[HN Gopher] Is Math Real?
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       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 ?
        
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