Timeline for Do complex numbers really exist?
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 12, 2020 at 7:54 | comment | added | theprogrammer | I think we cannot be sure if a tree exists either. Today the tree might exist. 10 years from now, deforestation might make it non-existent. 1000 years ago, it might not have been born yet. So the absolute notion of whether "this" tree exists cannot be answered. | |
| Apr 15, 2011 at 20:45 | history | made wiki | Post Made Community Wiki | ||
| Feb 19, 2011 at 14:16 | comment | added | Christian | @Jason: You can run very straightforward tests to see whether a particular tree exists. Thinking of a test that tests whether time exists is qualitatively different. | |
| Feb 19, 2011 at 14:12 | history | edited | Christian | CC BY-SA 2.5 | added 1 characters in body |
| Dec 22, 2010 at 7:16 | comment | added | isomorphismes | What about Quine's insight to define a natural number $n \in \mathbb{N}$ as the equivalence class of all sets with cardinality $n$? | |
| Dec 19, 2010 at 18:29 | comment | added | Andrew Marshall | Incidentally, this train of thought leads back to justifying complex numbers: take -1 as an involution on R. It's not clear what it means to iterate this function 1.5 times, but extending R to C now gives us (two) excellent choices. | |
| Dec 19, 2010 at 18:10 | comment | added | Andrew Marshall | some quantities can't be described even by real numbers, but necessarily by natural numbers only, such as performance of a process that doesn't scale (iteration of a function, even). Therein lies the answer to the complex number question: there is a context to what numbers can describe, and counting apples is not a meaningful context for complex numbers. | |
| Dec 19, 2010 at 18:03 | comment | added | Andrew Marshall | @Christian, agreement with Jason. Physical theories are as much abstractions as are mathematical theories. If we want to be precise, we don't even get to distinguish a type of object, i.e., atom, without implying a model. | |
| Dec 2, 2010 at 22:10 | comment | added | Jason Orendorff | @Christian: I wonder what you mean by "the way trees or atoms exist". What way is that, exactly? Any decent definition of "exist" has to at least admit that things like time, sounds, shadows, communication, and the color red exist, don't you think? It's hard to imagine any such definition would rule out the number six. | |
| Nov 29, 2010 at 12:41 | comment | added | Christian | @Mauro: There a long philosophical debate about whether numbers can exist in some Platonian heaven of ideas. Things that physics people use in their formulas have per definition a link to reality. | |
| Nov 27, 2010 at 20:32 | comment | added | SamB | @Christian, Mauro: but it certainly seems that something rather similar to the Peano numbers is the simplest way to explain the empirical behavior of a significant class of objects in the real world, and thus (by Occam's razor) the best one -- how is that different from, say, Newtonian physics? | |
| Nov 22, 2010 at 15:20 | comment | added | Mauro | I think this is a non-answer. Clearly the mathematical concept of numbers is not "real" and in the past concepts, as zero, that now we consider clear were misterious. Still people tend to understand and consider "real" positive, negative and fractional numbers because they see a link with reality. In this sense they "exist" and that's why basic algebra is normally understood by a vaste majority | |
| Jul 28, 2010 at 2:40 | comment | added | Vortico | Very good insight on this. | |
| Jul 20, 2010 at 23:39 | history | answered | Christian | CC BY-SA 2.5 |