Friday, January 25, 2019

Belief in infinite doppelgangers

I mentioned that Brian Greene is sympathetic to many-worlds theory without endorsing it, but he definitely believes in a multiverse that is almost as goofy:
Physicists Brian Greene and Max Tegmark both make variants of the claim that if the universe is infinite and matter is roughly uniformly distributed that there are infinitely many “people with the same appearance, name and memories as you, who play out every possible permutation of your life choices.”
Greene's 2011 book said:
“[I]f the universe is infinite there’s a breathtaking conclusion that has received relatively scant attention. In the far reaches of an infinite cosmos, there’s a galaxy that looks just like the Milky Way, with a solar system that’s the spitting image of ours, with a planet that’s a dead ringer for earth, with a house that’s indistinguishable from yours, inhabited by someone who looks just like you, who is right now reading this very book and imagining you, in a distant galaxy, just reaching the end of this sentence. And there’s not just one such copy. In an infinite universe, there are infinitely many. In some, your doppelgänger is now reading this sentence, along with you. In others, he or she has skipped ahead, or feels in need of a snack and has put the book down. In others still, he or she has, well, a less than felicitous disposition and is someone you’d rather not meet in a dark alley.”
I am not sure which is crazier, this, nonlocality, denial of free will, or many-worlds theory.

When some non-physicists like Deepak Chopra says stuff like this, they get mocked by physicists.

Greene would say that there is someone like in a distant universe, but he regularly blogs in favor of quantum computing instead of against it.

Why do physics professors like Greene and Tegmark get a free pass?

The above paper addresses several problems with the Greene-Tegmark view.

I think the problem is more basic. Once you start talking about infinities like that, you have left the realm of science. You as might as well be talking about angels dancing on the head of a pin.

You might be surprised that a mathematician like myself would be so hostile to infinities. After all, mathematicians use infinities all the time, and know how to deal with all the paradoxes. But the infinities are short-hands for logical arguments that make perfect sense.

What do you do with beliefs that you have no free will, and you have infinitely many copies of yourself in distant universes leading parallel lives? Or that what you think is a personal decision is really splitting yourself from an identical right here in this universe, but invisible? In some of these universes, bizarre things happen, like a tiger giving birth to a goat. But why don't we ever see such nonsense? You can say that those events are unlikely, but there are universes where they happen all the time. How do you know that we are not in one?

I am just scratching the surface of what a nonsensical world view this is.

Historians of science wonder how Galileo and Newton had such coldly rational views towards analyzing the mechanics of simple experiments or celestial observations, and yet they completely accepted all sorts of biblical religious that most scientists today say is just stupid mysticism. How is that possible?

Someday, Greene, Tegmark, and many other leading physicists will be seen similarly. They wrote some good scientific papers, but they also believed in total nonsense that a child could see was ridiculous.

Here are some mathematicians talking about infinities, from a recent podcast:
Dr. Garibaldi decided to talk about a theorem he calls the unknowability of irrational numbers. Many math enthusiasts are familiar with the idea of countable versus uncountable infinities. ...

The set of all real numbers—all points on the number line—is uncountable, as Georg Cantor proved using a beautiful argument called diagonalization. The basic idea is that any list of real numbers will be incomplete: if someone tells you they’ve listed the real numbers, you can cook up a number their list omits. ...

The end result is, in Dr. Garibaldi’s words, sort of hideous. Any classes of numbers you can describe explicitly end up being merely countably infinite. Even with heaping helpings of logarithms, trigonometry, and gumption, the number line is more unknown than known.
So all the real numbers we know anything about are countable. All our knowledge is countable. The reals are uncountable, so almost all real numbers are unknowable in some sense.

Mathematicians all understand this, and it is important in some mathematical arguments, but it doesn't really have any grand philosophical implications. Knowledge is countable because of they way knowledge is defined and accepted. Actual things are finite.

You could say that there is some real number that perfectly encodes your doppelganger, or records all your memories, or predicts all your future behavior, or any other weirdo fantasy you have. We cannot construct that real number, or say anything interesting about it.

You can fantasize all you want about alternate realities, but the physics and the math don't really add anything.


  1. Yes! If, for the sake of argument, against your very reasonable and to me agreeable idea that we as people can only construct models that have a finite number of components, infinite detail (countable or uncountable) is in fact required to specify one real object, then the combinatorics of possible real objects would require the number of universes to be a higher order of infinity for there to be even one copy. Dividing and multiplying and exponentiating infinities is not a decent game even for physicists.

    1. But the problem is really more fundamental. Completed infinities and impredicative definitions lead to logic contradictions and absurdities. Solomon Feferman has written a somewhat technical book on how transfinite mathematics is hogwash: "In his concluding chapters, Feferman uses tools from the special part of logic called proof theory to explain how the vast part--if not all--of scientifically applicable mathematics can be justified on the basis of purely arithmetical principles. At least to that extent, the question raised in two of the essays of the volume, Is Cantor Necessary?, is answered with a resounding no."

      Ultrafinists or strict finitists simply don't make silly assumption and they avoid the whole mess. A completed infinity is an immediate self-contradiction. Impredicative definitions are logical contradictions. From this you get "paradoxes" like Banach-Tarski or uncomputable numbers etc. Pure baloney and a waste of time.

  2. Yes, almost all the paradoxes of mathematics have to do with impredicative definitions or infinity. Strict finitists suffer no mysteries at all. However, the problem with mathematics modeling physics was apparent with Zeno quite a long time before any of these derivative topics. The paradoxes Zeno described have never really been answered by math. Joseph Mazur pointed this out in his book "The Motion Paradox: The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space." Zeno never received a proper answer. The nature of the mathematical continuum (false dichotomy of infinite discreteness vs discreteness) says nothing about physics. It's just circularity and invalid logic at that.

    My point about "nonlocality" (not signal nonlocality) is that people who reject it are engaging in mysticism. We have deterministic accounts, however much you might not like them for aesthetic reasons. I'm not sure people who try to change logic or blur our thinking with Copenhagen are any less mystical. If you like QM, you are still stuck with it violating Bell. You can debate this all you like but I have read the papers and Bell was following EPR and not making assumptions about classicality, realism, counterfactuals, etc.

  3. All numbers actually aren't real, they are just abstractions, locations on another imagined construct called a number line, none of them exist outside of abstraction (unless you are a mystic subscribing to numeric Platonism). Look all you want in the entire universe, you will never actually discover a '1', or a n + 1 anywhere, just various symbols which represent the abstraction. Nothing in nature works by math being done with numbers, or involving calculations, these are merely the synthetic tools humans have developed to measure, model, and describe aspects of reality we have the ability to measure, the reality itself is NOT math.

    The only ridiculous reason Greene has for pandering infinities is that he is unable to mentally deal with the actual improbability of his own existence (its an existential crisis of sorts). He simply can not deal with the sheer fact that when you apply a statistical likelihood of even being alive against the largely inert immensity of the tiny fraction of creation we have been able to observe, it is very statistically improbable bordering on miraculous of the random chances of such an event even being possible within a mere 14 billion years, so he attempts to deflect this numerical improbability by whistling up a literal infinite chorus of other universes to deflect the numerical improbability of his own unique existence into a mind numbing infinite number of universes. Greene needs to believe in randomness and mindless probability determining all outcomes in his world view, but alas, even by his own calculations, the observable universe indicates otherwise.

    Mathematicians are just as prone to self delusion as anyone else when confronted with what they don't want to accept, and mathematicians are also historically notorious card cheats, stacking the deck whenever they don't like the odds.

  4. Ah the paradox of Zeno. Few people get this. The problem with the paradox is that it isn't a paradox at all, it's a logical error of assumptions leading to impossible consequences. If you cross half way across the room, then half of that distance, then half of that etc, you never reach the other side of the room, logically it would seem, except that you have already revealed the contradiction in the premise itself, you crossed half the room, thereby proving movement is already finitely possible regardless of any other silly abstractions you layer on top of it , No distance ever travelled has anything to do with infinity, as any infinity is a purely numerical ABSTRACTION outside of time, and a measureable distance (like crossing a room)is a finite reality within time.

    1. Right but motion is still not explained. I think Zeno ultimately destroyed the idea of space & time as any ultimate abstraction a long time ago. People just started making illogical limit arguments and everyone forgot him.

  5. Zeno was trying to illustrate how poorly conceived arguments lead to nonsense. Employing infinity in an argument magically interacting with finite time or movement is utterly meaningless, as time and all movement is finite in measurable observation. Pretending you can do anything forever is a good way to get nowhere and accomplish nothing very unscientifically.

  6. I just had a thought about the entire 'multiverse' argument.

    If a physicist is going to agonize over what can be known through the event horizon of a imagined black hole... in this universe, how the hell are they going to even be able to touch a single thing through the paywall/firewall/???? of another universe entirely? Psychic friends network? Ouija board? Frog entrails? Oh.... I get it, lots and lots more money so they can 'think' big thoughts about how insignificant our universe really is in the 'greater scheme' of things. Sigh.

    There really is an easier (and much cheaper) way. Physicists who want to pursue the multiverse meme need to put down the physics books and read lots of fantasy novels until they overdose and want to puke. Each and every one of these books take place in another multiverse according to their own statements about an infinite number of different universes with different laws of physics...

    Or... we could start mandatory drug testing of all physicists and scientists who receive government funding. So much coming out of academia has the haze like tinge of pot induced fantasy.