1 Improved Spanreed for use in Multiple Reference Frames Author: u/skemp117 Date: Vevishes 1175 I. I NTRODUCTION Current spanreeds cannot transmit writing effectively be- tween two different frames of reference (1). Because of this, communication between land and ships is rendered impossible. This is because the single conjoiner fabrial on the device does not distinguish between the desired movement of the writing hand and the movement of the reference frame. We propose a solution to negate the effects of the different reference frames by adding another conjoiner as well as a reverser. II. I MPROVED D ESIGN Adding a reverser seems an obvious move. Place one half of the pair on the receiving spanreed and the other half somewhere in the reference frame of the transmitting spanreed, an ink-well perhaps. While adding this reverser will remove the effects of the transmitter’s reference frame, the receiving spanreed would be unable to account for the movement of its own frame. Figure 1 shows a simplified sketch of the proposed design. Fig. 1. Improved spanreed and ink-well Spanreeds are unique in that they act as a rigid connection (not dynamic), transmitting position and not velocity, accel- eration, or force. Conjoined masses act as rigidly connected masses subject to the forces upon them at the time. Although one could say you need more force to move these conjoined masses, it is equally valid to say that a conjoined items mass is increased by the dimension of the connection that binds the masses together through the Cosmere thus increasing the force needed to effect them. As such, in the following equa- tions, ̄ x will represent the infinitesimal 3D change in position composed of orthogonal delta position vectors (x,y,z) for an infinitesimally small period of time. This yields more accurate results than traditional dynamics as fabrial connections aren’t effected by time derivatives in non-inertial reference frames. Further notation definitions are that s indicates a spanreed, o indicates a reference frame, t is for transmitter, and r is for receiver. Equation (1) shows the standard form for the equation of a spanreed. The full motion of the receiving fabrial is the sum of the relative motion of the transmitter in its frame and the motion of the transmitter’s frame. This is not enough. Consider the receiving spanreed located on a moving ship, the position vector ̄ x r s = ̄ x t s/o + ̄ x t o (1) Adding the reverser between the receiver spanreed and the transmitter reference frame would remove the effects of the transmitter reference frame which are inevitably transmitted through the primary conjoiner. The motion of the receiving spanreed would now be mimicking exactly the handwriting of the transmitter. That works great if the receiver is stationary. Consider receiving a message on the deck of a ship. Your span- reed would mimic perfectly the handwriting of the transmitter; however, your ship would have sailed out from under the receiver while it hovers over the ocean writing away. Thus we need to add another conjoiner between the receiver’s reference frame and the receiver to add the motion of the ship back to the receiver. Equation (2) shows the new terms. The first parenthesized term is the primary conjoiner, the second term is the reverser, and the third term is the secondary conjoiner. ̄ x r s = ( ̄ x t s/o + ̄ x t o ) + ( − ̄ x t o ) + ( ̄ x r o ) = ̄ x r s/o + ̄ x r o (2) ̄ x t s/o + ̄ x t o − ̄ x t o + ̄ x r o = ̄ x r s/o + ̄ x r o (3) As you can see in equation (3), the motion of the transmitter reference frame is cancelled. Matching terms on both sides of the equation shows us that the handwriting of the transmitter, ̄ x t s/o , is successfully transmitted, and the receiver can continue to move in its reference frame as if rigidly connected to it. III. C ONCLUSION This paper presents a novel method for transmitting infor- mation across Roshar without needing to consider reference frames. We hope this will aid the Coalition with the liberation of Alethkar and other nations of Roshar. R EFERENCES [1] “Spanreed.” [Online]. Available: https://coppermind.net/wiki/Spanreed