There is an ongoing PBS TV series (additionally numerous books and additionally an internet site) referred to as “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 trendy cosmologists, physicists, philosophers, theologians, psychologists, and so forth. On all the Big Questions surrounding a trilogy of extensive topics – Cosmos; Consciousness; Meaning. The trilogy collectively treated truth, space and time, thoughts and focus, extraterrestrial beings, theology and on and on and on. Here are a few more of my feedback on one in every one of the general subjects included, mathematics.
Is Mathematics Eternal?
# The variety of capacity equations is as close to limitless as makes no odds. But handiest a relative few replicate our fact (anything that is). What role do the others play like as an instance an inverse cube law or say electricity equals mass instances the velocity of light (no longer squared)?
Is Mathematics Invented or Discovered?
# The idea that seven instances six equals 40- (7 x 6 = forty two) is best genuine due to the fact we all agree on that being the case, just like we will and do all agree that a twenty greenback bill a relative few ($20) is well worth twenty dollars despite the fact that the unique paper it is published on is probably well worth or have value most effective twenty cents. So we agree on that equation too – a twenty greenback bill equals twenty bucks. But, if all of a sudden the giant majority of the population said that seven instances six do now not equal 42, however, say 24, then that might be the case and seven instances six could now not equal forty-two. The same applies concerning the foreign money. If all of a sudden all shopkeepers stated your twenty dollar invoice turned into only well worth twenty cents, well, twenty cents it shall be. Thus, mathematics and mathematical equations are ruled with the aid of close to absolute majority settlement or consensus and for this reason arithmetic is an invention that does not exist in any experience of fact out of doors of that consensus. Seven instances six equals 40-two or seven instances six does no longer same forth-two – neither exist as a widespread truth aside from what we together decide via consensus is the case.
# I gather one ought to specific arithmetic within the English (French, Chinese, German, something) language. I suggest One Plus One Equals Two is as valid as 1 + 1 = 2. So, the language of arithmetic is a subset or a sub-part of the English (French, Chinese, and so on.) language, and people languages are used for all subjects. Of course, mathematics, written out or in image shape, is not just for physics and the sciences. I bet part of the normal, properly the human universe anyway, is using arithmetic to do your profits tax return, and your household budget, and figuring out on the grocery store what emblem of the product is most inexpensive per unit amount. Anyway, English isn’t widespread and French isn’t always conventional and Chinese is not regularly occurring, however, Englishmen and Frenchmen and Chinamen might agree that 1 + 1 = 2 is familiar whether expressed in symbols or letters; hieroglyphics or characters. Even the “Greys” would possibly agree that 1 + 1 = 2. However, is mathematics universal earlier than any aware minds had been conceived of in Mother Nature’s philosophy? Did 1 + 1 = 2 exist in any form, manner or shape nanoseconds after the Big Bang?
# Clearly there are standards that can not be expressed mathematically, like beauty or Wednesday, that’s why I advised that the language of arithmetic is a subset of a few broader language – like English, or French or Chinese or Klingon. There are probably trillions of thoughts that can be expressed in English, simply a number of which contain arithmetic.
By “widespread language”, I imply mathematics might be going to be the initial way through which we will begin to speak with an extraterrestrial intelligence anywhere throughout the Universe. We probably have Euclidean Geometry, mathematics, Pi, and so on down the line is not unusual. One would count on that one and simplest one immediately line can be part of two points on a flat surface and that would maintain true everywhere in our galaxy and our Universe. That might be generic. If all of an unexpected you noticed etched or carved into the Martian floor the conventional pictorial illustration of a Pythagorean Triangle, you would finish that a non-human intelligence did the etching or carving and that we have that something in commonplace that might kick-begin verbal exchange off.
# This might be being overly simplistic, but discoverable matters had actual life or reality previous to there being any life forms that developed from non-living structures and substances, especially lifestyles paperwork with minds which have self-cognizance, awareness, intellect, reasoning competencies, and so forth. Now even as Jupiter probable failed to exist previous to intellectual existence forms evolving in the Universe, the stuff that makes up Jupiter absolutely did. Jupiter became consequently discoverable hence observed, no longer invented.
Invented things had no actual lifestyles or reality previous to the evolution of lifestyles paperwork, in particular, existence bureaucracy with the mind. Those invented things are both physical things that by no means might of come to pass without an intellect to conceive consequently manufacture them like coffee makers, in addition to ideas (like language and mathematics and logic and splendor) that non-highbrow items (like Jupiter) could in no way, ought to by no means, invent. The Great Red Spot on Jupiter is unaware of coffee makers and calculus! Calculus was invented through intellect and a few intellects recall it lovely. Of path as soon as something is invented, then that something can, in turn, be observed. You failed to invent calculus and also you probably did not invent the coffee maker, but you discovered both as the end result of someone else’s mind. But, my bottom line is that if there may be no mind in the cosmos and by no means has been, then there would be no calculus and no espresso makers.
# Maybe other dictionaries are extraordinary to mine, however, my dictionary defines “invent” or “invention” along the traces of “to supply or create with the creativeness” or “the workout of imaginative or creative power”. “Inventor” is “a person who invents”.
Now the cosmos is much stuff to many human beings, but except absolutely everyone wants to get returned to the idea of Panpsychism, I alternatively doubt that the cosmos has an energetic “imagination” or “ingenious… Strength” and the cosmos really is not a “man or woman”. The act of invention seems to be a planned manner, one that calls for intellect.
Natural evolution is not directed; is not aim-oriented. Mother Nature didn’t dictate to the cosmos “let there be humans”. The artificial choice then again is directed; is goal oriented. Humans (now not Mother Nature) say “let there be a bionic ear”; “permit there be capsules that permit humans to live longer and more healthy”; “permit there be dressmaker babies without a start defects”; and “permit there be robots with ‘synthetic intelligence’ that could vacuum the carpets and robotic ‘pets’ which could provide consolation to the sick and elderly in establishments”.
Thus, I advocate something along those strains: In the absence of the herbal evolution of life forms on Earth, rocks and minerals and water (in a single or extra forms) existed awaiting to be observed when (and if) existence might stand up and evolve on Planet Earth. In the absence of the natural evolution of lifestyles bureaucracy on Earth, calculus and coffee makers did no longer exist. These summary ideas had to wait for the starting place and evolution of existence right here on Planet Earth to ultimately invent them. No lifestyles: rocks, minerals, and water exist. No life: calculus and coffee makers do now not exist.
Mathematics has absolutely advanced, but handiest inside an intellectual capacity. Ancient people migrating out of Africa 70,000 years ago probably did not realize a lot greater than bone-head mathematics. The historic Greeks brought geometry, however, did not recognize calculus. Calculus came later and arithmetic remains evolving these days way to human intellect and inventiveness.
# If flesh-and-blood human beings are part of nature, and who can argue against that announcement (aside from a few far proper-wing religious fundamentalists), then anything humans produce, or evolve into, or are outmoded via – cyborgs or androids or artificially sensible robots – should also be a part of the natural scheme of factors. No problem there. However, I nonetheless object to the phrase that nature “invented” the inventors. Why no longer just drop the term “invented” and just say that nature advanced inventors? Again, “invented” implies a selected course or intention that nature intended from the get-move, and I preserve that absolutely everyone might be difficult-pressed to pin “goal” on nature, except route you equate nature as synonymous with a deity or deities.
# As long as arithmetic has developed inside the confines of the intellect by highbrow beings (human beings or different self-conscious entities along with extraterrestrial intelligence even synthetic intelligence) then it is high-quality. I’d have a tough time adapting to the belief that arithmetic evolved from mathematics through to geometry for this reason set theory and calculus and fractals, and so on. All between the Big Bang event and the beginning of the very first life forms.
# Many an element existed earlier than intellectually derived arithmetic, arithmetic that presently describes things like orbits and collisions and velocities. All of which increases an interesting query. Only one form of chemistry, a neurological chemistry, can find out and invent things. There are dozens of other sorts of chemistries like soil chemistry, cooking chemistries, inorganic chemistries, natural chemistries, biochemistries, mineralogical chemistries, metallurgy, petrochemical chemistries, pharmaceutical chemistries, digestion, photosynthesis, nuclear chemistries, and so on. There are all kinds of chemical actions and reactions occurring 24/7/52, endothermic reactions and exothermic reactions, yet only one sort of chemistry finally ends up understanding and expertise and discovering and inventing. That’s a totally profound line-in-the-sand among the chemistry of the mind and the chemistries of the whole thing else.