This focus ties up the resources of the conscious mind, and it starts to lock up. This is the first stage. A hypnotic trance (or meditative trance if you prefer, it's the same thing) results from an excess of focus and stressful emotion.

As the scientist tries to solve the problem the focus is clung to. As it refuses to be solved frustration, anger, and fatigue build up. A feeling of rushing might start to occur even while standing still. The scientist will likely pace a lot, and raise the body's physical energy up high. The emotions start to spike upwards in strength at random. Breathing often becomes heavy. The scientist might start muttering constantly to himself or herself. There tends to be a wild exuberant feeling, accompanied by stress and even fear. Pictures will dominate the mind, usually having to do with the problem being focused on.

With the natural way of entering madspace, this is about half of the trick. The other half comes when the scientist tries to expand his mind by stilling his thoughts, in an effort not to lose the many thoughts racing around his or her head. This might be a conscious trick, of meditating while maintaining focus. It might be, like with Archimedes' taking a bath, an attempt to relax while being unable to let go of the problem.

If everything is just right, then madspace is entered into. If the solution to the problem does not just suddenly appear in a flash of insight then the flash of insight occurs anyways but in a more general sense. The scientist in madspace is being almost overwhelmed with powerful emotions. There is actually an impulse to laugh maniacally. It's driven by a need to express the sheer exuberance of being in that state. All emotions are incredibly powerful, transcendental versions of their normal selves. Everything seems to shine. The scientist might hear voices or see visions. It feels like being more awake than you've ever been before, of being AWAKE!!! In this state of hyper-awareness the intellect feels a million times more capable than ever before. You become capable of seeing solutions to problems without having to think about them. Every solution you see is like being hit with a lightning bolt of divine revelation. Focus is easy. However, anything that tends to interfere with your focus will tend to make you very angry indeed. It is very easy to enter the berserkergang from madspace.

Of course this state can't last forever. Eventually either fatigue of thinking the wrong thought will ruin the state, and the scientist will once again assume his mundane mindset. After this comes a period of great tiredness and stupidity. The scientist will likely be more irritable than ever. The negative consequences afterward seem proportional to the length and intensity of the madspace experience itself.