Spin of electron While reading 'The Universe in a Nutshell' by Stephen Hawking, I came across the example of cards and how he used it to explain concept of spin and fermions and bosons. There he defined 'Spin' as number of rotations required by a particle to regain its original state and "look" exactly "same". But since electron is an elementary parṭicle how are we supposed to define an axis around which it spins. I ṭried reasoning with it but wasn't able to. Can someone help me?
 A: 
There he defined 'Spin' as number of rotations required by a particle to regain its original state and "look" exactly "same". 
  But since the electron is an elementary parṭicle how are we supposed to define an axis around which it spins. I ṭried reasoning with it but wasn't able to. Can someone help me?

see an article in Scientific American-

"When certain elementary particles move through a magnetic field, they are deflected in a manner that suggests they have the properties of little magnets. In the classical world, a charged, spinning object has magnetic properties that are very much like those exhibited by these elementary particles. Physicists love analogies, so they described the elementary particles too in terms of their 'spin.'

"Unfortunately, the analogy breaks down, and we have come to realize that it is misleading to conjure up an image of the electron as a small spinning object. Instead, we have learned simply to accept the observed fact that the electron is deflected by magnetic fields. If one insists on the image of a spinning object, then real paradoxes arise; unlike a tossed softball, for instance, the spin of an electron never changes, and it has only two possible orientations. In addition, the very notion that electrons and protons are solid 'objects' that can 'rotate' in space is itself difficult to sustain, given what we know about the rules of quantum mechanics. The term 'spin,' however, still remains."
Professor Hawkins was also trying to communicate how one may look at the different spin states of an elementary particle and to communicate one uses analogies which helps in building a picture.
Similar is the features with colour states of quarks or flavours associated with quarks.

Spin has served as the prototype for other, even more, abstract notions that seem to have the mathematical properties of angular momentum but do not have a simple classical analogue. For example, isotopic spin is used in nuclear physics to represent the two states of a 'nucleon,' the proton and neutron. Similarly, quarks are paired as isospin 'up' and 'down,' which are the names given to the two quarks that make up ordinary matter. The rotational symmetry of space and time is generalized to include symmetries in more abstract 'inner' dimensions, with the result that much of the complex structure of the microworld can be seen as resulting from symmetry breaking, connecting profoundly to ideas describing the spontaneous formation of structure in the macroworld.

These terms ' spin', 'colour', 'flavour' though in common use as terms outside the 'physics'  domain do not carry its usual meaning.
