brilliant introduction to the integrity of spherical thinking as it relates to the areal accounting by triangling. i am looking forward to what may follow.
may i ask: why wouldn't one just replace the "square" in a "squared area" with the triangle, too? so two to the second power, two triangled, is four.
You are absolutely right. In this case, we are simply using the common usage of the term 'square' because people have already been well-trained in that concept. It also highlights the fact that language is often the least expressive of our three ways of communicating: visual, verbal, and mathematical. Of the three, a visual representation will always provide a higher level of fidelity as to what is actually going on! We do our very best to use commonly defined terms wherever possible, but I do believe that, in time, the language will get an upgrade. I have often said 'n^Δ' numbers, just as you posit here. Many of my notes use the Triangle just as you've described, but again, Delta in physics is already taken to mean the change of some variable, like Δ time, for instance. As we get more comfortable with the basic foundations, we will indeed develop other terms and new notations. I, too, look forward to watching your videos and posting more about these ideas. Luminal Mind 2.0 will be coming at you in 2025 in a big way. Your reflections are appreciated.
brilliant introduction to the integrity of spherical thinking as it relates to the areal accounting by triangling. i am looking forward to what may follow.
may i ask: why wouldn't one just replace the "square" in a "squared area" with the triangle, too? so two to the second power, two triangled, is four.
and on a related note, sphere are a few more reasons why a triangular paradigmshift may be very reasonable: https://youtu.be/AZF8zg9xTtA?si=H1xSawwAcXj9Ik2z
peace
struppi
You are absolutely right. In this case, we are simply using the common usage of the term 'square' because people have already been well-trained in that concept. It also highlights the fact that language is often the least expressive of our three ways of communicating: visual, verbal, and mathematical. Of the three, a visual representation will always provide a higher level of fidelity as to what is actually going on! We do our very best to use commonly defined terms wherever possible, but I do believe that, in time, the language will get an upgrade. I have often said 'n^Δ' numbers, just as you posit here. Many of my notes use the Triangle just as you've described, but again, Delta in physics is already taken to mean the change of some variable, like Δ time, for instance. As we get more comfortable with the basic foundations, we will indeed develop other terms and new notations. I, too, look forward to watching your videos and posting more about these ideas. Luminal Mind 2.0 will be coming at you in 2025 in a big way. Your reflections are appreciated.