By John Prytz There is an ongoing PBS TV series (also several books and also a website) called "Closer to Truth". It is hosted by neuroscientist Robert Lawrence Kuhn. He's featured in one-on-one interviews and panel discussions with the cream of the cream of today's cosmologists, physicists, philosophers, theologians, psychologists, etc. on all of the Big Questions surrounding a trilogy of broad topics - Cosmos; Consciousness; Meaning. The trilogy collectively dealt with reality, space and time, mind and consciousness, aliens, theology and on and on and on. Here are a few more of my comments on one of the general topics covered, mathematics.
Is Mathematics Eternal?
# The number of potential equations is as close to infinite as makes no odds. But only a relative few reflect our reality (whatever that is). What role do the others play like for example an inverse cube law or say energy equals mass times the velocity 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 on that being the case, just like we can and do all agree that a twenty dollar bill a relative few ($20) is worth twenty dollars even though the special paper it is printed on might be worth or have cost only twenty cents. So we agree on that equation too - a twenty dollar bill equals twenty dollars. But, if all of a sudden the vast majority of the populace said that seven times six does not equal 42, but say 24, then that would be the case and seven times six would no longer equal 42. The same applies regarding the currency. If all of a sudden all shopkeepers said your twenty dollar bill was only worth twenty cents, well, twenty cents it shall be. Thus, mathematics, and mathematical equations are ruled by near absolute majority agreement or consensus and thus 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 forth-two - neither exist as a universal truth apart from what we collectively determine by consensus is the case.
# I gather one could express mathematics in the English (French, Chinese, German, whatever) language. I mean One Plus One Equals Two is as valid as 1 + 1 = 2. So, the language of mathematics is a subset or a sub-part of the English (French, Chinese, etc.) language, and those languages are used for all subjects. Of course mathematics, written out or in symbol form, isn't just for physics and the sciences. I guess part of the universal, well the human universe anyway, is using mathematics to do your income tax return, and your household budget, and figuring out at the supermarket what brand of product is cheapest per unit quantity. Anyway, English isn't universal and French isn't universal and Chinese isn't universal, but Englishmen and Frenchmen and Chinamen would 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 minds were conceived of in Mother Nature's philosophy? Did 1 + 1 = 2 exist in any shape, manner or form nanoseconds after the Big Bang?
# Clearly there are concepts that cannot be expressed mathematically, like beauty or Wednesday, which is why I suggested that the language of mathematics is a subset of some broader language - like English, or French or Chinese or Klingon. There are probably trillions of ideas that can be expressed in English, just some of which involve mathematics.
By "universal language", I mean mathematics is probably going to be the initial means by which we can start to communicate with an extraterrestrial intelligence anywhere across the Universe. We probably have Euclidean Geometry, arithmetic, Pi, and so on down the line in common. One would assume that one and only one straight line can join two points on a flat surface and that would hold true anywhere in our galaxy and our Universe. That would be a universal. If all of a sudden you saw etched or carved into the Martian surface the traditional pictorial representation of a Pythagorean Triangle, you'd have to conclude that a non-human intelligence did the etching or carving and that we have that something in common that could kick-start communication off.
# This is probably being overly simplistic, but discoverable things had actual existence or reality prior to there being any life forms that evolved from non-living structures and substances, especially life forms with minds that have self-awareness, consciousness, intellect, reasoning abilities, etc. Now while Jupiter probably didn't exist prior to intellectual life forms evolving within the Universe, the stuff that makes up Jupiter certainly did. Jupiter was therefore discoverable hence discovered, not invented.
Invented things had no actual existence or reality prior to the evolution of life forms, especially life forms with intellect. Those invented things are both physical things that never would of come to pass without an intellect to conceive hence manufacture them like coffee makers, as well as concepts (like language and mathematics and logic and beauty) that non-intellectual objects (like Jupiter) would never, could never, invent. The Great Red Spot on Jupiter is ignorant of coffee makers and calculus! Calculus was invented by intellect and some intellects consider it beautiful. Of course once something is invented, then that something can in turn be discovered. You didn't invent calculus and you probably didn't invent the coffee maker, but you discovered both as the result of someone else's intellect. But, my bottom line is if there is no intellect in the cosmos and never has been, then there would be no calculus and no coffee makers.
# Maybe other dictionaries are different to mine, but my dictionary defines "invent" or "invention" along the lines of "to produce or create 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 all and sundry wish to get back to the concept of Panpsychism, I rather doubt that the cosmos has an active "imagination" or "imaginative... power" and the cosmos certainly isn't a "person". The act of invention seems to be a deliberate process, one which requires intellect.
Natural evolution isn't directed; isn't goal oriented. Mother Nature didn't dictate to the cosmos "let there be humans". Artificial selection on the other hand is directed; is goal oriented. Humans (not Mother Nature) say "let there be a bionic ear"; "let there be drugs that enable people to live longer and healthier"; "let there be designer babies with no birth defects"; and "let there be robots with 'artificial intelligence' that can vacuum the carpets and robotic 'pets' that can provide comfort to the sick and elderly in institutions".
Thus, I advocate something along these lines: In the absence of the natural evolution of life forms on Earth, rocks and minerals and water (in one or more forms) existed awaiting to be discovered when (and if) life would arise and evolve on Planet Earth. In the absence of the natural evolution of life forms on Earth, calculus and coffee makers did not exist. These abstract concepts had to await the origin and evolution of life here on Planet Earth to ultimately invent them. No life: rocks, minerals and water exist. No life: calculus and coffee makers do not exist.
Mathematics has certainly evolved, but only within an intellectual capacity. Ancient humans migrating out of Africa 70,000 years ago probably didn't know much more than bone-head arithmetic. The ancient Greeks added geometry but didn't know calculus. Calculus came later and mathematics is still evolving today thanks to human intellect and inventiveness.
# If flesh-and-blood humans are a part of nature, and who can argue against that statement (apart from some far right-wing religious fundamentalists), then whatever humans produce, or evolve into, or are superseded by - cyborgs or androids or artificially intelligent robots - must also be a part of the natural scheme of things. No issue there. However, I still object to the phrase that nature "invented" the inventors. Why not just drop the term "invented" and just say that nature evolved inventors? Again, "invented" implies a specific direction or goal that nature intended from the get-go, and I maintain that anyone would be hard-pressed to pin "intention" on nature, unless of course you equate nature as synonymous with a deity or deities.
# As long as mathematics has evolved within the confines of the intellect by intellectual beings (humans or other self-conscious entities including extraterrestrial intelligences even artificial intelligences) then that's fine. I'd have a hard time adapting to the notion that mathematics evolved from arithmetic through to geometry hence set theory and calculus and fractals, etc. all between the Big Bang event and the origin of the very first life forms.
# Many a thing existed before intellectually derived mathematics, mathematics that currently describes things like orbits and collisions and velocities. All of which raises an interesting question. Only one kind of chemistry, a neurological chemistry, can discover and invent things. There are dozens of other kinds of chemistries like soil chemistry, cooking chemistries, inorganic chemistries, organic chemistries, biochemistries, mineralogical chemistries, metallurgy, petrochemical chemistries, pharmaceutical chemistries, digestion, photosynthesis, nuclear chemistries, etc. There are all kinds of chemical actions and reactions going on 24/7/52, endothermic reactions and exothermic reactions, yet only one kind of chemistry ends up knowing and understanding and discovering and inventing. That's a very profound line-in-the-sand between the chemistry of the intellect and the chemistries of everything else.
# By the one kind 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 quite 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 it will eventually rule the roost. Of course that might be a cyborg or android composite in the initial stages; perhaps ultimately a fully-blown artificial intelligence (AI).
The interesting thing here is that while interstellar travel for that which houses our neurological chemistry (the human brain even detached from the human body) is difficult - vast distances, slow velocities, limited lifespans, massive amounts of environmental infrastructure required, etc. - interstellar travel for an AI is way more achievable. The distances and the velocities might be the same but the lifespans are now vast and way more indestructible and the infrastructure requirements reduced to a bare minimum - no need for toilets. Human hibernation for an interstellar voyage is going to be way more technologically difficult relative to a 'sleep' switch for an AI. Thus, when it comes to the UFO extraterrestrial hypothesis (ETH), the ET part might be far more likely to be an ETAI.
Science librarian; retired.
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