3 ms·

> The break from the common definition of "numbers are real because I can go buy 24 tangerines and 24 is a number" If I have two dogs, and you swap one of them

> The break from the common definition of "numbers are real because I can go buy 24 tangerines and 24 is a number" If I have two dogs, and you swap one of them out for a different dog; well, it's not the same and I'd notice. What I find interesting about "24 apples" is that all of those apples are in fact also unique individuals - none are identical, they have different weights, percentage moisture, sugar content, number and positioning of seeds, etc. Their exterior markings will be as unique as fingerprints. None of them are really interchangeable. Saying that "there are 24 of the same thing here" is an _abstraction_ of reality. It's our perception, our agreement that they can be considered "the same thing", but it is not a physical reality. It might be real for of protons, but not of people, cats, apples or tangerines. Macroscopic objects are not numbers.

katmannthree 5y ago
Exactly. Every instance of the belief that elements of some particular number systems are "real" is a mapping of the human abstraction representing that number system to another human abstraction of some other system of objects that are considered to be "actually real." The base case of that mapping is natural numbers representing possession of quantities of fungible objects. That mapping is broken by the negative integers, literally the next step up from the natural numbers. If you're concerned about the reality of the reals you can ramble on about finitism or the holographic principle and how something can possibly be real if you can't name or explicitly define every version of it, or you can recognize that every number system from the natural numbers to the complex numbers shares the property that elements of this system of numbers map to elements of physical systems and thus they are all exactly as real as each other.
ChainOfFools 5y ago
well, 1 = -1*-1 but the right hand side contains more "information" than the left hand side, being not simply a quantity but a route to getting there from other quantities.
scotty79 5y ago
Imagine 24 places separated by some distances. You have 24 somethings. The fact that they are not identical with regards to any physical quantity doesn't matter.
- SideburnsOfDoom 5y ago
  How do you know which items to include in that set of 24 items, and which to exclude? With different criteria it could be a set of 23 items, or of 25, or 1 or none or infinite. These 24 items are all unique, as are the excluded ones. The inclusion, the concept of set, the grouping, is not real, it is your criterion, mapping, your abstraction of reality.

katmannthree 5y ago

Exactly. Every instance of the belief that elements of some particular number systems are "real" is a mapping of the human abstraction representing that number system to another human abstraction of some other system of objects that are considered to be "actually real." The base case of that mapping is natural numbers representing possession of quantities of fungible objects. That mapping is broken by the negative integers, literally the next step up from the natural numbers. If you're concerned about the reality of the reals you can ramble on about finitism or the holographic principle and how something can possibly be real if you can't name or explicitly define every version of it, or you can recognize that every number system from the natural numbers to the complex numbers shares the property that elements of this system of numbers map to elements of physical systems and thus they are all exactly as real as each other.

ChainOfFools 5y ago

well, 1 = -1*-1 but the right hand side contains more "information" than the left hand side, being not simply a quantity but a route to getting there from other quantities.

scotty79 5y ago

Imagine 24 places separated by some distances. You have 24 somethings. The fact that they are not identical with regards to any physical quantity doesn't matter.

SideburnsOfDoom 5y ago
How do you know which items to include in that set of 24 items, and which to exclude? With different criteria it could be a set of 23 items, or of 25, or 1 or none or infinite. These 24 items are all unique, as are the excluded ones. The inclusion, the concept of set, the grouping, is not real, it is your criterion, mapping, your abstraction of reality.