Why 1+1=2 is beautiful
1+1=2
Yes. And?
I bet this was one of the first equations you wrote down. Without understanding it much, we would scribble it down on a piece of paper, and it would usually be followed by 1+2=3 or something of the sort. But there's much more to this seemingly simple equation than we could care to think when we were four.
Firstly, what is '1'? My philosophy teacher defined it as the existence of a single quantity.
Okay, so what is 'quantity'? Quantity means 'number', since a 'number' is just a name we assign to an arithmetical quantity.
So...what is 'number'?
This is the ultimate brick wall humanity hits. You see, we invented the concept of number as a way to describe the quantities we perceive, and somehow the universe works perfectly according to this system we invented.
Take 𝜋, for example. Most of us know that it is approximately 3.14, that it is irrational and (most importantly), it is the ratio between the circumference (length) of any circle and it's diameter. It works in all circles of the universe.
We could also take the formula F=ma. This formula gives us the resultant force acting on any object, and it works in all of the universe's objects.
Countless examples of constants, equations and theorems can be given, and 𝜋 and F=ma are just two of those that show that humans invented a system of 'numbers' and somehow the entire universe works according to the system; in a flawlessly ordered symphony according to various laws and quantities. So we invented a system we don't understand...but then proceeded to discover it existed in the universe in the first place. How strangely beautiful.
We ourselves do not have a definition for 'number', but we are able to realise space and time work according to this mysterious concept: 'number'.
A common misconception is to define number by it's own name, saying it's 'an arithmetical value expressed by a certain name'. This, however, is an error, because we simply call numbers a certain name by convention.
'1' does not have to be called 'one'. In fact, I'm now going to start my own number system and call it 'Table'.
'2' does not have to be called 'two'. From now on, I'll call it 'Jabble'.
Following this logic, I can still say 'Table'+'Table'='Jabble', because it was not the name that was important but the number/quantity it represents that was important.
If suddenly we re-wrote the rules and our way of thinking and now said 1+1 no longer =2 and form now on 1+1=3, it would lead to the breakdown of all science and mathematics as we know it.
Simple, unprovable equations like 1+1=2 are the bedrock of our understanding, despite the ironic fact that we ourselves do not understand what a 'number' is.
So next time you write down '1+1=2', just know this equation is not as easy or simple as you think; it is both the foundation of knowledge and also something we may never fully understand.
Yes. And?
I bet this was one of the first equations you wrote down. Without understanding it much, we would scribble it down on a piece of paper, and it would usually be followed by 1+2=3 or something of the sort. But there's much more to this seemingly simple equation than we could care to think when we were four.
Firstly, what is '1'? My philosophy teacher defined it as the existence of a single quantity.
Okay, so what is 'quantity'? Quantity means 'number', since a 'number' is just a name we assign to an arithmetical quantity.
So...what is 'number'?
This is the ultimate brick wall humanity hits. You see, we invented the concept of number as a way to describe the quantities we perceive, and somehow the universe works perfectly according to this system we invented.
Take 𝜋, for example. Most of us know that it is approximately 3.14, that it is irrational and (most importantly), it is the ratio between the circumference (length) of any circle and it's diameter. It works in all circles of the universe.
We could also take the formula F=ma. This formula gives us the resultant force acting on any object, and it works in all of the universe's objects.
Countless examples of constants, equations and theorems can be given, and 𝜋 and F=ma are just two of those that show that humans invented a system of 'numbers' and somehow the entire universe works according to the system; in a flawlessly ordered symphony according to various laws and quantities. So we invented a system we don't understand...but then proceeded to discover it existed in the universe in the first place. How strangely beautiful.
We ourselves do not have a definition for 'number', but we are able to realise space and time work according to this mysterious concept: 'number'.
A common misconception is to define number by it's own name, saying it's 'an arithmetical value expressed by a certain name'. This, however, is an error, because we simply call numbers a certain name by convention.
'1' does not have to be called 'one'. In fact, I'm now going to start my own number system and call it 'Table'.
'2' does not have to be called 'two'. From now on, I'll call it 'Jabble'.
Following this logic, I can still say 'Table'+'Table'='Jabble', because it was not the name that was important but the number/quantity it represents that was important.
If suddenly we re-wrote the rules and our way of thinking and now said 1+1 no longer =2 and form now on 1+1=3, it would lead to the breakdown of all science and mathematics as we know it.
Simple, unprovable equations like 1+1=2 are the bedrock of our understanding, despite the ironic fact that we ourselves do not understand what a 'number' is.
So next time you write down '1+1=2', just know this equation is not as easy or simple as you think; it is both the foundation of knowledge and also something we may never fully understand.
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