• Space/Science
  • GeekSpeak
  • Mysteries of
    the Multiverse
  • Science Fiction
  • The Comestible Zone
  • Off-Topic
  • Community
  • Flame
  • CurrentEvents

Recent posts

From one independent country to another Pebble July 4, 2022 1:41 pm (CurrentEvents)

Chicago …and on July 4th Pebble July 4, 2022 11:48 am (CurrentEvents)

Hey, Jude. ER July 3, 2022 2:19 pm (Off-Topic)

Shooting in Denmark Pebble July 3, 2022 12:50 pm (CurrentEvents)

The Orville - New Horizons BuckGalaxy July 2, 2022 9:21 am (Science Fiction)

Four hostile alien civilizations may lurk in the Milky Way BuckGalaxy July 2, 2022 9:18 am (Space/Science)

Sorry, I just couldn't resist this. ER July 2, 2022 6:37 am (Off-Topic)

And the latest in the anti abortion debacle Pebble July 1, 2022 4:52 pm (CurrentEvents)

Pod, clarified my question on anthropomorphic sea level rise on M of M RobVG June 30, 2022 2:55 pm (Off-Topic)

Erskine Childers (1870-1922), RIP ER June 30, 2022 12:00 pm (Off-Topic)

definition of the term "caliber" ER June 29, 2022 3:09 pm (CurrentEvents)

Home » Mysteries of the Multiverse

The unit circle September 24, 2020 5:51 am ER

When I was in high school, my trigonometry teacher drew a right triangle inside a unit circle and defined the sine and cosine functions as the ratios of the lengths of the opposite and adjacent sides of the triangle to the hypotenuse, vertical and horizontal values divided by 1.

As the radius vector spun around, he plotted the sine and cosine values on a Cartesian coordinate system where the x axis represented the angle of the vector and the y was the value of the function. The sine and cosine curves, identical but 90 degrees out of phase, marched off to the right, in an endless progression into infinity.

In a terrifying flash of insight, I realized triangles had been playing these games with each other long before there were human minds to contemplate them, indeed, even before there was a universe at all, and that this simple mathematical trick could be used to model any oscillating system: springs, guitar strings, waves, alternating current, sound. This was the meaning of the display on an oscilloscope. All these “real” things, matter and energy, space and time, could be represented precisely in a human mind by a process of pure thought, and it was based on a concept that didn’t seem to need human minds at all–it was simply a property of triangles.

I still haven’t come to grips with just what it all means.

  • I remember a science fiction story covering this! by Vitruvius 2020-10-02 02:40:55
    • Found it! by Vitruvius 2020-10-02 15:52:40
    • And many years later...in another place, another teacher......proved entirely to my satisfaction...t by ER 2020-09-24 06:02:35

      Search

      The Control Panel

      • Log in
      • Register