Geezerbiker
New member
I suppose I'm going to have to live with, it's better and not know exactly how much. Thanks for all the input...
Tony
Tony
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
Lock time?
- Thread starter Geezerbiker
- Start date
Mixing things.
The math is black and white. That's how it's designed.
Not mixing anything. If you go and read some of the papers of the most brilliant mathematicians, they will explain it in similar concepts. Math, designed by man is black and white, but it is not, in most applications precise. Sure, basic counting and math up through HS algebra is. Non-linear algebra, partial differential equations...the stuff actually used to solve the most complex problems, is not, even with the computers. It takes getting out of the box you have created in your head and mind, how math was taught. It's a long process and most, like your explanations, really don't want to delve too deeply into it.
Way off the topic, so I'll stop with that. But some reading on the subject might be illuminating to you if you have the interest.
Truly very interesting stuff, at least it is for me. My first two degrees were technology degrees, it wasn't until my third that I started getting into dealing more effectively with non-linear systems and it was a real eye-opener.But some reading on the subject might be illuminating to you if you have the interest.
Right. That's where we're getting the disconnect.Math, designed by man is black and white, but it is not, in most applications precise.
It's not the math that's imprecise, it's how it is sometimes applied. If I say that I'm going to approximate this non-linear process with a linear model, then the model's output will not match the output of the actual real-world process. NOT because the math is imprecise but because of how I chose (or was constrained by the limitations of current mathematical knowledge) to model the real-world process.
Again, in this particular case, there's absolutely nothing at all imprecise in the mathematics that mehavey provided. The imprecision comes in trying to apply that mathematical calculation to the real world. The issue isn't the math at all, it's in the fact that there were assumptions made and those assumptions are not completely realistic. That imposes limitations on the "model" and means that the results can't be relied on as anything more than to provide a very general idea of the sort of best case scenario.
Same thing. Those methods are quite precise, but if one tries to use them to model real-world phenomena, there's going to be some disparity between the results of the mathematical output and the real-world systems they are supposed to model. Not because of imprecision in the math but because of issues with trying to make a mathematical model that takes into account every possible aspect of a real-world system.Non-linear algebra, partial differential equations...the stuff actually used to solve the most complex problems, is not, even with the computers.
It would be like saying: This metric end-wrench is imprecise because it won't fit a rounded-off bolt or this SAE bolt. The problem isn't the wrench, it's that the wrench is made to fit metric bolts of one specific size that are not rounded off. It's not a problem with the wrench, it's that the real-world has generated a problem that the wrench can't solve, or that the user is trying to use the wrench for something that it can't do.
We all live in our own boxes, do we not?
Analytical solutions, in either close-form or open-form, are exact, even for complex problems. But they may not exit. Generations of mathematicians spent their whole lives search for such solutions. Despite the elegance of their works, the solutions they have found are tiny subset of problems present.
What do we do when we don't have the analytical solutions? Numerical methods are used. Following mathematical relationships among quantities, iterative algorithm is formulated to find out numerical values of the solution, point by point, starting from the initial and boundary conditions. Such numerical solutions are not exact. But with right methodology the error can approach zero, depending on number of iterations allowed. Such methods, although not exact, fit beautifully with computer, so they are widely used today. Before that, an office full of people are employed to crunch the numbers.
My high school friend Raymond was a brilliant mathematician, a real one. A beautiful mind behind he socially awkward appearance. He earned his post doctorate in pure maths before 30. I still remember the fear in the high school math teacher's eyes when Raymond raised his hand to ask question. He despised numerical analysis as it wasn't pure maths. Guess what his job is? He is top analyst with an internal financial firm in Tokyo, doing... Numerical analysis! He changed his mind after having wife and kids. He couldn't bear to see them being poor accompanying him in the search of perfect, exact, and elegant solutions in the endless ocean of mathematical symbols.
Back to the box of reality. Where the mass is removed from the hammer is important, if it is a rotating hammer. It is the moment of inertia that matters.
-TL
Sent from my SM-N960U using Tapatalk
Analytical solutions, in either close-form or open-form, are exact, even for complex problems. But they may not exit. Generations of mathematicians spent their whole lives search for such solutions. Despite the elegance of their works, the solutions they have found are tiny subset of problems present.
What do we do when we don't have the analytical solutions? Numerical methods are used. Following mathematical relationships among quantities, iterative algorithm is formulated to find out numerical values of the solution, point by point, starting from the initial and boundary conditions. Such numerical solutions are not exact. But with right methodology the error can approach zero, depending on number of iterations allowed. Such methods, although not exact, fit beautifully with computer, so they are widely used today. Before that, an office full of people are employed to crunch the numbers.
My high school friend Raymond was a brilliant mathematician, a real one. A beautiful mind behind he socially awkward appearance. He earned his post doctorate in pure maths before 30. I still remember the fear in the high school math teacher's eyes when Raymond raised his hand to ask question. He despised numerical analysis as it wasn't pure maths. Guess what his job is? He is top analyst with an internal financial firm in Tokyo, doing... Numerical analysis! He changed his mind after having wife and kids. He couldn't bear to see them being poor accompanying him in the search of perfect, exact, and elegant solutions in the endless ocean of mathematical symbols.
Back to the box of reality. Where the mass is removed from the hammer is important, if it is a rotating hammer. It is the moment of inertia that matters.
-TL
Sent from my SM-N960U using Tapatalk