One might think this means that imaginary numbers are just a mathematical game

One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?

Stephen Hawking

3 thoughts on “One might think this means that imaginary numbers are just a mathematical game”

  1. Is the distinction just in our minds?
    In the world of political activists and their ilk, yes.
    In the world of macroscopic physics, no. (Nd humans are definitely macroscopic.)
    In the quantum realm? Still being debated after a century…,themselves%20could%20depend%20on%20who%27s%20looking%20at%20them.

    I suspect we do live in a multiverse and one where the different “branes” intersect at the quantum level so that all the quantum weirdness is just leakage.

    Just as likely as some of the stuff we see in politics. (Trilion dollar coins indeed.) 😉

    • The study confirms what I have always “Observed”.

      That’s where the Mandela Effect comes in handy, for Story[1].

      The Mandela Effect

      It’s all about the Copenhagen interpretation of quantum physics. You have Heisenberg’s Uncertainty Principle, Schoedenger’s wave function and how the Observer Effect cascades reality moment by moment.

      The concept is best shown in the play by Michael Frayn.


      Copenaghen – Bohr & Heisenberg

      The DVD is out of print and overpriced. Keep an eye out for it in streaming. It will show up again, someday. The play is available in book form. Pay attention to the end when Bohr points out the possible results of Heisenberg knowing the bomb could be built, and realize that all of those possibilities shown actually happened.

      The reason the worldline ended up as it did, was both men were upset at the time, isolated from other “Observers”, and talking past each other, so their local “node” in the Zeitgeist chose the least destructive worldline.

      Also watch both versions of Donnie Darko by Richard Kelly. Each time Kelly tries to understand what he created, the further away from the truth he gets.

      Donnie Darko

      As in Donnie Darko some people “remember” the changes. Those “memories” will always be suspect due to the censorship function built in to the local Zeitgeist. The act of trying to record instances of the worldline being reset only enforces that censorship by broadening the local Zeitgeist node. The larger the “node” the more effective the censorship, the firmer the worldline becomes; i.e., more locked down, less subject to change. Thus the Mandela Effect.

      BTW, The NSA Security State isn’t about preventing terrorism, it’s about getting enough “Observers” to lock down this worldline by increasing the censorship on the Zeitgeist. I’m not so sure that’s a good thing.

      – I’ve noticed, that the more they try and lock down this worldline, the less stable it becomes.

      See the end of Lathe of Heaven as example.

      That’s my Story, and I’m sticking to it. HA!

      [1] I find discussing the concept “safer” in Story than in the Real because it upsets people. Story lets people consider a fun concept rather than face their own “quantum indeterminacy”.

      “It’s a poor sort of memory that only works backwards.”

      – White Queen

      That is so true. I find that “memory” works Forwards, Sideways, as well as Backwards.

  2. The term “imaginary” numbers is long outdated. They are thoroughly grounded in real, everyday phenomena – they encode rotations in two dimensions. ‘i’ can be interpreted as a 90 degree counter-clockwise rotation. Squaring it – doing it twice – reverses the direction of the original vector. In other words, i^2 = -1. There’s nothing mysterious about it.

    Hawking knew this perfectly well, so I can only conclude that he was making use of the traditional jargon to make a point about positivism.

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