Is 1 plus 1 equal to 2?
By Jack Don McLovin - Multidiscplinarian -- Jack Has Been writing pages a day for the past 10 years under varying anonymous accounts, always drifting from place to place trying to gain popularity in a group, and start again, and repeat.
If addition were linear, then maybe. If everything was in decimal, then sure.
But the thing with math is it's different depending on which system you follow.
Asking a quantum physicist to explain and they'll give you the answer they learnt.
But asking a mathematician who always challenges the authoritative narrative within the cultural narrative. This is where the fruit gets added to the punch. If you have 1 sheep in a yard and add another sheep to the yard, you might think you only have two sheep. But if one is male and the other female (assuming binary gender), then (assuming it takes time to add a sheep to the yard) you could have 3 sheep, or two sheep and a lamb. This is how the story goes for non-linear addition. And all addition is non-linear when you use units of some real kind. And addition must be linear in order for the rest of mathematics to work.
Then, in computer science we look at the difference between decimal, hexadecimal, octal, and binary, amongst others. And different bit size numbers. Ultimately there's a limit to real calculations.
And further, even the word calculation comes from calculus where we assume the distance between curved lines on an infinitesimal size zoom is itself linear (curves are made of straight lines), and yet we can repeat the process infinitely with further scales of zooming, in which case you can't measure anything, even the smallest circle would have infinite area and surface area.
It's a little ridiculous, but the idea of mathematics isn't to give straight answers to crooked questions, it's how we can show our prowess as mathematicians. Many ideas start in mathematics and then appear elsewhere as physics or dynamics or statics or mechanics.
You might think it's ridiculous to justify how mathematics is broken as a mathematician with mathematics, but this is all assuming that the addition is linear, and we can still break it up.
But my favourite punch of it is that in a different script or culture or font or language the meaning behind the mathematics changes. And meaning is just the effect caused by affect. If comic sans makes you feel different to times new roman, then it changes the effect of the language. And how do you describe that when the numerical script is made from it. And what about in say Mandorin or Hebrew where the numbers have different meanings, some are lucky some are unlucky. But that changes culture to culture, and similarly the effect of linear addition mathematics does also. Nothing is constant. Even nothing changes.
And this is just the beginning of the conversation on this topic.
The easiest one to challenge is that of money. If you buy two burgers is it one burger plus one burger in cost? Or is it a meal deal? The real one that no one denies is that of speed and time, the higher your speed the more dilated your time. They call this the relativity of simultaneity, but this applies to the micro scale for vibrations too, if your eyes are vibrating then technically each eye is in a different point in time. 1+1 never equals two, except on paper, it always does. Even the tax man will agree that 50k income in a year plus another 50k income is not 100k. If you think it DOES equal 2, then the onus is on you to argue with the tax man, not on me to prove you wrong.
Examples where things are assumed to be linearly additive include money (higher income is taxed higher, and larger money doesn't always mean equal payments for example with 1 person per purchase goods), fruits (more bananas ripen/go mouldy faster), water (deeper water tanks increase in pressure according to depth as well as volume). You see everything we count depends on the units we count with, and when we count with units, they are never linearly additive.
