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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.






  • 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.





  • General_Effort@lemmy.worldtoScience Memes@mander.xyzLarge flavored quark
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    4 days ago

    The physicist who named the particle apparently liked to come up with nonsense words in his head. Later, when trying to decide the spelling, he came across a quote by James Joyce and spelled it “Quark”. Unfortunately, the particle rhymes with fork, while the german cheese rhymes with Mark.

    According to his own account he was in the habit of using names like “squeak” and “squork” for peculiar objects, and “quork” (rhyming with pork) came out at the time. Some months later, he came across a line from Joyce’s Finnegans Wake:

    Three quarks for Muster Mark!

    Sure he has not got much of a bark

    And sure any he has it’s all beside the mark.

    The line struck him as appropriate, since the hypothetical particles came in threes, and he adopted Joyce’s spelling for his “quork.” Joyce clearly meant quark to rhyme with Mark, bark, park, and so forth, but Gell-Mann worked out a rationale for his own pronunciation based on the vowel of the word quart: he told researchers at the Oxford English Dictionary that he imagined Joyce’s line “Three quarks for Muster Mark” to be a variation of a pub owner’s call of “Three quarts for Mister Mark.” Joyce himself apparently was thinking of a German word for a dairy product resembling cottage cheese; it is also used as a synonym for quatsch, meaning “trivial nonsense.”

    https://www.merriam-webster.com/wordplay/quark


    However, there is another interpretation of the quote.

    This passage from James Joyce’s Finnegans Wake, part of a scurrilous 13-line poem directed against King Mark, the cuckolded husband in the Tristan legend, has left its mark on modern physics. The poem and the accompanying prose are packed with names of birds and words suggestive of birds, and the poem is a squawk against the king that suggests the cawing of a crow. The word quark comes from the standard English verb quark, meaning “to caw, croak,” and also from the dialectal verb quawk, meaning “to caw, screech like a bird.”

    https://www.ahdictionary.com/word/search.html?q=quark

    This sounds very learned and all, but I can’t find that standard English verb in the dictionary.



  • I have no intuition for how hot or bright these trees would be. They certainly would be very different from the sun. The sun is literally incandescent; white-hot glowing. Trees would presumably use a mechanism comparable to glow-worms to generate radiation only in a very narrow frequency band. The fair skin color of elves suggests that they do not come from a high-UV environment.

    Somewhat less than half of the sun’s energy reaches us as visible light (43%). There are a few other factors that might allow the trees to glow brighter than the equatorial sun at noon. Unfortunately, the intensity per area diminishes with the square of the distance, so that doesn’t get us far (no pun intended).

    It would be much better if that world was basically rectangular (with reflective sides and top); basically a terrarium. That would also explain why you would place 2 light sources at 1 end. The length of a long rectangular box would only be limited by absorption of the light. The trees should glow brighter at the top. Plants, animals and structures on the surface, near the trees, are hit with only “mild” power, while the high-intensity light near the top of the box is absorbed or scattered by the atmosphere over a long distance. I’m not sure how to work out how long such a box might be. Mainly, I don’t know what assumption to make about that high-intensity light at the top.

    Anyway, we should consider that elvish anime eyes originally evolved as an adaption to low-light environments and only later became useful for seeing over long distances, because originally there possibly were no long distances.


  • Hmm. That should allow us to estimate the size of that world. The light of the trees must not be so bright as to cook everything in the vicinity; just make it nice and balmy. But, on the opposite side of the world, there must still be enough light to see. Having the occasional photon bounce back would eventually be enough to make out a static scene, but, apparently, it’s possible to see things happening in real time, yes?

    Does flat mean that we are talking about something like a simple disc here, or just that a beam of light travels parallel to the ground? The latter would imply a rather strange geometry, which I can’t wrap my mind around. It would make more sense, though, as, obviously, we couldn’t assume that light intensity diminishes with the {ETA:] square of the distance.


  • Publications in peer-reviewed journals are how a career in science is built. It’s impossible to measure the productivity of a scientist. What is done, is that one looks at their publications. How many publications do they have? How often are they cited? What is the quality of the journal?

    This creates very bad incentives, leading to things like publication bias. It also means that you must publish in prestigious journals. You don’t have a choice but to accept their terms. Libraries don’t have a choice but to stock these journals. It’s a straight-forward monopoly racket. These publishers make fantastical profits.

    All that money can be used for PR campaigns and lobbying to keep the good times rolling.