Numbers are an unfortunate necessity of the limitations of the
   human cognition. Humans must put everything into patterns. We
   cannot absorb the Universe in all of its uniqueness. Brains too
   small. == They're our creation for our needs. They're also very
   pragmatic, as are words. == Objects don't need numbers. Humans
   categorize the world into patterns and our visual systems
   surround what we see with outlines that aren't really there. We
   look for similarities and differences. When we find
   similarities, we consider them the 'same'. Ok, what happens when
   you have this pattern matching that pattern? Gotta form numbers.
   It's how our brains function. == You want to see if my
   definition fits the pattern you've chosen to use to define
   "number". If it does not, that will mean that "I do not know
   what number means". == You want to know how much I agree with
   you? It's more likely, considering the type of language you've
   used to describe numbers and language, that we will be speaking
   past each other. This is why I hesitate. I do not speak in terms
   of "abstract vs concrete". For abstract, there needs to be a
   platonic realm. I do not believe in the existence of the
   platonic realm. I am a fan of embodied cognition, which uses
   cognition as the basis with regards to how it relates to the
   body it is situated in in relation to the environment it finds
   itself in, including the culture, societies, its information and
   other people. There's no line for me. So for me to explain
   "number" would go in an entirely different direction than you
   are accustomed to. == A number is a product of the human
   cognition. We have anthropomorphized this further and applied it
   to the systems around us including other life forms. Our brains
   are small. They must "compress" environmental information into
   "patterns". We have the native ability to find enough
   similarities between incoming sense data from our limited
   perspectives, to categorize things into OBJECTS. No language
   required. It's just what we do. Our basic abilities for numbers
   are in the numerosity sense. We can instantly identify up to 3-4
   'objects" at once. No processing required. It's pretty instant.
   Anything beyond 4, is handled by our linguistic systems ==
   You're using a linguistic basis. I'm doing deeper than
   linguistics here. I do not see words as atomic. == But the
   object does not HAVE a terminal form. The terminal form is
   CREATED BY the mind itself. == The formal proofs are based upon
   the limitations of Aristlean axioms + proofs system. Another
   human construction. This includes the famous "excluded middle".
   This need for non-contradiction when reality itself seems to
   indicate that contradiction is the norm and non-contradiction
   the fiction. == Axioms and proof systems are fundamentally
   limited. They're always split. It's artificial. Useful but
   artificial. == Yes, I'm quite familiar with this stuff. It's a
   built-in part of western civilization to know this stuff. All
   starts and ends with geometry ultimately and geometry is
   supported by axioms and proofs. It's a great system but has
   flaws. == Reality is subjective. Agreement with other
   subjectives makes it objective. == You have the source and end
   points mixed up as do most people. It's built-in to our culture.
   Reality is not objective until we make it so and decide to make
   it as such through human agreement. Through coming up with
   systems to explain the thing we see to others. Words did not
   fall form the sky magically. Logic is not a built-in part of the
   Universe. It comes from us. It's USEFUL but it's ours. == Yes.
   It is a useful fiction that is functional. == There's no space.
   Everything touches something. == From our pov, it does. From the
   moon's pov, we're not even here. From a electron point of view,
   it's charges flipping around and exchanging. There's no
   distinction there either. Just for us. Humans. == Defining is a
   product of our human cognition. Visual systems outline things. I
   already explained that earlier. == For us it does. What about
   the boundary area? Not so distinct. == Boundary between the
   object and its environment. To me, they're one thing with a bit
   of wonkiness at points where items seem be different from one
   another. = This air around me is a part of me. I'm a part of
   this computer. The information going from my brain to yours is
   connected to me. You're connected to me. It's all one thing. ==
   The air goes into my lungs, through my blood stream, used for
   purposes, goes back out again as co2. Systems. We're not
   independent objects. We're all a part of systems that function
   together. == Information is perfectly physical. == I'm dead
   without the air in me. It's me. == Sure I do, insofar as much of
   it passes through me and as far as my senses go. == I don't
   'use' air. I'm a part of this environment. == I'm me. I'm also
   the air I breath. I also don't have universal knowledge. My
   perspective is very limited. I don't know what the air is like a
   mile away from me. But I know what the air is like where I can
   sense it. == I'm the air that I know. There's a lot of air I
   don't know. == It's great for artists to draw it that's true.
   Lines are useful fictions. = A line could very well be a circle
   on its side, edge on. The line is a cognitive construct as is
   the whole system you're basing your truthvalues on. There is no
   such thing as a line in the manner that we describe it from our
   limited human cognition. == Thank you. I mean, they ARE facts,
   insomuch that we could PROBABLY at some future point, scan a
   brain and "see" what lines _really_ look like. But there's no 1
   dimensional objects in this universe. Or 2. Or 3. Everything's
   at least 4 dimensional (3D + time) and possibly 5. maybe more.
   == Yes. It is a useful fiction and handy for idealized
   construction plans. But when you go to home depot and buy the
   wood, you find that those idealised lines need modifications,
   especially when you forgot to include the humidity that swells
   the wood. == Nearly a line. Not quite. I did a Vine about that
   the other day. The gaps. One of my favorite subjects is the
   imperfections of reality vs our idealised notions of reality.
   Life grows in the gaps. That 'line' where the floor meets wall?
   Over time (another dimension) they separate due to the
   properties of materials and the environment. Dirt gets in there.
   A seed goes in there. Life grows in there. Splits it apart
   further. Within a few years, the line is long gone. It never
   existed in the first place exxcept as a fiction. == STOP
   EVERYTHING! Oh, you can't. Yes, time is valid. == Yes, according
   to the fictional and very useful definitions of geometry. == On
   your planet maybe. I live here. == Yes, Euclid was useful for
   his time. Very pragmatic stuff. Built and continue to build a
   lot of things using his methodologies and those that supplanted
   them. = Time certainly delimits forms. What's a static form?
   Where was that line before you drew it? What will it be when the
   paper is gone? == You may be able to eliminate time for your
   purposes but it's not seeing the whole picture. == Not correct
   for your purposes. Correct for mine. I'd fail whatever class you
   teach. I'd be teaching a different class that includes
   everything and does not eliminate uncomfortable things that
   dont' fit into neat schemas. == Metaphorical class. I don't
   teach one either, but in a sense, we are acting as each other's
   teachers to unruly, uncooperative students. == The Universe is
   the Universe. Three examples are: True, False, I don't know. ==
   will in a few minutes I was involved in a rousing debate
   combating the purity of geometric forms vs my thing of "include
   everything", which tends to grate on ppls nerves but we parted
   shaking hands for a good discussion. I'll read, process and
   answer shortly smile emoticon ==