There is an ongoing PBS TV series (also several books and also a website) called “Closer to Truth”. It is presented by neuroscientist Robert Lawrence Kuhn. He has appeared in individual interviews and panel discussions with the cream of the crop of cosmologists, physicists, philosophers, theologians, psychologists, etc. from the actuality. about all the big questions surrounding a trilogy of broad topics: Cosmos; conscientiousness; Sense. The trilogy collectively dealt with reality, space and time, mind and consciousness, aliens, theology, etc. Here are some more comments on one of the general topics covered, math.
Is mathematics eternal?
# The number of potential equations is the closest thing to infinity that has no probabilities. But only a few reflect our reality (whatever that is). What role do the others play, such as an inverse cube law or saying that energy equals mass times the speed of light (not squared)?
Is Mathematics Invented or Discovered?
# The idea that seven times six equals forty-two (7 x 6 = 42) is only true because we all agree that is the case, just as we can and do all agree that a dollar bill twenty dollars is relatively little ($20) is worth twenty dollars even though the special paper it is printed on may or may have cost only twenty cents. So we also agree on that equation: a twenty dollar bill equals twenty dollars. But, if suddenly the vast majority of the population were to say that seven times six does not equal 42, but 24, then that would be the case and seven times six would no longer equal 42. The same applies with regard to currency. . If suddenly all the merchants said that your twenty dollar bill was only worth twenty cents, well, it will be twenty cents. Therefore, mathematics and mathematical equations are governed by almost absolute majority agreement or consensus, and therefore mathematics is an invention that does not exist in any sense of reality outside of that consensus. Seven times six equals forty-two or seven times six does not equal four-two, neither of which exists as a universal truth apart from what we collectively determine by consensus.
# I suppose one could express mathematics in the English language (French, Chinese, German, whatever). I mean that One Plus One Equals Two is just as valid as 1 + 1 = 2. So the language of mathematics is a subset or a subpart of the English language (French, Chinese, etc.), and those languages are used for all subjects. Of course, mathematics, written or in the form of symbols, is not just for physics and science. I guess part of the universal, well, the human universe anyway, is to use math to do your tax return and household budget, and find out at the supermarket which brand of product is cheapest per unit of quantity. Anyway English is not universal and French is not universal and Chinese is not universal, but the English, the French and the Chinese would all agree that 1 + 1 = 2 is universal whether expressed in symbols or letters; hieroglyphics or characters. Even the “greys” would probably agree that 1 + 1 = 2. However, is mathematics universal before any conscious mind was conceived in the philosophy of Mother Nature? Did 1 + 1 = 2 exist in some form, mode, or nanoseconds after the Big Bang?
# Clearly, there are concepts that cannot be expressed mathematically, such as beauty or Wednesday, so I suggested that the language of mathematics is a subset of a larger language, such as English, French, Chinese, or Klingon. There are probably trillions of ideas that can be expressed in English, some of which involve math.
By “universal language,” I mean that mathematics will likely be the initial means by which we can begin to communicate with an extraterrestrial intelligence anywhere in the Universe. We probably have Euclidean geometry, arithmetic, Pi, etc. in common. One would assume that one and only one straight line can join two points on a flat surface and that would be true anywhere in our galaxy and our Universe. That would be a universal. If you were to suddenly see the traditional pictorial representation of a Pythagorean Triangle engraved or carved on the Martian surface, you would have to conclude that a non-human intelligence did the engraving or carving and that we have something in common that could trigger communication.
# This is probably overly simplistic, but discoverable things had actual existence or reality before there were life forms that evolved from non-living structures and substances, especially life forms with minds that have self-awareness, intellect, abilities of reasoning. , etc. Now, while Jupiter probably didn’t exist before intellectual life forms evolved within the Universe, the things that make up Jupiter certainly did exist. Therefore, Jupiter was detectable, therefore discovered, not invented.
Invented things had no real existence or reality before the evolution of life forms, especially life forms with intellect. Those invented things are both physical things that would never have happened without an intellect to conceive of them, hence making them like coffee pots, as well as concepts (like language, math, logic, and beauty) that non-intellectual objects (like Jupiter) would. never, never could, invent. The Great Red Spot on Jupiter ignores coffee pots and calculus! Calculus was invented by the intellect and is considered beautiful by some intellects. Of course, once something is invented, that something can in turn be discovered. You didn’t invent calculus and you probably didn’t invent the coffeepot, but you discovered both as a result of someone else’s intellect. But, my conclusion is that if there is no intellect in the cosmos and there never has been, then there would be no calculus and no coffee pots.
# Other dictionaries may be different than mine, but my dictionary defines “invent” or “invention” along the lines of “producing or creating with the imagination” or “the exercise of imaginative or creative power”. “Inventor” is “a person who invents”.
Now the cosmos is many things to many people, but unless everyone wants to go back to the concept of panpsychism, I doubt the cosmos has an active “imagination” or “imaginative…power” and the cosmos certainly doesn’t. . it is not a “person”. The act of invention appears to be a deliberate process, requiring intellect.
Natural evolution is not directed; it is not goal oriented. Mother Nature did not dictate to the cosmos “let there be humans”. Artificial selection, on the other hand, is targeted; it is goal oriented. Humans (not Mother Nature) say “let there be a bionic ear”; “that there are medicines that allow people to live longer and with better health”; “let there be designer babies without birth defects”; and “let there be ‘artificial intelligence’ robots that can vacuum carpets and robotic ‘pets’ that can provide comfort to the sick and elderly in institutions.”
Therefore, I advocate something along these lines: In the absence of the natural evolution of life forms on Earth, rocks, minerals, and water (in one or more forms) existed waiting to be discovered when (and if) life would arise and evolve on Earth. Planet Earth. In the absence of the natural evolution of life forms on Earth, calculus and coffee pots did not exist. These abstract concepts had to wait for the origin and evolution of life here on Planet Earth to finally invent them. There is no life: there are rocks, minerals and water. There is no life: calculation and coffee pots do not exist.
Certainly, mathematics has evolved, but only within an intellectual capacity. The ancient humans who migrated from Africa 70,000 years ago probably didn’t know much more than basic arithmetic. The ancient Greeks added geometry but did not know calculus. Calculus came later, and mathematics continues to evolve today thanks to human intellect and inventiveness.
# If flesh and blood humans are part of nature, and who can argue against that claim (other than some far-right religious fundamentalists), then any humans that produce, evolve, or are replaced by – cyborgs or androids or artificially intelligent robots – must also be part of the natural scheme of things. No problem there. However, I still object to the statement that nature “invented” inventors. Why not just drop the term “invented” and simply say that nature evolved inventors? Once again, “invented” implies a specific direction or goal that nature intended all along, and I submit that anyone would be hard-pressed to attribute “intention” to nature, unless, of course, one equates nature with it. as a synonym for a deity or deities
# As long as mathematics has evolved within the limits of the intellect by intellectual beings (humans or other self-aware entities, including extraterrestrial intelligences and even artificial intelligences), then it’s fine. I would have a hard time adjusting to the notion that mathematics evolved from arithmetic to geometry, thus set theory and calculus and fractals etc. everything between the Big Bang event and the origin of the first forms of life.
# Many things existed before intellectually derived mathematics, mathematics that actually describe things like orbits, collisions, and velocities. All of which raises an interesting question. Only one type of chemistry, neurological chemistry, can discover and invent things. There are dozens of other types of chemistry such as soil chemistry, cooking chemistry, inorganic chemistry, organic chemistry, biochemistry, mineralogical chemistry, metallurgy, petrochemical chemistry, pharmaceutical chemistry, digestion, photosynthesis, etc. nuclear chemistry etc There are all kinds of chemical actions and reactions that happen on 7/24/52, endothermic reactions and exothermic reactions, but only one type of chemistry ends up knowing and understanding and discovering and inventing. That is a very deep line between the chemistry of the intellect and the chemistry of everything else.
# By the type of chemistry, I should have qualified that by stating that it was, for lack of a better phrase, Mother Nature’s chemistry – a natural chemistry that evolved, well, naturally.
Now, I completely agree that yet another chemistry, a chemistry discovered, invented and designed by that neurological chemistry, our neurological chemistry, will be a metallurgical based chemistry, and will eventually rule the roost. Of course, that could be a cyborg or android composite in the early stages; perhaps ultimately a full-fledged artificial intelligence (AI).
What’s interesting here is that while interstellar travel for what our neurological chemistry houses (the human brain even separated from the human body) is difficult – great distances, slow speeds, limited lifespan – a lot of environmental infrastructure is required, etc. – Interstellar travel for an AI is much more feasible. The distances and speeds may be the same, but the life expectancy is now enormous and much more indestructible and the infrastructure requirements are reduced to a minimum, without the need for toilets. Human hibernation for interstellar travel is going to be much more technologically difficult relative to a “sleep” switch for an AI. Therefore, when it comes to the Alien UFO Hypothesis (ETH), the ET part is much more likely to be an ETAI.