Skip Navigation
61 comments

  • Me, a nerd: its just a joke don't go off on a tangent, dont go off on a tangent, dont go - just let it be.... I just.. I just...

    I NEEEED IT

    So achtbually, nature works with transcendental real numbers on the complex plane with uncountably infinite precision.

    Lets break this math nerd statement down in a way normal people might understand. First, most numbers are multi-dimensional and live on a plane instead of a line. The straight integer number line like 0, 1, 2 is just a small slice of the plane. In this plane, imaginary numbers occupy their own dimension. Complex numbers which are made of both real and imaginary parts occupy another dimension.

    Moreover, most numbers are also infinitely precise thus being uncalculatable. Their decimal places go on forever and ever without repeating or being representable with a ratio of integers. Its why we only have good approximations for pi instead of an exact pinpoint knowledge of it. There are methods to get closer and closer approximations but you need an infinite time frame to complete that unending process.

    Theres actually somehow more uncountably real numbers than countable integers and ratios, even though they are both infinite. There are more decimal numbers between 0-1 than there are integers between 0-infinity. One form of infinity is literally bigger than another, and that bigger infinity is the one nature likes working with.

    Moreover, most of our universal physical and mathematical constants are transcendental reals because nature gets a hard-on for baking multidimensional fractal holomorphic topology and complex nonlinear equations into its magical abstraction bullshit logic.

    Theoretical physicist during the 20th century were VERY salty about finding complex and imaginary real numbers in their physical equations. Since it implies that complex numbers arent just imaginary tools of abstrction but somehow "real" and affects the universes physical machinery. Nonlinear dynamic equations put a bullet through the brains of classical scientific determinism. Thank you very much, chaos theory and entropy.

    It's not that we invented imaginary numbers, its that they were the missing piece to fully complete our understanding of algebra. With them, we finally graduated from cave man linear algebra, to discovering holomorphic dynamics which model the way natural systems actually work. After 2000 years of banging basic logical abstractions together to make a enough decent sparks of discovery for a real smoldering fire.

    Computer processing power sure helped to visualize these higher dimensional topologies for our little monkey brains to process with our eyeballs in real time instead of just thinking about this stuff in the minds eye. I sure cant visualize a 4D hypercube let alone a 20ishD hyperstructure that AI image network picture forms brought down to three dimensions.

    Really its a miracle that we have even a thin narrow portion of numbers we can compute, all our regular integers and ratios are islands distanced apart by an infinitely deep ocean.

    In case you were wondering about the stuff in the image: Multidimensional AI activation map showing how and image AI organizes its knowledge on a neural network. Similar concepts or images are closer together.

    3D mandelbrot set with the logistic map highlighted along its real number line axis. https://github.com/jonnyhyman/Chaos

    minibrot zoom in

    algae colony arranging itself into conjoined 2nd iteration sierpinski triangle, screenshot from a journey to the microcosmos video.

    pascals algebraic triangle encoding the sierpinski triangle by if the number is even or odd (base/mod 2)

    the dynamic map of where a pendulum will land if pulled upon by three magnets equally spaced given its initial starting spot. https://youtu.be/C5Jkgvw-Z6E

  • https://lemmy.blahaj.zone/post/15648655

    I wrote a piece about why imaginary numbers are actually important. It's in german though.

    To sum it up, to every polynomial equation, there exists at least one solution to it, if you allow complex numbers to be solutions.

    • I used that text as a little test for the AIs at DDG. Here's from Claude 3 Haiku.

      Here is the translation to English:

      Complex Numbers and Polynomials

      Something that hardly anyone knows is that complex numbers, in addition to their application in Complex AC Calculations (known to HTL students), also have a second, important use.

      In mathematics, there is often the problem of finding a number x for a given function f(x) such that f(x) = 0 holds.

      This is often the case for polynomials, as many important mathematical functions can be well approximated by polynomials.

      The Fundamental Theorem of Algebra states that if we allow x to be a complex number, then there is always a solution to the problem such that f(x) = 0.

      Restriction: but the polynomial must not consist of only a constant term, i.e., f(x) = 5 would be inadmissible. The x must appear at least once in the polynomial. Otherwise, there are really no restrictions :-)

      PS: In the example given in the image (f(x) = x^2 + 2 = 0), a solution would be approximately x = √2 i ≈ 1.4 i.

      Then I asked: "Please make it understandable to a general audience and phrase it like a pop-science author would."

      Here is the translation in a more accessible, pop-science style:

      The Hidden Power of Complex Numbers

      Most people think complex numbers are just some obscure math concept, useful only for electrical engineers. But these mysterious numbers actually have a hidden superpower - they can solve all sorts of important math problems.

      You see, in math, we often want to find a number x that makes a function f(x) equal to zero. This comes up a lot when working with polynomials - those nice, smooth equations made up of powers of x.

      The problem is, sometimes there just doesn't seem to be any real number x that does the trick. That's where complex numbers swoop in to save the day!

      The Fundamental Theorem of Algebra proves that as long as we allow x to be a complex number (a number with both a real and imaginary part), then there will always be a solution that makes f(x) equal to zero. No exceptions!

      So complex numbers unlock the ability to solve all kinds of polynomial equations that would be impossible with just regular old real numbers. It's like they have a secret mathematical superpower.

      Of course, there is one small catch - the polynomial can't be a simple constant, like f(x) = 5. It has to actually contain the variable x somewhere. But other than that, complex numbers can tackle any polynomial problem you throw at them.

      So the next time you see an imaginary number like √(-1), remember - it's not just some weird math trick. It's a powerful tool for solving important equations. Complex numbers may seem strange, but they're secretly the heroes of the math world!

  • Imaginary numbers: proof that mathematicians don't understand branding.

61 comments