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The knoweledge has evolved. We know more than what we knew yesterday.It has branched off into many different areas.It has created many concepts .... and all of those concepts can be learned by any newcomer.But some of the concepts are abstract , purely abstract.How can one learn these creations of mind if they do not suggest any thing real ?For example infinity , 0 , complex number i , extended number systems which allow divisions and multiplication of infinity .Can we(or should we) define them in a way which purely abstract?If not then how will we define the conpcepts mentioned above?
I am referring to the Extended Real Numbers which includes infinity as a Number.When you say 2people +3 people = 4 people there is a evolutionary link with the method of empirical understanding to understand an abstract idea using associations with real world instances. people are real .. they are not abstract .And the real objects found in nature are used to develop a understanding of addition.infinity , 0 and i are simple from the point of evolutionary thought. Try to define infinity , 0 or i to a student without using purely Abstract constructs. To begin with , suppose a person who doesnt understand Numbers asks :What is Number? What will be your answer?
In roman letter we represnet seven as VII. Whereas in Arabic it is represent as 7.How do we know that we talking about the same concept?
Because people have used the two notions interchangeably without any loss or gain of meaning.
The growth of knowledge has some evolutionary aspects notably where people are interested in things there can be a competition for ideas and the good ideas survive and the bad ideas fail there are also problems with ideas that are very attractive an interesting and interesting that people wish they would happen and try to create them even though most of the physics says they are impossible ideas like this are multiple intercommunicating universes, time travel and faster than light travel including instantaneous teleportation. These are the subject of many thought experiments and fantasy stories.
The very attractiveness of ideas like this does not make them useful or valid scientifically and scientist are often considered as bigoted when they put them down for very good scientific resons. in an evolutionary context these ideas are a bit like an unstable ecosystem where one species is multiplying out of control because the normal controls that apply to stable ecosystems have for some reason been bypassed.
I am sorry to say that human self awareness and skills is one of these occasions.REP:I dont think so .. I explain your disappointment as absence of purpose.. The purpose is TSP (i.e Towards Sustainable Pleasure)
Mathematics on the other hand is a special sort of language to describe things that do not have to have any physical reality although where mathematics aligns with physics it is a very useful discipline and a fundamental tool for researchers. Ideas in mathematics are as subject to fashion and selection as much as other sciences though.REP: The problem is where mathematics works Physics doesnt and where Physics works Maths doesnt.