[HN Gopher] Is Math Real? ___________________________________________________________________ Is Math Real? Author : hhs Score : 16 points Date : 2023-09-25 21:55 UTC (1 hours ago) (HTM) web link (maa.org) (TXT) w3m dump (maa.org) | tabtab wrote: | Math is merely a mutual agreement. First an agreement on root | principles, and then an agreement on notation for these root | principles. The rest is built on top of those. Nobody is forced | to accept the premises. (Unless you don't want an F in math | class.) | dekhn wrote: | One imagines two intelligent alien races would be able to | communicate that pi is the ratio of the circumference to the | ratio of a circle without coming to any real agreements over | postulates or axioms. But I suppose that's natural philosophy, | not math. | | See https://computingbiology.github.io/docs/hamming1998.pdf | "Mathematics on a Distant Planet" for more thinking. Many | physicists think that math is instrinsic and absolute | (objective) in the universe, not "merely a mutual agreement" | A_D_E_P_T wrote: | Mathematics is, in part, the study of universal traits: | | (1) Ratios between things in the world. | | (2) Logical relations between things in the world. | | (3) Absolute distinctions between things in the world, in a | nominative sense, which is to say in the sense that numbers can | be assigned to things or elements of things. | | Mathematics that relates to one of the three use-cases above is | absolutely real, hence its unreasonable effectiveness in the | natural sciences. (See Wigner: | https://www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf ) | | When mathematics does not relate to one of the three -- for e.g., | in Cantor's theories of "countable" and "uncountable" infinite | sets -- it is totally unreal. A construct or game played with | logic that has no prior or intrinsic relevance to the material | world. | bawolff wrote: | So when an application is found to a previously pure theory | area (e.g. number theory and RSA) does math becone real? | | Is realness not an instrinsic property but just a judgement on | how useful something is? | | Is being real a real property of something or just a construct? | kdottt wrote: | "The question "is math real?" is answered in the epilog of this | book. Cheng tells us that math is real because it is an idea and | ideas are real." | | Alright great lol | dasil003 wrote: | What is "real"? Well, it's just an idea... really | RagnarD wrote: | You might as well ask "Are ideas real?" in the broader | philosophic sense. Yes, they (with math as a subset) are real | existents within consciousness. The question of mathematical | ideas' connection to reality is _epistemological_. "Real | reality" pertains to metaphysics - the externally perceivable | stuff of reality that exists independent of our minds (as in, | eternally prior to, and subsequent to, the existence of any | humans or other beings with conceptual consciousness.) Math is an | epistemological tool to abstract the causality of existence into | a simplified structure amenable to consideration and manipulation | by human consciousness. | | A quadratic equation can be used to approximate the coordinates | of the trajectory of a thrown object in a gravity field. I think | the really interesting question is why that particular equation | reflects that trajectory. Arithmetic operators - multiplication | and addition in that case - in a particular order, are | approximating the causal operations of existence that are | actually at work. I think of this as the philosophy of | mathematics and much more should be done to investigate it. | tracerbulletx wrote: | Brains model patterns in signals, math could be described as the | brain's language for expressing higher order manipulations on all | those models with communicable symbols. So it's kind of both real | and invented, because brains invent, and brains are also just | real objects and any models they form came from somewhere. | moritzwarhier wrote: | This introduction is a very pleasant read and adequately dense | and easy at the same time. | agumonkey wrote: | is math memory ? ___________________________________________________________________ (page generated 2023-09-25 23:00 UTC)