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Cake day: December 18th, 2023

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  • I perceived an uninterrupted stream of fantastic pictures, extraordinary shapes with intense, kaleidoscopic play of colors. After some two hours this condition faded away.

    This was, altogether, a remarkable experience - both in its sudden onset and its extraordinary course. It seemed to have resulted from some external toxic influence; I surmised a connection with the substance I had been working with at the time, lysergic acid diethylamide tartrate. But this led to another question: how had I managed to absorb this material? Because of the known toxicity of ergot substances, I always maintained meticulously neat work habits. Possibly a bit of the LSD solution had contacted my fingertips during crystallization, and a trace of the substance was absorbed through the skin. If LSD-25 had indeed been the cause of this bizarre experience, then it must be a substance of extraordinary potency. There seemed to be only one way of getting to the bottom of this. I decided on a self-experiment.

    Exercising extreme caution, I began the planned series of experiments with the smallest quantity that could be expected to produce some effect, considering the activity of the ergot alkaloids known at the time: namely, 0.25 mg (mg = milligram = one thousandth of a gram) of lysergic acid diethylamide tartrate.

    From LSD: My Problem Child by Albert Hofmann. I will leave it to others to explain all the ways in which this is absolutely hair-raising.


  • In February 1993, the University of Minnesota announced that it would charge licensing fees for the use of its implementation of the Gopher server.[11][9] Users became concerned that fees might also be charged for independent implementations.[12][13] Gopher expansion stagnated, to the advantage of the World Wide Web, to which CERN disclaimed ownership.[14] In September 2000, the University of Minnesota re-licensed its Gopher software under the GNU General Public License.[15]

    https://en.wikipedia.org/wiki/Gopher_(protocol)#Decline

    It’s probably not quite right to call it an open source alternative, though. I don’t think that gopher or anything was established in a monopolistic way, but that was before my time. Besides, the internet was all universities back then.








  • General_Effort@lemmy.worldtomemes@lemmy.worldIt's true.
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    2 days ago

    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!


  • General_Effort@lemmy.worldtomemes@lemmy.worldIt's true.
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    2 days ago

    Electrical engineers use them for calculating AC-circuits. In a DC circuit, you only have to worry about how much volt and amperes are in each part of the circuit. In an AC circuit, you also have to worry about the phase, cause the voltage goes up and down. The phase means where in that up and down you are.

    The complex number is interpreted as a point on a 2-dimensional plane; the complex plane. You have the “normal” number as 1 axis, and orthogonal to that the imaginary axis. The angle of the vector to that point gives the phase.

    They can be generally used for such “wavy” (ie periodical) processes. But I think this particular field of electrical engineering is the main application.