You'd need a supercomputer that's the most badass of the badassest supercomputers, 'cause there's a whole lot of calculations that's just annihilate each other when it's all said and added, multiplied, divided, integrated, subtracted, differentiated, exponentiated, divided, and otherwise evaluated. Aside from the simple difficulties of computation, it's quite possible.
But just try to imagine calculating the probable locations of each and every atom in a large piece of metal that's being subjected to constant stress over a long time, succumbing to creep all the while, all its atoms trying to jump slightly off to the side here and there, dislocations wiggling their way through the lattice--shifting, attracting, repelling. OoooOOOoooOOOOooh. That'd be awesome but it's too damn much work.
Our understanding doesn't extend much beyond our ability to observe and measure. As our instruments become more complex with higher degrees of precision , our approximations become closer to 100% (maybe 99.9999...%).
I'm sure there is a direct connection between the quantum reality and the macro reality but have no idea what that is and apparently I'm not alone.
Classical physics can be derived from quantum physics--it's just a matter of taking limits. They aren't the ordinary x --> L limits, quite, though; rather, they're x/y --> L, with that L usually being 0.
The real difference between classical and quantum is that quantities are allowed only to be in/at certain explicit, discrete (not discreet) values given by an expression that includes an increment number, n.
Such as the energy levels of a "particle in a (1-dimensional) box": E = n^2*h^2/(8*L^2*m), where m is the particle's mass, h is Planck's constant, L is the width of the "box", and n is some integer. E can be 0 or, at the second-least, h^2/(8*L^2*m) when n = 1 or -1. As the width of the box increases out of the tiny world that you've heard that quantum mechanics applies in, the box becomes of classical size, so to speak, and that minimum nonzero E becomes less and less and the increments between energy levels also decrease more and more, approaching a good approximation of a continuum of energy levels which is what classical physics holds as true.
Quantum theory is by design such that the classical mechanics follows as a consequence. Why would anyone even consider a theory whose macroscopic predictions disagree with our best-verified observations?
People speak about quantum weirdness probably because most textbooks on the topic discuss special cases where the difference to the classical systems is very clear, with an emphasis on the technical aspects. The popular books are also focused on the weird stuff because this is what people want to hear and what boosts up the sales.
You could say that the classical world is not weird, because basically it is just an average of the microscopic world and in massive systems the deviations from the average become increasingly small. But probably the evolution of our senses is also related to the issue.
"Where does the common sense come from and how can it be derived from a weird fundamental system?"
I'll try to answer this. The basic quantity of classical mechanics is the trajectory of a particle, while quantum mechanics deals with probability distributions of measurement results. The process of getting classical mechanics from the quantum theory usually involves either making things heavier or taking a quantum parameter multiplying the mass to infinity. With increasing mass the distributions become sharper and in the end any measurement outcome will be indistinguishable from a single value - the classical result.
It is not true that quantum mechanics allows only discrete quantities - for instance spatial coordinates or energies after a scattering event have a continuum of possible values. The discrete values are often seen under confinement when the probability distribution adopts the form of a standing wave.
OK, but I'm not a physicist so it is difficult for me to discuss this on a higher level. Can you therefore answer these two more simple questions:
1) Can you derive F=ma from quantum principles?
2) What size group of atoms would be necessary for the more classical laws to begin to be manifest? 100, 1 million?
"1) Can you derive F=ma from quantum principles?"
Here's my take on it: F = ma follows from the conservation of energy, because mav is the rate of change in the kinetic energy, while Fv is the rate of change in the potential energy. In quantum mechanics the energy principle holds always by construction.
The probabilities of possible measurement results depend on time and space coordinates. When the maximum of the probability moves, the measurement outcomes matching with the new maximum become more likely. That is how in the classical limit it will look like there is a trajectory coming from the equation F = ma.
"2) What size group of atoms would be necessary for the more classical laws to begin to be manifest? 100, 1 million?"
This depends a bit on which classical laws we are considering.
If you take an atom as a whole, it is already quite massive and moves around in classical manner. You don't expect it to spread out in free space, form standing waves in a box or tunnel through obstacles. The quantum phenomena are more important for electrons and for light.
In atoms, the electrons are trapped into the "box" of nuclear Coulomb attraction. The chemical and optical properties of atoms, which are usually beyond classical explanations, come from the quantum mechanics of these trapped electrons.
When atoms form larger clusters, each constituent makes some properties more probable than the others. In very large clusters only the conventional elastic, thermodynamic and optical properties survive. People say that this starts to be manifest already in clusters of about 1000 atoms.