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Another bad way to check for non-coincidences is to use a value like g which changes depending on your location. Pi is the same everywhere in the universe. g

Another bad way to check for non-coincidences is to use a value like g which changes depending on your location. Pi is the same everywhere in the universe. g on Earth: 9.8 m/s² g on Earth's moon: 1.62 m/s² g on Mars: 3.71 m/s² g on Jupiter: 24.79 m/s² g on Pluto: 0.62 m/s² g on the Sun: 274 m/s² (Jupiter's estimate for g is at the cloud tops, and the Sun's is for the photosphere, as neither body has a solid surface.)

TheRealPomax 2y ago
Fun fact: pi is both the same, and not the same, in all of those places, too. Because geometry. If you consider pi to just be a convenient name for a fixed numerical constant based on a particular identity found in Euclidean space, then yes: by definition it's the same everywhere because pi is just an alias for a very specific number. And that sentence already tells us it's not really a "universal" constant: it's a mathematical constant so it's only constant given some very particular preconditions. In this case, it's only our trusty 3.1415etc given the precondition that we're working in Euclidean space. If someone is doing math based on non-Euclidean spaces they're probably not working with the same pi. In fact, rather than merely being a different value, the pi they're working with might not even be constant, even if in formulae it cancels out as if it were. As one of those "I got called by the principal because my kid talked back to the teacher, except my kid was right": draw a circle on a sphere. That circle has a curved diameter that is bigger than if you drew it on a flat sheet of paper. The ratio of the circle circumference to its diameter is less than 3.1415etc, so is that a different pi? You bet it is: that's the pi associated with that particular non-Euclidean, closed 2D plane. So is pi the same everywhere in the universe? Ehhhhhhhh it depends entirely on who's using it =D
- mr_mitm 2y ago
  In non-euclidean spaces, your definition of pi wouldn't even be a value. It's not well defined because the ratio of circumference to diameter of a circle is dependent on the size of the circle and the curvature inside the circle. It's probably true that it's only well defined in euclidean space. Your relaxed definition, which I have never seen before, is not very useful.
  - _a_a_a_ 2y ago
    I don't agree, I thought what he said was very interesting. It never occurred to me that pi might vary, and over a non-flat space I can see what they're saying. I think it's intrinsically interesting simply because it breaks one of my preconceptions, that pi is a constant. Talking about it being 'not very useful' just seems far too casually dismissive.
    - mr_mitm 2y ago
      Pi doesn't vary. The ratio of circumference to diameter of a circle may vary depending on the geometry. Clearly everyone means euclidean space unless specified otherwise. Any other interpretation will only lead to problems, which is why it's not useful. There is really no ambiguity about this in mathematics. Mathematicians still use the pi symbol as a constant when they compute the circumference of a circle in a given geometry as a function of the radius.
      - TheRealPomax 2y ago
        There is no "clearly" in Math. The fact that pi is a constant while at the same time not being "the same constant" in all spaces, and not even being "a single value, even if we alias it as the symbol pi" is what makes it a fun fact. Heaven forbid people learn something about math that extends beyond the obvious, how dare they!
        travisjungroth 2y ago
        > There is no "clearly" in Math. Sure there is. You don’t expect a paper to explain that the numbers are in decimal and not hexadecimal.
        TheRealPomax 2y ago
        I don't know which ones you read so I can't comment on that, but the ones I read most definitely specify which fields of math they apply to, and which axioms are assumed true before doing the work, because the math is meaningless without that? Papers on non-Euclidean spaces always call that out, because it changes which steps can be assumed safe in a proof, and which need a hell of a lot of motivation. And of course, that said: yeah, there are papers for proofs about things normally associated with decimal numbers that explicit call out that the numbers they're going to be using are actually in a different base, and you're just going to have to follow along. https://en.wikipedia.org/wiki/Conway_base_13_function https://en.wikipedia.org/wiki/Conway_base_13_function is probably the most famous example?
- travisjungroth 2y ago
  Just sounds like you’ve confused yourself. It’s like spinning in circles and acting like no one else knows which way is up. That isn’t a different pi. That’s a different ratio. Your hint is that there are ways to calculate pi besides the ratio of a circle’s circumference to its diameter. This constant folks have named pi shows up in situations besides Euclidean space.
  - TheRealPomax 2y ago
    Good job, you completely missed the point where I explain that pi, the constant, is a constant. And that "pi, if considered a ratio" (you know, that thing we did to originally discover pi) is not the same as "pi, the constant". Language skills matter in Math just as much as they do in regular discourse. Arguably moreso: how you define something determines what you can then do with it, and that applies to everything from whether "parallel lines can cross" (what?) to whether divergent series can be mapped to a single number (what??) to what value the circle circumference ratio is and whether you can call that pi (you can) and whether that makes sense (less so, but still yes in some cases).
    - travisjungroth 2y ago
      I haven’t missed your point. I’ve criticized it. You’re treating your non-consensus definition not as a hypothetical, but as a fact. Your comment started with “fun fact”.
    - matt-attack 2y ago
      FWIW I enjoyed your original comment :)
- Tainnor 2y ago
  Modern mathematics is more likely than not going to define pi as twice the unique zero of cos between 0 and 2, and cos can be defined via its power series or via the exp function (if you use complex numbers). None of this involves geometry whatsoever.
  - aydyn 2y ago
    What do you mean? Cos is an inherently geometric function.
    - IsTom 2y ago
      There are many equivalent definitions and many of them do not refer to geometry at all. If you don't want to go through cos you can always define pi as sqrt(6 * sum from 1 to inf 1/n^2).
      - TeMPOraL 2y ago
        You can also define it as `3.14159...` just because. Obviously, a π definition entirely divorced from geometry becomes irrelevant to it - instead, in geometry, you'd still use π = circumference/diameter, or π = whatever(cos), and those values would happen to be the same as a non-geometric π, but only if the geometric π is the one from Euclidean geometry.
        Tainnor 2y ago
        > You can also define it as `3.14159...` just because. That's not a rigorous definition, though, because it doesn't tell you what those "..." expand to.
    - Tainnor 2y ago
      To quote myself: > cos can be defined via its power series or via the exp function (if you use complex numbers).
      - aydyn 2y ago
stkdump 2y ago
My physics prof said g is actually a vector field. Because the acceleration has a direction and both magnitude and direction vary from point to point.
- deleted 2y ago
  [deleted]
- jvanderbot 2y ago
  Your physics Prof is correct of course, and so is GP. "Standard" values for g exist for these bodies, but it also varies everywhere.
- DistractionRect 2y ago
  This is correct, gravitational constants are a good approximation/simplification since the mass of solar bodies is usually orders of magnitude greater than the other bodies in the problem, and displacement over the course of the problem is usually orders of magnitude smaller than absolute distance between them. In other words, we assume spherical cows until that approximation no longer works.
- TheOtherHobbes 2y ago
  Absolutely true on astronomical scales. An unnecessary complication if you're dropping a brick out of a window.
  - wongarsu 2y ago
    It's funny how much of physics we do assuming a flat earth. If you did it "properly" you would calculate the orbit of the brick (assuming earth was a point mass), then find the intersection between that orbit and earth's surface. But for small speeds and distances you can just assume g points down as it would in a flat earth
    - dudinax 2y ago
      To do it properly you have to account for the gravitational pull of the building.
TheCleric 2y ago
I volunteer for the Mars mission as a weight loss tool.
- kevindamm 2y ago
  Surviving on Mars will probably involve some mass loss, too.
  - TeMPOraL 2y ago
    With the current technology, even getting on a rocket to Mars will involve some weight loss - the mass budget is tight, and each kilogram they can trim off the crew bodies is a kilogram that could be put towards fuel, life support, or scientific equipment.

TheRealPomax 2y ago

Fun fact: pi is both the same, and not the same, in all of those places, too. Because geometry. If you consider pi to just be a convenient name for a fixed numerical constant based on a particular identity found in Euclidean space, then yes: by definition it's the same everywhere because pi is just an alias for a very specific number. And that sentence already tells us it's not really a "universal" constant: it's a mathematical constant so it's only constant given some very particular preconditions. In this case, it's only our trusty 3.1415etc given the precondition that we're working in Euclidean space. If someone is doing math based on non-Euclidean spaces they're probably not working with the same pi. In fact, rather than merely being a different value, the pi they're working with might not even be constant, even if in formulae it cancels out as if it were. As one of those "I got called by the principal because my kid talked back to the teacher, except my kid was right": draw a circle on a sphere. That circle has a curved diameter that is bigger than if you drew it on a flat sheet of paper. The ratio of the circle circumference to its diameter is less than 3.1415etc, so is that a different pi? You bet it is: that's the pi associated with that particular non-Euclidean, closed 2D plane. So is pi the same everywhere in the universe? Ehhhhhhhh it depends entirely on who's using it =D

mr_mitm 2y ago
In non-euclidean spaces, your definition of pi wouldn't even be a value. It's not well defined because the ratio of circumference to diameter of a circle is dependent on the size of the circle and the curvature inside the circle. It's probably true that it's only well defined in euclidean space. Your relaxed definition, which I have never seen before, is not very useful.
- _a_a_a_ 2y ago
  I don't agree, I thought what he said was very interesting. It never occurred to me that pi might vary, and over a non-flat space I can see what they're saying. I think it's intrinsically interesting simply because it breaks one of my preconceptions, that pi is a constant. Talking about it being 'not very useful' just seems far too casually dismissive.
  - mr_mitm 2y ago
    Pi doesn't vary. The ratio of circumference to diameter of a circle may vary depending on the geometry. Clearly everyone means euclidean space unless specified otherwise. Any other interpretation will only lead to problems, which is why it's not useful. There is really no ambiguity about this in mathematics. Mathematicians still use the pi symbol as a constant when they compute the circumference of a circle in a given geometry as a function of the radius.
    - TheRealPomax 2y ago
      There is no "clearly" in Math. The fact that pi is a constant while at the same time not being "the same constant" in all spaces, and not even being "a single value, even if we alias it as the symbol pi" is what makes it a fun fact. Heaven forbid people learn something about math that extends beyond the obvious, how dare they!
      - travisjungroth 2y ago
        > There is no "clearly" in Math. Sure there is. You don’t expect a paper to explain that the numbers are in decimal and not hexadecimal.
        TheRealPomax 2y ago
        I don't know which ones you read so I can't comment on that, but the ones I read most definitely specify which fields of math they apply to, and which axioms are assumed true before doing the work, because the math is meaningless without that? Papers on non-Euclidean spaces always call that out, because it changes which steps can be assumed safe in a proof, and which need a hell of a lot of motivation. And of course, that said: yeah, there are papers for proofs about things normally associated with decimal numbers that explicit call out that the numbers they're going to be using are actually in a different base, and you're just going to have to follow along. https://en.wikipedia.org/wiki/Conway_base_13_function https://en.wikipedia.org/wiki/Conway_base_13_function is probably the most famous example?
travisjungroth 2y ago
Just sounds like you’ve confused yourself. It’s like spinning in circles and acting like no one else knows which way is up. That isn’t a different pi. That’s a different ratio. Your hint is that there are ways to calculate pi besides the ratio of a circle’s circumference to its diameter. This constant folks have named pi shows up in situations besides Euclidean space.
- TheRealPomax 2y ago
  Good job, you completely missed the point where I explain that pi, the constant, is a constant. And that "pi, if considered a ratio" (you know, that thing we did to originally discover pi) is not the same as "pi, the constant". Language skills matter in Math just as much as they do in regular discourse. Arguably moreso: how you define something determines what you can then do with it, and that applies to everything from whether "parallel lines can cross" (what?) to whether divergent series can be mapped to a single number (what??) to what value the circle circumference ratio is and whether you can call that pi (you can) and whether that makes sense (less so, but still yes in some cases).
  - travisjungroth 2y ago
    I haven’t missed your point. I’ve criticized it. You’re treating your non-consensus definition not as a hypothetical, but as a fact. Your comment started with “fun fact”.
  - matt-attack 2y ago
    FWIW I enjoyed your original comment :)
Tainnor 2y ago
Modern mathematics is more likely than not going to define pi as twice the unique zero of cos between 0 and 2, and cos can be defined via its power series or via the exp function (if you use complex numbers). None of this involves geometry whatsoever.
- aydyn 2y ago
  What do you mean? Cos is an inherently geometric function.
  - IsTom 2y ago
    There are many equivalent definitions and many of them do not refer to geometry at all. If you don't want to go through cos you can always define pi as sqrt(6 * sum from 1 to inf 1/n^2).
    - TeMPOraL 2y ago
      You can also define it as `3.14159...` just because. Obviously, a π definition entirely divorced from geometry becomes irrelevant to it - instead, in geometry, you'd still use π = circumference/diameter, or π = whatever(cos), and those values would happen to be the same as a non-geometric π, but only if the geometric π is the one from Euclidean geometry.
      - Tainnor 2y ago
        > You can also define it as `3.14159...` just because. That's not a rigorous definition, though, because it doesn't tell you what those "..." expand to.
  - Tainnor 2y ago
    To quote myself: > cos can be defined via its power series or via the exp function (if you use complex numbers).
    - aydyn 2y ago

stkdump 2y ago

My physics prof said g is actually a vector field. Because the acceleration has a direction and both magnitude and direction vary from point to point.

deleted 2y ago
[deleted]
jvanderbot 2y ago
Your physics Prof is correct of course, and so is GP. "Standard" values for g exist for these bodies, but it also varies everywhere.
DistractionRect 2y ago
This is correct, gravitational constants are a good approximation/simplification since the mass of solar bodies is usually orders of magnitude greater than the other bodies in the problem, and displacement over the course of the problem is usually orders of magnitude smaller than absolute distance between them. In other words, we assume spherical cows until that approximation no longer works.
TheOtherHobbes 2y ago
Absolutely true on astronomical scales. An unnecessary complication if you're dropping a brick out of a window.
- wongarsu 2y ago
  It's funny how much of physics we do assuming a flat earth. If you did it "properly" you would calculate the orbit of the brick (assuming earth was a point mass), then find the intersection between that orbit and earth's surface. But for small speeds and distances you can just assume g points down as it would in a flat earth
  - dudinax 2y ago
    To do it properly you have to account for the gravitational pull of the building.

TheCleric 2y ago

I volunteer for the Mars mission as a weight loss tool.

kevindamm 2y ago
Surviving on Mars will probably involve some mass loss, too.
- TeMPOraL 2y ago
  With the current technology, even getting on a rocket to Mars will involve some weight loss - the mass budget is tight, and each kilogram they can trim off the crew bodies is a kilogram that could be put towards fuel, life support, or scientific equipment.