DarkAntimatter

4 hours ago, vlaiv said:

Although those concepts are related to math, understanding them is related to physics more - why those particular mathematical constructs are used when they are used.

Out of larger class of mathematical constructs, each having certain features, these are used in physics because of their suitability - they fit underlying physics.

Maybe this analogy will help - consider vectors - little arrow ones. We have vectors in 2d, 3d and higher dimensions. Once you understand basic concepts related to them - like their addition, dot product and so on - you have mathematical knowledge of vectors, but calculating mechanical system in 3d requires 3d vectors - particular kind of vectors and you need to know what sort of mathematical manipulations yield physical results - that is related to physics rather than mathematics.

So better to learn these directly and why they are needed I suppose.  

1 hour ago, vlaiv said:

Actually no, that is what you in principle need:

- calculus

- algebra (meaning algebraic structures like vector spaces and groups/rings/ ....)

- Fourier analysis

- complex numbers

Important thing is ability to think in abstract terms - which should be covered by second above - algebraic structures. Most of QM formalism is expressed in these abstract structures. For example, when we speak about vector spaces - most people imagine plain old vectors - little arrows that have origin, direction and magnitude. But vector space does not mean those vectors - it can mean space of real functions where you can use certain operations on members of the space. Vectors are thus members of a set - or in simple terms some entities that behave in certain way.

Here is what wiki lists as set of math tools needed:

Thanks, that is a good list.  My background is as an engineer so I have a (very) little bit of familiarity with the above.  But I found it slow going when things turned to Pauli (which seem to be important to really understand spin), and especially gamma (Dirac) matrices.  I was not sure if this is something that I should just be expected to learn from the information in the QM book or if there is a particular math subject that would cover this better.  

Thank you. By "good understanding" I meant what particular math so that QM becomes not very complicated. I expect that will mean more than algebra, ode, and some Fourier analysis. 

On 07/08/2019 at 05:57, vlaiv said:

QM is not that complicated at all, what is problematic to most people is math behind it - you need to understand the math in order to understand the QM.

If you have math knowledge, then there is a very good set of lectures online by Leonard Susskind that cover many aspects of physics including much of QM. Lectures are based on his book and titled the same: Theoretical minimum

There is a website with link to videos of lectures on youtube:

https://theoreticalminimum.com/

I find lectures very good although sometimes a bit slower paced than I would like (some concepts are explained multiple times because lectures are recorded in actual class and people have questions, etc ...).

Out of curiosity, which maths do you recommend in order to have a good understanding of QM?

Well, to partially answer my own question, I did a little googling and did not uncover any in range of amateur scopes but this APOD from 2012 is a Hubble image of a galaxy 150 M ly away.:  https://apod.nasa.gov/apod/ap120304.html  

It looks similar to the above diagram of our galaxy to me.

Does anyone know of any examples of other warped spiral galaxies that are visible in amateur scopes?

Another possibility is Autostakkert. As!3 works well for me in wine on Ubuntu and I've been happy with it. 

Yes, they start nearer the poles and gradually get closer to the equator as the cycle progresses. The northern and southern hemisphere spots tend to have opposite polarity and this reverses with each new cycle as mentioned. 

One can find a summary of the day's activity on several sites. I like the one at http://www.solen.info/solar/. This is indeed a cycle 25 spot, but not the first. 

It's open source but looks like it is Windows - only?

18 minutes ago, Alien 13 said:

Maybe its just me but linux cant handle the latest high end graphics cards and has difficulties with most ancillaries like Canon cameras, printers and other drivers...it seems to default to some kind of generic option without all the proper options. I do use Linux mint on one of my laptops but find it limited, would be nice if I could use Photoshop and play the latest PC games with it.

Alan

I agree about photoshop.  Gimp is really powerful, but probably not quite as full-featured as ps and less user friendly.  The main drawbacks of non-WIndows, to me, are no photoshop, fewer games, and no office for the case when you need to collaborate with office users (there are good alternatives if office compatibility is not important).  Well, OSX has ps and office, so I guess that is a linux drawback.

I do use high-end NVIDIA graphics cards for both visual and CUDA applications and don't have trouble with them at all.  NVIDIA provides and frequently updates their drivers in linux as well as windows.  The HPC (high-performance computing) world is dominated now by computers with CUDA GPUs and almost all of them run linux - GPU support is solid, at least for NVIDIA GPUs.

I've found network printers are supported very well and linux finds them without any hints and gets the proper drivers for any printers I select.  Haven't tried connecting a printer directly to the computer.  My Nikon DSLR works well; haven't tried Canon.  

I guess operating systems are something of a personal preference issue and they all have their pros and cons.  

2 hours ago, Alien 13 said:

I often wonder about Linux users that perhaps spend days/weeks/months trying to iron out issues for a system that is pretty useless for everyday things when Windows just works...

Alan

Well, there are a lot of things that just work in linux too.  Speaking as a person who uses computers to get stuff done but doesn't enjoy trying to iron out issues I find linux more productive overall for me.  Try installing a recent linux desktop, such as Ubuntu, and a fresh copy of Windows 10 on a new computer from scratch and you might have a different outlook on which comes the closest to just working.  In the old days linux had a lot more problems but I suspect it now works out of the box much better than WIndows.  The reason Windows has an "easy" reputation now is that the new computer almost always comes with Windows already installed for you.  Granted there will be the occasional new device which needs a special driver and for which the manufacturer hands you a Windows driver but doesn't have one for linux, but it is getting rarer.  

I would also cast a vote in favor of a getting started with Kstars/ekos thread, thanks.