I didn't mean to imply "therefore". I just mean that if you can come up with the idea of numbers out of the nothingness, mathematics kind of just falls out of it. 1 + 1 = 2 because logics demands it. I wonder though if you could come up with a "fuzzy number system" that would jack that all up. I dunno. Hmm... yeah that works for me I think. It's all in how you play it. In your case, when 1+1=2.. is that math? In a sense it's just counting, but it's once removed from counting in that is an observation about counting. Hmmm.
If mathematics is perspective-dependent, as you write, then the laws of physics are also -- regarding that you can't even formulate them without using math. To take a simple example: s=1/2a*t^2. It would be impossible to describe the relationship between the time passed and the distance covered in even the most elementary forms of motions without using equations, which is to say, math. Definitions are linguistic entities existing exclusively in the mind. I agree with this. But it doesn't follow that the thing defined is also of linguistic nature, or exists in the mind. Why should that follow? Besides, our interpretation of the input had better be in accordance with the reality around us, otherwise we would have been eliminated from the tree of evolution very early. Physics has turned the relevant properties of the environment into precise statements. If its definitions don't "hit" reality in a very fundamental sense, its power to manipulate nature is absolutely incomprehensible.
/If mathematics is perspective-dependent, as you write, then the laws of physics are also -- regarding that you can't even formulate them without using math. nature doesn't need man to put laws on it. it just works. /To take a simple example: /s=1/2a*t^2. It would be impossible to describe the relationship between the time passed and the distance covered in even the most elementary forms of motions without using equations, which is to say, math. Why is it impossible without the math? I could use english to describe it with less accuracy. You think your equation is an absolute truth? The math was developed to describe something that works perfectly fine without the math. It's just if you want to understand it or give it meaning that numbers and such become important... and thus perspective become important. Do you think that s=1/2*t^2 is the only way to describe the relationship you're talking about? Why does it necessarily need to be described? I certainly appreciate that it is, but don't see it as necessary, nor wholly accurate. Your equation is an approximation. Stuff just exists. We use numbers and such because we want to understand our environments and numbers are allow a high degree of accuracy when doing so. I could say "hey build me a cube" or i can say "hey build me a 3'x3' cube with +/- 1% on all measurements. Either way I get a cube (unless you're a slacker :bugeye: ) but math sure helps me say how I need the cube to be. /Definitions are linguistic entities existing exclusively in the mind. I agree with this. But it doesn't follow that the thing defined is also of linguistic nature, or exists in the mind. Why should that follow? because you are describing something that already exists... you are not making up gravity. you are using the language of mathematics to attempt to describe it. /Besides, our interpretation of the input had better be in accordance with the reality around us, otherwise we would have been eliminated from the tree of evolution very early. Brother, I'm with you there. /Physics has turned the relevant properties of the environment into precise statements. If its definitions don't "hit" reality in a very fundamental sense, its power to manipulate nature is absolutely incomprehensible. Please don't take my assertions as disrespectful of the power of physics. I've been an engineering student, that's enough to give one great respect I'd think! Please Register or Log in to view the hidden image! I wholly agree that math is beautiful, but you must see that it is a language.. a very precise one, which is why it is favored when describing physical systems. Oh, and just to clear one thing up: If it's power to manipulate nature was incomprehensible, it wouldn't be very usefull would it?? Please Register or Log in to view the hidden image!
I'm sure its been answered, but I will repeat it anyway because I don't have enough time to read through. 1+1=2 because we say it does. It's a statement, NOT a truth, not a product of logic. It is a product of expedience. All that matters is that every expedient used to form the paradigm of perception stays consistent. SO basically...1+1 doesnt have to equal two. In fact....such silly entities don't have any more significance than what our minds have been conditioned to believe they should.
wow I just cant believe you guys got seven pages of rabble (or truely intelligent explanations) on such a trivial concept such as 1+1=2. *standing ovation* *sits down*
are you joking, have you ever been to a forum before? They're exclusively made up of trivial discussions, that's what they're for.
Triviality? I just like to question my assumptions. Yes has a point you know. 1 + 1 = 2, is context dependent.
Cool thread! For those who are interested in the idea there was an excellent short story published by Ted Chiang in the Story of My Life and Others( a collection of his fiction). In it a mathematician was able to prove the very types of points made here in the sense that 1=0. She later went insane. More broadly, 1 + 1 = 2 needs IMO certain concepts to be proveable. First, the concept of '1', second the concept of '+", third the concept of another '1' and lastly the concept of '=' Once we establish these concepts we can infer the existence of 1 + 1 = 2 as valid in the context of these definitions. Cheers!
