We view reality in many different ways,changing interpretation of it regularly while every point of view remains partially in the memory as a separate sheet of information . So in a sense our perception of reality is a multi-valued function (observation) from our memories of information to the actual reality .However the reality and our interpretation of it is a dynamic process changing in time ,usually in a continuous way but at moments of big emotions also very suddenly and unpredictable . The different sheets are connected at places ,say two-by-two, for each connection a different set of places but every two sheets are connected by at least one wormhole allowing to change from one sheet of interpretation to another in a continuous way ; moreover the sheets are in constant movement being reshuffled in reaction to new events experienced. So your actual interpretation of reality is the sheet in front of you and yo do not observe the interpretations on other sheets unless they move to the front position. It is like a rubber building with many stores connected by wormholes at many places ,always moving and reshuffling the floors with the stairs flexing and staying connected . This picture is exactly the one of a Riemann surface used to make a multi-valued function on some space into a single valued one on some new constructed space , i.e. the many layered kind of construction jut described.We view a multi-valued reality as observed in our mind and perceive it as a single-valued function on a very complex dynamic Riemann surface,guided by your emotions and rational ideas . The use of Riemann surfaces in Math can be seen for example in considering the function of a complex variable z ,say the (multi-valued) function “square root of z” which has a positive and a negative complex value everywhere except at z=0 ,as a single-valued function on two complex planes glued together in one point (here the 0) taking on one sheet the positive value and on the other the negative while both agree in 0. Thus our interpretation of the reality seems unambiguous because we actually use a much bigger space for the interpretation than the actual dimension of the reality necessitates .
At specific times you observe the reality on the sheet in front of you ,not on the ones in the back of the deck unless they move to the front. Some sheets contain a lot of horrible facts from reality together with your feelings of sadness and anger,some contain the lovely things in life like grandchildren,mothers,friends,…,together with your feelings of joy and happiness. Yet every sheet is connected in at least one place to any other and so you can move almost unaware from the good to the bad, from spiritual to concrete,from optimistic to pessimistic,from scientific to religious,or conversely. So at moments you can be completely at peace with the universe ,like I am now,even knowing there are so many horrors on other sheets. So we see reality as a one-valued observation at the price of letting our brain value “facts” on a multi-sheeted domain ,where all the mystery is in the connections between sheets ,we only realize the connections exist when we experience them by moving from one sheet to another . Hence we did not construct those connecting wormholes in an aware way.
It is the system’s way of surviving conflicting interpretations in our own evaluation of events in reality.
It is important to stress the role of the memory in the process of understanding reality ,indeed it is obvious that all our interpretations of reality are based on past information . The creation of an interpretation of the universe takes time in the brain,it mixes very many observations combined with related emotions ,either experienced at the time of “learning” about the assumed structure of reality or emerged at the moments of contemplation of the observations in the framework of the larger picture. The interpretation takes the form of a “theory” about life or the universe and is remembered for longer periods while the emotions influencing the construction are mostly forgotten after a while or at least the connection between the aspects of the interpretation and the emotions at the moment is forgotten.The effect of the role of the memory is that the psycho-Riemann surface we gradually develop over years of living is at the same time decomposing while being constructed, it is a surface made out of Swiss cheese ,decaying Swiss cheese! When getting older there are more holes and in the end the layers of the construction may become separated completely because the areas of the connecting points are being forgotten!So at the end of our cognitive life the interpretation of reality may be a very conflicting set of interpretations without obvious relations and no flexibility for moving around in it ,the world shrinks and yet looks disconnected!
We do use free will in the construction of the psycho-Riemann surface and also,but less(!) in the choice of paths we follow in it by remembering what (we think ) the world is . Unlike in Physics we use no measuring in the construction of our model but since our model takes into account immeasurable effects also from our own and other people’s emotions as well as from all kinds of human interactions it is in many ways a deeper model than the one constructed in scientific ways . In fact depending on the ability of each individual the scientific “facts” known to him or her are used in the construction of the model .The interactions in society allow to obtain an interactive social structure obtained by gluing the interpretation domains even further ,thus we may actually use a social-emotional -rational-global model of interpretation if people can only agree to talk and communicate peacefully . That would be a great reality.