That isn't an approximation. It is a core principle, not just of math, but of the laws of our universe. It is so core, that it's impossible to imagine a universe without it.
or maybe it is an approximation. Maybe there is some essence of the universe that gives is additiveness - and maybe if you could see closer/bigger/faster, maybe that too would break down.
We should take nothing for granted.
1 river + 1 river = 1 river
1 stick - 1/2 stick = 2 stick
But try the first two with the following substitutions:
"drop of water" => "volume of a drop of water"
"river" => "flow rate of a river"
And you're back to addition and correct answers.
2 = 2 is true
2 ≠ 2 is false
1 river = 1 river is true
1 river ≠ 1 river is also true under some circumstancesThen as 1 and 1 totaling two rivers they come together then exist as 1.
Representation is relative on an arbitrary border of quantity. The rules leak for any rule that exists.
One father and one mother have a kid. One and one make another one totaling three.
• and • make •.
Usually a person will substitute 1 for the observation of a “thing” so • will be father, and another • mother +1+1=+1
One unit and another one unit makes a third unit. Yet one unit plus another unit is two units.
Not really. If I look at a map and see the Amazon river, and then see the Nile, Amazon + Nile ≠ 1 river. They're still two separate rivers. Adding rivers means merging sets of rivers under consideration, not merging actual rivers.
All you're doing now is playing with different operations that are not what the symbol "+" stands for.
All definitions are nuanced and subjective based on path of least resistance heuristics.
It’s often miscommunication is happening because expected results are misaligned despite using same rules/language.
It’s quite complex. It’s really interesting but also leads to poor communication. Do we try to embed in our cultures to align on expectation and values to improve this or always doomed to potentially fatal inconsistencies? I guess the dynamics of any rules naturally incentivize behavior whether it’s negative or positive.
Math is our reality, and not a universal reality/law/principal (while science conservation of energy/matter is universal). There are no addition/subtraction happening in the universe.
Addition is not conservation. But that's how we see it.
The point mostly being, any symbolic representation is only that. It is never universal. And to think it’s an objective representation of anything is serious error.
1 is an abstract concept applied to many things that share this "singleton property".
Nothing is equal in universe. Everything is its own thing. 1 drop of water != another 1 drop of water. Two different entities.
Only in math we have 1=1 or 1+1=2. And math doesn't work for universe, it works for science.
There’s different ways to count based on the dynamics of the system you’re interacting with.
One interaction interacting with another interaction can create a third interaction causing the system to interact as as pieces totaling 3 that came from a 1 and a 1.
1+1=3.
Also, my brain may be split into two spheres however is it better to reason about it as 1+1=2 me’s or 1^2? Funny joke if I use i^2 then I’m just imaginary. Hah.
Ultimately anything we describe as “is” isn’t anything other than agreement of some type of axiom which requires consciousness / imagination.
Lots to ponder. Ha.
If we can't agree on what the words mean, we can't really have a conversation.
More or less consistent enough is certainty.
Nuances exist, as well as unknown side effects.
When has any definition you thought were fixed expanded?
It’s a weird space.
When I figure out I have misunderstood something, it's not the definition that changes. It's my map of it. The map is not the territory.
Setting 1+1=2 creates patterns that often useful in real life (e.g. counting discrete objects). But it's by no means some universal law.
In this case setting 1+1=0 creates other patterns useful for error correcting codes.