**Our Mathematical Universe: My Quest for the Ultimate Nature of Reality**

Knopf (January 2014)

Max Tegmark just published his second book, “Life 3.0.” I gracefully declined reviewing it, seeing that three years weren’t sufficient to finish his first book. But thusly reminded of my shortfall, I made another attempt and finally got to the end. So here’s a late review or, if you haven’t made it through in three years either, a summary.

Tegmark is a cosmologist at MIT and his first book, “Our Mathematical Universe,” is about the idea that the world is not merely described by mathematics, but actually made of mathematics.

I told you ten years ago why this is nonsense and haven’t changed my mind since. It was therefore pretty clear I wouldn’t be fond of Max’s message.

But. Well. People like Max don’t grow on trees. I have much sympathy for his free-range ideas and also, even though I’ve met him several times, I never really figured out what he was tenured for. Probably not the mathematical universe. Once upon a time, I was sure, he must have done actual physics.

Indeed, as the book reveals, Tegmark did CMB analysis before everyone else did it. This solid scientific ground is also where he begins his story: With engaging explanations of contemporary cosmology, the evolution of the universe, general relativity, and all that. He then moves on to inflation, eternal inflation and the multiverse, to quantum mechanics in general and the many worlds interpretation in particular. After this, he comes to the book’s main theme, the mathematical universe hypothesis. At that point we’re at page 250 or so.

Tegmark writes well. He uses helpful analogies and sprinkles some personal anecdotes which makes the topic more digestible. The book also has a lot of figures, about half of which are helpful. I believe I have seen most of them on his slides.

Throughout the book, Tegmark is careful to point out where he leaves behind established science and crosses over into speculation. However, by extrapolating from the biased sample of people-he-spends-time-with, Tegmark seems to have come to believe the multiverse is much more accepted than is the case. Still, it is certainly a topic that is much discussed and worth writing about.

But even though Tegmark’s story flows nicely, I got stuck over and over again. The problem isn’t that the book is badly written. The problem is that, to paraphrase John Mellencamp, the book goes on long after the thrill of reading is gone.

Already in the first parts of the book, Tegmark displays an unfortunate tendency to clutter his arguments with dispensable asides. I got the impression he is so excited about writing that, while at it, he just also has to mention this other thing that he once worked on, and that great idea he had which didn’t work, and why that didn’t work, and how that connects with yet something else. And did I mention that? By the way, let me add this. Which is related to that. And a good friend of mine thinks so. But I don’t think so. And so on.

And then, just when you think the worst is over, Tegmark goes on to tell you what he thinks about alien life and consciousness and asteroid impacts and nuclear war and artificial intelligence.

To me, his writing exhibits a familiar dilemma. If you’ve spent years thinking about a topic, the major challenge isn’t deciding what to tell the reader. It’s deciding what to not tell them. And while some readers may welcome Tegmark’s excursions, I suspect that many of them will have trouble seeing the connections that he, without any doubt, sees so clearly.

As to the content. The major problems with Max’s idea that the universe is made of mathematics rather than merely described by mathematics are:

- The hypothesis is ill-defined without explaining what “is real” means. I therefore don’t know what’s the point even talking about it.

- Leaving this aside, Max erroneously thinks it’s the simplest explanation for why mathematics is so useful, and hence supported by Ockham’s razor (though he doesn’t explicitly say so).
The argument is that if reality is merely described by mathematics rather than actually made of mathematics, then one needs an additional criterion to define what makes some things real and others not.

But that argument is logically wrong. Saying that the universe is accurately described by mathematics makes no assumption about whether it “really is” mathematics (scare quotes to remind you that that’s ill-defined). It is unnecessary to specify whether the universe is mathematics or is something more, evidenced by scientists never bothering with such a specification. Ockham’s razor thus speaks*against*the mathematical universe.

- He claims that a theory which is devoid of “human baggage” must be formulated in mathematics. I challenge you to prove this, preferably without using human baggage. If that was too meta: Just because we don’t know anything better than math to describe nature doesn’t mean there is nothing.

- Max also erroneously thinks, or at least claims in the book, that the mathematical universe hypothesis is testable. Because, so he writes, it predicts that we will continue to find mathematical descriptions for natural phenomena.

But of course if there was something for which we do not manage to find a mathematical description, that would never prove the mathematical universe wrong. After all, it might merely mean we were too dumb to figure out the math. Now that I think of it, maybe our failure to quantize gravity falsifies the mathematical universe.

There. I’ve done it again. I set out with the best intention to say nice things, but all that comes out is “wrong, wrong, wrong.”

To work off my guilt, I’ll now have to buy his new book too. Check back in three years.

## 171 comments:

Hello Sabine,

Generally speaking, I would always argue the 'the universe' or 'matter' or anything else, can never be made from abstract concepts, such as mathematics. The same notion appears when some physicists claim that everything is made of information, or 'in the end it all boils down to pure energy'. What does pure mean here ? Nobody can draw me a scetch of what energy is, or information or mathematics as building blocks.

Therefore I would agree that mathematics or information can only entail a means of representation of reality, whatever reality may mean.

It's like Plato's cave : information or mathematics don't get past the level of the shadows on the cave wall. Whereas the stuff happening between the flame and the wall is always more fundamental. Even though, again, more fundamental descriptions of that stuff could exist.

Bottom line is : In science one should worry about producing testable claims about things unknown or badly understood around us, if one aspires to avoid, as you called it somewhere, blablaland.

Best, Koenraad

I liked this review a lot. I'm actually in the middle of this book right now but took a break right around page 250-275 as you mentioned. Glad I wasn't the only one who got a little exhausted at that point! I am curious on what you mean by this though:

Even more perplexing, he argues that the multiverse explains why the constants of nature seem finetuned for the existence of life. This is a misunderstanding of both finetuning and the anthropic principle.' I thought his explanation of that was pretty enlightening, but if it is a misunderstanding, I'd like to know why. Thanks!

Hi Sabine,

I would agree with most of what you say; even though a philosopher might say that the criterion for something to emerge from nothingness and be maintained is its self-coherence - for which "some maths" are relevant.

Also I do not understand why physics failure to discuss anything that is not a differential equation means that differential equations are the end of the story (which is what I understand from your text - pls correct me if I am wrong). After all, those are human made.

Best,

J.

https://youtu.be/h04CH9YZcpI

Peter Woit and Max Tegmark had an interesting discussion about the book a few years ago:

https://www.math.columbia.edu/~woit/wordpress/?p=6551 (see some of the early comments)

Not a fan of his "math first" ontology either, but I think his taxonomy of multiverse (type I, II, III, IV) should be broadly adopted. Whether any multiverse is real or not at least when we talk about it we would be talking about the same thing..

Every time I've read Tegmark's Mathematical Universe Hypothesis, my primary thought has been "How come this nutcase has tenure at MIT ?".

Thank you for answering that question !

As for MUH, I wish that at least magazines like Scientific American - where Tegmark's nonsense has appeared earlier - would filter articles based on their scientific content, rather than the author's institutional affiliation.

But going further, my main question for Tegmark would be:

How would you distinguish an universe that "IS mathematics" from one that is merely "perfectly described by mathematics" ?

I've never seen him give a coherent answer to this question anywhere.

I read the book 2 years ago. I am not sure if I agree with Tegmark, but find the question of why mathematics is so usefull in describing reality very fascinating.

Love it! Max thinks mathematics makes our minds. I think our minds make mathematics.

I generally agree. I liked the book and got through it pretty easily but I found it utterly unconvincing. One major issue I had that you don't mention is that he literally says that accurate theories of the universe should be expected to be weird and anti common sense merely b/c we live in an unusual locale on the surface of a spherical planet. If your default is that the weirder the theory is the more likely it is to be true then we have simply no grounding at all for judging theories. The moon is indeed made of cheese. Or the universe made of mathematics. To me, it seems pretty obvious that mathematics is simply a human-created tool for understanding the basic phenomena of the universe. There is no mathematics in the universe. It's all in our mind.

yuuuup. I would almost venture to say that if the universe IS Mathematics why can we only get approximations and what is the point of a mathemetical model of a reality based system if that reality is already math, just copy it over why change anything. no make sense. "Never confuse the symbol of an object for the object itself" I take honest over nice any day at least you know where everyone stands and THAT'S nice :)

-Jes

"I never really figured out what he was tenured for. ". An insight into Tegmark's modus operandi is provided by the following statement in Woit's blog "Not Even Wrong".: "Tegmark’s talent [is] as an impresario of physics and devotion to making a splash. Before publishing his first paper, he changed his name from Shapiro to Tegmark (his mother’s name), figuring that there were too many Shapiros in physics for him to get attention with that name, whereas “Tegmark” was much more unusual. In his book he describes his method for posting preprints on the arXiv, before he has finished writing them, with the timing set to get pole position on the day’s listing." Tegmark also says that he is "known as Mad Max for my unorthodox ideas and passion for adventure." I seriously doubt that anyone refers him as Mad Max; it is much more likely he has bestowed this moniker upon himself. btw - i've read Tegmark's latest book and i think you can safely put off reading it three (or more) years without missing anything of value. Sorry if this comment is harsh but i think that fantastical nonsense such as Tegmark's, do a great disservice to serious science and harms the field. As the saying goes "with friends like these, who needs enemies?"

Some people that are extremely bright/intelligent/high IQ most of the time they get a pass on their analysis and conclusion. We need people that are just as bright/intelligent/high IQ call them out for their liberal conclusion.

With that said, I will buy the book because I might find a nugget of gold even though the book has its flaws.

Thank you for the review.

I think he means that if the universe is fully described by mathematics, it becomes unnecessary to postulate a "real" universe that is different from its description, one that merely "follows" it, whatever that means. Clearly that satisfies Occam's razor, as it eliminates the metaphysical concepts in the scare quotes, making things a lot simpler.

Our universe is no more "real" than the number Pi, with all it's glorious infinity of digits. What we mean when we say 'real' is 'in the same mathematical description as I', thus reducing "real" to another metaphysical concept: "I"

That sounds like brutal reading. I don't mind a bit of digression in a book, but it can get annoying real fast. Worse, Tegmark is one of those people who thinks philosophical questions are important and lets that dominate his or her work. I'm one of those people who thinks that mathematics is something that people do because it is useful, so 'why mathematics works?' is not a real question. Mathematics is just a we can comprehend and predict things about reality. Either we can't comprehend and predict or we can. If we can, then mathematics or whatever we choose to call it.

You've clearly tried to give Tegmark a fair review. You did. That you gave a negative review is on him, not on you. You don't owe him.

I have the book ... signed copy even that I purchased from the man himself at his lecture at the IAS. Got to talk with him for a minute or two after. Very nice man and patient with the inane musings of lay people. That being said, I thought it was me and my lack of formal training but I had a massively hard time getting through this book and I read a lot of science books. [Penrose is another example of an author I just am at a loss to understand] I got buried in the maelstrom of ideas several times (as did my friend Randy) but I am going to give it another try and perhaps take another stab at Penrose's book on AI. Thanks Sabine ... now I don't feel like a complete clone ... :)

Tam,

I'm with Max on that point. I even have a chapter dedicated to this in my book. Not with regards to the mathematical universe (which appears briefly in my conversation with Garrett Lisi) but with regards to quantum mechanics. I don't see any reason why humans should find the fundamental laws of nature intuitive.

Andreas W,

I explained in my blogpost why that argument is wrong. I suggest you read it.

akidbelle,

I think this is a misunderstanding. First, physicists of course discuss things other than differential equations. What I said what merely that Tegmark claims in the book that if our universe is a mathematical structure and it's determined by a differential equation then that removes the need for initial conditions. Or so I understood. Which doesn't make any sense. Of course it's still the case that if you want to know which solution describes the universe you need to specify initial conditions. Whether or not the universe is moreover "made of" mathematics doesn't change anything about how the mathematics works.

Conner,

It's my #1 point of things that people misunderstand about the anthropic principle. It has *nothing* to do with the multiverse. It's just as true if there's no multiverse. And of course, to claim that something is unlikely, you need a probability distribution. (I go on about this in more detail in my book.) Best,

B.

Matthew,

It's not good to lump together the multiverse from eternal inflation with the string theory landscape. This makes people believe that eternal inflation actually tells you something about which constants vary in which way, but that isn't so.

Sabine,

Tegmark’s mathematical universe hypothesis is not, as you said, wrong, wrong, wrong. Wolfgang Pauli said it right, it’s not even wrong! Tegmark is stuck in the 6th century BC with the Pythagoreans. They started this mathematical universe hypothesis with their five Pythagorean solids. They also believed the square root of two is evil. The scientific world had moved on since then except Tegmark.

On more serious topic, what do you think of this article on the biggest debate on cosmology?

https://www.quantamagazine.org/colliding-neutron-stars-could-settle-cosmologys-biggest-controversy-20171025/

Here’s my take on the discrepancy in the value of the Hubble constant. The discrepancy should not be a surprise. The cosmic distance ladder method should have a higher value than the CMB method and this is indeed the case (73 vs. 67 km/s/Mpc). This is due to the accelerating expansion of the universe. CMB measures the expansion since 380,000 years after the Big Bang. The other method does not go this far back in the past.

Imagine a graph of recessional velocities. Distance in the x-axis, velocity in the y-axis. The slope of the line is the Hubble constant. But because the expansion is accelerating, it’s not a straight line. It’s slightly concave. The farther back in the past (greater distance) the more concave the curve will be. CMB goes farther back so the regression line of its curve will have a lower slope than the other method.

Enrico,

I did not say the hypothesis is wrong. I said these particular statements I mentioned are wrong. I would appreciate if you do not post off-topic comments.

I picked up Tegmark's book from by bookshelft to take and other look after 2 years. Well, I must agree the ideas in it are not what I would call established science. It is, to say the least, very speculative.

Since I am not a scientist (I do have MSc in Theoretical Physics, but I have been working for tech industry for 30 years), I can only try to read thoughts from people, who have time to think and write. It is very interesting and keeps me thinking I still understand something about physics, although what I learned has rusted away long since.

I find it interesting, that very intelligent people are frequently capable of coming into opposite conclusions about almost any speculative idea. Therefore, I can only conclude that scientific truth cannot be found with speculations and theories only.

The only thing that can judge is nature itself. That is why we need observations to match the theories, if not to gain complete understanding, but at least to get a glimpse of reality.

It should be more than obvious from history, that human brain is not able to produce truths by means of speculation and theory alone.

"Max erroneously thinks it’s the simplest explanation for why mathematics is so useful, and hence supported by Ockham’s razor (though he doesn’t explicitly say so). "

That sounds a lot like the old ontological proofs of God's existence, e.g., the one from Anselm.

https://plato.stanford.edu/entries/ontological-arguments/

What's the problem with mathematical structures being "initial conditions"?

For example: Let's say a gravitational acceleration in respect of general inertial frame from proper acceleration a0 would be a = e^(cH/a0) * a0, derivative e^(cH/a0) * (1-cH/a0) dimensionless parameter. It seems to be possible make a mathematical structure for any initial condition, isn't it so?

Eusa,

Right. So how does that mean you don't need initial conditions?

Obviously, Max Tegmark is not a mathematician.

I think Max means that we must find the mathematical structure instead of initial conditions, indeed. Of course we make observations and see conditions - but: are there really any other *initial* conditions but mathematical structure as basis of the reality?

Another example of fundamental physics raises from the conditions behind the big bang. There are people who think that fundamental structure is hierarcically ordered so that starting point is totally empty; no degrees of freedom, nothing. Then what the reality needs are built logically which means *mathematically*.

Conclusion: Everything can be math, really. Maybe notational layout makes us thinking math as something "human". Is it still vice versa: Human beings and all we can observe are something mathematical?

Eusa,

You either don't understand what I say, haven't read the book, or don't know what an initial condition is. Or all of the above. In any case, I think we're talking past each other.

I'm only trying to say that there is no indicated need for any seed for reality to exist. We can always see the math behind phenomena - why not all is based on pure mathematics?

If I rememeber, in book it's said that mathematical structure is by definition a

complete description of the physical world. I'd say it might be by definition... but we have no way to prove it.

Maybe it's about an attitude too. I see no possibilities but statistical quantities.

Addition: Of course we need initial conditions in every-day work. No need to questioning that. But do nature need? That's the question.

Ouch! Maybe you should replace Michiko at the New York Times?

Sabine: I would never comment on a post I have not read. I did not understand your argument on why he is wrong. When you say "It is unnecessary to specify whether the universe is mathematics or is something more, evidenced by scientists never bothering with such a specification.", isn't that exactly supportive of Tegmarks argument that you do not need the "something more"? Where "something more" presumably is the so-called real world which is only described by mathematics? I apologize if I just do not understand your argument.

I recall reading a comment by a physics Nobel Prize winner, many years ago, to the effect that not only is the universe queerer than we suppose, it may well be queerer than we are capable of supposing. Perhaps a little humility is in order when talking about the way the universe must be.

Andreas,

Tegmark makes the assumption "The world really is mathematics." This assumption is superfluous. The assumption "The world is not merely mathematics" is equally superfluous. His claim that physicists make the latter assumption merely by using mathematics is plainly wrong.

That quarks and gluons transform as the fundamental and adjoint representations of SU(3) is a highly non-trivial prediction that supports Max Tegmark's mathematical universe claim.

Sabine: If so, you have a point. However, from my reading of Tegmark (and I have not read the entire book), his main point is the same as yours: "The world is not merely mathematics" is superfluous. Perhaps rather than phrasing it as "The world really is mathematics", he should have said "The world is merely mathematics", and he might have stressed that there are no reasons to reject "The world is not merely mathematics" other than Occam's razor.

Metatron,

If you think so you don't even understand the point of his hypothesis.

Andreas,

Occam's razor is a *very* strong reason to reject a hypothesis. Without Occam's razor everything that's unfalsifiable would count as scientific.

Sabine,

So, I am left with the conclusion that you agree with "The world is merely mathematics", but not with "The world is really mathematics"?

Because I just said that there is no reason other than Occam's razor to reject the opposite of the former, and you said Occam's razor is a good reason. Therefore "The world is not merely mathematics" can be rejected, therefore "The world is merely mathematics".

Forgive me if I am confused. I don't mean to nitpick, but I am feeling we have gotten close to why I did not understand your original argument.

I think that Max, and others like him, have fallen into the trap of mistaking the map for the terrain.

A claim like "the universe is mathematics" doesn't seem very meaningful (to me), because (to coin a phrase) it depends on what the meaning of "is" is. More interesting is the very old idea that every mathematical structure (eventually) characterizes or is embodied by some physical entity or process. So, for example, if some mathematician dreams up an aperiodic tiling pattern, by this principle we would expect to find some crystals or something that conforms to this tiling pattern. I think of it like the equi-partition of energy in thermodynamics, which says every available energy mode will eventually become occupied. Likewise we might suppose that every available mathematical structure will eventually become "occupied" by some physical phenomena. This sounds superficially plausible, but there are (for example) structures in number theory involving integers with more decimal digits than there are particles in the visible universe, and there's really no limit to this kind of structure. Consider for example just the digits of an arbitrary real number (which a mathematician can say exists, even though he can't identify one). Could the physical universe ever exhaust all the structure in those digits? I have a feeling that the degrees of freedom of mathematical structure greatly exceed the degrees of freedom of physical entities and processes (unless we define mathematics as constructionists do). On the other hand, I think it's plausible that the physical world 'tends toward' exploiting more and more mathematical structures.

Maybe the idea is to deny the distinction between mathematical ideas and physical entities, but I think Einstein's comments on this are good:

"A basic conceptual distinction, which is a necessary prerequisite of scientific and pre-scientific thinking, is the distinction between "sense-impressions" (and the recollection of such) on the one hand and mere ideas on the other. There is no such thing as a conceptual definition of this distinction (aside from circular definitions, i.e., of such as make a hidden use of the object to be defined). Nor can it be maintained that at the base of this distinction there is a type of evidence, such as underlies, for example, the distinction between red and blue. Yet, one needs this distinction in order to be able to overcome solipsism."Sabine, I think the argument is that no specific initial conditions are needed because in a multiverse, all initial conditions are simultaneously fulfilled. There would thus be no deep reasons for the initial conditions we happen to infer in "our" reality (more than, perhaps, something akin to the anthropic principle).

Sabine, if we can't rely on common sense or intuition for judging the merits of fundamental scientific theories (along with whatever testable aspects of such theories are present) what criteria do we have available? It does seem to me to unmoor science and philosophy from whatever moorings we have available if we drop the default common sense/intuition criteria.

On math, my opinion is that math is simply thinking, thinking is math. It can be done poorly or well, but to say that we understand something about the universe (or think we do) is to say that we have either used some existing math to describe it, or else discovered some new math that describes it. (Also when I decide in what order to do three errands, or what words to use in this comment I am doing math - maybe not well).

Sabine,

Popper, Pauli, and Podolski claim falsifiability is fundamental to science without qualification. Thus according to Occam's razor Occam's razor isn't necessary.

And then there is String Theory and this nifty article:

http://www.pbs.org/wgbh/nova/blogs/physics/2015/02/falsifiability/

Andreas:

No, as I have now said several times the assumption "The world really is mathematics" is superfluous, and so is its negation. Look, no one (except Tegmark) ever makes such an assumption. Isn't this sufficient to tell you that it's superfluous? If you do not use the assumption "The world is merely mathematics" you instead have no assumption, neither this nor the contrary. This is what Occam's razor tells you: Make no such assumption because it's unnecessary. You do not need it.

Now you said there is no reason other than Occam's razor to reject Tegmark's hypothesis. For all I can tell this is correct. But as I emphasized above, this is a strong reason.

alphapsa,

No, that's not the argument. Did you even read the book?

Tam,

Their power to describe observation. This includes a requirement of simplicity - the simpler, the more power. Of course simplicity in practice correlates with intuition, but I don't think the two should be conflated. Quantum mechanics is simple. But people complain it's unintuitive. I think that's an unreasonable complaint and I agree with Tegmark on that. (Though I don't agree that the logical consequence is the many-worlds interpretation.)

Zafa,

In the areas I work, Popper has done more harm than good.

Andreas:

It occurs to me that the confusion you have is the same as the confusion I sometimes come across that science rules out the existence of god because you do not need such an assumption. But that you don't need an assumption doesn't mean that the negation of the assumption is correct. It means science makes no statement about whether it is or isn't correct and the assumption itself is just unnecessary. You can believe in god or not believe in god, that's up to you. In the same way, you can believe or not believe that the world "really is" mathematics. But its a belief and not science.

Still, one day we might be forced to face the issue there are no initial conditions any more. Only way to go forward can depend on finding math seeding math, merely...

We cannot rule out that possibility, can we?

No, I listened to it as an audiobook. I missed the figures sometimes but not too bad.

well, then listen to it again

Hello Sabine,

"But that you don't need an assumption doesn't mean that the negation of the assumption is correct. It means science makes no statement about whether it is or isn't correct and the assumption itself is just unnecessary. You can believe in god or not believe in god, that's up to you. In the same way, you can believe or not believe that the world "really is" mathematics. But its a belief and not science."

I certainly agree that if you want to engage in 'science', you will have to make falsiable claims. But the notion that assumptions (in this case unfalsiable ones) are unnecessary for science, is something I wouldn't always agree with. Because these 'beliefs' play a crucial role in arriving at a falsiable assumption.

Building a scientific hypothesis also entails a few leaps of faith, as part of the problem solving process I believe, but only worthwhile if they are stepping stones towards a falsiable claim.

For example, a more explanatory theory cannot arise from merely the existing knowledge, assumptions, tools, equasions that we currently have.

History shows it takes 'stubborn believers' who's brittle new philosophy turns into science one day, and mainly because they drove those assumptions to the level of falsiable claims by means of raising the bar (read severe analysis of accepted stepping stones).

P.S. I see very few papers engaging in the latter, we are mostly hanging on to the adagio of 'standing on the shoulders of giants', whereas standing on a ladder next to the giant, gives you that extra angle on the unknown, the giant stays deprived of.

What is your take on that ?

(I'm obviously deliberately excuding new observational findings here as stepping stones towards a new hypothesis).

Best, Koenraad

Sabine, IMHO you're wasting your time talking about tosh like this. I think you'd be better off doing some physics instead.

Although I liked the audiobook, I have better things to spend 15 hours on right now :)

Since I also have a hard copy of the book, however, I looked in it and can refer you to the section “Initial conditions reinterpreted” in Chapter 12 under “Implications of the Level IV Multiverse”; I think it is pretty clear in light of the preceding sections “The illusion of initial conditions/randomness/complexity” that he argues the initial conditions to merely be our address, as he calls it, in the Level IV multiverse. It is a multiverse of both mathematical structures and initial conditions, and our address identifies which one we happen to inhabit. The anthropic principle rules out addresses that are incompatible with us, but other than that, there is no reason provided why we have the address we do.

If this is not his argument, what is? Please don’t make me listen to the book again :(

You know, what's crazy, in my mind, is the number of competent mathematicians who embrace mathematical realism! I just finished two Siobhan Roberts books, one about Coxeter the other Conway, and they are both, the books I mean, unashamedly Platonic. In the Coxeter book Sir Roger Penrose is quoted as saying something like, "Mathematics seems to just conjure itself into being . . . " I mean, why is math so effective for describing "reality?" I, and it would seem Occam as well, prefer the constructivist explanation:

1)Constructivist approaches question the Cartesian separation between the objective world and subjective experience;

2)Consequently, they demand the inclusion of the observer in scientific explanations;

3)Representationalism is rejected; knowledge is a system-related cognitive process rather than a mapping of an objective world onto subjective cognitive structures;

4)According to constructivist approaches, it is futile to claim that knowledge approaches reality; reality is brought forth by the subject rather than passively received;

5)Constructivist approaches entertain an agnostic relationship with reality, which is considered beyond our cognitive horizon; any reference to it should be refrained from . . .

http://www.univie.ac.at/constructivism/journal/faq.html#denominators

A good idea need only be testable. It is believable afterward.

When theory that does not predict excludes falsifying observations, that is cowardice.

Sabine,

You said, "In the areas I work, Popper has done more harm than good."

That is fascinating. Could you elaborate? Are you in agreement with Sean Carroll, who called for the “retirement” of the falsifiability principle. (see the article I linked to above)

BTW, your responses are enlightening and fun, but it sure would nice when you respond to a comment I could easily find the comment.

alphapsa,

Exactly. So how does this mean the initial condition is unnecessary if it's part of the address?

Zafa,

Please direct complaints about the comment section to Google, not to me.

As to your question, I may be writing a blogpost about this next week or so. It's too long to stuff it into a comment. Best,

B.

Well yes, to describe our particular address we need both the natural laws and their initial conditions, or more generally a set of defining parameters (as may be argued are integral parts of the laws). I don’t think Tegmark denies that. I think his point is rather that, in the multiverse view, there is no deeper reason other than chance and the anthropic principle that we inhabit a universe with our particular parameters (our “address”). So it becomes not necessary (or even possible) to explain how it comes that we have the particular initial conditions we do, other than that it is one of the uncountable realities compatible with our existence.

To describe our universe, the speculation is thus that a TOE may need a set of parameters (including initial conditions) that cannot be derived from deeper principles, with their only constraint being the anthropic principle. This may be a bit of a pessimistic outlook, but exploring the range of parameters compatible with the anthropic principle may still prove interesting. Assuming a suitable TOE is found in the first place, that is.

Sabine

1) I love this blog.

2) Is it any wonder one ends up with a multiverse when mathematics inherently contains infinities and infinitesimals (hidden by the epsilon delta definition of a limit - Hilbert's view, see 'Philosophy of mathematics')and this leads to more incorrect mathematical statements (strictly speaking a larger cardinality of)than there are correct mathematical statements.

The bother in Tegmark's foundation is that mathematical foundations are inherently founded on the world as it appears to be to us (von Neumann's view, see 'Works of the mind'). As Wigner identified ('The unreasonable effectiveness of mathematics in the natural sciences') there is line that divides mathematics from reality. Until the two are shown to be ontologically fused, Tegmarks proposition that mathematics is reality and vice versa, are, like most arguments, presumptive. But then, so are arguments that he is wrong.

As for Popper - how can identifying a problem (fallibilism and falsification) be harmful in and of itself. The same would go for Quine's 'Word and object' according to which no word is ever properly founded. As such, neither can we be sure of anything we see, or the theories that come from this (i.e. empiricism) neither can we talk about it with any precision. Yet this does not seem to have driven the philosophers, physicists or mathematicians to hold back on new theories. Oops, there goes string theory. Indeed, the talk increases exponentially. But I wait to read your weblog on Popper.

Stephen,

It's prescheduled for tomorrow, so check back then :)

Raed the book, I like his style of writing.

He has some good points.

What was first, the hen or the egg?

But of course, Sabine, all your conclusions stand.

For me, Popper is still the law.

Wow, (nice blog and comments!) I'm waiting with baited breath for the Popper pop-off.

As a Physics type who does mostly engineering/ trouble shooting/ de-bugging, making a guess at the problem and having a test for that guess is my bread and butter. Sometimes the 'test' (the data) comes first, but that's the way of science.

Hi Sabine,

I'm glad to hear that you read my book! I read your review with interest. I have no issues with you disliking my writing style. In terms of your arguments, I feel that you're repeatedly using the technique of attributing to me something that I didn't claim and then pointing out that it is wrong. See for example what you attribute to me about initial conditions - a topic where I feel that you're also being overly dismissive of what some of your commenters have written.

Let's turn to the core of the matter: your critique of the mathematical universe hypothesis.

Your being your critique thus:

"The hypothesis is ill-defined without explaining what 'is real' means. I therefore don’t know what’s the point even talking about it." I'm very interested to hear what *you* mean by "is real". In particular, do you accept or reject the external reality hypothesis that there's an external physical reality completely independent of us humans?

Thanks in advance for clarifying!

Max

:-)

Hi Max,

On page 340, after explaining what initial conditions are, you write:

"In contrast, the Mathematical Universe Hypothesis leaves no room for such arbitrary initial conditions, eliminating them altogether, as a fundamental concept. This is because our physical reality is a mathematical structure that is

completelyspecified in all respects by its mathemathical definition in the master list."(Emphasis as in book.)

So please explain how writing an initial condition into the "master list" removes the need for an initial condition, or in which sense our "address" in the mathematical universe is any less arbitrary than specifying an initial condition in the same way as we always do.

As I have said elsewhere, I think the only way to avoid the need for initial conditions is to posit that nature fundamentally isn't described by differential equations, so I could agree on that, but that doesn't seem what you have in mind.

I do have a definition for what I mean by "real" which I wrote about here. But I don't think it makes sense to impose this definition on other people. Do I believe in an external physical reality? I think the question isn't decidable and hence isn't in the realm of science. Personally, sometimes I do, sometimes I don't. Best,

B.

Sabine, it seems the comment I posted yesterday in response to your question was lost in cyberspace – I hope you didn’t moderate it out for being too offensive or nonsensical, if so please tell me. I post it here again, in case you didn’t see it, although it may be less relevant now that Tegmark himself has joined the discussion:

Well yes, to describe our particular address we need both the natural laws and their initial conditions, or more generally a set of defining parameters (as may be argued are integral parts of the laws). I don’t think Tegmark denies that. I think his point is rather that, in the multiverse view, there is no deeper reason other than chance and the anthropic principle that we inhabit a universe with our particular parameters (our “address”). So it becomes not necessary (or even possible) to explain how it comes that we have the particular initial conditions we do, other than that it is one of the uncountable realities compatible with our existence.

To describe our universe, the speculations is thus that a TOE may need a set of parameters (including initial conditions) that cannot be derived from deeper principles, with their only constraint being the anthropic principle. This may be a bit of a pessimistic outlook, but exploring the range of parameters compatible with the anthropic principle may still prove interesting. Assuming a suitable TOE is found in the first place, that is.

On this interesting question by Max Tegmark:

'In particular, do you accept or reject the external reality hypothesis that there's an external physical reality completely independent of us humans?'

I believe indeed it isn't the realm of science, but from a philosophical perspective, I would propose a thought experiment to learn more:

Suppose we eliminated all human beings from the universe, would the universe still be there, planets, your car, dental floss, the Eiffel Tower ?

Yes, I would answer, so that's an objective reality independent of humans. But that doesn't mean we humans are able to describe it objectively, only subjectively, through a.o. mathematics.

Best, Koenraad

Koen,

You realize that the point of thought experiments is to carefully think about what can be measured? Now tell me how you want to measure something if you're not there.

You've got me temporarily cornered there,).

Dear Dr B

"You realize that the point of thought experiments is to carefully think about what can be measured? Now tell me how you want to measure something if you're not there."

Indeed a difficult question. However, we can try to make the question empirical.

Max Tegmark asked:

"In particular, do you accept or reject the external reality hypothesis that there's an external physical reality completely independent of us humans?"

I cannot test this question purely regarding myself or "all humans". However, we can add the assumption that there is no special vantage point in the universe. That is, every observer is "equal".

Then the question becomes:

Is there an objective reality outside of observer X, where we let X be any human (or non-human) observer?

Then we add the observation that the observable universe never did change when observers died, for any observer (X) that has died during the observation period, say, all of historic times. As the universe did not change after the death of any observer ever recorded, for any observer witnessing this death.

By extrapolation, or generalisation, we can now predict that the universe will not change due to the dead of any observer now living. By induction, the universe will stay put after all humans have died. By definition, this universe that stays put after all observers have died must be an objective reality (as there are no subjects left to be subjective).

We can add to this that humans are not the only observers. It is well known from biology that every living thing is an observer, i.e., reacts to changes in the environment, ie., the universe. There was a universe before humans arrived, and there will be living things on earth, or elsewhere, after humans have died out. So, even if we assume observers are required for the universe to exist, there will be observers after all humans have disappeared.

The one weak point in this analysis is that I have to assume that I myself am not in a special position. If I really am special, the universe might end when I die. But, from my analysis, I know that other people are not special enough to let the universe disappear when they die.

I am sure there are logical fallacies in the above argument. But I hope others can improve on it.

Rob,

I can't believe we're seriously discussing this. Philosophers have been all over this ground millenia ago - even I know this and I'm not much of a philosopher. What do you think Descartes meant when he said "I think therefore I am."? The logical fallacies in your argument? Try to prove to yourself that I am not a figment of your imagination, that indeed *anything* existed before you were born. Or try to prove to me that you exist for that matter. You are arguably special to yourself, so the assumption that you are not special is rather peculiar, don't you think?

@Dr B

"Philosophers have been all over this ground millenia ago"

Indeed, we still are discussing this.

What I wanted to say is that Max Tegmark's question was not about "Is there an external physical reality completely independent of us humans?", but about "Is there an external reality outside of *me*?"

The question Max asks, about *all* humans, can be trivially answered empirically by assuming that no human is special. I was overly worded about it, I admit. But that seems not to be the real question he seems to be asking.

What Max seems to conflate is "Is there an objective reality for everyone of us?", which is trivially easy to answer, and "Is there an objective reality external to *me*?" which we know is not an empirical question at all.

We can consider every one of interacting entities as a measurer. I think this is a fundamental point of view in the mathematical universe concept.

"I never really figured out what he was tenured for. Probably not the mathematical universe. Once upon a time, I was sure, he must have done actual physics."Max, describing himself as Dr Jekyll and Mr Hyde, candidly describes how he did real physics in order to get tenure, in part to have the freedom to pursue things like this. And he did do real physics. Off the top of my head, he was one of the main figures in pinning down the power spectrum of matter fluctuations (from non-CMB sources), almost all modern CMB analyses use his scheme for converting the sky into pixels (the paper has its abstract in heroic couplets!), he has done a lot of nuts-and-bolts stuff for CMB analysis. Definitely deserved tenure.

I also recommend reading his new book, whether or not you agree with it. :-)

"It's my #1 point of things that people misunderstand about the anthropic principle. It has *nothing* to do with the multiverse. It's just as true if there's no multiverse."Yes, you can still have the anthropic principle without the multiverse. But then you are left with a "just so" story. With the multiverse, the anthropic principle becomes a sensible explanation.

Or do you disagree with Weinberg on this? :-)

"

Here’s my take on the discrepancy in the value of the Hubble constant. The discrepancy should not be a surprise. The cosmic distance ladder method should have a higher value than the CMB method and this is indeed the case (73 vs. 67 km/s/Mpc). This is due to the accelerating expansion of the universe. CMB measures the expansion since 380,000 years after the Big Bang. The other method does not go this far back in the past.

Imagine a graph of recessional velocities. Distance in the x-axis, velocity in the y-axis. The slope of the line is the Hubble constant. But because the expansion is accelerating, it’s not a straight line. It’s slightly concave. The farther back in the past (greater distance) the more concave the curve will be. CMB goes farther back so the regression line of its curve will have a lower slope than the other method."

I can assure you that this is not the reason for the discrepancy. Read any text on observational cosmology!

For what it's worth, I wrote a more positive review, though I agree with you that the last chapter should have been left out.

"I think, therefore I am," was not really about thought, but establishing a secure place for the thinker from within the ontology from which to think about the world. Broughton (2002?) argues that Descartes's 'cogito' is not true because of the thinking, but because to doubt one's own existence requires first the existence of the one who doubts. Hence it is indubitable exactly because it defeats Descartes's Method of Doubt.

Unfortunately, as Dr B identifies (if I am reader her correctly) is that there is no other aspect about which one can be sure. It doesn't really even explain what 'to exist' actually means! Ultimately this implies a disjunction between noumenon (Kant - a thing as it is in itself) and phenomenon (a thing as it appears to be to us) which implies that empiricism is no path to knowledge, full stop (which is why I am an endpoint rationalist). In that context, the physicist ought to be a little humble, though I don't see a lot of evidence of such.

But this then extends to mathematics because, while mathematicians think of it being wholly rational, its foundations are very closely associated with the world of presentations. Then Tegmark's MUH remains a hypothesis and what we think of as real is an ephemeral mirage.

Rob,

Despite re-reading your comment several times I failed to make sense of it.

First, while conceivably possible that I've misunderstood Max for ten years, I believe his external reality is indeed supposedly independent of humans and not just independent of him.

Maybe more importantly, since none of us can prove that the rest of humans are independent of our own existence, it's not possible to disentangle the both, hence my remark about Descartes.

Indeed, the question "Is there an objective reality for everyone of us?" is trivial to answer, and the answer is "No" by the very definition of "objective."

Stephen,

Yes, you understood me correctly, thanks.

Phillip,

Of course I disagree with Weinberg. Look, if you want to describe the world that we observe, you *always* have to select assumptions "just because" they describe what we see. The only other logical alternative is Tegmark's mathematical universe, but in this case "picking assumptions" turns into "defining your position in the mathematical universe" which is the same thing by a different name.

The anthropic principle doesn't explain any more or any less if you have a multiverse. The only difference is psychological, in that some people seem to believe it's different to constrain a location in a fictional multiverse rather than to put constraints on the axioms (including the values of parameters) of a theory.

Really I think that we should have a principle in physics similar to what the economists call "revealed preferences." We could call it "revealed irrelevance." An axiom that is never used (such as "mathematics is real" or "there is an unobservable universe for any value of the cosmological constant") is irrelevant and has no place in science.

Best,

B.

Dear Dr. B

"Despite re-reading your comment several times I failed to make sense of it. "

My bad. You are right about "I can't believe we're seriously discussing this.", so I will not further delve into it.

"Of course I disagree with Weinberg."I'll go out on a limb here and agree with Weinberg. :-D

"The only difference is psychological, in that some people seem to believe it's different to constrain a location in a fictional multiverse rather than to put constraints on the axioms (including the values of parameters) of a theory."I think that the key word here is "fictional". If the multiverse is real, then there is a huge difference between saying that the world is conducive to our existence because there are many (perhaps infinitely many) and so no surprise that we are where we are, even if it is improbable in some sense, and on the other hand saying that the world is as it is since otherwise we wouldn't be here to think about it.

An analogy is the bizarre fact that the Earth just happens to be at the right distance from the Sun to allow our existence etc. If there were just one solar system, this would be believable only if one could somehow show that our distance from the Sun is a generic outcome, but it is no puzzle if there are many solar systems.

It's nice to see so much discussion about the fascinating relationship between math & physics! Here are a few quick responses before turning to prepare this mornings electromagnetism lecture:

Sabine:You write"Do I believe in an external physical reality? I think the question isn't decidable and hence isn't in the realm of science. Personally, sometimes I do, sometimes I don't."Then we're actually in agreement: my book argues that the external reality hypothesis (ERH) implies the mathematical universe hypothesis (MUH). ERH=>MUH. You don't buy the ERH (at least not every day), so the MUH therefore doesn't follow. Rejecting the ERH is perfectly respectable and you're in good company: Niels Bohr arguably rejected it too when stating "no reality without observation".

Contrary to what some commenters seem to think, my book doesn't claim that the ERH or the MUH is true, or that parallel universes exist, or that inflation happened. My job as a scientist isn't to believe in hypotheses, but to investigate the logical relation between hypotheses and to evaluate them against evidence.

As to initial conditions, we both agree that a partial differential equation governing time evolution of a physical system won't on its own give a unique solution, but rather a family of different solutions. The traditional way to get uniqueness is to impose initial conditions. What I'm saying is that in a multiverse (e.g. the Level III multiverse generated by inflationary quantum fluctuations), a whole family of solutions becomes realized in different branches of the wavefunction, so that what we've traditionally called initial conditions simply becomes our address in Hilbert space, not any fundamental fact about the full physical reality. In other words, you and I have no disagreements about the mathematics of differential equations, about what constitutes a well-posed Cauchy initial value problem, etc. Do you feel that we now understand each others point of view on the this issue?

:-)

David B:You write"I think that Max, and others like him, have fallen into the trap of mistaking the map for the terrain."Thanks for raising this important point about the distinction between the description and what is described, which I explore in great detail in chapters 11 and 12 of the book ( http://mathematicaluniverse.org ). This distinction is crucial *both* in physics and in mathematics. Our *language* for describing the planet Neptune (which we obviously invent - we invented a different word for it in Swedish) is of course distinct from the planet itself. Similarly, as I mentioned above, we humans invent the *language* of mathematics (the symbols, our human names for the symbols, etc.), but it’s important not to confuse this language with the *structures* of mathematics. For example, any civilization interested in Platonic solids would discover that there are precisely 5 such structures (the tetrahedron, cube, octahedron, dodecahedron and icosahedron). Whereas they’re free to invent whatever names they want for them, they’re *not* free to invent a 6th one – it simply doesn’t exist. It's in the same sense that the mathematical structures that are popular in modern physics are discovered rather than invented, from 3+1-dimensional pseudo-Riemannian manifolds to Hilbert spaces. The possibility that I explore in the book is that one of the *structures* of mathematics (which we can discover but not invent) corresponds to the physical world (which we also discover rather than invent).

:-)

Max,

Well, then please tell me what I learn from calling an initial value an address. Is this any more than verbal gymnastics? I can't see the difference. In the book you clearly seem to try to convince the reader that there is some benefit to this, but excuse me for being utterly unconvinced.

I also think that MUH doesn't follow from ERH, but I believe we've been through this previously. Just because you cannot think of anything besides mathematics to describe reality doesn't allow you to conclude there is nothing.

Koenraad Van Spaendonck:You write

" 'the universe' or 'matter' or anything else, can never be made from abstract concepts, such as mathematics.Thanks for raising this interesting point about "MADE OF" and "STUFF"! As a thought experiment, imagine that we one day develop super-advanced AI, and that you're a character in a future computer game that's so complex and realistic that you're conscious and mistakenly think you exist in a physically real world made of "stuff". Now you start studying your virtual world like a physicist, and gradually discover that the entities in your world seem to fundamentally have no properties except mathematical properties (since that's how your world is programmed), just as we've discovered here in our world. If you could perceive your virtual world as made of stuff even thought it was purely mathematical, then why can't the same be the case here in our cosmos?

Sure, the computer in this example is itself made of stuff, but the feeling that the objects in the game were made of "stuff" was completely illusory and independent of the substrate out of which the computer was built.

:-)

Thanks Sabine for clarifying! It sounds like we're converging: you're no longer saying that my statements about initial conditions are wrong, merely that you view them as uninteresting and without benefit. In contrast, some of your readers seemed to conclude that they were wrong and proved that I don't understand mathematics. :-)

"Well, then please tell me what I learn from calling an initial value an address. Is this any more than verbal gymnastics?"Isn't this a similar objection to yours mentioned above regarding the anthropic principle? To me, it does seem different, if one takes the many words seriously.

It will be interesting to see if rational people of good will (as I believe are having this discussion) can agree on a consensus.

"Just because you cannot think of anything besides mathematics to describe reality doesn't allow you to conclude there is nothing."

In my, perhaps idiosyncratic, view you can, because as I said above, I define mathematics as just rational thinking, usually in the attempt to solve problems and gain understanding. What we study in school as mathematics are past results of such efforts which have been generalized. If there is something besides rational thinking which can be used to describe (understand) reality, it seems as irrelevant to me as the concept of unobservable parallel universes does to others. If it is not rational, I will never be able to understand it, so it will not help me understand; if it is rational, it is a form of mathematics (albeit perhaps a new one).

(I am not sure this argument rules out something else but it causes me to give long odds against it.)

The benefit of the multiverse concept vis-a-vis initial conditions is that it is an answer to creationists who claim that the universe was deliberately made for us due to a love of human beings, rather than that human beings were created randomly by a universe in which it happened to be possible that humans could exist. For people who don't care about anything they can't observe there is no benefit, since as Dr. Hossenfelder says the initial conditions of our universe were arbitrary with or without a multiverse.

In a general sense, any new concept which broadens the range of possibilities might be considered useful - although again, not to those who don't like speculation beyond observation.

Sabine,

"Now you said there is no reason other than Occam's razor to reject Tegmark's hypothesis."

I must have misexpressed myself, I meant to say just the opposite. What I meant to say was there is no reason to reject the real world hypothesis (ERH, I suppose, the opposite of Tegmark's) other than Occam's razor. It is MUH vs. MUH + ERH, and Occam would have preferred the former. In other words: You can have the math without the external reality, but you cannot have the external reality without the math. I (following Occam) pick the former.

So I think we more or less agree on this: Both assumptions are unnecessary, but one is "cleaner". None has observable consequences, therefore this is not really physics, but philosophy.

And I love your blog.

Wait the *issue* is suddenly changing. My impression was that Dr. Tegmark is *not* saying that mathematics merely describes reality (Unger/Smolin "Singular Universe" which seems to have been written at least partly with Dr. Tegmark in mind) agree that math "describes" if imperfectly but Dr. Tegmark is saying something stronger, that math is metaphysically prior. For example the difference between "there are 5 possible solids because we happen to live in a universe of 3 spatial dimentions" (Unger/Smolin) verses "the universe has 3 spatial dimensions *because* there are only 5 possible solids" (Tegmark).

Max is 100% correct. In the past people thought that the earth was the center of the universe, today it seems many people want to claim that the human brain is the origin of reality( a spin on QM) and mathematical truths. Max has challenged people who criticize him, if reality is not literally mathematical structure then what is it. And if it is not mathematical structure how did it come about.

The Only answer is that reality is exactly mathematical structure. Because mathematical structures are ultimate truths in themselves and they don't have to be created. Problem solved:)

Max,

What I said about the initial conditions was that I don't understand your point. What you say is either correct but interesting or interesting but wrong.

Phillip,

My point about the anthropic principle was that this principle delivers a constraint on the parameters of our theories and is correct regardless of whether a multiverse exists. Hence, the anthropic principle does not speak in favor of the multiverse, that's just faulty logic. No, this is not verbal acrobatics.

As to your faith in Weinberg. Look, what Weinberg does (assuming we're talking about his CC argument) is to invent a probability distribution and then conjecture there's a multiverse and then bla-bla-bla-math he comes up with a prediction for the CC. The only thing this does is to replace guessing the value of a constant with guessing a probability distribution. It has no explanatory value. Hence my comment about "revealed irrelevance".

Btw, it seems even Max agrees that the measure problem turns the whole multivese idea ad absurdum, though I might have read that overly favorably... It's right of course, but you could have seen that from the outset that the multiverse it trying to achieve the logically impossible. Why is that so hard to understand? Best,

B.

Andreas,

I think you have confused yourself about what Occam was concerned with. He was concerned with science, meaning describing observations. To describe observations with mathematics you do not need to assume that mathematics is real (or that reality exists for that matter), hence Occam's razor tells you to discard these assumptions as superfluous.

Max,

I appreciate you taking the time to respond to my rather terse comment about the trap of mistaking the map for the terrain. I'd like to elaborate on this (esp. in light of your response to Koenraad). I am in no way agreeing or disagreeing with your comments, rather, I am attempting to clarify my concern. The "trap", as I see it, is that our brains have evolved over time and developed various underlying processes for rendering what we perceive as our experiences. I suspect that those processes are quite efficient and, I suspect, those same processes could very well have been co-opted into the evolution of the language of mathematics. This may explain why math "feels" right when we use it to describe reality. The real questions is: is mathematics a part of the underlying structure of reality or is it a processing trick of the brain?

Can I ask a 'laymen's' question? Is the multiverse the same as the many worlds theory of QM? Wiki seems to say there's subtle differences, https://en.wikipedia.org/wiki/Multiverse. As a solid state experimentalist, I have no problem with Max Tegmark's level 1. or level 2... things are different in a universe far far away. But 'many worlds' is just to weird for me. (I realize many physics types much smarter than I, like the idea.)

George,

The short answer is "no". For a long answer, I recommend Max Tegmark's book...

George... "many worlds" of QM is Dr. Tegmark's type IV multiverse. Why I pointed out that whether one agrees or disagrees with his central thesis, his taxonomy is very useful

Hi Sabine,

I was using Occam as a justification for dropping unnecessary assumptions. Perhaps I am confused, I am not really an expert philosopher. The assumption I was talking about was "The world is not merely mathematics" (which I take to be the same as ERH), and all I am saying that it can and should be dropped. At this point, I feel myself to be in agreement with both yourself and Max on this, but I may be simply deluded.... :-)

Maybe a better phrasing is in terms of the map/terrain thing: If a map describes the terrain completely, there is no need for the terrain. For any practical purpose, the map alone will suffice. So, to simplify things (whether this is Occam's razor or not), let's do away with the terrain.

I cannot make it any clearer, thanks for putting up with me.

George,

The principle is the same, but the MUH, or multiverse IV, goes much further than the many worlds quantum interpretation.

Looking at the future, people have no problem thinking of the future as an ensemble of many possible outcomes. Many potential worlds. Even for the present and past, we can easily conceptualize what would be or what might have been. What the many worlds interpretation does, and all it does, it discard the notion that amongst all the potential worlds there is one that is "real". Rather, the universal wavefunction is seen as a superposition of all possible worlds, and "reality" only comes into play when you put a marker on one of the superimposed components and call it "I", or "the observer". Reality then becomes relative, dependent on how you define the observer, and the wave function collapse becomes an illusion caused by the progression of "the observer" from a pure to a mixed state when interacting with the observed.

This view still relies on one specific Hamiltonian that determines the unitary time evolution of the universal wave function, and also one specific initial condition. The MUH goes two steps further: In addition to many superimposed components, there is also many potential initial conditions, and even many potential Hamiltonians, none of which are special in any way. If you look at it this way, the MUH is really the ultimate exercise of the Copernican Principle.

Thanks Sabine, (Please excuse my laziness, it's too easy these days to send off an email (or blog) question w/o doing any looking on your own.) Here's your 'medium' length answer.

http://backreaction.blogspot.com/2015/12/ask-dr-b-is-multiverse-science-is.html

This is what I find so crazy! Tegmark says:

"Similarly, as I mentioned above, we humans invent the *language* of mathematics (the symbols, our human names for the symbols, etc.), but it’s important not to confuse this language with the *structures* of mathematics. For example, any civilization interested in Platonic solids would discover that there are precisely 5 such structures (the tetrahedron, cube, octahedron, dodecahedron and icosahedron). Whereas they’re free to invent whatever names they want for them, they’re *not* free to invent a 6th one – it simply doesn’t exist. It's in the same sense that the mathematical structures that are popular in modern physics are discovered rather than invented, from 3+1-dimensional pseudo-Riemannian manifolds to Hilbert spaces."

This is very similar to the argument Conway presents to his biographer in Genius at Play; he goes on and on about the obstinacy of mathematical objects, which, if I remember correctly, Tegmark does in MUH as well. Conway asks, "Where does this obstinacy come from?" Well, it comes from the axioms! The reason why there are only five Platonic solids is due to the axioms, the rules, which define what a Platonic solid can be. But we INVENT the goddamn rules - the axioms! We invent these axioms and then discover the consequences - as we all well know, different axioms, different consequences! I mean, how many of the Platonic solids are 3+1 psuedo-Riemannian manifolds? Exactly my point . . .

What Tegmark, Conway, Coxeter, Connes, etc. etc. do is precisely reify mathematical structures and I see no RATIONAL justification for this! Allow me a short quote from a paper by William Tiller (https://www.tillerinstitute.com/pdf/White%20Paper%20XXXVI.pdf):

"The Danish author, Torr Norretrander(3) reminds us that the human conscious mind can only process less than 50 bits of information per second while the human unconscious mind can process more than 50 million bits of information per second. Thus, it is the latter that actually gathers the multiple data streams of information flowing through a human at any point in time. It appears that our unconscious system gathers such information, organizes such information and refines such information. It then appears to create small kernels of prepared relevant information to send to the conscious mind. However, it appears to do so only if the conscious mind has previously given meaning to that topic. If the conscious mind has not given serious meaning to that topic, such information kernels appear to be “dumped” by the human unconscious mind."

It seems unquestionable that all mathematical realists find the process of doing mathematics mysterious and I would suggest that the reason is due to a failure to account for this 50 million bits of subconscious processing! I would like to see Tegmark respond to Gilbert Simondon's "Process of Individuation" argument (http://www.columbia.edu/cu/arts/vad/critical_issues_on_art/Simondon.PDF) as well as its extension (https://arxiv.org/abs/1505.06366) by David Weinbaum and Viktoras Veitas.

"A long time ago, Descartes said, 'I think, therefore I am.' … But if you are not thinking, what?" - Seung Sahn

https://scholar.harvard.edu/sara_lazar/press-2

From the meditation perspective, on a conventional level mathematics exists in the same insubstantial way as dogs, cats, trees, people, etc.; these things depend on other things for their existence, hence, they have no inherent existence . . .

It's my #1 point of things that people misunderstand about the anthropic principle. It has *nothing* to do with the multiverse. It's just as true if there's no multiverse.Indeed, just as true without a multiverse, which is why the anthropic principle is virtually tautological.

However, without a multiverse we're still left with the question of

whyvarious parameters have their anthropic values. With the multiverse, no such questions remain becausesomeuniverse(s) in the multiverse simplymusthave those values.Sandro,

No, the anthropic principle is not tautological, that's #8 on my list of common misunderstandings about the anthropic principle. (Please read the full list before you reply.)

Sabine, I said

virtuallytautological for a reason.What Tegmark, Conway, Coxeter, Connes, etc. etc. do is precisely reify mathematical structures and I see no RATIONAL justification for this!Wes, I would hazard a guess that you're simply unfamiliar with the body of work in the philosophy of mathematics. Suffice it to say, non-Platonist theories are rife with problems. Platonist theories like the mathematical universe are completely unproblematic. Accounting for mathematics with matter appears to be

significantlymore difficult than accounting for matter with mathematics.We may yet find a naturalist or other non-Platonist account for mathematics, but we definitely don't have it yet. Thus, calling Platonist theories absurd or irrational is simply untenable given these facts. In fact, Platonist theories are currently the

onlyrational choices available.These facts certainly shouldn't concern practicing scientists like Sabine though. Max seems to be engaging a wider philosophical topic rather than a strictly scientific subject.

Similar to interpretations of quantum mechanics, this sort of debate will likely only spur ideas, and hopefully thought experiments, which is great, but they have little immediate calculational value.

Andreas,

No, what you say is still incorrect. If you drop an assumption, the consequence is *NOT* that you use the negation of this assumption. You just make no assumption.

Look, consider the follow "set of axioms"

1) x is an element of the real numbers

2) x is larger than five

Now if you drop assumption two, you are left with

1) x is an element of the real numbers

This does *not* mean that x is now smaller or equal than five.

Hope that is clear.

Same with the mathematical universe. If you drop the assumption "The world is not merely mathematics" it does not mean that now you have the assumption "The world is merely mathematics." Or the other way round, doesn't matter. The point is that either assumption is unnecessary.

Also, I think you are confused about what Max means by the external reality hypothesis. It clearly does not means what you think it does. Best,

B.

"George... "many worlds" of QM is Dr. Tegmark's type IV multiverse. Why I pointed out that whether one agrees or disagrees with his central thesis, his taxonomy is very useful"No, the many worlds in the many-worlds interpretation of QM is Tegmark's Level III.

"My point about the anthropic principle was that this principle delivers a constraint on the parameters of our theories and is correct regardless of whether a multiverse exists. Hence, the anthropic principle does not speak in favor of the multiverse"Yes, I'm talking about his CC argument.

I agree that the constraints are the same in both cases. What matters is the plausibility. This actually ties in with your post after this one on Popper. Go back to the solar-system example. Are you saying that if there were only one solar system in the universe, ours, then we would require no explanation for what is arguably an improbable case (Earth at just the right distance from the Sun, etc)?

This line of argument seems similar to saying that one can explain

anythingby initial conditions, so why seek any scientific explanation at all?On a related note, do you really think that you have it right and everyone else got it wrong? This does occasionally happen, but usually not when your opponents try to counter your arguments.

Phillip,

You cannot explain anything

equally wellby initial conditions. (I meant to write a separate post about this but haven't found the time.)I don't understand what point you are trying to make with the solar system. It's always good and advances science to have better explanations. What I am saying is that inventing a probability distribution over a multiverse is not any better than just inventing a parameter. Indeed, it's worse, because now you have the whole clutter with the multiverse and a distribution over it. (Same issue, but much more clutter, with naturalness arguments in particle physics.)

As to the rest of your comment. I don't understand what you mean. I am far from certain I am right of course. But no one seems to have any counter argument to my argument, so I'll be dragged along by its momentum until someone stops me. Where is your argument? Why do you think a probability distribution over a multiverse is any better an explanation than just a parameter. (Both of which, we seem to agree, are equally constrained by anthropic considerations.) Best,

B.

"What I am saying is that inventing a probability distribution over a multiverse is not any better than just inventing a parameter."It does seem to be the case that in some sense the universe is fine-tuned for life. Sure, if it weren't, we wouldn't be here. But that still leaves the question why it is the case. With the multiverse, with parameters different in different universes, one shouldn't be surprised that we find ourselves in a universe conducive to life.

It doesn't matter if our universe is unlikely if likely universes don't support life, so it doesn't matter what the probability distribution is. (A different question concerns the values of parameters for which a wide range is compatible with life. Here, we would expect to observe likely values, though we might not necessarily know what they are.)

There are other explanations, of course. Maybe it is just coincidence (such as the angular sizes of the Sun and Moon, making total solar eclipses possible, and moreover for only a relatively short time since the Moon is receding from the Earth), maybe this is the only possible case (but that remains to be shown), maybe there is some creator, maybe we are in some simulation, and so on. The question is, what explanation is the best?

Phillip,

Any mentioning of finetuning rests on a notion of probability. On the risk of sounding like a broken record (assuming you are old enough to understand the metaphor) where does the probability distribution come from?

"Any mentioning of finetuning rests on a notion of probability. On the risk of sounding like a broken record (assuming you are old enough to understand the metaphor) where does the probability distribution come from?"I'm older than you. :-( Although I switched to CDs relatively early because of better sound quality, I still have about 100 vinyl albums and even a record player (but well over 1000 CDs by now*).

I don't think that one needs the actual distribution. Suppose you come upon a pink elephant dancing something out of

Swan Lakewhile it is singing the Stones' "You can't always get what you want". Would you just shrug and say that, since you don't know the distribution, this might not be improbable? I think not.Yes, many examples of fine tuning are bogus, but that is because people assume a wrong probability distribution. If one can calculate the correct one, and the observed outcome is not unlikely, then fine-tuning goes away. But that doesn't mean that all claims of fine-tuning are bogus.

---

*If I hear one CD per day, I can hear each one twenty more times in my life, if I live to be old but not improbably old. Ars longa, vita brevis. (Yes, I'm even old enough to know Latin!)

Phillip,

Suppose I'm an alien who just arrived on this planet and I encounter your pink singing Elephant, I would indeed not make an assumption about this being likely or unlikely. Why would I? But having lived on this planet for some while and never having encountered a pink elephant, a picture of a pink elephant, a singing elephant, a dancing elephant, or anyone or anything singing the Stones while dancing swan lake, I think I can reasonably estimate the probability for this to be exceedingly tiny.

No, not all fine-tuning claims are bogus. They are fine if you know the probability distribution. Unfortunately, none of the examples for fine-tuning examples some people (cough) believe to speak for the multiverse are of this case. Because, well, in this case you don't have the probability distribution. And worse, you also have no way to ever get it.

Best,

B.

"With the multiverse, with parameters different in different universes, one shouldn't be surprised that we find ourselves in a universe conducive to life."

One shouldn't be surprised, period [Appendix 2].

Phillip,

I don't know if the universe is finetuned for life. Because I have no probability distribution for the parameters...

I haven't read the book in question, but I can tell you what's wrong with the argument. They have no probability distribution.

Getting sick of it yet? Why don't you try and answer my question. Where does the probability distribution come from? Best,

B.

Sabine, just to clarify your argument why a probability distribution is needed: If, for instance, the parameters compatible with life were very probable (even inevitable), then we would not need any finetuning at all, so without having the probability distribution we cannot have a discussion about finetuning. Do I understand it correctly?

I think Philip’s point is that in the multiverse, the anthropic principle puts us in a habitable universe no matter what the probability distribution is.

The difference as I see it is that in the first case (single universe), we don’t know if our universe is subject to remarkable finetuning or not. If it is, it’s a bit of a mystery how we can exist.

In the second (multiverse) case, even if remarkable finetuning is indeed needed, habitable universes would always be produced, so our existence is expected.

Sandro Magi says:

"In fact, Platonist theories are currently the only rational choices available."

Are you kidding me! And you accuse ME of being unfamiliar with the literature! I would suggest you peruse the link to the Radical Constructivist paper in my earlier comment; I'll re-paste it here for your convenience:

http://www.univie.ac.at/constructivism/journal/guidelines/denominator.pdf.

I would also challenge you, like Tegmark, to respond to Simondon's "process of individuation" argument and the Weinbaum/Veitas "Open-ended Intelligence" argument. And no where in my comment do I suggest we account for mathematics with matter - ridiculous, but they are co-dependent arising! Perhaps you should actually read the Tiller paper I link to; there's always more to the story.

I am more than happy to concede Tegmark the implication, External Reality implies Patterned Universe, but there is no rational reason to equate the patterns in the Universe with patterns in the human endeavor which is mathematics! Mathematics is messy, imperfect, and filled with human-ness and with human-ness I include Platonist's attempts to obfuscate the messiness and imperfection!

I'm through here until Tegmark addresses, at the very least, Simondon; and I may be through even then . . .

Here's a question for you: In the Platonist Realm, how does Euclidean two-space distinguish itself from the Complex Plane? Since Gauss supposedly rid mathematics of "metaphysical difficulties" with his ordered pair representation, it's a legitimate question. Gee whiz . . .

https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From

https://www.amazon.com/What-Mathematics-Really-Reuben-Hersh/dp/0195130871

Hello Sabine, Phillip, Max et al,

Thank you for continuing this very interesting discussion about the anthropic principle and multiverses! I have much to learn about the anthropic principle, but I have one question about your point about probability distributions. Does this mean even if you know all the various options for these parameters/observed laws of physics (as I believe Max does explain in the book), unless you know the likelihood of each parameter/collection of parameters, you cannot say that the universe is finetuned for life? Through our existence, I believe that it does, although I may be misunderstood, which was my original point. However, because there is no probability distribution for these parameters, is this your rationale for why the anthropic principle has nothing to do with the multiverse theory, or are they simply unrelated?

Finally, last question to Max (if I may, Dr. B) because this is something I've always been caught up with - when you say that your job is to present the hypotheses without saying what you believe, how does this coalesce with the fact that you published a book arguing that the MUH is unfalsifiable because it can not be proven that there are aspects of the Universe that aren't mathematical. Simply put, I guess, did you publish the book to argue that the MUH is true, or to educate people on the possibility of it being a possible explanation? (Your books have inspired a lot of my recent interest in AI, astrophysics and cosmology, so I thank you. I am also looking forward to meeting you at the ANMH on 1/7).

Dr. B - Sorry if any of the above is nonsensical, in that case, feel free to ignore or delete. I will also be looking forward to your book as well!

Thank you very much,

Conner

Sabine, it seems you missed approving one of my comments where I addressed this paragraph of yours, so I assume that was an accidental oversight given the comment volume over the past few days:

But that argument is logically wrong. Saying that the universe is accurately described by mathematics makes no assumption about whether it “really is” mathematics (scare quotes to remind you that that’s ill-defined). It is unnecessary to specify whether the universe is mathematics or is something more, evidenced by scientists never bothering with such a specification. Ockham’s razor thus speaks against the mathematical universe.Firstly, that scientists never bothered addressing an issue does not entail that an issue doesn't exist, or that any such issue doesn't matter. I think it's a little bizarre that you'd even make such a statement. There are plenty of boring

scientificquestions that have not yet received any attention. Philosophical issues that aren't even in the typical scientists' sphere of interest would obviously be far from any scientist's mind -- which again, says nothing about their actual importance.Secondly, you're seriously understating the problems inherent to the philosophy of mathematics if you take a position that mathematical structures aren't actually real. Philosophers have now spent almost a century on non-Platonic philosophical theories, and while some progress has been made, many gaping holes the likes of quantum gravity yet remain.

By contrast, Platonic theories are completely unproblematic. And once you accede existence to mathematical structures, it's multiplying entities unnecessarily to suggest that matter deserves its own distinct place in our ontology, rather than simply being yet another mathematical structure. Ergo, Ockham's razor speaks quite strongly in favour of a mathematical universe.

Obviously I cannot do the philosophy of mathematics justice in a blog comment, so I'll direct you to this overview of the types of problems that a mathematical metaphysics either solves, or makes meaningful progress on when other approaches have repeatedly failed.

alphapsa,

Yes, that's correct. The probability distribution could be anything. If you believe in a theory of everything (which I don't, but that's another story), then the probability distribution is peaked at one particular set, for example. But that's a rather esoteric point. My main point is that you do not gain anything from introducing a probability distribution (which has to be conjectured) and then doing some calculation just to find a set of parameters which you could have assumed equally well. It's unnecessary and I can see no way you can possibly ever justify it.

Of course the anthropic principle says we live in a universe hospitable to life. But that has nothing to do with the multiverse. As Paul Hayes says, above, you shouldn't be surprised to find yourself in a place that allows beings that are surprised...

Sandro,

Sorry in case I missed your comment. Well, thanks for pointing out that mathematical metaphysics is a thing, but maybe your comment should be addressed at Max. That I don't think the question has any relevance in practice (yet) is, for all I can see, not in contradiction with you saying it's an important topic for philosophers. Best,

B.

"I think Philip’s point is that in the multiverse, the anthropic principle puts us in a habitable universe no matter what the probability distribution is."Exactly.

Phillip,

Ok, then, congrats for noticing that we live in a universe hospitable to life.

"Ok, then, congrats for noticing that we live in a universe hospitable to life."I'm not sure whether that is cynicism or whether you really don't get it. Yes, maybe that Weinberg guy has no idea what he is talking about. Doing astronomical cosmology and particle physics while continuing to teach and write books about science and the history of science and contemporary politics well past retirement age might cause him to overlook something, I don't know. :-|

In any case, I have an extra copy of the book by Lewis and Barnes (please post my lost comment if you can find it) which you are welcome to have in exchange for posting a review (positive or negative) on your blog. :-)

Phillip,

Cynicism. I totally get you're repeating what everyone else says too. Not the first time I'm having this argument.

You are not doing well defending your point. I have given you good reasons for why the argument is bunk, all you have to offer are remarks about Weinberg.

Let me try this once again because I've gotten to know you as a reasonable and not-dumb person: It is entirely useless to introduce a probability distribution over a space of which qua definition all but one element - corresponding to one particular realization of the presumed random number - is unobservable. There is no way to ever infer the probability distribution. And postulating it (or further assumptions from which to compute it or assumptions to compute these assumptions) are unnecessary and should be stripped by that guy's razor. You can simply throw away the probability distribution and take the parameter, done.

If you manage to come up with a probability distribution that gives you a likely value for observed combinations of parameters from fewer assumptions than the parameters themselves, you could just take whatever equation it is that allows you to compute that. You don't need a probability distribution over some ensemble to go with it.

Tbh, in the latter case I would probably accept that the multiverse is a possible interpretation of the math, like I accept many worlds as a possible interpretation of (the present version of) quantum mechanics. But we're far from that point. (And I would still complain it's useless.)

And either way you put it, the anthropic principle doesn't change anything about it.

Best,

B.

"Cynicism."That's a relief! For a moment there you had me worried. ;-)

"I totally get you're repeating what everyone else says too. Not the first time I'm having this argument."Just because others believe it doesn't mean that it is wrong. I certainly don't believe it just because others believe it and, as the "inflation" thread shows, I am on record disagreeing with the mainstream.

"You are not doing well defending your point. I have given you good reasons for why the argument is bunk, all you have to offer are remarks about Weinberg."OK, I'll try harder. :-|

"Let me try this once again because I've gotten to know you as a reasonable and not-dumb person:"I'm even more reasonable and less dumb offline. :-)

"It is entirely useless to introduce a probability distribution over a space of which qua definition all but one element - corresponding to one particular realization of the presumed random number - is unobservable. There is no way to ever infer the probability distribution. And postulating it (or further assumptions from which to compute it or assumptions to compute these assumptions) are unnecessary and should be stripped by that guy's razor. You can simply throw away the probability distribution and take the parameter, done."Take an example: relative masses of up and down quarks. If they were slightly different, then one can show that life not only as we know it but at all similar to what we know would not be possible. True, one doesn't have a probability distribution, so we can't say precisely how unlikely the observed relative masses are. Two points. First, I don't think it is unreasonable to assume that the probability distribution is not sharply peaked around the observed value. It might be, but the burden of proof is on those who claim that that is the case, who need to present a calculation. Second, even if we don't know the probability distribution, as long as it is not essentially a delta function representing the observed value (in which case we would know it), then it makes sense to say that the observed value is unlikely. Perhaps we can't say how unlikely it is, but that it is unlikely. Where the multiverse comes to the rescue is that the probability distribution doesn't matter. It doesn't mater at all whether the observed value is likely or unlikely; as long as it is not infinitely unlikely, it will exist somewhere in the multiverse, and perhaps we are there. Some people don't like this explanation, but that doesn't mean that it can't be correct. People used to look for some reason for why the planets have the distances from the Sun that they have (Kepler's scheme with the Platonic solids is a good example); it later turned out that there is nothing special about the distances (though they are not completely random), as orbits are possible at all distances*. Again, with just our Solar System, the question arises as to why the Earth is at just the right distance from the Sun to allow life, while this question has a trivial answer if there are many solar systems. Of course, one can say that things just happen to be the way they are with no further explanation; presumably it is a personal philosophical issue whether one is happy with this or not. (If this is the source of our difference in opinion, then we have to agree to disagree.)

To be continued...

...continued:

The interesting thing about the multiverse is that one doesn't have to know anything about the probability distribution.

This is distinct from the concept of assuming or calculating (somehow) a probability distribution in the multiverse to explain some observed value. There might be convincing examples of this, but I can't think of any offhand.

Note also that the multiverse wasn't just postulated in order to allow these sorts of anthropic explanations, but arises in other contexts (Linde's eternal inflation, for example). (Again, though, the universe is independent of the steps we take to understand it.)

"If you manage to come up with a probability distribution that gives you a likely value for observed combinations of parameters from fewer assumptions than the parameters themselves, you could just take whatever equation it is that allows you to compute that. You don't need a probability distribution over some ensemble to go with it."True, but this is the second example I mentioned above, and doesn't enter into the multiverse-explains-why-the-universe-is-fine-tuned-for-life argument.

Maybe the point is hard to make; perhaps that is why Lewis and Barnes wrote an entire book about it. I don't agree with everything in the book, as my review indicates, but I do think that it argues my case well, in a couple of hundred pages better than I can do in a comment box. Worth reading even if you don't agree with everything.

Of course, if you believe that the universe is not fine-tuned for life, or that the concept has no meaning, then there is little point in discussing possible explanations for the fine-tuning.

---

* A journalist once overheard Wernher von Braun (whom my mother worked for before I was born; one of my earliest memories is drawing a rocket on his blackboard) say something about putting a satellite into orbit at such and such a distance from the Earth, and was impressed: "How does he know so quickly that there even is an orbit at that distance?!" :-D

"Well, then please tell me what I learn from calling an initial value an address."

To me, at least, initial values demands an explanation: 'Why

theseimprobable constants?', with any number of unhelpful answers supplied by the world's religions.An address in Hilbert space answers this with, 'There is an infinite set of numbers that produce a universe hospitable to self-conscious matter'. There is no fine tuning. Victor Stenger's 'MonkeyGod' demonstrated (the plausibility of) this.

ferren,

To the extent that this answer explains anything, it's not a scientific explanation. You don't learn anything from it. Saying "this is our address in an infinite multiverse" isn't any more of an explanation than "these are the values of parameter in our universe."

Phillip,

No, that many people believe it doesn't mean it's wrong, but it explains my cynicism.

First, as I already said above, I don't agree that the universe is finetuned for life because (drums please) you cannot speak about finetuning without a probability distribution, so why do you continue to insist on it? (Let me emphasize, because people tend to misunderstand it, that I didn't say the universe is not finetuned. I simply said no statement can be made about it.)

Second, I know most of the examples for finetuning (and mention some in my book), but I don't think these are relevant for anything.

Besides, as it's been said often enough, twiddling one parameter of some dozen doesn't scan much of parameter space. There are also various examples in the literature (also quoted in my book) for universes entirely different from ours that can give rise to complex chemistry (not quite life, but a precondition for).

You write

"True, one doesn't have a probability distribution, so we can't say precisely how unlikely the observed relative masses are."You can't say how likely they are, period.

"First, I don't think it is unreasonable to assume that the probability distribution is not sharply peaked around the observed value.""I don't think so" is not an argument. Please try a little harder. This is the important point.

"the burden of proof is on those who claim that that is the case, who need to present a calculation"Anyone who claims they have any probability distribution has a burden of proof, that includes you. Why is a smooth distribution any more, dare I say it, likely than a peaked distribution? Allow me to mention that smooth function have measure zero in the space of all functions. Too bad, huh? Not that I mean to say this bears any relevance, this is just to show how ridiculously easy it is to pull away the carpet under this type of argument.

Can't you see how you are just shifting from "why this parameter" to "why this probability distribution"? It's the same thing in green, as the German idiom goes. (You can go one step further and shift the choice from the probability to the priors as some people are doing recently.)

The whole idea that you can get rid of an observer-dependent choice is entirely idiotic. There is NO way to get rid of it. You can merely reformulate it into something else. (And we could talk about reformulation, but the problem is that with the multiverse in the present form it's not only a reformulation, it also adds superfluous assumptions.)

Look, you can say about Tegmark what you want, but at least he is logically coherent. If you want to claim you can do only with consistency as a premise, then the only option is the mathematical multiverse. And in this case you go full circle by rewriting the question "why these laws" to "why this place in the mathematical universe."

"Note also that the multiverse wasn't just postulated in order to allow these sorts of anthropic explanations..."Once again, anthropic explanations are correct regardless of whether you have a multiverse or not. This is an entirely irrelevant point.

Best,

B.

"Besides, as it's been said often enough, twiddling one parameter of some dozen doesn't scan much of parameter space."Lewis and Barnes also have a chapter on common objections to the fine-tuning argument, which they discuss in detail and rebut. This is one of them.

Read the book. It won't cost you anything except a bit of time. :-) It is well written and most of the jokes are actually funny.

In any case, since you feel so strongly that you are right (something that I can sympathize with!), why not write up your objections, not in a book but in a paper? This will encourage rebuttals to be in the form of papers, which take much more time than writing comments (although both are enjoyable).

Since you've given up on tenure, you have nothing to lose! :-)

Phillip,

I am writing them up in a paper, though it will take a few more months to finish it (I have another paper that needs to be finished before that). It'll not contain much about finetuning in cosmology though, mostly naturalness in particle physics. But it's the same problem, just that the (missing) probability distribution is over a different space.

Does this mean you give up? Seems too easy, I was expecting more ;)

"I am writing them up in a paper, though it will take a few more months to finish it (I have another paper that needs to be finished before that)."I know the feeling.

"It'll not contain much about finetuning in cosmology though, mostly naturalness in particle physics. But it's the same problem, just that the (missing) probability distribution is over a different space."I'm not sure that we would agree that it is the same problem. :-|

I do note that there are papers which say "the expected, natural ratio should be of order 1; the observed one is vastly different; we need an explanation" and others which say that "if it is not a strange coincidence that this ratio is of order 1, we need an explanation". Really. (I'm not sure if there are both types of papers about the same ratio, but it wouldn't surprise me.) My guess is that it is a ratio of order 1 which needs an explanation, not a vastly different one.

"Does this mean you give up? Seems too easy, I was expecting more ;) "Give up? I won! :-D

Phillip,

I told you why finetuning arguments are bunk. They are mathematically ill-defined because you have no probability distribution. The only thing you had to reply to this was that you don't think it's unreasonable to assume something you would like to assume. This isn't an argument, this is a joke, and it's not even funny.

Unfortunately, that's what always happens. If the person I'm arguing with has any brain, they come to agree with me pretty quickly and not surprisingly so, because what I say is obviously correct. But then they refuse to accept the consequences and continue to hold on to their beliefs. Hence my cynicism.

Best,

B.

PS: You are right that naturalness arguments in particle physics are different from finetuning arguments in cosmology. I merely meant they are both wrong for the same reason.

"If the person I'm arguing with has any brain, they come to agree with me pretty quickly"I hope that this is cynicism. :-|

No, that's a status report. People agree with my argument against naturalness and finetuning because, well, the argument is obviously right. But then they keep on doing what they've been doing as if nothing has ever happened. It's not even confirmation bias. It's just... bizarre.

That I don't think the question has any relevance in practice (yet) is, for all I can see, not in contradiction with you saying it's an important topic for philosophers.I agree it's not relevant to typical scientific practice. This line is a little fuzzy since Max attempts to make the argument that it's somewhat falsifiable, at least in principle, which would make it a relevant scientific question.

While Max's argument that the continued relevance of math to physics is weak evidence for this position, it may also serve as evidence for an as-yet formed naturalistic mathematics.

Sabine: "And in this case you go full circle by rewriting the question "why these laws" to "why this place in the mathematical universe.""

I think this is the crux of the matter. The first question, to me, seems like an actual mystery. The second is kind of obvious: It is "this place" because that is where I am. The question is obvious and moot at the same time, similar to "Why was I born in this country, this state, this little town, and at exactly that time?"

You might be right in that the first question ("why these laws") is similarly obvious and moot, but to some (me and apparently others) that is harder to see.

The first question, to me, seems like an actual mystery. The second is kind of obvious: It is "this place" because that is where I am. The question is obvious and moot at the same time, similar to "Why was I born in this country, this state, this little town, and at exactly that time?Suppose you were one of several children born on the same day in the same place. No mystery.

Suppose you were the only child born in Antarctica. Wouldn't that demand more explanation? Getting back to the pink elephant dancing Swan Lake and singing a Stones song, Sabine would say "only if I have reason to think that the situation is improbable", which is possible in our own experience but not, she would argue (I think) with respect to the multiverse. I would argue that one can speak of "unlikely" values of parameters without knowing the probability distribution. I think that is the main point of dispute.

"I would argue that one can speak of "unlikely" values of parameters without knowing the probability distribution. I think that is the main point of dispute."Exactly.

"People agree with my argument against naturalness and finetuning because, well, the argument is obviously right. But then they keep on doing what they've been doing as if nothing has ever happened."

Maybe this is because their argument is with people (not you) who feel strongly that everything happens for a reason, so that (to them) if this universe has physical properties that allow for DNA-life, whereas randomly-chosen physical properties would not, then this universe must have been created for us, making us special. The multiverse is then posed as an alternative logical possibility, in which complete randomness still allows us to exist, and we are not special at all. Then Mario's Sharp Rock (the principle that whichever explanation is humblest is likely to be right) says that the latter possibility is the more likely of the two.

I would argue that one can speak of "unlikely" values of parameters without knowing the probability distribution. I think that is the main point of dispute.Exactly.

So finally we agree! ;-)

Phillip: "I would argue that one can speak of "unlikely" values of parameters without knowing the probability distribution. I think that is the main point of dispute."

This sounds self-contradictory to me. Speaking of "likely" or "unlikely" is the same as specifying aspects of a probability distribution, unless you and I have different understanding of the meaning of the words.

The point about the "obvious and moot" question is not about probabilities. I was born where I was born, and if I had been born somewhere else, that would still be true. The actual probability of someone being born at that place and that time is irrelevant. The important word in the question "Where was I born" is not the "where", but the "I".

Going back to the mathematical universe: The thing to understand is that there is no one true "version" of reality. What looks real to me is special only to me. Just like my hometown is not different from any other town, except from my point of view, all the different potential universes are equally valid. None of them is special, or real, except by the virtue of containing me. Many other potential universes contain thinkers who are convinced theirs is the one, true reality.

Phillip,

Well, now you only have to come to realize that a probability without probability distribution is ill-defined and we will agree.

"(Let me emphasize, because people tend to misunderstand it, that I didn't say the universe is not finetuned. I simply said no statement can be made about it.)"

Sabine, Thank you for this clarification, btw.

Conner

The clearest avenue to a "naturalist" philosophy of mathematics, by which I mean a philosophy which doesn't include some sort of "supernatural Platonic realm," is suggested by Paul Ernest with his book, "Social Constructivism as a Philosophy of Mathematics." This philosophy is, of course, grounded in radical constructivism:

Here's the problem with Platonic theories. Suppose mathematical entities have, as Tegmark suggests, inherent existence, then why is our access to those entities limited to representations? If they have inherent existence then we should be able to grasp them by that inherent existence without the necessity of representation. So then Mr. Magi states:

"By contrast, Platonic theories are completely unproblematic. And once you accede existence to mathematical structures, it's multiplying entities unnecessarily to suggest that matter deserves its own distinct place in our ontology, rather than simply being yet another mathematical structure. Ergo, Ockham's razor speaks quite strongly in favour of a mathematical universe."

But this is bullshit because we don't have access to these so-called inherently existing entities, rather, all we have access to are the representations. So even if the Universe is a mathematical structure, without matter to represent that structure, we would have no perceptual access to that structure. Hence, the Occam's razor argument is bunk. QED

Why Are We Here?

God: The Supreme Kvetch put us here so he would have beings to berate.

Super Determinism: We are a solution of the Great PDE with initial conditions from the Big Bang.

Anthropic Principle (generalized): Things are the way they are, because if they were different, they wouldn't be the way they are.

The Multiverse (in iambic parameter): There are many a possible environment,

and we are in one compatible with our predicament.

Dumb Luck: We are a trial from the Great Random Variable whose pdf will forever remain hidden.

Benign Mommy: Oh, good question honey, I don't know, but you are smart and strong and if you work hard one day you might figure it out and tell me.

The Hossenfelder: I answered that in a previous blog, but the complete answer can be found in my upcoming book.

PS: "If the person I'm arguing with has any brain, they come to agree with me pretty quickly and not surprisingly so, because what I say is obviously correct."

This is why I love your blog, because what you say is true a.e.

Zafa

But this is bullshit because we don't have access to these so-called inherently existing entities, rather, all we have access to are the representations. So even if the Universe is a mathematical structure, without matter to represent that structure, we would have no perceptual access to that structure. Hence, the Occam's razor argument is bunk. QEDWell that's just nonsense. Firstly, we can only deal with representations of mathematical entities because that's how our mathematical reality is structured. You don't have access to the law of the excluded middle in intuitionistic logics, but you can represent it by embedding other logics within intuitionistic logic. Similarly, the mathematical structure governing our reality gives us access to some mathematical entities, but not all, and the remainder we access via embeddings in the same fashion.

Secondly, your argument is seriously confused. Our perceptions are also governed by matter, so you're suggesting that matter can't interact with matter, which is axiomatically false.

Another (and last) thought on why some of us cling to the multiverse (type IV, per Dr. Helbig) concept despite that the arbitrariness it gives in initial conditions is something we had already (although, it is nice for intuition's sake to have a mechanism for arbitrariness along with the arbitrariness):

Einstein, I am told, at first thought the universe would be in a steady-state under General Relativity, until other mathematicians overcame his cognitive bias with evidence. I cite this as an example that people tend to prefer a steady-state universe, I think due the biological imperative that our genes must go on.

The multiverse restores a pseudo-steady-state! As our universe becomes inhospitable to our form of life due to Heat-Death and/or a Big Rip, other universes are being born, and at any time there is a range of universes in various states from Big Bang to Heat Death.

"Einstein, I am told, at first thought the universe would be in a steady-state"He thought that it was static. Indeed, this is what most astronomers thought at the time, essentially thinking that the Milky Way was the entire universe. Though there had been speculation, going back at least to Herschel, that at least some "nebulae" were distant "island universes" like our own Galaxy, this wasn't the consensus, was a minority opinion at the time, and wasn't resolved until several years later, in the famous "Great Debate" between Harlow Shapley (who lost) and Heber Curtis (who won)---at least in retrospect, though both were both wrong and right about various aspects and a the time it wasn't seen as so decisive.

The term "steady state" has a very specific meaning in cosmology: a universe with exponential expansion in which matter is created so that the mean density remains constant. This was a contended with, and at times even more popular than, the big-bang model from the later 1940s to the early 1960s. Technically, a static universe is also in a steady state, but the latter term is already taken in cosmology.

There is reason to believe that "all that there is" or "what everything is made of" or "reality" is nothing but fields. And ... what are fields "made of"? Are fields any more than mathematics? The community has long since abandoned discussion of what fields are fields of. Would it help exploration of MUH ideas to first of all (or also) feel comfortable about whether what many believe everything is comprised of (i.e. fields) is anything more than a mathematical structure?

Dr. Helbig, thanks for the enlightening corrections: I should have used static instead of steady-state, and the Einstein example was probably not a good one because it may have been motivated by contemporaneous evidence rather than personal preference.

To all,

It would be helpful if you give your opinion about this question.

Suppose There is a mathematical structure that can be constructed from first principle and without and regards to experiment that mimics QM gives the mass of the electron and the proton and all other predictions, would you then accept that reality is a mathematical structure. Or would you want to see more proof, and what kind.

Ok, one answer is, it depends... but let's not complicate it:)

qsa,

Could you elaborate on what you mean by first principle(s).

Zafa Pi

I sure can.

from wiki

"A first principle is one that cannot be deduced from any other. The classic example is that of Euclid's (see Euclid's Elements) geometry; its hundreds of propositions can be deduced from a set of definitions, postulates, and common notions: all three types constitute first principles."

Also, automata systems exhibit similar traits which includes rules. Now suppose you have a circle and a point, you can see that you can have an automatic rule. The point is inside the circle or outside it or on it, so the rule that you can have is inherent to the elements. My guess is that nature is a mathematical structure that is made up of some simple element(s) that carry its own possible rules.

Example. a world with only line segments. Suppose you only have a small segment, now you choose another segment that should lay inside it. Obviously, if it is bigger, then an automatic rule can be generated that is to discard it or keep it. you can have a bit more complicated setup with these line segments but they are nicely limited but they can produce a plethora, just take my word for it:)

qsa,

If from the 1st paragraph, common notions are the undefined terms (e.g. point and line) then I understand.

QM itself is a mathematical structure with several postulates/definitions, e.g. state (a unit vector in Hilbert space), time evolution of state (Schrodinger), measurement of state (observables and their eigenvalues as random variables). Then there are a lot of definitions and theorems. If this abstract structure was sent back to the early 18th century, it would be considered a bizzare useless edifice.

It is true that QM doesn't capture all what you asked for, but it does predict over a more restricted domain. Do you accept it as a limited reality?

For me it is necessary to have "common notions (?)", that is, to know, for example, the correspondence between the QM mathematical measurement and what is done in the lab for it to make any realistic sense.

The Pythagorean Theorem isn't reality, but is useful in carpentry which is real.

Probability Theory isn't reality, but is useful in modeling the flipping of a well balance coin.

I wonder what Sabine thinks.

Max Tegmark, I have question. I have read about your mathematical universe hypothesis. I have become a believer so to speak. But I ran into a problem. It seems that the different multiverses clash together. In one quantum mechanical multiverse everything is described with probability distributions. But out there in the mathematical universe there is another such multiverse with different probability distributions. This could be because the constants of nature in the other universe are different, or because the initial conditions are different. In both these quantum mechanical multiverses there is a probability that the very same configuration of particle locations and/or momentums come into existence. But then, which probability is right? The one or the other? Both multiverses are equal in the mathematical universe. Do we have to add them up together and treat them as a single multiverse? But how? Should we give one more weight than the other? But how do we determine the weights?

I haven given it some thought again. I think if in a different multiverse a particle has a different mass, then it is distinguishable from this multiverse. The two multiverses won't clash. Two particles with different masses are two entirely different particles after all, you can't swap them like bosons.

And I think I have found a solution to the problem of the initial states. If you pick an initial state, somewhere out there in the mathematical universe there is another initial state that could be a precursor to the first initial state you picked. This other initial state will have a lower entropy. Just like when you take this time slice of the universe and calculate back how the universe could have been a hundred million years ago. Then you will conclude that some of the fossils in the Earth once had been living dinosaurs.

Eventually if you go back further in time, the entropy decreases and decreases until you reach a point when the entropy can't drop any further. You have reached a state of maximum order, and you assign to this state a probability of 100%. From there you can calculate the probability of all the other initial states. You simply let the clock run forward in time, and you calculate a probability for each 'initial state'.

A "perfect" description is one that omits nothing, by definition; there is a 1:1 correspondence between the described and the described. Therefore a perfect description (as opposed to an abstraction) is an identity. So if the universe is perfectly described by mathematics, it is identical to that mathematics.

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