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  1. M.C. Escher and CP Violation

    I’ve had these pictures for quite a while and can’t remember where I got them from, but I used to show them in my lectures on Theoretical Particle Physics when I was in Nottingham to illustrate CP-violation and used them in this morning’s lecture at Maynooth.

    The following picture by M.C. Escher is called Day and Night:

    If you look at it you can see two kinds of symmetry emerging. One is a kind of reflection symmetry about a vertical axis drawn through the centre of the picture that applies to shapes but not to colour. The other is between black and white. But it is obvious that the picture doesn’t display these symmetries separately: to get a picture unchanged from the original you would have to do the mirror reflection and change black to white (and vice-versa).

    The mirror reflection in the image can be taken to represent parity (P). Strictly speaking parity refers to a reflection through the origin in 3D rather than a mirror reflection, but it’s just for illustration. We know that a parity symmetry is violated in weak interactions just as it is in the picture.

    The other possible symmetry, between black and white can be taken to represent charge-conjugation (C), the operation that converts particles into anti-particles and vice-versa.

    While P is not an exact symmetry of weak interactions, it was long thought that the combination of C and P (CP) would be. Actually it isn’t. The story of the discovery of CP-violation is fascinating but I don’t have time to go into it here. It suffices to say that the Escher print also displays CP violation.

    First lets do `C’, i.e. convert black to white and vice-versa. The result is:

    Now reflect about the vertical mid-line to illustrate `P’:

    If `CP’ were an exact symmetry then that image would be identical to the original, which I reproduce here:

    You can see, however, that while some elements of the picture do look the same after this combined operation (e.g. the birds), others (e.g. the buildings at the bottom) do not. Although CP is not an exact symmetry of this picture, it is almost (just like it is in particle physics).

    #CPViolation #DayAndNight #MCEscher #ParticlePhysics
  2. M.C. Escher remains the undisputed king of visual paradoxes. 🎨

    Even when modern tech decodes his illusions, the real magic is how he dreamt up such complex compositions using nothing but a pencil and pure imagination. It is a humbling reminder that while computers are fast, the human mind is the original engine of infinite complexity. 🧠

    youtube.com/watch?v=ldxFjLJ3rVY

    Which Escher piece has always left you scratching your head?

    #MCEscher #OpticalIllusion #ArtHistory #CreativeGenius #HandDrawn

  3. Wonderful analysis and animated recreation of M.C. Escher's "Picture Gallery" by 3B1B: youtube.com/watch?v=ldxFjLJ3rVY

    The 2003 paper by De Smit and Lenstra who as number theorists were intimately familiar with elliptic functions ("doubly periodic complex functions") at the heart of the image pub.math.leidenuniv.nl/~smitbd

    I grew up in Baarn where Escher lived for a while but only learned later that he lived on the same street! D'oh. Of course we were separated by 35 years.

    #mathematics #escher #mcescher

  4. If you're a fan of #MCEscher's drawings and/or #demoscene productions, or just want to relax to some chill music, I can highly recommend “Mrs. Escher's Nightmare”, a #demo / #musicvideo by #AndromedaSoftwareDevelopment aka #ASD: youtu.be/G7dpLcIaUTs

    Released at #Euskal Encounter 22 back in 2014

    Code by #Navis
    Music by #aMUSiC
    Handmodel & Photography by #Ch3
    Graphics by #Amoivikos

    More demos by asd at www.asd.gr