4 ms·

Human limitations is one reason, but there's something much deeper going on here. Navier and Stokes worked before we were sure that atoms existed, certainly be

Human limitations is one reason, but there's something much deeper going on here. Navier and Stokes worked before we were sure that atoms existed, certainly before we had any idea of how many there were. Nevertheless they were able to write down useful theories for describing fluids. This is how all of science works. The things about which we are totally ignorant are much smaller today, of course... but useful theories of any set of phenomena always omit a great many things we do in fact know about. From these theories, we can understand what's going on, and use this to extrapolate to things we have not seen yet. An atom-by-atom computational model would (in some sense) be no more useful than what we had before N-S, just blind experiment. To try out any given swirl of smoke etc. we can equally well walk next door to the lab and videotape it... but this doesn't help us imagine what else might be possible. The "blowup scenario" discussed is an example of this kind of imagining.

oldandtired 9y ago
> The things about which we are totally ignorant are much smaller today, of course One would have to disagree with this idea. The more we study the universe around us, the less we actually know. As a somewhat philosophical point, there are many times when our mental (mathematical) models get in the road of understanding. Very often, people believe that because we have a model that works and appears to give good predictive results about some phenomena then we understand the how and the what (and even the why) of those phenomena. When this happens, we get into a situation where alternative models are actually discouraged. If one looks the the history of the 19th, 20th and 21st centuries, one can see that more and vaster avenues of investigation have arisen as time passes. Our increasing knowledge is continuing to be shown as ever smaller in relation to what we are now seeing. No theory is ever complete, nor is it ever accurate to the extent that it describes the reality of the universe around us. All theories make those simplifying assumptions that when taken too far lead into inaccurately describing and predicting what we should see. Too often people get enamoured by the beauty of the mathematics and forget it is only an attempt at reflecting reality. Mathematics is a magnificent and useful tool, but it is a foolish master. Too often we forget that. Theories and models help us gain some understanding of the nature of the universe around us. This understanding, however, is always subject to change, no matter how "perfect" the theory may appear to be. There are too many scientists, both theoretical and practical, who are so infatuated and enamoured with their current models that they have forgotten that the models are approximations only and are subject to change or even overturning.
- improbable22 9y ago
  "much smaller today" meaning literally smaller: Navier didn't know about atoms, 10^-10 m, but now we know about things at 10^-18 m or so. Sure, our awareness of how much we don't know has grown over time. The point I was trying to make is that theoretical models (like N-S) not only don't have to be perfect to be useful, but more, are useful precisely because they are not complete. By ignoring irrelevant details we get theory, not just simulation.
  - oldandtired 9y ago
    I don't disagree with the idea that a model doesn't have to be perfect to be useful. But I do disagree with the prevalent idea that such theories are the "truth" when they are not. Understanding that a model or theory is useful even when we ignore certain aspects of reality is quite different to the often displayed belief that a specific theory is "gospel" even in the face of anomalies and discrepancies of the real world compared with prediction. Too much of the "theoretical physics" genre (word specifically chosen) is based on the idea that mathematics is the means of finding the "truth". As I said above, mathematics is a wonderful and useful tool, but it is not a good master. It provides a possible insight into what is going on. However, those insights are not "truth" as such. I have been doing a review of my old mathematics texts for scientists and engineers, as well as other resources. It is interesting that all of them talk of and demonstrate that all the mathematical models are simplified and incomplete. Yet, if one raises the various problems with the various models in use today, one is shouted down. This does not bode well for our advancement in understanding of the universe around us.
    - improbable22 9y ago
      It's certainly possible to find such views in theoretical physics. But typically not from very serious people. In my understanding the big shift was the understanding of renormalisation, Kadanoff and Wilson, around 1970. This took airy ideas about useful approximation and turned them into serious tools, which are both useful for everyday things and illuminating about why any of it works.

oldandtired 9y ago

> The things about which we are totally ignorant are much smaller today, of course One would have to disagree with this idea. The more we study the universe around us, the less we actually know. As a somewhat philosophical point, there are many times when our mental (mathematical) models get in the road of understanding. Very often, people believe that because we have a model that works and appears to give good predictive results about some phenomena then we understand the how and the what (and even the why) of those phenomena. When this happens, we get into a situation where alternative models are actually discouraged. If one looks the the history of the 19th, 20th and 21st centuries, one can see that more and vaster avenues of investigation have arisen as time passes. Our increasing knowledge is continuing to be shown as ever smaller in relation to what we are now seeing. No theory is ever complete, nor is it ever accurate to the extent that it describes the reality of the universe around us. All theories make those simplifying assumptions that when taken too far lead into inaccurately describing and predicting what we should see. Too often people get enamoured by the beauty of the mathematics and forget it is only an attempt at reflecting reality. Mathematics is a magnificent and useful tool, but it is a foolish master. Too often we forget that. Theories and models help us gain some understanding of the nature of the universe around us. This understanding, however, is always subject to change, no matter how "perfect" the theory may appear to be. There are too many scientists, both theoretical and practical, who are so infatuated and enamoured with their current models that they have forgotten that the models are approximations only and are subject to change or even overturning.

improbable22 9y ago
"much smaller today" meaning literally smaller: Navier didn't know about atoms, 10^-10 m, but now we know about things at 10^-18 m or so. Sure, our awareness of how much we don't know has grown over time. The point I was trying to make is that theoretical models (like N-S) not only don't have to be perfect to be useful, but more, are useful precisely because they are not complete. By ignoring irrelevant details we get theory, not just simulation.
- oldandtired 9y ago
  I don't disagree with the idea that a model doesn't have to be perfect to be useful. But I do disagree with the prevalent idea that such theories are the "truth" when they are not. Understanding that a model or theory is useful even when we ignore certain aspects of reality is quite different to the often displayed belief that a specific theory is "gospel" even in the face of anomalies and discrepancies of the real world compared with prediction. Too much of the "theoretical physics" genre (word specifically chosen) is based on the idea that mathematics is the means of finding the "truth". As I said above, mathematics is a wonderful and useful tool, but it is not a good master. It provides a possible insight into what is going on. However, those insights are not "truth" as such. I have been doing a review of my old mathematics texts for scientists and engineers, as well as other resources. It is interesting that all of them talk of and demonstrate that all the mathematical models are simplified and incomplete. Yet, if one raises the various problems with the various models in use today, one is shouted down. This does not bode well for our advancement in understanding of the universe around us.
  - improbable22 9y ago
    It's certainly possible to find such views in theoretical physics. But typically not from very serious people. In my understanding the big shift was the understanding of renormalisation, Kadanoff and Wilson, around 1970. This took airy ideas about useful approximation and turned them into serious tools, which are both useful for everyday things and illuminating about why any of it works.