Pi doesn't exist? Are you serious? That's not philosophy, it's just silly. I would suggest that you go to high school and take some math. Then you might do well to take some science and engineering courses.

Dude, I'm a math major.

EDIT: er, I meant I was a math major in college. It's so hard getting used to being graduated.

Pi doesn't exist? Are you serious? That's not philosophy, it's just silly. I would suggest that you go to high school and take some math. Then you might do well to take some science and engineering courses.

He means in a literal state, in our base ten number system, it is not a number we can absolutely verify.

Actually I mean that the universe as a whole is discrete, and therefore a concept like Pi has no bearing on reality.

This isn't GD though, and I'm sorry if I set up a huge offtopic discussion.

Really, no math has a basis in reality. It has a basis in a small number of basic axioms, which can not be verified. So integer computations are pretty useless too

Really, no math has a basis in reality. It has a basis in a small number of basic axioms, which can not be verified. So integer computations are pretty useless too

Sigh. This whole sort of discussion is perpetuated by the sort of academic who doesn't actually do anything. Lets keep this in the realm of mathmatics or engineering, please.

Sigh. This whole sort of discussion is perpetuated by the sort of academic who doesn't actually do anything. Lets keep this in the realm of mathmatics or engineering, please.

Hmm.. way to take a joke too seriously. I do quite a bit though, and if you want to keep it in the realms of mathematics or engineering, that was very much in the realm of mathematics. If you don't believe me you clearly have never studied advanced mathematics and if you'd read between the lines you'd have picked up on the fact that I was making the point that increased floating point precision does matter, whether Pi is "real" or not, in a round-about way because if we make that kind of distinction about irrationals, we have to make it about every number, since they are all just human constructs, not "real". Anyway, sorry to go off on a rant, but comments like this tick me off.

Hmm.. way to take a joke too seriously. I do quite a bit though, and if you want to keep it in the realms of mathematics or engineering, that was very much in the realm of mathematics. If you don't believe me you clearly have never studied advanced mathematics and if you'd read between the lines you'd have picked up on the fact that I was making the point that increased floating point precision does matter, whether Pi is "real" or not, in a round-about way because if we make that kind of distinction about irrationals, we have to make it about every number, since they are all just human constructs, not "real". Anyway, sorry to go off on a rant, but comments like this tick me off.

Advanced mathematics is much, much different than Advanced Engineering Mathematics (at least it was in my day, Bessel Func., LaPlace Transforms, Churchill mapping, and of course the the two kings of pain, Topology and Viscous Flow, etc)

Hmm.. way to take a joke too seriously. I do quite a bit though, and if you want to keep it in the realms of mathematics or engineering, that was very much in the realm of mathematics. If you don't believe me you clearly have never studied advanced mathematics and if you'd read between the lines you'd have picked up on the fact that I was making the point that increased floating point precision does matter, whether Pi is "real" or not, in a round-about way because if we make that kind of distinction about irrationals, we have to make it about every number, since they are all just human constructs, not "real". Anyway, sorry to go off on a rant, but comments like this tick me off.

So you're ticked off by the engineer and I'm ticked off by the "pure" mathematician philosopher. We're even, except that we were discussing computer math which is a practical construct, not a pure mathematical one. If you are doing pure math on a computer you have to do everything in symbolic terms and never actually evaluate a numerical result, so precision is only relevent when you want to extract a concrete answer (which is never if you're only interested in the pure side of things).

No need to resort to hand waving about how numbers are "human constructs" and not "real". A computer's representation of floating point numbers corresponds only loosely to traditional numerics, never mind some notion of what is "real". Precision and representation are essential parts of the floating point system, although they are ignored by developers all too often -- leading to unstable systems or inaccurate results.

So you're ticked off by the engineer and I'm ticked off by the "pure" mathematician philosopher. We're even, except that we were discussing computer math which is a practical construct, not a pure mathematical one. If you are doing pure math on a computer you have to do everything in symbolic terms and never actually evaluate a numerical result, so precision is only relevent when you want to extract a concrete answer (which is never if you're only interested in the pure side of things).

No need to resort to hand waving about how numbers are "human constructs" and not "real". A computer's representation of floating point numbers corresponds only loosely to traditional numerics, never mind some notion of what is "real". Precision and representation are essential parts of the floating point system, although they are ignored by developers all too often -- leading to unstable systems or inaccurate results.

Wouldn't hardware that understood symbolic manipulation give us the best of both worlds? Mabye an OpenGL type thing where if you need the extra performance you buy the card, and if not it all gets done in software. I understand that there's not enough demand for this kind of thing to warrant CPU-level hardware support, but it really bugs me that there's no easy standard way to do this stuff. Ok, I'm done ranting for a good 30 minutes or so.

So you're ticked off by the engineer and I'm ticked off by the "pure" mathematician philosopher. We're even, except that we were discussing computer math which is a practical construct, not a pure mathematical one. If you are doing pure math on a computer you have to do everything in symbolic terms and never actually evaluate a numerical result, so precision is only relevent when you want to extract a concrete answer (which is never if you're only interested in the pure side of things).

No need to resort to hand waving about how numbers are "human constructs" and not "real". A computer's representation of floating point numbers corresponds only loosely to traditional numerics, never mind some notion of what is "real". Precision and representation are essential parts of the floating point system, although they are ignored by developers all too often -- leading to unstable systems or inaccurate results.

Gee, I thought Pi was a number that was generated when you divide a circles circumference by it's diameter, therefore, it exists but is transcedental.

Yes, but there are no circles in nature. Circles are only concepts. A CD is real, and it has an edge, and that edge evokes in us the concept of a circle.

Enlarge it enough, and you'll see that it's made of molecules and atoms, so it can't be perfectly round. If you take the circumference of a CD (whatever way you measure it) and divide it by the diameter (however you measure that) you'll get some number. Both PI and 3.14150265 are approximations of that number, and there's no reason to think that PI is better.

Yes, but there are no circles in nature. Circles are only concepts. A CD is real, and it has an edge, and that edge evokes in us the concept of a circle.

Enlarge it enough, and you'll see that it's made of molecules and atoms, so it can't be perfectly round. If you take the circumference of a CD (whatever way you measure it) and divide it by the diameter (however you measure that) you'll get some number. Both PI and 3.14150265 are approximations of that number, and there's no reason to think that PI is better.

Pi is better in the sense that the better and bigger the circle, the closer that number will be to Pi. OTOH, in a real-world setting you're more likely to get errors from incorrect measurements than from rounding Pi to the 10,000th decimal place.

The G5 is faster with floating point operations than with integer operations, so I would expect to see more use of floating point operations, not less.

Eh? I've done my fair share of integer and floating point math, and I can safely say that you use one or the other. VERY few situations come up where you could use either interchangably. Come to think of it, I can't think of one non contrived situation where one wouldn't be obviously better than the other. If you need floats, you use floats. If you need integers, then you use integers.

Quote:

The main reason Photoshop and multimedia apps are so fast on G4 and G5 machines is their extensive use of AltiVec. I don't see the 64-bit integer capability in the G5 changing that equation.

Aside from making larger memory partitions available to the OS (and hence the software), yes, there will be no performance benefit to the software.

Quote:

The 64-bit integers and address pointers use twice as much memory as their 32-bit counterparts. Moving 10000 64-bit integers around takes twice as long as moving 10000 32-bit integers.

I am confused about what you mean by move around. I am not aware of how it takes twice as long- the processor doesn't move bits around one at a time, but in "bulk" (i.e. parallel), so it takes the same number of CPU cycles to move a 32 bit number as well as a 64 bit number. Motherboards work the same way. Now it may be the case that you are wasting bits on a 64 bit number when a 32, 16, or heck, even an 8 bit number would be better, but that is a problem for 32 bit numbers as well. No big deal.

The benefits of 64 bit computing TOTALLY outweigh the limitations. If you talk to any video editing people and ask them if they would like to have 6GB of RAW video in memory instead of on disk, they will tell you that they do indeed want this.

Wouldn't hardware that understood symbolic manipulation give us the best of both worlds? Mabye an OpenGL type thing where if you need the extra performance you buy the card, and if not it all gets done in software. I understand that there's not enough demand for this kind of thing to warrant CPU-level hardware support, but it really bugs me that there's no easy standard way to do this stuff. Ok, I'm done ranting for a good 30 minutes or so.

Man what did I miss in this conversation!

First of all, pi is a symbol and there is no such thing as a pi in the material world. Secondly, a machine that operated at the symbolic level would be dirt slow... and worthless. For example, it could only return symbolic results and on its own would be incapable of even running a GUI (a circle on screen after all is not a symbol, but a particular rendering of the abstract concept- a symbol- on a pixelated surface). There is no standard way to do symbolic math on hardware because it would be nearly impossible.

For headache's sake, you can find a perfect circle if you look at the event horizon of a black hole, but you would somehow have to have a frame of reference that is not moving relative to the blach hole.

Yes, but there are no circles in nature. Circles are only concepts. A CD is real, and it has an edge, and that edge evokes in us the concept of a circle.

Enlarge it enough, and you'll see that it's made of molecules and atoms, so it can't be perfectly round. If you take the circumference of a CD (whatever way you measure it) and divide it by the diameter (however you measure that) you'll get some number. Both PI and 3.14150265 are approximations of that number, and there's no reason to think that PI is better.

Pi is not an approximation. Pi ratio that the number 3.141592654... is an approximation of. Pi is a symbol and as such can never be an approximation.

Eh? I've done my fair share of integer and floating point math, and I can safely say that you use one or the other. VERY few situations come up where you could use either interchangably. Come to think of it, I can't think of one non contrived situation where one wouldn't be obviously better than the other. If you need floats, you use floats. If you need integers, then you use integers.

It is perfectly reasonable to do use the FPU to do math on numbers which happen to be integers. On the 970 it would probably be significantly faster.

Quote:

I am confused about what you mean by move around. I am not aware of how it takes twice as long- the processor doesn't move bits around one at a time, but in "bulk" (i.e. parallel), so it takes the same number of CPU cycles to move a 32 bit number as well as a 64 bit number. Motherboards work the same way. Now it may be the case that you are wasting bits on a 64 bit number when a 32, 16, or heck, even an 8 bit number would be better, but that is a problem for 32 bit numbers as well. No big deal.

Uh... you'll note how there is a lot of discussion of memory bandwidth and it is measured in "bytes per second". A 32-bit number is 4 bytes. A 64-bit number is 8 bytes. If you have to copy 1000 32-bit pointers then you have to transfer 4000 bytes from one memory location to another. If you have to copy 1000 64-bit pointers then you have to transfer 8000 bytes from one memory location to another. If your bandwidth is 1000 bytes/sec then it will take 4 seconds if you have 32-bit pointers and 8 seconds if you have 64-bit pointers. That could be a big deal if it represented a significant fraction of what you were doing. Fortunately the number of pointers is usually relatively small so the impact will be relatively slight... but the fact remains that all other things being equal a 64-bit program will require slightly more bandwidth than a 32-bit program and will therefore run more slowly.

Quote:

The benefits of 64 bit computing TOTALLY outweigh the limitations. If you talk to any video editing people and ask them if they would like to have 6GB of RAW video in memory instead of on disk, they will tell you that they do indeed want this.

Read my previous point and consider the plight of most software (i.e. that which requires far less than 4 GB of RAM to run).

Pi is not an approximation. Pi ratio that the number 3.141592654... is an approximation of. Pi is a symbol and as such can never be an approximation.

Take a CD. Measure the length of its edge. Now measure its diameter. Now divide these two numbers. You got some ratio. This ratio is close to Pi, and also close to 3.14159265. There is no reason to thing that it is closer to Pi than to 3.14159265. This is what people mean by Pi not being in nature. It is because perfect circles are not part of nature, but rather an abstract concept.

## Comments

174memberOriginally posted by Mr. MePi doesn't exist? Are you serious? That's not philosophy, it's just silly. I would suggest that you go to high school and take some math. Then you might do well to take some science and engineering courses.Dude, I'm a math major.

EDIT: er, I meant I was a math major in college. It's so hard getting used to being graduated.

256memberOriginally posted by Mr. MePi doesn't exist? Are you serious? That's not philosophy, it's just silly. I would suggest that you go to high school and take some math. Then you might do well to take some science and engineering courses.He means in a literal state, in our base ten number system, it is not a number we can absolutely verify.

174memberOriginally posted by robsterHe means in a literal state, in our base ten number system, it is not a number we can absolutely verify.Actually I mean that the universe as a whole is discrete, and therefore a concept like Pi has no bearing on reality.

This isn't GD though, and I'm sorry if I set up a huge offtopic discussion.

76memberOriginally posted by Anonymous KarmaActually I mean that the universe as a whole is discrete, and therefore a concept like Pi has no bearing on reality.

This isn't GD though, and I'm sorry if I set up a huge offtopic discussion.

Really, no math has a basis in reality. It has a basis in a small number of basic axioms, which can not be verified. So integer computations are pretty useless too

3,409memberOriginally posted by DelphikiReally, no math has a basis in reality. It has a basis in a small number of basic axioms, which can not be verified. So integer computations are pretty useless tooSigh. This whole sort of discussion is perpetuated by the sort of academic who doesn't actually

doanything. Lets keep this in the realm of mathmatics or engineering, please.1,224memberOriginally posted by Anonymous KarmaActually I mean that the universe as a whole is discrete, and therefore a concept like Pi has no bearing on reality.

This isn't GD though, and I'm sorry if I set up a huge offtopic discussion.

Gee, I thought Pi was a number that was generated when you divide a circles circumference by it's diameter, therefore, it exists but is transcedental.

76memberOriginally posted by ProgrammerSigh. This whole sort of discussion is perpetuated by the sort of academic who doesn't actuallydoanything. Lets keep this in the realm of mathmatics or engineering, please.Hmm.. way to take a joke too seriously. I do quite a bit though, and if you want to keep it in the realms of mathematics or engineering, that was very much in the realm of mathematics. If you don't believe me you clearly have never studied advanced mathematics and if you'd read between the lines you'd have picked up on the fact that I was making the point that increased floating point precision does matter, whether Pi is "real" or not, in a round-about way because if we make that kind of distinction about irrationals, we have to make it about every number, since they are all just human constructs, not "real". Anyway, sorry to go off on a rant, but comments like this tick me off.

1,224memberOriginally posted by DelphikiHmm.. way to take a joke too seriously. I do quite a bit though, and if you want to keep it in the realms of mathematics or engineering, that was very much in the realm of mathematics. If you don't believe me you clearly have never studied advanced mathematics and if you'd read between the lines you'd have picked up on the fact that I was making the point that increased floating point precision does matter, whether Pi is "real" or not, in a round-about way because if we make that kind of distinction about irrationals, we have to make it about every number, since they are all just human constructs, not "real". Anyway, sorry to go off on a rant, but comments like this tick me off.Advanced mathematics is much, much different than Advanced Engineering Mathematics (at least it was in my day, Bessel Func., LaPlace Transforms, Churchill mapping, and of course the the two kings of pain, Topology and Viscous Flow, etc)

3,409memberOriginally posted by DelphikiHmm.. way to take a joke too seriously. I do quite a bit though, and if you want to keep it in the realms of mathematics or engineering, that was very much in the realm of mathematics. If you don't believe me you clearly have never studied advanced mathematics and if you'd read between the lines you'd have picked up on the fact that I was making the point that increased floating point precision does matter, whether Pi is "real" or not, in a round-about way because if we make that kind of distinction about irrationals, we have to make it about every number, since they are all just human constructs, not "real". Anyway, sorry to go off on a rant, but comments like this tick me off.So you're ticked off by the engineer and I'm ticked off by the "pure" mathematician philosopher. We're even, except that we were discussing computer math which is a practical construct, not a pure mathematical one. If you are doing pure math on a computer you have to do everything in symbolic terms and never actually evaluate a numerical result, so precision is only relevent when you want to extract a concrete answer (which is never if you're only interested in the pure side of things).

No need to resort to hand waving about how numbers are "human constructs" and not "real". A computer's representation of floating point numbers corresponds only loosely to traditional numerics, never mind some notion of what is "real". Precision and representation are essential parts of the floating point system, although they are ignored by developers all too often -- leading to unstable systems or inaccurate results.

735memberOriginally posted by ProgrammerSo you're ticked off by the engineer and I'm ticked off by the "pure" mathematician philosopher. We're even, except that we were discussing computer math which is a practical construct, not a pure mathematical one. If you are doing pure math on a computer you have to do everything in symbolic terms and never actually evaluate a numerical result, so precision is only relevent when you want to extract a concrete answer (which is never if you're only interested in the pure side of things).

No need to resort to hand waving about how numbers are "human constructs" and not "real". A computer's representation of floating point numbers corresponds only loosely to traditional numerics, never mind some notion of what is "real". Precision and representation are essential parts of the floating point system, although they are ignored by developers all too often -- leading to unstable systems or inaccurate results.

Wouldn't hardware that understood symbolic manipulation give us the best of both worlds? Mabye an OpenGL type thing where if you need the extra performance you buy the card, and if not it all gets done in software. I understand that there's not enough demand for this kind of thing to warrant CPU-level hardware support, but it really bugs me that there's no easy standard way to do this stuff. Ok, I'm done ranting for a good 30 minutes or so.

475memberOriginally posted by ProgrammerSo you're ticked off by the engineer and I'm ticked off by the "pure" mathematician philosopher. We're even, except that we were discussing computer math which is a practical construct, not a pure mathematical one. If you are doing pure math on a computer you have to do everything in symbolic terms and never actually evaluate a numerical result, so precision is only relevent when you want to extract a concrete answer (which is never if you're only interested in the pure side of things).

No need to resort to hand waving about how numbers are "human constructs" and not "real". A computer's representation of floating point numbers corresponds only loosely to traditional numerics, never mind some notion of what is "real". Precision and representation are essential parts of the floating point system, although they are ignored by developers all too often -- leading to unstable systems or inaccurate results.

Remember,

there is no spoon.248memberOriginally posted by BigcGee, I thought Pi was a number that was generated when you divide a circles circumference by it's diameter, therefore, it exists but is transcedental.Yes, but there are no circles in nature. Circles are only concepts. A CD is real, and it has an edge, and that edge evokes in us the concept of a circle.

Enlarge it enough, and you'll see that it's made of molecules and atoms, so it can't be perfectly round. If you take the circumference of a CD (whatever way you measure it) and divide it by the diameter (however you measure that) you'll get some number. Both PI and 3.14150265 are approximations of that number, and there's no reason to think that PI is better.

735memberOriginally posted by synpYes, but there are no circles in nature. Circles are only concepts. A CD is real, and it has an edge, and that edge evokes in us the concept of a circle.

Enlarge it enough, and you'll see that it's made of molecules and atoms, so it can't be perfectly round. If you take the circumference of a CD (whatever way you measure it) and divide it by the diameter (however you measure that) you'll get some number. Both PI and 3.14150265 are approximations of that number, and there's no reason to think that PI is better.

Pi is better in the sense that the better and bigger the circle, the closer that number will be to Pi. OTOH, in a real-world setting you're more likely to get errors from incorrect measurements than from rounding Pi to the 10,000th decimal place.

1,148memberOriginally posted by TidrisThe G5 is faster with floating point operations than with integer operations, so I would expect to see more use of floating point operations, not less.

Eh? I've done my fair share of integer and floating point math, and I can safely say that you use one or the other. VERY few situations come up where you could use either interchangably. Come to think of it, I can't think of one non contrived situation where one wouldn't be obviously better than the other. If you need floats, you use floats. If you need integers, then you use integers.

The main reason Photoshop and multimedia apps are so fast on G4 and G5 machines is their extensive use of AltiVec. I don't see the 64-bit integer capability in the G5 changing that equation.

Aside from making larger memory partitions available to the OS (and hence the software), yes, there will be no performance benefit to the software.

The 64-bit integers and address pointers use twice as much memory as their 32-bit counterparts. Moving 10000 64-bit integers around takes twice as long as moving 10000 32-bit integers.

I am confused about what you mean by move around. I am not aware of how it takes twice as long- the processor doesn't move bits around one at a time, but in "bulk" (i.e. parallel), so it takes the same number of CPU cycles to move a 32 bit number as well as a 64 bit number. Motherboards work the same way. Now it may be the case that you are wasting bits on a 64 bit number when a 32, 16, or heck, even an 8 bit number would be better, but that is a problem for 32 bit numbers as well. No big deal.

The benefits of 64 bit computing TOTALLY outweigh the limitations. If you talk to any video editing people and ask them if they would like to have 6GB of RAW video in memory instead of on disk, they will tell you that they do indeed want this.

1,148memberOriginally posted by WhisperWouldn't hardware that understood symbolic manipulation give us the best of both worlds? Mabye an OpenGL type thing where if you need the extra performance you buy the card, and if not it all gets done in software. I understand that there's not enough demand for this kind of thing to warrant CPU-level hardware support, but it really bugs me that there's no easy standard way to do this stuff. Ok, I'm done ranting for a good 30 minutes or so.Man what did I miss in this conversation!

First of all, pi is a symbol and there is no such thing as a pi in the material world. Secondly, a machine that operated at the symbolic level would be dirt slow... and worthless. For example, it could only return symbolic results and on its own would be incapable of even running a GUI (a circle on screen after all is not a symbol, but a particular rendering of the abstract concept- a symbol- on a pixelated surface). There is no standard way to do symbolic math on hardware because it would be nearly impossible.

For headache's sake, you can find a perfect circle if you look at the event horizon of a black hole, but you would somehow have to have a frame of reference that is not moving relative to the blach hole.

1,148memberOriginally posted by synpYes, but there are no circles in nature. Circles are only concepts. A CD is real, and it has an edge, and that edge evokes in us the concept of a circle.

Enlarge it enough, and you'll see that it's made of molecules and atoms, so it can't be perfectly round. If you take the circumference of a CD (whatever way you measure it) and divide it by the diameter (however you measure that) you'll get some number. Both PI and 3.14150265 are approximations of that number, and there's no reason to think that PI is better.

Pi is not an approximation. Pi ratio that the number 3.141592654... is an approximation of. Pi is a symbol and as such can never be an approximation.

1,224member3,409memberOriginally posted by YevgenyEh? I've done my fair share of integer and floating point math, and I can safely say that you use one or the other. VERY few situations come up where you could use either interchangably. Come to think of it, I can't think of one non contrived situation where one wouldn't be obviously better than the other. If you need floats, you use floats. If you need integers, then you use integers.It is perfectly reasonable to do use the FPU to do math on numbers which happen to be integers. On the 970 it would probably be significantly faster.

I am confused about what you mean by move around. I am not aware of how it takes twice as long- the processor doesn't move bits around one at a time, but in "bulk" (i.e. parallel), so it takes the same number of CPU cycles to move a 32 bit number as well as a 64 bit number. Motherboards work the same way. Now it may be the case that you are wasting bits on a 64 bit number when a 32, 16, or heck, even an 8 bit number would be better, but that is a problem for 32 bit numbers as well. No big deal.

Uh... you'll note how there is a lot of discussion of memory bandwidth and it is measured in "bytes per second". A 32-bit number is 4 bytes. A 64-bit number is 8 bytes. If you have to copy 1000 32-bit pointers then you have to transfer 4000 bytes from one memory location to another. If you have to copy 1000 64-bit pointers then you have to transfer 8000 bytes from one memory location to another. If your bandwidth is 1000 bytes/sec then it will take 4 seconds if you have 32-bit pointers and 8 seconds if you have 64-bit pointers. That could be a big deal if it represented a significant fraction of what you were doing. Fortunately the number of pointers is usually relatively small so the impact will be relatively slight... but the fact remains that all other things being equal a 64-bit program will require slightly more bandwidth than a 32-bit program and will therefore run more slowly.

The benefits of 64 bit computing TOTALLY outweigh the limitations. If you talk to any video editing people and ask them if they would like to have 6GB of RAW video in memory instead of on disk, they will tell you that they do indeed want this.

Read my previous point and consider the plight of most software (i.e. that which requires far less than 4 GB of RAM to run).

248memberOriginally posted by YevgenyPi is not an approximation. Pi ratio that the number 3.141592654... is an approximation of. Pi is a symbol and as such can never be an approximation.Take a CD. Measure the length of its edge. Now measure its diameter. Now divide these two numbers. You got some ratio. This ratio is close to Pi, and also close to 3.14159265. There is no reason to thing that it is closer to Pi than to 3.14159265. This is what people mean by Pi not being in nature. It is because perfect circles are not part of nature, but rather an abstract concept.