Philosophy of Mathematics of the Future

The philosophy of mathematics, in its aspiration for timeless eternity like its subject, does not take into account developments in physics as changing fundamental perceptions of mathematics. If not for its success in the sciences - which is most peculiar according to the current scientific picture (meaning this picture is likely incorrect) - the entire perception of mathematics would be different, as chess is perceived, that is, as arbitrary and not as an eternal truth at the foundation of the universe. Mathematics can be viewed as a type of physical experiment that reveals a basic, low-level physical truth that is also expressed at the higher level of thought, meaning a physical law that is not limited to a specific horizontal order of magnitude in the universe but vertically crosses all orders of magnitude in the universe, and is therefore accessible to us also at the level of thought, which allows us to conduct a physical experiment in the brain at the level of elementary particles and thus penetrate the secrets of the universe

By: The Account Is Not Yet Settled

Does mathematics' ability to create complete spiritual universes actually rely on physics? (__Source__)

Love is a wonderful human invention - perhaps the most beautiful invention of culture, except perhaps for the spiritual world - but it is not an invention of biology. Just as the fact that art is a wonderful invention doesn't mean it's an invention of biology. Therefore, beyond the scientific decoding of the brain and intelligence, even if successful - stands the scientific challenge of decoding culture, which is the product of dynamics between many intelligences - of an imagined world.

But why can such a world exist in the universe at all? What even allows a spiritual world in a physical world? Because of mathematics. Why is there even a symbolic dimension? Because information is the physical basis of the world. Why is there information in the world? Why is there a capability for representation? Because there is a difference between 0 and 1, meaning a stable (and not analog) difference between two states, which doesn't suddenly quantum leap between them, or mix in such a way that there's no ability to distinguish between 0 and 1.

If quantum theory is correct, then there's a small chance that suddenly 0 will equal 1 and all our checks will show that 0 equals 1, a chance that diminishes to infinity with each check but is not zero. Meaning there's a chance that every incorrect proof is correct and vice versa. And therefore there's also a chance that this entire reasoning is flawed, because the conclusion can jump from 0 to 1, and one bit is enough to change from truth to falsehood. So if every mathematician can make a mistake, why can't mathematics make a mistake? There was a long-standing attempt to turn the basis of the world from laws to particles, and from fields to geometry. A kind of attempt to make physics more immanent, necessary, aesthetic, stemming from the structure itself, and not imposed on it from outside. The question is whether this can't happen to mathematics as well?

The gap between the processor and information (memory, and even software) creates for us a dualistic universe - whereas in the brain they are connected. The question arises whether the genome is similar to a computer (the genome is memory on which the cell computer operates) or if it's like a brain and the genome's memory is itself a computer. And perhaps learning of the computer type - like the genome - is much slower than brain learning, and that's why evolution took a thousand times longer than culture (that's the order of magnitude). Billions of years to produce humans compared to millions to produce their culture, and millions to develop humans compared to thousands to develop their culture, and thousands of years to grow a culture compared to a few years to raise a child, meaning to create a human who is a product of that culture only through brain learning. Therefore, the universe can be more like a brain and not like a computer. Meaning mathematics can be its upper product and not its lower basis.

Additionally - between computer and brain there's the Internet network, which is both decentralized-networked and digital, meaning it's an intermediary medium between brain and computer. And it is precisely there that culture resides in all its glory - the shared imaginary space - more than in the human itself or in the computer. And this might continue to be true even if artificial intelligence is added to the system. The very fact that it's possible to build artificial intelligence still doesn't allow building artificial culture, and vice versa. One can also think of a super genius (or a brilliant literary computer) that isn't intelligent. Culture doesn't necessarily require intelligence - but culture. Could there be, similar to the Internet network, an intermediary medium between physics and mathematics, where the connection between them resides, and where the content of the universe is found - between two systems of laws? In fact, one could argue that this is the universe itself, or the universe as a computer - that is, including the data, the software, where physics is the processor and mathematics is the computer language and its logic. But perhaps this is actually a network connection that connects mathematics to physics, like the nature of many connections in nature - which are a network?

Do prime numbers reveal something fundamental about the universe? Because this is the most primitive place in mathematics where there seems to be information, not just structure. Is there information in them? Apparently not, because they can be deduced from the initial conditions. But not easily. The meaning of the difficulty is that what is easily defined in one system does not translate to an easy definition in another system. That is - a short definition and a long proof (or definition). Which means there are systems more suitable and less suitable for dealing with problems that are identical. Are mathematics and physics actually two such systems, which differ only in perspective but deal with the same engine of the universe? Does mathematics even stem from the laws of physics, according to which each time anew 1 is different from 0?

For the universe to converge to complexity and not chaos (like gas), fine-tuning is needed that stems from learning, or from planning. Is it possible that physics will prove that our universe was created by design? Or from learning? Design would be a metaphysical earthquake, where science would prove intelligent design, and reverse the direction of secularization, and this can certainly happen. And can something similar happen to mathematics? Is mathematics the product of design? Or of learning? Or something even stranger - logical necessity? What does logical necessity actually mean, other than that in our universe there is a natural rule that forbids violating mathematics, or that every mathematical experiment will always come out the same, that one plus one will always equal two. And why, for example, in the universe, generally, symmetry and circular shape prevail, from sun, galaxy, to the entire universe?

Pi is noise in the decimal system, but not in other systems. And if we discover that the entire universe is arranged according to some mathematical pattern, which caused, for example, the galaxies to be in their place according to a certain formula, or that the laws of nature are the result of some algorithm, what will be the metaphysical significance of such a conspiracy? Or once it's a law of nature, is it no longer a conspiracy? Are there laws of nature that we won't be willing to accept as reasonable? There can still be many scientific and mathematical revolutions that will make us think that the spiritual world is more basic than the material world, that mathematics is beneath the world, and that there are spiritual laws beneath the physical laws. Our perception is ultimately a derivative of what is discovered in that period in physics about the basis of the world. When there are laws there is a transcendent God (as opposed to immanent in Aristotelian physics of the Middle Ages) and when there are particles there is no God but matter. And when the physical basis for the world (as in the direction of strings) is mathematics, then God is pure spirit.

But why can such a world exist in the universe at all? What even allows a spiritual world in a physical world? Because of mathematics. Why is there even a symbolic dimension? Because information is the physical basis of the world. Why is there information in the world? Why is there a capability for representation? Because there is a difference between 0 and 1, meaning a stable (and not analog) difference between two states, which doesn't suddenly quantum leap between them, or mix in such a way that there's no ability to distinguish between 0 and 1.

If quantum theory is correct, then there's a small chance that suddenly 0 will equal 1 and all our checks will show that 0 equals 1, a chance that diminishes to infinity with each check but is not zero. Meaning there's a chance that every incorrect proof is correct and vice versa. And therefore there's also a chance that this entire reasoning is flawed, because the conclusion can jump from 0 to 1, and one bit is enough to change from truth to falsehood. So if every mathematician can make a mistake, why can't mathematics make a mistake? There was a long-standing attempt to turn the basis of the world from laws to particles, and from fields to geometry. A kind of attempt to make physics more immanent, necessary, aesthetic, stemming from the structure itself, and not imposed on it from outside. The question is whether this can't happen to mathematics as well?

The gap between the processor and information (memory, and even software) creates for us a dualistic universe - whereas in the brain they are connected. The question arises whether the genome is similar to a computer (the genome is memory on which the cell computer operates) or if it's like a brain and the genome's memory is itself a computer. And perhaps learning of the computer type - like the genome - is much slower than brain learning, and that's why evolution took a thousand times longer than culture (that's the order of magnitude). Billions of years to produce humans compared to millions to produce their culture, and millions to develop humans compared to thousands to develop their culture, and thousands of years to grow a culture compared to a few years to raise a child, meaning to create a human who is a product of that culture only through brain learning. Therefore, the universe can be more like a brain and not like a computer. Meaning mathematics can be its upper product and not its lower basis.

Additionally - between computer and brain there's the Internet network, which is both decentralized-networked and digital, meaning it's an intermediary medium between brain and computer. And it is precisely there that culture resides in all its glory - the shared imaginary space - more than in the human itself or in the computer. And this might continue to be true even if artificial intelligence is added to the system. The very fact that it's possible to build artificial intelligence still doesn't allow building artificial culture, and vice versa. One can also think of a super genius (or a brilliant literary computer) that isn't intelligent. Culture doesn't necessarily require intelligence - but culture. Could there be, similar to the Internet network, an intermediary medium between physics and mathematics, where the connection between them resides, and where the content of the universe is found - between two systems of laws? In fact, one could argue that this is the universe itself, or the universe as a computer - that is, including the data, the software, where physics is the processor and mathematics is the computer language and its logic. But perhaps this is actually a network connection that connects mathematics to physics, like the nature of many connections in nature - which are a network?

Do prime numbers reveal something fundamental about the universe? Because this is the most primitive place in mathematics where there seems to be information, not just structure. Is there information in them? Apparently not, because they can be deduced from the initial conditions. But not easily. The meaning of the difficulty is that what is easily defined in one system does not translate to an easy definition in another system. That is - a short definition and a long proof (or definition). Which means there are systems more suitable and less suitable for dealing with problems that are identical. Are mathematics and physics actually two such systems, which differ only in perspective but deal with the same engine of the universe? Does mathematics even stem from the laws of physics, according to which each time anew 1 is different from 0?

For the universe to converge to complexity and not chaos (like gas), fine-tuning is needed that stems from learning, or from planning. Is it possible that physics will prove that our universe was created by design? Or from learning? Design would be a metaphysical earthquake, where science would prove intelligent design, and reverse the direction of secularization, and this can certainly happen. And can something similar happen to mathematics? Is mathematics the product of design? Or of learning? Or something even stranger - logical necessity? What does logical necessity actually mean, other than that in our universe there is a natural rule that forbids violating mathematics, or that every mathematical experiment will always come out the same, that one plus one will always equal two. And why, for example, in the universe, generally, symmetry and circular shape prevail, from sun, galaxy, to the entire universe?

Pi is noise in the decimal system, but not in other systems. And if we discover that the entire universe is arranged according to some mathematical pattern, which caused, for example, the galaxies to be in their place according to a certain formula, or that the laws of nature are the result of some algorithm, what will be the metaphysical significance of such a conspiracy? Or once it's a law of nature, is it no longer a conspiracy? Are there laws of nature that we won't be willing to accept as reasonable? There can still be many scientific and mathematical revolutions that will make us think that the spiritual world is more basic than the material world, that mathematics is beneath the world, and that there are spiritual laws beneath the physical laws. Our perception is ultimately a derivative of what is discovered in that period in physics about the basis of the world. When there are laws there is a transcendent God (as opposed to immanent in Aristotelian physics of the Middle Ages) and when there are particles there is no God but matter. And when the physical basis for the world (as in the direction of strings) is mathematics, then God is pure spirit.