michael.h.f.wilkinson

Then I suggest you study chaos theory in more detail

That is akin to invoking magic, but unless it has infinite accuracy (or the infinite tape of a Turing machine) it won't be able to predict the long-term behaviour of even a simple chaotic pendulum, let alone the universe. They won't be able to solve the Halting problem either

You are talking limits of infinite precision, which in the real world doesn't work (many students of my course on Modelling and Simulation within our CS Master programme have found this out the hard way ). In fact, we often suggest that if you are studying chaotic system, forget about high precision solvers as all they do is waste computer time trying to impose numerical stability on an inherently (physically) unstable system.

Wrong. The pseudo-orbit starts at Z0, and ends at ZN at an epsilon distance from Zx, the true orbit starting at Z0 is unknown. All you know is that there exists some point in an epsilon surroundings of Z0 that ends in an epsilon surroundings of ZN, which contains Zx. When you iterate these kinds of maps at various resolutions to see where the orbits end up, e.g. to compute fractal images like those of the Mandelbrot and Julia sets you will notice that as you zoom in, and increase the number of iterations N, each pixel on the boundary region of the set gets split up into smaller and smaller regions ending up in different regimes. Thus, if I pick any point in an epsilon surroundings of Z0, I will then not necessarily end up anywhere near the ZN I found in the first run, and therefore not anywhere near Zx. Incidentally, how do you intend to store the state in phase space of the entire universe in a physical computer which must therefore be part of that same universe (i.e. a strict subset). How could that computer even hold that information?

But it will be a pseudo-orbit, not a true orbit.

Amazing scopes, both of them. Just have to mop up some drool from my keyboard

It is possible, but the orbit found, ending up at Zx (or ZN if you like) does not actually start at Z0, but at some epsilon distance from it. The actual orbit starting from Z0 may end up elsewhere. See https://en.wikipedia.org/wiki/Shadowing_lemma

A Turing machine is infinite, so must be ruled out. The more general answer is that even assuming classical, deterministic mechanics, the computation you propose is impossible on any finite precision device.

If modelling of physics through any form of differential equations is correct, the kind of design needed would be mathematically impossible for any finite computational device, because the kind of design you want requires a precision which is impossible in such a device. So either you need an infinite computer, or you need a totally different kind of physics.

The shadowing lemma states that when performing calculations with limited accuracy (at least limited by numerical precision of your floating point representation), starting from point P in phase space, what you get is a reasonably close trajectory starting from some unknown point P' close to P. However, it may deviate arbitrarily far from the true trajectory starting at P. This is why we always make simulations with many starting points around P, and see where they end up. If they all end up roughly the same, we have a good idea where the trajectory starting at P should end up. If they diverge wildly, all bets are off. After sufficient time, wild divergence is rule rather than exception, and 4.5 billion years is generally sufficient.

I always use the word infinity with care (studying astronomy and physics at university teaches a certain rigour in that area). Chaos theory states that we cannot calculate the future of a system with positive real parts of the Lyapunov exponents unless there is zero error in both observation of the initial state, and zero round-off error in the calculations. This holds true even for a spring-mass magnet system of a handful of elements. Zero round-off error is impossible on finite bit resolution machines. Any error will make the calculations deviate further and further from the system's "true" orbit. We can do ensembles of simulations, as the shadowing lemma states that the computed orbits will be a reasonable representation of some possible orbit of the system at some starting point near the initial state. My point is therefore, that even without quantum mechanics, the future if the solar system would by very unpredictable, and that it would therefore not be feasible to design it. Turing machines don't come into this as these are essentially about integer computation.

Predicting the future behaviour of a non-linear dynamical system the size and complexity of the solar system (leaving aside any influence from nearby exploding stars) is mathematically impossible even when using classical mechanics (without all that newfangled uncertainty stuff), unless you have perfect knowledge of the initial state (infinite precision), and infinite precision in your numerical solution (not possible on any finite machine). Mathematically speaking just a single positive Lyapunov exponent means that any non-zero error will explode. In other words, the only way to know how the story ends is to set up some initial state, and wait for it to evolve for 4.5 billion years. We might feel that the solar system is special in that life could evolve in the first place, but then (as stated in the weak anthropic principle) we could not have evolved in any solar system that didn't allow life to evolve. Given the trillions upon trillions of stars out there, statistics doesn't just allow for the existence of special places, it quite literally demands them. Among a trillion stars, a million are one-in-a-million long shots (but then one-in-a-million chances come up 9 times out of ten )

That is superb. Like the very natural look

But posing with e.g. a nice bouillabaisse wouldn't smell too fishy

Feel free to differ in opinion, but please keep the tone friendly. I tend to agree with some of the early posts in this thread that all is fine as long as you are honest about the sources of the data. Astronomy is a science, so you can use other peoples' work provided you give credit where credit is due. If getting data from a rented remote telescope is "cheating", does this mean we can take credit for the kit we have, having just bought it off the shelf? Should we all build our own scopes, mounts, and cameras? So provided you mention the source of the data, and only take credit for the processing, all is well in my book. Moreover, if I plan the imaging (targets, instrumentation used, exposure times), I can take credit for that part as well. I recently got into a discussion with an astronomer from the Instituto Astrofisica de Canarias, and we got into a discussion on the potential of lucky imaging on really big scopes. He actually suggested donating 5 minutes of time on a seriously fast camera on a seriously large telescope. Unfortunately, powers higher up didn't want to "waste" even such a short time on the instrument for an experiment they thought would fail, but had I got the data and turned it into a neat image, would that be cheating? In the analogy of fishing posted earlier: I personally don't have the patience to go fishing, but I can cook some seriously good fish and seafood dishes. I can take full credit for the cookery, not the capture or culture of the fish, scallops, clams, etc involved. I would never pose with the fish, but I would happily pose with the resulting dish!

Midnight, in my case

I only spotted my first NLCs (from 53 deg N), last year, on the night of July 15. To the naked eye they were only a ghostly blur just above the horizon, but the camera showed them in their full glory. A shot with my Canon EOS 80D and Samyang 10mm F/2.8 Same clouds with the Canon EOS 80D and 50mm F/1.4

I always use the Baader Solar Continuum filter. The added contrast is worth the green colour. When imaging, you do need to add an IR-blocking filter of some kind, as the continuum filter had quite an IR leak. No problem for visual, but an issue when using a camera.

I got mine from dls-store.com Cheers, Michael

This time with copies of the signatures of Neil Armstrong, Buzz Aldrin, and Michael Collins on it, and one of the heart of darkness Will have a listen to the Sound of Silence, in the version by Disturbed (check it out, if you don't know it). Will wear one of these at an outreach event tomorrow.

I keep using GIMP, especially now it supports 16bits per pixel properly. The kit is expensive enough, so free software is most welcome

Interesting

The APM 80mm F/6 was sold under quite a few names when I bought it, including TS. I chose the APM one simply because of their reputation for good optical standards. Haven't regretted it at all

I still haven't spent a huge load on deep sky imaging, and still enjoy visual stuff a lot. Ideally, I have my EQ3-2 with APM 80mm F/6 triplet (often with 0.8x reducer) with modded EOS550D (just 175 euro) ticking away whilst the C8 sits on the Great Polaris mount for visual work. My DSO imaging set-up is (still) cheaper than my visual kit. Flats are essential, I find. I also find I leapt ahead once I started using AstroPixelProcessor rather than Deep Sky Stacker. I still have the latter, but the former gets me much better results without too much tweaking. My favourite results so far are M42, the Flame and Horse-Head, and the Pleiades. I have also experimented with the planetary cameras, and got some decent results with the ASI178MM

Apparently there are still MaxVision 40 mm 68 deg EPs around. I would be tempted by those if I hadn't already got the LVW 42. Link here: https://www.bresser.de/en/Sale/Display-Items/0215240-1.html I gather these have the same optics and mechanical construction as the Meade SWA 40mm