three-body problem

No it doesn't, actually. For instance, a galaxy with a large peculiar velocity (wrt to the expansion of the universe as a whole) has an enormous kinetic energy. As it travels, it passes slower galaxies and gradually moves into groups whose velocities are more similar to its own.

Result: an enormous decrease in its kinetic energy, that didn't go anywhere.

Cheers

Phil Hobbs

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Dr Philip C D Hobbs 
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Phil Hobbs
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LT Spice simulates a comparator with inputs connected to two identical resistive voltage dividers just fine. Rock-stable equality. No amount of simulation can substitute a moment of thinking.

Best regards, Piotr

Reply to
Piotr Wyderski

The usual problem with LTSpice is that many oscillators which work fine in the real world pathologically refuse to un-Buridan's ass themselves without a lot of coaxing.

Reply to
bitrex

I won't. Not until 'bad' gets a definition (that word is just SO generic, it could mean... anything). Agreeing to something like that, is like writing a blank check.

Reply to
whit3rd

If a computer program was coded to predict the dynamics of a physical system, and it doesn't in any useful manner, it's a bad program.

How about that?

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John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  
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John Larkin

I know you didn't use the word 'chaos' above. Still,

I just want to say that IMHO chaos is over used. The weather and other stuff (fluid dynamics, etc..) is complex. If you chase computer models down there is all sorts of beautiful stuff. All those beautiful butterflies. The real world is scrambled, patterns are lost in the noise... My only real world example of this: We sell this Lorentz chaos analog circuit, that I copied from Paul Horowitz, (I tired to make it 'better' by upping the gain in the multiplier stages.) I wanted to see the period doubling as chaos is approached. In the analog world, I had to struggle to see more than two period doublings, at high frequency noise blurred things, and getting close to DC you bump into 1/f noise.

On a 'puter you can dive down as far as you program.

George H.

Reply to
George Herold

in ANY useful manner? So, you've never really seen a bad program!

Think like an engineer, the value of a program relates to its functions, and there can be a TEST of those functions. The Pentium divide bug would skate totally past that definition of 'bad'.

It's a hard issue, to really define a software test. The Pentium divide bug DID skate past testing.

When a projection of an orbit gives an inaccurate value, it's usually because of the input observational errors, and there's a mathematical relationship of the output errors to those input observations... a time derivative. For something like an orbit, where the position values are cyclic, the positions don't change much cycle to cycle, but the small error times derivative times the delta-time grows, grows, grows... maybe faster than linear when the error becomes no-longer-small.

It's not the 'program' at fault there; it's input data, and the sensitivity of megayear projections to the measured values of the orbits of everything nearby...

It's easy to make a mathematical formula that gives completely accurate 1% predictions to one set of 1% values, and blows up with signal-to-noise estimates of -120dB to a slightly different set of values. Any program using such a formula inherits the noise sensitivity. And, there's NO REASON to believe that such a formula is not the correct physics.

Reply to
whit3rd

I've always found that the "real work" gets done when one goes about the sometimes difficult task of identifying the reasons that the simulation and the prototype work differently.

Only then do you really understand how it works.

m
Reply to
makolber

Computer simulation can be a great way to check whether your math applies to the real world. i.e. if you have a mathematical model on how light interacts and reflects from objects, and you do a render using that model and every shadow is upside-down or something, clearly that mathematical model can't be representative of the real world.

Reply to
bitrex

The isolated unconstrained three-body problem doesn't exist in nature, and there is no closed-form solution to the ODEs. It is meaningless to talk about 'bad' and 'good' solutions to the problem, like there is actually some closed-form reference-standard solution hiding out there but it's known only to God and our puny computer simulations can only approximate it badly or goodly.

Reply to
bitrex

I guess that every bad program is useful as a bad example.

But if people spend enormous sums coding a sim, and base trillions of dollars of public policy on the results, and it's not usefully predictive, that's a bad program.

Unless the orbital mechanics are strongly chaotic, as some 3-body cases are. You could write theroetically perfect differential equations, and maybe even work out analytic solutions, but they wouldn't be predictive of any real system. And a numerical sim ould be hopelessly polluted by finite math precision.

Some systems simulate beautifully; some don't.

--
John Larkin         Highland Technology, Inc 

lunatic fringe electronics
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John Larkin

Wow, I never knew they spent that much money on the three-body problem!

Reply to
bitrex

Nonsense. There aren't large sums involved (on the Solar system scale) by the paltry few people employed in calculating orbits. Public policy on (for instance) placement of geosynchronous communications hardware has been a big-money-payback success.

Again, you just Don't Get It. Place two oscillators side-by-side, and a SPICE model will predict frequency and phase. But if you look at the relative phase of the two after a few million cycles, I'm reasonably certain your model won't have the right number.

The phase REALLY matters for predicting an eclipse, or a collision, and George Airy (a century or so ago) correctly identified this as an insoluble long-range-simulation problem for orbital motion.

There aren't any megabucks being spent on naiive notions either in SPICE, or in orbital prediction, or weather models. The folk who USE the models, as you use SPICE, aren't naiive.

Your own experience ought to have taught you that much.

Reply to
whit3rd

John Larkin doesn't understand the scientific evidence for anthropogenic global warming, doesn't like what that evidence demonstrates, and is happy to condemn the computer programs involved on that basis.

It's a bit silly.

John Larkin hasn't noticed that many chaotic systems simulate beautifully in the short term. Short term weather prediction works and we can predict solar planetary orbits up to about a million years ahead.

--
Bill Sloman, Sydney
Reply to
bill.sloman

Of course, you could do the math and really understand it. ;)

Cheers

Phil Hobbs

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Dr Philip C D Hobbs 
Principal Consultant 
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Reply to
Phil Hobbs

I'm different from you. I don't get much insight from a page of equations. I have to think about a system until I can *feel* it. Feeling it is my concept of truly understanding. My deconvolution thing, and my new weird PLL, and other things came from the subconscious, from just thinking about the problem. The math came after that.

Simulation helps me think about system dynamics. Sometimes I abandon a sim before I actually run it; I've learned from sort of just formulating the problem.

You can teach people to solve equations. I don't know if you can teach instinct. Maybe.

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John Larkin         Highland Technology, Inc 

lunatic fringe electronics
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Reply to
John Larkin

It depends on how you do the math. The way it's usually taught, it's almost like public-key crypto: easy to do in one direction (analysis) and next to impossible in the other (synthesis).

The way I like to do it is to keep the contributions separate, and write things like convolutions in Bracewell's short form, i.e.

a, b, c constants g, h, i,... real-space functions G, H, I,... k-space functions

g*h convolution g star h correlation F(a) Fourier transform

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Reply to
Phil Hobbs

Convolution, to me, is visualizing two waveforms sliding past one another and interacting. The Fourier transform is drawing a sine wave on top of another waveform and asking how similar they look. Don't need no eee-jay-omega things.

Some things are so complex that just analog-brain visualization doesn't work. I get help with that stuff. Or simulate them.

I've got to show you the PLL one day.

What if they started using numbers *before* formulas? That's what I did. When I was an EE undergrad I had a job designing stuff, like

32000 HP control systems and flight hardware for the Saturn moon rocket. I never took a course in control theory or digital logic... I was too busy doing it. My professors didn't approve of students having jobs (or wives) because that distracted them from the academics. They said that undergrads didn't design stuff; design was for grad students. I got out of there ASAP.

No, no, formulas have to be exact!

EE schools, post WWII, developed an inferiority complex re physics (and dollar envy) so switched from being hands-on to being closed-form academic. A mix would be better, instinct and math learned together.

--
John Larkin         Highland Technology, Inc 

lunatic fringe electronics
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Reply to
John Larkin

Not all. UIUC was very hands on, at least when I was there. Most of the profs were of the WWII generation who, for the most part, were a hands-on generation. UIUC grads were highly sought after because they did know which end of a soldering iron to pick up. I have no idea how it is now. I haven't been back for 20 years (no one I know there, any more). GT seems to be quite hands-on. They have a pretty big coop program, too.

Reply to
krw

l

I wonder how many times the US coast will need to be pounded by hurricanes before you accept that the climate has changed for the worse as predicted b y the models. I was at a site last weekend where you can see sustained peri ods of certain prehistoric sea levels as raised beaches from a warmer era w hen the seas were much deeper than today.

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A fair amount of effort has gone into planetary ephemeris simulations both at JPL and in Paris where VSOP87 was the first semianalytic perturbation so lution that really cut the mustard. It really only affects lunar and interp lanetary missions (and observing pulsars close to the sun or Jupiter/Saturn ).

Russia had much worse computers and weaker rockets back in the days of the Moon race and so had to find ingenious slower but lower energy transfer orb its to get their probes there. Numerov developed some cute tricks for them. A more recent take on the subject which might interest some readers is her e:

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Likewise a fair amount of computational power has been expended on computi ng the development of the universe from the Big Bang with a remarkable degr ee of agreement with what we observe. They were still struggling to get ind ividual galaxies to behave themselves properly in my day. It only takes one really close encounter and you very easily end up with a choice of incredi bly stiff equations with infinitesimal time steps or failure to conserve en ergy. Various tricks were developed over the years that allow such things t o work within the limits of what can sensibly be computed.

It is only where climate simulations are concerned that the right whingers want to shoot the scientific messengers because they don't like the message .

Regards, Martin Brown

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Martin Brown

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