It appears that all of the good ideas I’ve had in the past will find themselves back into my theory, even if I try to get rid of them. This is what happened again to me with bicones, even though my last post on them was written two months ago.
The reason for me scrapping the bicones for two months was that I got stuck with them, so I started looking more at vectors and reflections. Cones seemed to be too abstract. However, now that I have my reflection model pretty much ready, something interesting happened: a bicone emerged from the folding model without me trying to actively insert it there. Only this time, when inserted into the folded model, the bicone folded as well. At first, I was going to say something fancy, but then decided to let the model speak for itself. So, I tried to make the model as accurate as possible, but then something really odd happened: the model ‘self-corrected’ itself. I had worked under the assumption that any flyby path along (or more precisely through) the unit sphere of reflection should fly through the center of a circular cutoff of the unit sphere. But this isn’t what the model said.
The model shows quite unequivocally that the flyby path has a tilt. It’s quite hard to explain what this means, as I’ve just realized it from the model myself. Perhaps the best we to explain this is just to show the folding model with the bicone:
There are a lot of things going on in this model, and much of it is things I’ve only had a couple of hours to ponder upon myself. You might wonder how these things would reveal themselves to me. Didn’t I invent them? Well yes and no. It’s all to do with the initial assumption of a spherical cow, which allowed me to begin somewhere. But in correcting the false assumptions in the initial model needs to be done one step at a time. And usually, you only observe new errors once you’ve corrected the old ones.
While all of this seems like a protracted Zeno’s paradox which has lasted for five years, it also seems that there can’t be too many surprises waiting. But who knows, it might takes months longer to reach the final solutions for all that I know.
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