a genius generates as many alternative approaches as one can but an average person thinks exclusively focusing on specific information and excluding all else. ,exclusive thinking leads us to neglect potentially important pieces of the problem .
First, what is a genius? A person with a high IQ? Not necessarily. A genius is a person who posseses what I and others call "creative insight". It is seeing something in a new light, in a new way from a new point of view, of thinking "outside the box". It may spawn a "Eureka moment". High intelligence aids and abets the process but is not a formal prerequisite. In the brain of the genius, however, thought processes likely are better organized and efficient than in the brains of us "average" folk. This contributes both to increased insight and to creativity.
A subsidary question might be "Is homo sapiens sapiens currently evolving in the direction of increasing mental prowess"?
Does a genius have a different sense of time than average men and women? What was going on in Einstein's mind during the time he worked as a postal clerk?
They undoubtedly think, but how? I am not familiar with any genius, therefore I can't answer. This kind of people is so rare... I know many talented, smart, knowledgeable, calm, creative people, but so that these properties all together will be in same pot...
Genius differ from quite good individual due to their knowledge ,skill dexterity in their action of life .For this any other individual of average level should not be underestimated due to the genius of the person in the sense that genius cannot be an all round performer as his knowledge & skill remains in his areas & in this line any average person may be man or woman can not be underestimated .
Both the genius and the average person think. But the mentality of the genius is not similar to that of the average person. Their views, interpretation, ways of analysis are different. That is why there are individual differences between one person and another.
I can imagine one individual processing information "faster". One individual doing pattern matching "faster". One skipping steps in a proof better. But what more is there to "seeing things differently" is there?
Geniuses are often stupid regarding practical matters. Paul Erdös never buttered his own bread until he was 21 and then was astounded by how easy it was.
For the record I beg to differ with your summary list of three thought-processing characteristics that define a "genius". A genius might think faster (that is, more "efficiently") than the rest of us and may have a better memory ( I don't know what you mean by "Ability to skip steps"; isn't that connected with speed?) but I would maintain that the key to being a genius is the ability to grasp the essence of a problem (insight) and the ability to see the problem in a new way, to think outside the box (creativity).
Discussion Summary so far. I have been placing concepts as they make sense to me interpreting what others have said and my thoughts as well. Please feel free to offer new points or cross out my interpretations all together:
Compared to average individuals thought processing:
1. Is faster (can be interpreted as "more efficient");
I considered "faster" in reference to "speed only. Thought processing of one individual compared to another individual can differ in terms of:
POSITIVES
1. Speed only.
2. Faster due to "skipping steps" e.g. seeing a "shorter (more elegant) proof.
3. Better memory (e.g., ability to retain more logical theories).
4. Better insight, e.g., can see more clearly what will and what will fail.
5. Better able to see outside the box.
NEGATIVES
1. Possible lack of common sense in certain areas.
The main difference is in the pin - point concentration given by the genious in the particular subject of interest added with somewhat better merit with a key to open the new doors.