Mathematics differs from sensory science in that it draws its subject from structural construction to abstract abstraction of quantitative quantities, while other sciences rely on the description of actual sensory objects already in existence.
What do you think?
Yes, mathematics has a high degree of mental science but it is also more of applicable science.
Mathematics stimulates thinking but our students have attitude towards the subject. Maybe due to teachers' belief impacted on students. The subject is difficult.
Mathematics stimulates thinking but our students have attitude towards the subject. Maybe due to teachers' belief impacted on students. The subject is difficult.
I would say that subjects like convex analysis, topology, algebra, complex analysis, and geometry definitely have strong connections to physical objects - abstract as well as objects that we can observe in the real world.
It is also the subject of logic, memory , problem solving , calculation and also odering the solution steps.
It used for managing economic and social needs and also widely used for solving puzzles of physics.
Yes, that's exactly the point. The numbers exist for the observer who draws information through the measurement and define causal relationships called logical relationships from a mundane world of degenerate infinite world information that seems to exist before Βig Bang. Every good definition should be based on the theory of numbers and their totals, not to feeling means like likehapening in clasic Geometry
Mathematics is calculative planning for better technology development.
Or to solve one of the millenium problems:
https://en.wikipedia.org/wiki/Millennium_Prize_Problems
Mathematics shows an unchanging world. For example, no mathematical theorem has changed since the universe was born, while the universe being chang continusly into the observer's eyes. Can the objects being mathematically defined (ie the energy that builds their forms) based on the numbers, And how is the substance of the numbers connected with the information which flowing expressing the change and the transfer of energy? Seem the numbers not so intangible and matter is not so materialist ?.....
Oh yes, theorems have changed - as in being extended to hold for more general topologies, for example, or with sharper estimates. Math does NOT stand still. What do you mean by energy in this context? And substance? What have you been smoking? :-)
The generalizations of the theories simply reveal that the twigs are part of larger branches and so on as the cognitive evolution of our species extends its visibility into more general numbers relations. But the tree is a tree, and the mental forest is forest, no matter how much of it we know every moment. In this sense the forest of infinite information of numbers, of their infinite potential relations, seems to have always existed. Like the unmistakable events in the four dimensional world are immovable and unalterable events of the observer's past, composing one of the infinite number of parallel pasts that could been happened if they could been coordinated with the paradoxical observer. Outside the observer, however, is not defined the past, there is the infinite information of inexperienced conjugated worlds. This world is unchanging, indipentendly to the evolution of only the observer. The energy in its variations transfers information dS = dE / dT. This information flow in the energy flow (E = M.c ^ 2) containing all the objects inside it is expressed by number relations. So energy must also be the expression of the transfer of information to the observer by one inexperienced other sea of relationships.
And something else. Euclid's geometry, for example, never ceased to be valid under the flatness conditions of the place where the observations had documented it. Just when new conditions were found, ie the non-flatness of the space, it turned out that the old geometry was part of a wider geometry, such as a key can screw 5 different kinds of screws, but another key of wider use can screw these 5 types and yet 100 kinds that the first key can not screw. But that does not mean that the first key has changed. Each scientific theory is relevant to a number of phenomena that it explains, and is acceptable because it does not produce contradictions in terms of its reference phenomena, as opposed to religious theories that explain strange phenomena in a reasonably inconsistent manner. Every scientific point of view must be substantiated on the basis of definitions of phenomena and logical proof, and not by instictional and psychological ways of the type "What have you been smoking?". Thus, for the above question, it is necessary to define the concepts that refer to "pure mental skimming" by using examples, ie phenomena of reference to these concepts by those who input the initial guestion, so that they do not understand every one and something different about these concepts of abstrac question.
Corection in the above: "pure mental science?' instead of "pure mental skimming "
Yes, mathematics has a high degree of mental science but it is also more of applicable science.
I often think that anything we discover is a representation of an objective law within the observer's consciousness. What else could it be? But if it is so, then our conscience is a picture of an unchanging world. I do not imply anything religious. Can one doubt the usefulness of these depictions, for example, the usefulness of the Mathematical tool, etc?. Certainly no one doubt, but this is another matter.
Τhe language problem is a mathematical problem where the sentences takes on a special meaning from the other sentences around of their place. That is why we could not made until to day the perfect translator. I imagine that every theme must has its own translator. So we need to have a translator of Physics, another translator for biology, and so on. One technique I do is to reverse the translator for one language to another until the two texts remain unchanged. In Mathematics this is called self-consistent method and it is used for solving specific equations, where the output returned as input and so on until input and output become the same.
Mathematics is basic skill of engineering. It make science applicable.
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