May 28, 2019 at 13:10Do people need math?
I will express a rather paradoxical opinion that right up to the era of steam (hello, Steam punk!)
Mathematics, although it was very desirable and helped people, was not required . That is, it is possible, theoretically, to imagine a civilization that built steam locomotives, but only knows how to divide and multiply.
No, but really. You will say heat engines, thermodynamics, but: if you do not go into the depths (entropy), gases expand linearly with temperature, and to understand that the piston will push the steam, the set theory is not needed. It is possible to grind all this and assemble by trial and error. All Lefties on a hunch will do a lot (and many physicists worked on a hunch almost without any formulas - the same Faraday).
Of course, you can’t do a microcircuit on a hunch - here you need to understand quantum mechanics. But again, knowledge of the non-trivial zeros of the Riemann zeta functionWell, no effect on the construction of the engine does not have! That is, it’s great that now all of this is there, but how did the mathematics manage to hold out until the time when it became really needed?
This question haunted me when I tried to understand Suslin’s hypothesis from set theory, and drew attention to the dates of this person’s life. A small village, an early death ... Life in the villages looked like this:
But what he thought about:
And the contrast between the flight of thought and the situation is amazing and makes you wonder: why? why did they do this? So will you pore over the formulas? Most likely, you will not do what you are not paid for at all. Yes, there are enthusiastic people. But then the population was much smaller, and among this population of educated people - a very thin layer. And this layer has always been under the negative selection of evolution. Galois, Suslin, and even the happy Erdosh , who did not leave offspring because he was a virgin.
Digging deeper. Cardano formula (1500 years). They don’t pass it at school, because for modern schoolchildren it is too complicated. How did people live then? Yes, I remember from school, slops poured on the heads of passers-by.
However, as we go deeper into history, we continue to see the extreme importance of mathematics in human civilization (Maya, Ancient Greece) at a time when there was practically no use for it.
I hear exclamations: a calendar! eclipse! crops! Say, the poor inhabitants of the south (for us that Rome, that Egypt, that Peru is a hot south) had to carefully follow the calendar, because almost what was wrong, the crop was gone. Complete, absolute nonsense! Let’s see what kind of mathematics the inhabitants of the risky farming zone used, where life and death really depended on the crop, and swelled from hunger. Here are the rules of our ancestors:
It’s wet on Makey - all summer is like this
On Pakhoma it’s warm - all summer is warm
If on top of Fedot on the oak top with the edge, you will measure oats as a tub
Here is such a higher mathematics.
Why did mankind so rapidly disproportionately develop mathematics, despite the fact that for the time being there was little practical benefit from it? Partly sacred, priests, this is true. But there is a phrase that I once read in Chemistry and Life - (there was a wonderful magazine). Now I can’t find a quote, so I will recall from memory:
When evolution comes up with a new trait (for example, deer horns), this trait is created immediately in a large number of variants in many species, and in some species this trait is so hypertrophied that it begins to harm survivability.As an example, a rapidly extinct giant deer was cited - the poor horns interfered more than helped:
It seems that the human mind and its penchant for mathematics turned out to be these very horns, because of which we can die out (hello, Fermi paradox! ). Mathematics, as before, is ahead of practical needs by whole eons, and we are engaged in unattainable capacities . Should someone come up with yet another beautiful, complex and useless construction, another mathematician will come and generalize it to the case of arbitrary n-dimensional spaces , and then it’s a sin not to generalize to the case of non-Euclidean spaces either, right?
What is it if not a classic runaway ?
It's useless, but damn it, so interesting.
Mathematics, although it was very desirable and helped people, was not required . That is, it is possible, theoretically, to imagine a civilization that built steam locomotives, but only knows how to divide and multiply.
No, but really. You will say heat engines, thermodynamics, but: if you do not go into the depths (entropy), gases expand linearly with temperature, and to understand that the piston will push the steam, the set theory is not needed. It is possible to grind all this and assemble by trial and error. All Lefties on a hunch will do a lot (and many physicists worked on a hunch almost without any formulas - the same Faraday).
Of course, you can’t do a microcircuit on a hunch - here you need to understand quantum mechanics. But again, knowledge of the non-trivial zeros of the Riemann zeta functionWell, no effect on the construction of the engine does not have! That is, it’s great that now all of this is there, but how did the mathematics manage to hold out until the time when it became really needed?
This question haunted me when I tried to understand Suslin’s hypothesis from set theory, and drew attention to the dates of this person’s life. A small village, an early death ... Life in the villages looked like this:
But what he thought about:
And the contrast between the flight of thought and the situation is amazing and makes you wonder: why? why did they do this? So will you pore over the formulas? Most likely, you will not do what you are not paid for at all. Yes, there are enthusiastic people. But then the population was much smaller, and among this population of educated people - a very thin layer. And this layer has always been under the negative selection of evolution. Galois, Suslin, and even the happy Erdosh , who did not leave offspring because he was a virgin.
Digging deeper. Cardano formula (1500 years). They don’t pass it at school, because for modern schoolchildren it is too complicated. How did people live then? Yes, I remember from school, slops poured on the heads of passers-by.
However, as we go deeper into history, we continue to see the extreme importance of mathematics in human civilization (Maya, Ancient Greece) at a time when there was practically no use for it.
I hear exclamations: a calendar! eclipse! crops! Say, the poor inhabitants of the south (for us that Rome, that Egypt, that Peru is a hot south) had to carefully follow the calendar, because almost what was wrong, the crop was gone. Complete, absolute nonsense! Let’s see what kind of mathematics the inhabitants of the risky farming zone used, where life and death really depended on the crop, and swelled from hunger. Here are the rules of our ancestors:
It’s wet on Makey - all summer is like this
On Pakhoma it’s warm - all summer is warm
If on top of Fedot on the oak top with the edge, you will measure oats as a tub
Here is such a higher mathematics.
Why did mankind so rapidly disproportionately develop mathematics, despite the fact that for the time being there was little practical benefit from it? Partly sacred, priests, this is true. But there is a phrase that I once read in Chemistry and Life - (there was a wonderful magazine). Now I can’t find a quote, so I will recall from memory:
When evolution comes up with a new trait (for example, deer horns), this trait is created immediately in a large number of variants in many species, and in some species this trait is so hypertrophied that it begins to harm survivability.As an example, a rapidly extinct giant deer was cited - the poor horns interfered more than helped:
It seems that the human mind and its penchant for mathematics turned out to be these very horns, because of which we can die out (hello, Fermi paradox! ). Mathematics, as before, is ahead of practical needs by whole eons, and we are engaged in unattainable capacities . Should someone come up with yet another beautiful, complex and useless construction, another mathematician will come and generalize it to the case of arbitrary n-dimensional spaces , and then it’s a sin not to generalize to the case of non-Euclidean spaces either, right?
What is it if not a classic runaway ?
It's useless, but damn it, so interesting.