How can you say their are 100 marbles in the box? It involves someone counting and then saying that their are 100 marbles. How reliable that person is? Is he capable of counting? Did he make a mistake? Is he truthful? Did we hear clearly when he pronounce the result? Well the questions can be endless. Suppose we are going to employ a machine to do it. Is the machine reliable? Due to wear and tear it may not give the correct result. The same countless questions can be asked.
So how can we know the number of marbles in the box?
The truth is we can never know definitely. We can only get a probable result.
When the concept of color is formed in the human brain, say dark red and light red, these concepts are formed in the brain, and will be different from individual to individual.
Contrast this with the number 106, the human brain do not form a concept.(here again it should be said this is the normal case, but a brain excellent in maths will have more concepts than a normal person. Sometimes looking at 100 marbles arranged in 10 x10 rows will instantly recognize it. Sometimes there may be smart people who can identify 106 unarranged marbles instantly.)
The conclusion we can come to is maths is there to do a fine tuning our understanding.
Because of mathematics capacity of brain had increased immensely. We can go into details of our environment that is impossible for the brain to comprehend.
When you see 7 marbles human brain can distinguish it is different from 8 marbles. Even when randomly arranged it will be able to visually separate to 5 and 2 or 5 and 3. But it won't be able to distinguish 96 and 97 randomly arranged marbles. Though there is no sharp boundary, when the numbers get large it gets increasingly difficult to comprehend. Mathematics is the tool we use to understand large numbers.
Wittgenstein criticise the proposition 'there are two apples on the table' but it is possible to picture it by the brain. But it can't picture 'there is one million in my bank account'.
Human brain cannot keep time - this is obvious. It needs a tool and mathematics.
Then regarding mass it is the same, but have some ability in evaluating weight. Lifting heavy and light objects human brain can compare.
Distance, brain can get some idea, but to measure accurately you need a tool and mathematics.
The situation becomes more complicated when very small measurements are made, quantum theory need to fine tune mathematics.
Measurements disturbs the environment. Therefore what we get is not a measurement of the environment, but an approximation. When measuring a length the mark of the ruler has some width, without that width we are unable to see the mark therefore it is impossible to get the exact measurement. Heisenberg uncertainty principal gives the limit of accuracy in certain measurements.The reason for this limit is not because of shortcomings of the measuring apparatus but due to the structure of the world itself.It is impossible to separate world and the observer. Recent findings show that traveling photos and electrons behaves like a wave when no observer is present and behaves like particles when observed.
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