativity, which makes sense given that his simple programs generate abstract spaces and those theories are essentially theories of space. Some ideas that come out of contemplating his models—like an interpretation of quantum mechanical measurement as shifting into a "quantum observation frame" or the acceptance of a "many worlds" view of quantum mechanics without accepting multiple timelines because of a kind of causal-invariance conservation law—are thought-provoking and could lead to new avenues of exploration in physics.

But, if you drink the Kool-Aid and think that models of this kind will actually reveal the fundamental theory of physics, there seems to be little hope for progress. The problem is that Wolfram's model runs square up against another of his cherished ideas: what he calls the principle of computational equivalence. This is the idea that, for any non-trivial computational system (like the simple hypergraph-modifying programs he entertains), there is no way to predict the outcome of the computation without going through all the intermediate computational steps. But, if this is meant to be a theory of the universe that, to explain cosmology, would have to start from the beginning, how do you ever do all that computation? Even to make what might seem to be one of the simplest connections with established quantum physics that you might hope to make—to model a single electron—he estimates that you would need to simulate a hypergraph with 10^35 elements. Storing the state of that electron would require, by my estimate, more than all the total storage capacity of all the computers on Earth.

Wolfram is aware of this problem of scale, and offers two Hail-Mary solutions at the end of the book (or the middle, more on that below). The first is the hope that there might be regions of computational reducibility offering shortcuts around computational equivalence. This seems like a cop out, coming from the progenitor of that theory. The second—to address the problem that the underlying "simple" program might be arbitrarily complex—is to introduce the notion that the universe might not be governed by one program, but by a superposition of all possible programs. Again, this is food for thought. But it means that—contrary to what you might read in the introduction (dubbed "The Announcement")—this project is not exactly on the verge of discovering any fundamental theories.

As I said, there is certainly food for thought in these models, and interested physicists will probably enjoy reading the 70-page "Announcement", which summarizes all the main ideas (which have not, incidentally, been published in a peer-reviewed journal). I am not sure who should actually read this entire book, though. For those who want to understand the central concepts, those are all in the "Announcement", which is available online. The bulk of this nearly-800-page book is meant for those who mean to contribute to the "Project" of furthering Wolfram's models. But, there is such a gulf between the simple details of the book (much of which is a picture-filled explanation of how to build and describe hypergraphs) and the leviathan task of reproducing real physics that I don't think reading this primer will help in the slightest.

Those who nonetheless persist in reading it, however, should know that it is laid out in such a way that the historical background comes after the new developments. I would instead suggest working through in this order: Preface, Announcement, History, Foundations, Background, Technical Introduction.

Note: My review copy of this book was provided without charge by the publisher.

[Douglas Summers-Stay · Rating 4 out of 5]

Wolfram's writing style is odd. He doesn't cite people properly, he starts half his sentences with conjunctions, he likes to show example after example without telling what the example is supposed to show, etc... I feel like reading his books is like hanging out with your brilliant, slightly-on-the-spectrum friend. You're not demanding scientific rigor, you just want to see what he's thinking about, because it is interesting.
His idea is a way to explain space, energy, matter, relativity, conservation laws, and quantum mechanics, and so on in terms of directed-graph rewriting rules. For people like me who have just a little physics (in high school) it is really nice to have a notion of what energy is, or what momentum is, that isn't just a mysterious rule for the universe.
He's really good at making pretty graphics in Mathematica, which I appreciate. I don't do nearly as much mathematical recreations stuff as I used to, so its fun to go visit that world once in a while.
Most of the idea are not very far developed beyond what he described in A New Kind of Science, but I feel like the explanation is clearer.

[William Darian · Rating 5 out of 5]

It is very exhilarating to see the "Project to Find the Fundamental Theory of Physics" (A.K.A. Wolfram Physics) at its inception. Starting by introducing elementary components and operations of the framework, one can derive quite a lot of things related to contemporary physics.

The primary model is based on mathematical graphs (or shall we say hypergraphs for its analog in higher dimensions). Its nodes connect with unweighted, directed edges that—on a large scale—can show unprecedented emergent phenomena such as special and general relativity and quantum physics. Physical concepts such as energy, rest mass, momentum, and quantum entanglement can be identified in the model quite clearly.

The structure of the graph evolves by an underlying graph transformation rule(s) (that is specific for each "universe" and its progression). With an initial graph as a seed to run the model, one can iterate through the application of the rule(s) in a predetermined ordering to see the succeeding states of the model. Even with this simple setup, the possibilities are truly endless.

Space and its dimensionality can be measured within the model after some generation of the state. On the other hand, time is represented in the model by the action of the rule application itself. Other, higher concepts in physics are explained further in the book, but many of the derivations of them are based on analytical observations of the model, rather than using a mathematical line of reasoning.

That said, the main purpose of the book is to introduce an unconventional approach to the fundamental theory of physics to those who are interested in exploring. That is, by treating the universe as a state in an irreducible computational process that has been going on since the dawn of time.

There are, however, some well-known concepts in physics that were not evident in the models explored in this book. A notable example is the fundamental force of electromagnetism.

Ultimately, the book was a blast to read. More so considering most of the illustrations are beautiful. The illustrations include many high-quality depictions of the graphs that are relevant to the topic. The book was quite exhaustive regarding the exploration of the possible simple rules that might govern our universe, but there's lots and lots more to explore.

I would recommend this book to computer scientists, mathematicians, and physicists who are looking to widen their perspectives towards the universe which we, as observers, are living in. Stay curious.

[Anthony O'Connor · Rating 5 out of 5]

Fascinating, and very readable. An account of one aspect of his life's work.
Wolfram leads the many and various attempts to base physics on simple computational rules. First it was cellular automata and now time-evolution of hyper-graphs. The subject in itself is interesting enough but he claims that he can derive as emergent properties the basics of relativity ( special and general ) and quantum mechanics and much else - which gives it enormous importance. He seems to think of time as emergent too but let's face it that is built in from the start. The steps in the computations. Need something more subtle there.
Setting up and promoting a project in this manner is not the usual way it's done so it will be interesting to see how Academia responds. Such uber-ambitious projects outside conventional bounds would usually be sneered at and their authors dismissed as cranks. But Wolfram more than anyone has the street cred, the intelligence, the background, the resources and the independence to get it going. It's going to be interesting.

[Stephen Muires · Rating 5 out of 5]

With Stephen Wolfram’s new 2020 book we are witnessing the evolution of science happening before our eyes in real-time. It is like watching Isaac Newton write the Principia. Wolfram is Newton before Newton knew he was Newton.

When I received the book in the mail I showed it to my son who is majoring in astrophysics at university. I wondered if this stuff could ever be part of the curriculum. He looked through the pages for a few minutes and said, “No, it doesn’t contain any mathematics.” There you go, a simple insight and a simple indictment against modern science. Something that contains no math is not science, is the modern belief. In my own view the fact that Wolfram’s work, on the surface, is free of mathematics just makes it digestible. It makes it possible for a mere human to follow along and get hold of the basic insights. A Project to Find the Fundamental Theory of Physics is so full of insights that it seems overwhelming after just a few pages. But since there are no math equations to throw spokes in the wheel, I can enter this world, and so can you. Also, and more importantly, mathematics may today constitute prison bars on further scientific developments.

When Wolfram’s first large work, A New Kind of Science, came out in 2002 I must have been one of the first readers. It was a fascinating journey through cellular automata that illuminated tantalizing properties of the universe we live in. The relentless approach from all directions of life and science, left me deeply impressed by rule 30. Rule 30 is the cellular automaton that most obviously produces irreducible randomness from a simple and supremely graspable set of instructions. I did not understand it fully. I wondered how and if this could ever become practically applicable, a rather reasonable requirement for a scientific effort.

The new insight that did not leave me alone, and that did not leave Wolfram alone, was that of computational irreducibility. A simple concept to explain, but very hard to understand the implications of. In simple words, irreducibility means there’s no shortcut. A bit like we know from life, from skill training, from building relationships or a career. It stands in contrast to the reducibility that science has been striving for. A formula that yields everything, instantly. Mathematical equations are like that: they have a solution, one answer that is arrived at instantly. But rule 30, and others, demonstrate behavior that cannot be arrived at through prediction. There is no way to know if the middle cell in iteration #3456 of the cellular automaton is going to be black or white, 1 or 0. Unless you compute the rule through all of the 3456 steps and then observe the result. The computation cannot be reduced. Exactly like in real life. We cannot know what will happen tomorrow other than live through it.

The computation becomes life-like. Not imitating life, but rather being structured from the inside out as life is structured from the inside out. From there it is a short distance to proposing that the universe is a result of an ongoing and irreducible computation.

In my novel Ordained (2015) I described a fanciful and fictional application of rule 30 in decrypting passwords. That was fun, but of course unrealistic. I understood that Wolfram’s work would not be a hit. It does after all propose a radical new way of doing things. You can’t fight city hall, even in the exploration of the universe.

With the publication of this new project I was pleased to realize that Wolfram not only has gone it alone, but has been doing this successfully and with increasing support from brilliant younger scientists. Instead of a dud, the 2002 project was merely a wedge in the door. Now stuff is slipping through the cracks.

The new project goes an order of magnitude further and faster than A New Kind of Science. It is still written in loosely edited, informal English. No academic principles of paper writing were adhered to, thank God. The pictures are in color and are the main argument why, in my opinion, Wolfram is certainly on the heels of very large prey. The prey is as large as the universe itself. The pictures have a disturbing quality, as if looking inside the structure of life. As if looking into a mirror.

This is an easy book to read, yet not easy to accept, to absorb. It probably helps if you have plodded through the even thicker A New Kind of Science. Like a ship, you have to be willing to climb aboard. I feel that the rewards of doing so could be the discovery of a whole new world.

[Vasil Kolev · Rating 5 out of 5]

I really liked this.

First, let me note that 1) I'm biased, as every such theory based on computation, and relatively simple is in the domain of things I work and am familiar with, and 2) I don't fully understand a lot in the physics part (which is to be expected for someone who has failed Calculus 2).

The overall theory is simple enough, that the universe is a graph/hypergraph that evolves based on preset rules. A lot of things, like relativity come out as natural effects of the model, and even without the specific rules (which are being looked for) there's a lot of reasoning that can be done.

This is very preliminary - the book is mostly a description of the idea, a technical description and some taxonomy of different systems/rules and observations on them, but should be looked at more like the introductory math textbook for physics that is being discovered right now, not as something complete and full. There's a lot of work remaining (which the author says multiple times), and this is its beginning.

Humongous amount of questions remains (even I have a few separate in my head, which might get answered on a second read), and one direction hasn't been even started yet, which would be really important for accepting this theory, which would be how to experimentally prove it. With the expected sizes of things (stuff like 10^-81 m for the smallest discrete size, 10^500 for the number of "updates" since the beginning of the universe), it might be practically impossible, and I don't think there's even an idea where to start on that (or I haven't been able to find any mentions).

Still, the whole idea of the universe as a computational "device" and all that follows it looks extremely promising and with very interesting ramifications (and might also prove p!=np as some random side-effect).

[Paul Schrum]

The concepts are fascinating and Wolfram's work is exhaustive.

Yet where he tries to apply his theory to an explanation of the event horizon of black holes, he astonishes me. He seems not to understand what the theory actually is. I know this can't be possible, so I am baffled at why he applies his theories in the way that he does. It's just wrong.

Wolfram's application of graph theory as the fundamental quanta of space to how an event horizon works does not allow for the signal of gravity bending spacetime to pass the boundary. When I realized this, I read the section a second time to be sure I understood. I did, and I was astonished that he would not provide a way for that to happen.

This basically crashed my confidence in his work. He may figure it out one day, but the seeds of that are not in this book.

[Łukasz Stafiniak · Rating 5 out of 5]

I haven't really read the whole book, but I own a physical copy. I listened to more stream discussions than it's worth though, and I've read parts of Jonathan Gorard's papers (as much as I had time for at the time...)

For technically minded people, I don't recommend reading this book, but it's still a good book for its art value. Read these articles instead: https://www.wolframphysics.org/people...

A note on Scott Aaronson negative reaction: one person's modus ponens is another's modus tollens, makes me deduce a couple authority points. I think he is responding to a straw-man shaped by his understanding of Wolfram Physics from "A New Kind of Science" instead of engaging with the results (e.g. the ZX-Calculus approach).

[Gile · Rating 3 out of 5]

A preposterously overbearing title for an otherwise rather interesting atlas of generic graphs.
Is he talking about a structure equivalent to an universal automata (Turing machine)?! If so, everything from that point can be claimed and some of that even demonstrated because it is universal, so why not...

[Will Peterson]

My brain only has a slight, tenuous hold on comprehension (and even sanity) when reading this book. But I'm pretty sure he's on track for the fundamental theory of physics and the whole universe.

[Carlos Augusto Méndez Alvarado]

INTERESTING