I thought I'd share my pet theory about the 25th-century warp scale recalibration, to see whether anyone else had similar thoughts (also, maybe someone wants to use this in their fan-fiction or something, idk)
I know this was discussed by scientific advisor Andre Bormanis and he suggested that the scale was recalibrated to make Warp 15 equate to infinite velocity and that Warp 13 on the new scale equated to roughly Warp 9.95 on the old, but that doesn't really make sense to me.
First of all, I can't think of any sensible mathematical function that maps 13 to 9.95 and 15 to 10, especially if we want to (as we presumably do) map 1 to 1 so that Warp 1 is still c. Secondly, throwing out the 9.95 figure, if you are going to simply stretch the scale so as to still have a Warp 10-like "infinite barrier" somewhere on the scale, the only obvious thing to do would be just to multiply the whole thing and scale it evenly.
The problem is that this would result in relatively slow and conventional warp speeds suddenly being much higher. Warp 13 divided by the rescaling coefficient that moves 10 to 15 (so, 1.5) is 8 2/3. Why exactly anyone would want to go at exactly warp 8 2/3 so often that it merits being given an integer designation is anyone's guess.
In fact, we know that integer warp factors on the TNG scale are more energy efficient than fractional ones, so such a scale would be tremendously inconvenient, as 5 out of the 9 usable integer warp factors would now end in .5 - and what's even worse is that old Warp 1 is new Warp 1.5, meaning that Warp 1 to 1.5 describes sub-light speeds. That's...just dumb.
So, my solution: Don't rescale Warp 1-8.99999..., but adopt a definition where for Warp >= 9, the new warp factor is defined as 9 - log_10(10-X), where X is the old warp factor.
Sounds complicated and random, but what this means is that Warp 9.9 -> Warp 10, Warp 9.99 -> Warp 11, Warp 9.999 -> Warp 12 and so on. This seems like a sensible change - as maximum speeds kept increasing, Captains would grow tired of saying things like "Warp 9.999". It also removes any kind of infinite barrier, which just isn't helpful (so now you can have arbitrarily large warp speeds; a new warp factor of 50 would simply be a 9 followed by 51 decimal 9s in the old system.
Crucially, no warp factor would be more complicated than it used to be. Granted, technically the Intrepid max cruise speed of 9.975 would now be 10.60205999132796..., but obviously this could just be stated as 10.6 without much of an impact; calculating 10.6 in reverse gives us 9.97488..., which is clearly close enough. Similarly for Intrepid's max rated speed, 9.992, we can state this as 11.1, which reverse-calculates to 9.9920567..., which again seems close enough.
So basically this recalibration keeps existing integer warp speeds as they are, but makes higher warp speeds a whole lot easier to express.
Thoughts?
I know this was discussed by scientific advisor Andre Bormanis and he suggested that the scale was recalibrated to make Warp 15 equate to infinite velocity and that Warp 13 on the new scale equated to roughly Warp 9.95 on the old, but that doesn't really make sense to me.
First of all, I can't think of any sensible mathematical function that maps 13 to 9.95 and 15 to 10, especially if we want to (as we presumably do) map 1 to 1 so that Warp 1 is still c. Secondly, throwing out the 9.95 figure, if you are going to simply stretch the scale so as to still have a Warp 10-like "infinite barrier" somewhere on the scale, the only obvious thing to do would be just to multiply the whole thing and scale it evenly.
The problem is that this would result in relatively slow and conventional warp speeds suddenly being much higher. Warp 13 divided by the rescaling coefficient that moves 10 to 15 (so, 1.5) is 8 2/3. Why exactly anyone would want to go at exactly warp 8 2/3 so often that it merits being given an integer designation is anyone's guess.
In fact, we know that integer warp factors on the TNG scale are more energy efficient than fractional ones, so such a scale would be tremendously inconvenient, as 5 out of the 9 usable integer warp factors would now end in .5 - and what's even worse is that old Warp 1 is new Warp 1.5, meaning that Warp 1 to 1.5 describes sub-light speeds. That's...just dumb.
So, my solution: Don't rescale Warp 1-8.99999..., but adopt a definition where for Warp >= 9, the new warp factor is defined as 9 - log_10(10-X), where X is the old warp factor.
Sounds complicated and random, but what this means is that Warp 9.9 -> Warp 10, Warp 9.99 -> Warp 11, Warp 9.999 -> Warp 12 and so on. This seems like a sensible change - as maximum speeds kept increasing, Captains would grow tired of saying things like "Warp 9.999". It also removes any kind of infinite barrier, which just isn't helpful (so now you can have arbitrarily large warp speeds; a new warp factor of 50 would simply be a 9 followed by 51 decimal 9s in the old system.
Crucially, no warp factor would be more complicated than it used to be. Granted, technically the Intrepid max cruise speed of 9.975 would now be 10.60205999132796..., but obviously this could just be stated as 10.6 without much of an impact; calculating 10.6 in reverse gives us 9.97488..., which is clearly close enough. Similarly for Intrepid's max rated speed, 9.992, we can state this as 11.1, which reverse-calculates to 9.9920567..., which again seems close enough.
So basically this recalibration keeps existing integer warp speeds as they are, but makes higher warp speeds a whole lot easier to express.
Thoughts?
