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Some corrections/nitpicks on your weather forecasting example: * there are most definitely some overarching equations that explain it all. We just can't solve

Some corrections/nitpicks on your weather forecasting example: * there are most definitely some overarching equations that explain it all. We just can't solve them analytically. But we use them to write the code. * when you say "one processor per cube": if you mean cube = grid cell you're way off. You want to have at least ~ 10 000 grid cells per processor to have any level of performance. * it is definitely not quantum mechanics that makes weather hard to predict. It's what's popularly called "chaos", or mathematically, "exponential sensitivity to variations in initial data". * getting more performance for this type of application is not about getting more cores, it's about getting more memory bandwidth. That's why e.g. GPUs are useless for speeding up weather forecasting. * funfact: weather simulations today are not running any faster than in 1994; it's at about 15 minutes per simulation. The increases in computing power are used to a) increase grid resolution and b) run more replicas. * The last point is what makes modern weather simulations tick. You don't run one simulation, you run 1000, each with slightly different initial data, and you analyse the ensemble results.

lutusp 11y ago
> * there are most definitely some overarching equations that explain it all. Not so, not for Earth's atmosphere, the topic I was discussing. There are first principles, but no overarching equations, analytically expressible or not. Prove me wrong -- show me the equation that tracks arctic temperature, rainfall, and snow cover, including the feedback effects that join them all, as an equation. > * when you say "one processor per cube": if you mean cube = grid cell you're way off. You want to have at least ~ 10 000 grid cells per processor to have any level of performance. It was part of a simple explanation, but in the future, in the name of increased throughput and as processor costs continue to fall, it will be literally true. I say this on a day when the Raspberry Pi Zero is so much in demand that I can't find one for sale. > * it is definitely not quantum mechanics that makes weather hard to predict. It's what's popularly called "chaos", or mathematically, "exponential sensitivity to variations in initial data". Both play a part. Quantum mechanics is thought to be the final obstacle to long-term weather forecasting, and chaos theory (extreme sensitivity to initial conditions) is the mechanism by which small initial causes lead to large effects. Your last three point weren't corrections, so no need for comment.
- semi-extrinsic 11y ago
  > show me the equation that tracks arctic temperature, rainfall, and snow cover, including the feedback effects that join them all, as an equation. The reader is referred to "Chapter IV: The Governing Equations" of Richardson's classical book "Weather Prediction by Numerical Process" [1]. > It was part of a simple explanation, but in the future, in the name of increased throughput and as processor costs continue to fall, it will be literally true. No. You didn't read what I wrote. Unless some radical paradigm shift occurs in both hardware and algorithm design, strong scaling is never going to pay off once you get less than about 10 000 grid cells per CPU. Core cost is not tge issue, power usage over the cluster lifetime is already a huge cost. Memory bandwidth is the issue, Linpack (peak float) performance is so irrelevant even management has started to ignore it. > Quantum mechanics is thought to be the final obstacle to long-term weather forecasting [By whom?][Citation needed]. Of course QM is behind how atoms and molecules behave, but that doesn't mean any QM result will ever improve weather prediction. And, why stop at quantum mechanics? Why not invoke quarks and gluons and the Higgs field if you're going all the way down to fundamental particles? [1] https://books.google.com/books?hl=en&lr=&id=D52d3_bbgg8C&oi=fnd&pg=PA3&dq=equations#v=onepage&q&f=false https://books.google.com/books?hl=en&lr=&id=D52d3_bbgg8C&oi=...
  - lutusp 11y ago
    >> show me the equation that tracks arctic temperature, rainfall, and snow cover, including the feedback effects that join them all, as an equation. > The reader is referred to "Chapter IV: The Governing Equations" of Richardson's classical book "Weather Prediction by Numerical Process" [1]. I will say this one more time: "As an equation". There is no equation that describes the system I described, there are only algorithms that cannot be expressed in closed form. The fact that they cannot be expressed or solved in closed form is revealed by the language of your reference: "by Numerical Process". Numerical algorithms are used -- must be used -- for system that don't have a closed-form solution, i.e. an equation that describes the system. Weather and atmospheric physics are in that category. My specific example -- arctic temperature, rainfall and snow cover -- represents a system that we can't even model with any reliability, much less hope to express as an equation. Another example, one that surprises many people, is the fact that there is no equation able to describe an orbital system with more than two masses. Those systems must also be solved numerically. (https://en.wikipedia.org/wiki/Three-body_problem https://en.wikipedia.org/wiki/Three-body_problem) > ... but that doesn't mean any QM result will ever improve weather prediction So? I made the exact opposite claim -- that the effect of QM on weather systems may prevent accurate forecasts past a certain time duration. >> It was part of a simple explanation, but in the future, in the name of increased throughput and as processor costs continue to fall, it will be literally true. > No. You didn't read what I wrote. Who cares what you wrote? You tried to say that 10,000 cells per processor is required for reasonable throughput. This is already false, and it will become more false in the future. >> Quantum mechanics is thought to be the final obstacle to long-term weather forecasting > [By whom?][Citation needed]. I didn't make an evidentiary claim, I expressed a commonly heard opinion, so I don't have to provide a citation. > Why not invoke quarks and gluons and the Higgs field if you're going all the way down to fundamental particles? The evidentiary burden is yours to try to support the idea that weather isn't affected by fundamental particles.

lutusp 11y ago

> * there are most definitely some overarching equations that explain it all. Not so, not for Earth's atmosphere, the topic I was discussing. There are first principles, but no overarching equations, analytically expressible or not. Prove me wrong -- show me the equation that tracks arctic temperature, rainfall, and snow cover, including the feedback effects that join them all, as an equation. > * when you say "one processor per cube": if you mean cube = grid cell you're way off. You want to have at least ~ 10 000 grid cells per processor to have any level of performance. It was part of a simple explanation, but in the future, in the name of increased throughput and as processor costs continue to fall, it will be literally true. I say this on a day when the Raspberry Pi Zero is so much in demand that I can't find one for sale. > * it is definitely not quantum mechanics that makes weather hard to predict. It's what's popularly called "chaos", or mathematically, "exponential sensitivity to variations in initial data". Both play a part. Quantum mechanics is thought to be the final obstacle to long-term weather forecasting, and chaos theory (extreme sensitivity to initial conditions) is the mechanism by which small initial causes lead to large effects. Your last three point weren't corrections, so no need for comment.

semi-extrinsic 11y ago
> show me the equation that tracks arctic temperature, rainfall, and snow cover, including the feedback effects that join them all, as an equation. The reader is referred to "Chapter IV: The Governing Equations" of Richardson's classical book "Weather Prediction by Numerical Process" [1]. > It was part of a simple explanation, but in the future, in the name of increased throughput and as processor costs continue to fall, it will be literally true. No. You didn't read what I wrote. Unless some radical paradigm shift occurs in both hardware and algorithm design, strong scaling is never going to pay off once you get less than about 10 000 grid cells per CPU. Core cost is not tge issue, power usage over the cluster lifetime is already a huge cost. Memory bandwidth is the issue, Linpack (peak float) performance is so irrelevant even management has started to ignore it. > Quantum mechanics is thought to be the final obstacle to long-term weather forecasting [By whom?][Citation needed]. Of course QM is behind how atoms and molecules behave, but that doesn't mean any QM result will ever improve weather prediction. And, why stop at quantum mechanics? Why not invoke quarks and gluons and the Higgs field if you're going all the way down to fundamental particles? [1] https://books.google.com/books?hl=en&lr=&id=D52d3_bbgg8C&oi=fnd&pg=PA3&dq=equations#v=onepage&q&f=false https://books.google.com/books?hl=en&lr=&id=D52d3_bbgg8C&oi=...
- lutusp 11y ago
  >> show me the equation that tracks arctic temperature, rainfall, and snow cover, including the feedback effects that join them all, as an equation. > The reader is referred to "Chapter IV: The Governing Equations" of Richardson's classical book "Weather Prediction by Numerical Process" [1]. I will say this one more time: "As an equation". There is no equation that describes the system I described, there are only algorithms that cannot be expressed in closed form. The fact that they cannot be expressed or solved in closed form is revealed by the language of your reference: "by Numerical Process". Numerical algorithms are used -- must be used -- for system that don't have a closed-form solution, i.e. an equation that describes the system. Weather and atmospheric physics are in that category. My specific example -- arctic temperature, rainfall and snow cover -- represents a system that we can't even model with any reliability, much less hope to express as an equation. Another example, one that surprises many people, is the fact that there is no equation able to describe an orbital system with more than two masses. Those systems must also be solved numerically. (https://en.wikipedia.org/wiki/Three-body_problem https://en.wikipedia.org/wiki/Three-body_problem) > ... but that doesn't mean any QM result will ever improve weather prediction So? I made the exact opposite claim -- that the effect of QM on weather systems may prevent accurate forecasts past a certain time duration. >> It was part of a simple explanation, but in the future, in the name of increased throughput and as processor costs continue to fall, it will be literally true. > No. You didn't read what I wrote. Who cares what you wrote? You tried to say that 10,000 cells per processor is required for reasonable throughput. This is already false, and it will become more false in the future. >> Quantum mechanics is thought to be the final obstacle to long-term weather forecasting > [By whom?][Citation needed]. I didn't make an evidentiary claim, I expressed a commonly heard opinion, so I don't have to provide a citation. > Why not invoke quarks and gluons and the Higgs field if you're going all the way down to fundamental particles? The evidentiary burden is yours to try to support the idea that weather isn't affected by fundamental particles.