Alpha particle emissions are common causes of single-bit errors, especially from ceramic enclosure materials in integrated circuits. Mitigating soft errors from circuit packaging is an active area of research in materials science. Parity bits and CRC error checking are needed precisely to reduce the impact of these errors down to manageable levels.

"Alpha particles can be stopped by a sheet of paper, beta particles by aluminum, and gamma radiation by a block of lead."

This is what I read online. A typical hardware components is enclosed in a aluminum case so really gamma radiation is of concern right?

GP is saying the radiation is emitted by the component package itself, i.e. the random decay of particles in the ceramic surrounding an IC can cause errors.

Lantz, "Soft errors induced by Alpha Particles", 1996. http://ieeexplore.ieee.org/document/510798/?reload=true

It comes from within.

Concrete and brick are significant sources of radiation. Especially when new.

I don't know if the sort of radiation they give out is of much risk to computers however.