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The mathematics depend heavily on physics. If physics outside of our universe differ - the math wouldn't add up. I can make 2 + 2 = 5 in a simulation. That doe

by Nadya 10y ago

The mathematics depend heavily on physics. If physics outside of our universe differ - the math wouldn't add up. I can make 2 + 2 = 5 in a simulation. That doesn't mean 2 + 2 = 5 outside of the simulation.

ajuc 10y ago
> I can make 2 + 2 = 5 in a simulation I'm not sure you can. Yes you can make a chest with 2 apples contain 5 apples if you put 2 more, but it's impossible (IMHO) to make it consistent. How many apples do you have if you place 2 chests besides 2 other chests and put 1 apple in each? What if you repeat the process 2 times and then another 2 times? Also - when some things in physics aren't intuitive (QM for example, but even adding velocities in relativity) we don't think math is wrong - we think math doesn't apply in that way to this particular phenomena.
- aswanson 10y ago
  Sure he can. He can overload the "=" or "+" operator and make them do whatever he wants in that domain. Taking it further, what if rules and logic, and by extension, math as we know it, is just a construct that is not applicable in the "real" universe. What if, in that "real" space, 7+7=5, or mathematical operations are not possible. What if causality and time dont exist?
  - ajuc 10y ago
    You can change symbols all you want, but when life appears in your simulation they won't care. If they put 2 items and then another 2 items, and 4 items are there - for all they care 2+2=4. And if sometimes its 5 - they will do what we did with relativity when it turned out velocities doesn't add up like they "should". We haven't changed addition - we changed the equations used in physics. I guess you could hand-made an intelligent life that is designed never to discover the true math.
    - mcbits 10y ago
      If you put 2 male mice in a box with 2 female mice and wait a while, you may find 5 or more mice in the box. Or if you put 2 clouds in a box and later put 2 clouds in the box, you probably won't find 4 or 5 clouds in the box. The act of putting things in boxes (after first perceiving and classifying them as discrete entities) and the abstract notion of addition are only as related as you need them to be for a given purpose.
      - ajuc 10y ago
        > The act of putting things in boxes (after first perceiving and classifying them as discrete entities) and the abstract notion of addition are only as related as you need them to be for a given purpose. Yes. That was my point. How would you change the abstract notion invented by creatures in your simulation if not by changing reality to shape their abstractions? And how do you change enough instances that their math develops in such way that 2+2=5? I think our basic math (logic, set theory, integer math) with some exceptions (choice theorem) is the only useful consistent basic math there is.
    - aswanson 10y ago
      The point I was trying to raise, though, is what if the concept of "adding two things" has no basis in the "real reality". I know its hard to grasp...but imagine a reality where there is no "+" or "-" operation.
      - eastindex 10y ago
        But "+" and "-" operations are inherently time bound.
        aswanson 10y ago
        why? and what is "time?"
        eastindex 10y ago
mcherm 10y ago
> The mathematics depend heavily on physics. I do not believe that to be true. While physics is heavily dependent on math, the reverse is not true. > I can make 2 + 2 = 5 in a simulation. No, I am fairly confident that you absolutely can not. You can make a simulation where putting 2 oranges in a box and adding two more oranges results in 5 oranges in the box (rather like putting together certain nucleons together into a nucleus results in a mass different than the sum of their individual masses). But in that simulation it would be a peculiar property of oranges, not a property of mathematics -- just as we don't claim addition is invalidated by the behavior of nucleon masses.
- aswanson 10y ago
  Suppose a "reality" where every observation of "addition" yielded unpredictable results. Would your confidence still be warranted?
  - dasil003 10y ago
    There's no direct observation of addition, it's just a symbolic construct to model something we observe. I suppose a reality where such a model never made sense is possible, but it would be a very foreign environment that is completely outside the scope of our intuitive understanding. If it made sense only for a subset of the cases it does in our current understanding, then that would be the context in which it was discovered/understood.
  - baq 10y ago
    Addition is defined in such a way that the universe it's performed in doesn't matter (in fact, no universe is required at all), which is true for most if not all of formal mathematics. See set theory 101 for the very beginning on how's that possible.

by Nadya 10y ago

ajuc 10y ago

> I can make 2 + 2 = 5 in a simulation I'm not sure you can. Yes you can make a chest with 2 apples contain 5 apples if you put 2 more, but it's impossible (IMHO) to make it consistent. How many apples do you have if you place 2 chests besides 2 other chests and put 1 apple in each? What if you repeat the process 2 times and then another 2 times? Also - when some things in physics aren't intuitive (QM for example, but even adding velocities in relativity) we don't think math is wrong - we think math doesn't apply in that way to this particular phenomena.

aswanson 10y ago
Sure he can. He can overload the "=" or "+" operator and make them do whatever he wants in that domain. Taking it further, what if rules and logic, and by extension, math as we know it, is just a construct that is not applicable in the "real" universe. What if, in that "real" space, 7+7=5, or mathematical operations are not possible. What if causality and time dont exist?
- ajuc 10y ago
  You can change symbols all you want, but when life appears in your simulation they won't care. If they put 2 items and then another 2 items, and 4 items are there - for all they care 2+2=4. And if sometimes its 5 - they will do what we did with relativity when it turned out velocities doesn't add up like they "should". We haven't changed addition - we changed the equations used in physics. I guess you could hand-made an intelligent life that is designed never to discover the true math.
  - mcbits 10y ago
    If you put 2 male mice in a box with 2 female mice and wait a while, you may find 5 or more mice in the box. Or if you put 2 clouds in a box and later put 2 clouds in the box, you probably won't find 4 or 5 clouds in the box. The act of putting things in boxes (after first perceiving and classifying them as discrete entities) and the abstract notion of addition are only as related as you need them to be for a given purpose.
    - ajuc 10y ago
      > The act of putting things in boxes (after first perceiving and classifying them as discrete entities) and the abstract notion of addition are only as related as you need them to be for a given purpose. Yes. That was my point. How would you change the abstract notion invented by creatures in your simulation if not by changing reality to shape their abstractions? And how do you change enough instances that their math develops in such way that 2+2=5? I think our basic math (logic, set theory, integer math) with some exceptions (choice theorem) is the only useful consistent basic math there is.
  - aswanson 10y ago
    The point I was trying to raise, though, is what if the concept of "adding two things" has no basis in the "real reality". I know its hard to grasp...but imagine a reality where there is no "+" or "-" operation.
    - eastindex 10y ago
      But "+" and "-" operations are inherently time bound.
      - aswanson 10y ago
        why? and what is "time?"
        eastindex 10y ago

mcherm 10y ago

> The mathematics depend heavily on physics. I do not believe that to be true. While physics is heavily dependent on math, the reverse is not true. > I can make 2 + 2 = 5 in a simulation. No, I am fairly confident that you absolutely can not. You can make a simulation where putting 2 oranges in a box and adding two more oranges results in 5 oranges in the box (rather like putting together certain nucleons together into a nucleus results in a mass different than the sum of their individual masses). But in that simulation it would be a peculiar property of oranges, not a property of mathematics -- just as we don't claim addition is invalidated by the behavior of nucleon masses.

aswanson 10y ago
Suppose a "reality" where every observation of "addition" yielded unpredictable results. Would your confidence still be warranted?
- dasil003 10y ago
  There's no direct observation of addition, it's just a symbolic construct to model something we observe. I suppose a reality where such a model never made sense is possible, but it would be a very foreign environment that is completely outside the scope of our intuitive understanding. If it made sense only for a subset of the cases it does in our current understanding, then that would be the context in which it was discovered/understood.
- baq 10y ago
  Addition is defined in such a way that the universe it's performed in doesn't matter (in fact, no universe is required at all), which is true for most if not all of formal mathematics. See set theory 101 for the very beginning on how's that possible.