I've come back to this idea of "differences" from many angles...
From images: information _is _ the differences between pixels
From opinions: my opinion alone is worthless, but a difference of opinions? now we've got something
From relationships, graphs, networks: edges are _differences_ between nodes. the edges are everything. nodes alone... are meaningless
From music: this one is a little easier to take at face value, you can't have a sound without a change (difference) over time. the speaker cone can only wobble...
Not sure about the absoluteness or correctness of this intuition, please criticize
For images, you need a reference pixel to get the color right. You can apply differences from there but you’re effectively working with absolutes because of that so it’s a meaningless distinction.
Any time an absolute reference point is assumed, all downstream calculations are effectively absolutes
I have a blue/black (or possibly white/gold) dress that says it's relative.
You can also ask a UI designer about "absolute" colors. One color needs to be different depending on the context it's in order to LOOK the same (it's size/thickness, background, what it's next to).
Suppose you have a reference pixel but don’t know its value. You don’t get the color right but there is plenty of other information there, right? Which pixel also probably limits the range of values since your highest and lowest values are probably within a certain range.
Or said another way, forces carry the structure of G-torsors! The terminology is way too pompous for such a simple concept, though. John Baez has a really clean writeup on them, accessible to anyone interested: https://math.ucr.edu/home/baez/torsors.html.
Heck, even differences are usually non-physical; it's their ratio that matters. I.e. choosing feet or meters doesn't change the physics; the same goes for energy. So we have two free parameters: choice of origin and choice of units.
Baez only hints at this near the end of the above article, but we can actually fuse translations and scalings into a single group of elements that are combined translation + scale operations, an affine group. It turns out that this combined group is just a certain combination (semidirect product[0]) of the translation and scaling groups, as one would hope.
And once we are thinking about affine groups, it's natural to consider more complicated ones. Most famous is probably the Poincaré group[1]. That is, points in space are physically described by G-torsors over the Poincaré group!
Excellent comment. The only thing I can add is the obligatory "why stop there?", Poincaré true to form gives a beautiful description of the symmetries of flat spacetime, but we know that spacetime is only locally flat, the measurement symmetries at large scale are carried by the (unfortunately named) Killing fields[0].
there most certainly are absolutes. theres an absolute maximum amount of distance a massive object can travel through spacetime. theres an absolute maximum amount of mass/energy that can exist within a volume of space before an event horizon forms. universal constants which have dimensions are more or less measurable absolutes. differences maybe more apparent but that doesnt mean absolutes dont exist.
An absolute on the upper bound of velocity that a massless object can travel through space at maybe?
Although - I had it explained to me that the fabric of space was entering a black hole faster than light could travel, which is why light couldn't escape.
Which made me wonder - is light (the massless object) travelling, or is it space travelling and carrying things at different velocities.
Heh, i wonder what the mean free space between blackholes is?
Now, given that in quadrillions of quadrillions of years all black holes will evaporate and potentially even protons decay there could be a time in the universe where everything is mass less radiation.
I agree OP misspoke, but are we sure the time axis has no upper bound? Or that it doesn’t loop back round on itself? Or that it even exists meaningfully as an axis?
there's something about this quote that i really like, going to have to use it out of context on people