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1+1=2. 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

1+1=2. 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.

codegladiator 6y ago
1 drop of water + 1 drop of water = 1 drop of water 1 river + 1 river = 1 river 1 stick - 1/2 stick = 2 stick
- TeMPOraL 6y ago
  Now you're cheating, because + and - no longer mean "addition" and "subtraction", but merging and... well, weird division - the last example would be better as 1 stick / 2 = 2 sticks. 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.
  - codegladiator 6y ago
    Sure we can measure something else to keep a track of whats happening and fit our definitions, but the math remain true, isn't it? It is still 1 river and 1 drop and 2 sticks.
    - Tagbert 6y ago
      But 1 river is not a defined measurement. It is has a range of meanings whereas 2 is defined. 2 = 2 is true 2 ≠ 2 is false But 1 river = 1 river is true 1 river ≠ 1 river is also true under some circumstances
      - dfischer 6y ago
        It’s one of something. When one of something and one of another thing are observed it’s expressed as 1 and 1 so two rivers become one they represent a quantity of observation. Then 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.
        TeMPOraL 6y ago
        > It’s one of something. When one of something and one of another thing are observed it’s expressed as 1 and 1 so two rivers become one they represent a quantity of observation. 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.
        dfischer 6y ago
        I don’t think that you’d be able to communicate the observation of units in a way that’s consistent as a written form of symbology in the rule space of mathematics and the language space used to communicate the mathematics and observation of reality around oneself which leads to relativity. 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.
      - codegladiator 6y ago
  - dfischer 6y ago
    You added additional axioms that require a quantity. Not all things exist as quantities with properties of addition, multiplication, division, or subtraction. Various debates can be had that any quantity is largely an arbitrarily defined border. 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.
- proc0 6y ago
  1 does not equal "1 of <something>", the latter is a concrete example only (and as mentioned the quantity error, you would have 2 drops of water if the volume of 1 drop stays consistent). 1 is an abstract concept applied to many things that share this "singleton property".
  - codegladiator 6y ago
    If you think about it really hard (since we are at abstract) "1 of <something>" is never equal to any other "1 of <something>" 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.
    - proc0 6y ago
      I disagree, computation has equality, unless you think computer files are not real. Two computations can be equal, and as far as we know we are leveraging this property of the universe. Electrons move and produce patterns which have equality and gives rise to computer state and thus equality of values, not to mention electrons themselves must be indistinguishable given they behave the same.
willis936 6y ago
Do you see addition in the universe, or only in an observer taking account of things in the universe?
- dfischer 6y ago
  I like this question. Addition is closer to experience sounds interacting. For example one person playing a note then two notes at once or maybe two instruments start interacting. Either way, it’s our experience of some dynamics based on observation.
- JohnStrangeII 6y ago
  The observers are part of the universe, too, as is my pocket calculator.
  - willis936 6y ago
    Turtles all the way down. I think we should try to nail down answers on simple cases before trying to unravel apparent paradoxes.
dfischer 6y ago
Yeah except it’s not that easy. 1+1=2 but could 1+1=3 too? Yes, even 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.
- aliceryhl 6y ago
  It is that easy. If you got the result 1+1=3, then you changed the meaning of either 1, 3, + or =.
  - dfischer 6y ago
    In that raw written symbolic form, perhaps. However the nuances exist where the symbols don’t apply but the language is still used. You can observe effects/interactions and say one thing added with another thing makes three things. There is not two things, there’s three things happening now. Also one can be added to another and make one. The “adult” costume for two kids hiding in adult clothing. Two became one interacting as three as a system represented by one. The values are relative. There’s a danger in having such zoomed in views. On one hand we must know when to zoom in, and on the other know how to capture vagueness.
    - aliceryhl 6y ago
      That isn't really about mathematics anymore. With the meanings of the words/symbols that koheripbal intended, 1+1=2 is definitely true, and similarly, with the meaning koheripbal intended, 1+1=3 is definitely false. If we can't agree on what the words mean, we can't really have a conversation.
      - dfischer 6y ago
j7ake 6y ago
For error correcting codes (Hamming), you make 1+1=0 as a starting point. 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.

codegladiator 6y ago

1 drop of water + 1 drop of water = 1 drop of water 1 river + 1 river = 1 river 1 stick - 1/2 stick = 2 stick

TeMPOraL 6y ago
Now you're cheating, because + and - no longer mean "addition" and "subtraction", but merging and... well, weird division - the last example would be better as 1 stick / 2 = 2 sticks. 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.
- codegladiator 6y ago
  Sure we can measure something else to keep a track of whats happening and fit our definitions, but the math remain true, isn't it? It is still 1 river and 1 drop and 2 sticks.
  - Tagbert 6y ago
    But 1 river is not a defined measurement. It is has a range of meanings whereas 2 is defined. 2 = 2 is true 2 ≠ 2 is false But 1 river = 1 river is true 1 river ≠ 1 river is also true under some circumstances
    - dfischer 6y ago
      It’s one of something. When one of something and one of another thing are observed it’s expressed as 1 and 1 so two rivers become one they represent a quantity of observation. Then 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.
      - TeMPOraL 6y ago
        > It’s one of something. When one of something and one of another thing are observed it’s expressed as 1 and 1 so two rivers become one they represent a quantity of observation. 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.
        dfischer 6y ago
        I don’t think that you’d be able to communicate the observation of units in a way that’s consistent as a written form of symbology in the rule space of mathematics and the language space used to communicate the mathematics and observation of reality around oneself which leads to relativity. 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.
    - codegladiator 6y ago
- dfischer 6y ago
  You added additional axioms that require a quantity. Not all things exist as quantities with properties of addition, multiplication, division, or subtraction. Various debates can be had that any quantity is largely an arbitrarily defined border. 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.
proc0 6y ago
1 does not equal "1 of <something>", the latter is a concrete example only (and as mentioned the quantity error, you would have 2 drops of water if the volume of 1 drop stays consistent). 1 is an abstract concept applied to many things that share this "singleton property".
- codegladiator 6y ago
  If you think about it really hard (since we are at abstract) "1 of <something>" is never equal to any other "1 of <something>" 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.
  - proc0 6y ago
    I disagree, computation has equality, unless you think computer files are not real. Two computations can be equal, and as far as we know we are leveraging this property of the universe. Electrons move and produce patterns which have equality and gives rise to computer state and thus equality of values, not to mention electrons themselves must be indistinguishable given they behave the same.

willis936 6y ago

Do you see addition in the universe, or only in an observer taking account of things in the universe?

dfischer 6y ago
I like this question. Addition is closer to experience sounds interacting. For example one person playing a note then two notes at once or maybe two instruments start interacting. Either way, it’s our experience of some dynamics based on observation.
JohnStrangeII 6y ago
The observers are part of the universe, too, as is my pocket calculator.
- willis936 6y ago
  Turtles all the way down. I think we should try to nail down answers on simple cases before trying to unravel apparent paradoxes.

dfischer 6y ago

Yeah except it’s not that easy. 1+1=2 but could 1+1=3 too? Yes, even 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.

aliceryhl 6y ago
It is that easy. If you got the result 1+1=3, then you changed the meaning of either 1, 3, + or =.
- dfischer 6y ago
  In that raw written symbolic form, perhaps. However the nuances exist where the symbols don’t apply but the language is still used. You can observe effects/interactions and say one thing added with another thing makes three things. There is not two things, there’s three things happening now. Also one can be added to another and make one. The “adult” costume for two kids hiding in adult clothing. Two became one interacting as three as a system represented by one. The values are relative. There’s a danger in having such zoomed in views. On one hand we must know when to zoom in, and on the other know how to capture vagueness.
  - aliceryhl 6y ago
    That isn't really about mathematics anymore. With the meanings of the words/symbols that koheripbal intended, 1+1=2 is definitely true, and similarly, with the meaning koheripbal intended, 1+1=3 is definitely false. If we can't agree on what the words mean, we can't really have a conversation.
    - dfischer 6y ago

j7ake 6y ago

For error correcting codes (Hamming), you make 1+1=0 as a starting point. 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.