Capacitance Updated 2025-07-16
CERN Updated 2025-07-16
Capoeira Updated 2025-07-16
It is not a practical fighting style. But it is an awesome game/exercise.
Catalysis Updated 2025-07-16
Stop codon Updated 2025-07-16
Twin paradox Updated 2025-07-16
The key question is: why is this not symmetrical?
One answer is: because one of the twin accelerates, and therefore changes inertial frames.
But the better answer is: understand what happens when the stationary twin sends light signals at constant time intervals to each other. When does the travelling twin receives them?
By doing that, we see that "all the extra aging happens immediately when the twin turns around":
  • on the out trip, both twins receive signals at constant intervals
  • when the moving twin turns around and starts to accelerate through different inertial frames, shit happens:
    • the moving twin suddenly notices that the rate of signals from the stationary twin increased. They are getting older faster than us!
    • the stationary twin suddenly notices that the rate of signals from the moving twin decreased. They are getting older slower than us!
  • then when the moving twin reaches the return velocity, both see constant signal rates once again
Figure 1.
Twin paradox illustration with twins sending light signals at regular intervals
. Source.
Another way of understanding it is: you have to make all calculations on a single inertial frame for the entire trip.
Supposing the sibling quickly accelerates out (or magically starts moving at constant speed), travels at constant speed, and quickly accelerates back, and travels at constant speed setup, there are three frames that seem reasonable:
  • the frame of the non-accelerating sibling
  • the outgoing trip of the accelerating sibling
  • the return trip of the accelerating sibling
If you do that, all three calculations give the exact same result, which is reassuring.
Another way to understand it is to do explicit integrations of the acceleration: physics.stackexchange.com/questions/242043/what-is-the-proper-way-to-explain-the-twin-paradox/242044#242044 This is the least insightful however :-)
Bibliography:
Twin prime conjecture Updated 2025-07-16
Let's show them how it's done with primes + awk. Edit. They have a -d option which also shows gaps!!! Too strong:
sudo apt install bsdgames
primes -d 1 100 | awk '/\(2\)/{print $1 - 2, $1 }'
gives us the list of all twin primes up to 100:
0 2
3 5
5 7
11 13
17 19
29 31
41 43
59 61
71 73
Tested on Ubuntu 22.10.
TwinsUK Updated 2025-07-16
Two.js Updated 2025-07-16
Examples at: two-js/.
JavaScript library, works both on browser and headless with Node.js to SVG.
Feels good. Maybe not ultra featured, and could have more simple examples in docs, but still good.
One of the main features of Two.js appears to be the fact that it can natively render to either SVG and canvas, rather than creating SVG through DOM hacks as done by other projects.
CC BY-NC-ND Updated 2025-07-16
CC BY-SA 4.0 Updated 2025-07-16

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