Earlier quoted context omitted.
That's just "Exist as physical objects exist" Ie., you're asking someone to find you an object with spatio-temporal properties which, as an object, does not have spatio-temporal properties. Likewise you could ask, "find me a smile?!!" and then deny every example was a smile because "it was only a face smiling!". "Existence" is defined relative to a context in which it can be evaluated, and it -- in general -- does no…
This reminds me of my Italian grammar teacher telling me that nouns can be broken into two categories: ‘concrete’ and ‘abstract’ (for example, ‘chair’ and ‘love’ respectively). Then came a totally mind bending digression for my eight-year-old mind when she mumbled “well actually all nouns are abstract because there’s no such thing as a chair divorced from reality, there’s nobly instantiations of these abstract concep…
What Even Is a Number?
161–170 of 173 posts
Re: What Even Is a Number?
#162Earlier quoted context omitted.
Yes, that's what qubex said, in correcting the error in your previous comment.
ℤ︎ with * is not a group, there is no inverse for 0. When being pedantic it's good to be correct.
You are perfectly correct, I was wrong. Upon closer reflection it appears impossible to have a nontrivial set (meaning other than {0}) that forms a group both under addition and under multiplication because the identity element of the former does not have an inverse in the latter. However, take this with a grain of salt, because I haven't had time to prove this to my own satisfaction yet (and I am loathe to go googling for answers in my own field of expertise).
My abstract algebra professor would be horrified by my misstatement, and I shall go to bring flowers as a sign of atonement and rememberance to his grave at the earliest available opportunity.
Re: What Even Is a Number?
#163Earlier quoted context omitted.
I’m all for reification. It’s not even limited to mathematics: ‘democracy’ is just another example of a reification from another realm of human endeavor: it gets implemented in different countries with slightly different axioms and varying degrees of success but in aggregate those nations that abide by some form of it are accepted as functional equals by other whom have likewise implemented their own instantiation of…
That's not what reification means, it's more a form of Platonism (Idealism), plus. See The Meno and it's discussion of the forms (say, the "form" of a spoon.) Plato would reify democracy (although he hated it) but most of us certainly do not. A nominalist (even a Berkeley follower) could discuss democracy perfectly well.
I'm pretty well versed in what reification means. Fundamentally it entails taking a theoretical concept and treating it as if it were a tangible, almost embodied, thing.
Maybe my example wasn't the best but this “democracy thing” gets discussed as if it has material properties: that it can expand, that it can be transported from one place to another, that it can be expelled from a locale, and so forth. Those are pretty material attributes to assign to something that is actually notional.
Re: What Even Is a Number?
#164Earlier quoted context omitted.
> How is it any different than believing that unicorns exist as physical objects, just in their own universe? We have very well-developed representations of the number universe that we can embed into our own universe. These things are governed by precise axioms. By contrast, we don't have such well-developed "unicorn universe". (For starters, what is the definition of "unicorn"? If it's just a horse with a horn, then…
We have very well-developed representations of the number universe that we can embed into our own universe. These things are governed by precise axioms. By contrast, we don't have such well-developed "unicorn universe". Indeed. The current better known attempts at a "unicorn universe" have problems with power scaling and the square-cube law. https://www.reddit.com/r/mylittlepony/comments/mrs81/accordi... Do you have…
>Do you have a good definition of what constitutes a "well-developed" universe?
An easy definition would be one where everyone agrees on the exact mechanics and sequence of states. The fibonacci sequence is well-developed: it has an exact definition that every competent simulator can simulate the same way. If I say my favorite number is the 1000th item in the sequence (starting with 0, 1, 1 as items #1, #2, #3), then everyone can calculate the 1000th item the same way.
If we all try to talk about what happens in the "unicorn universe", everyone has their own different ideas about that. There's no unambiguous rules for how the unicorn universe is calculated. Everyone has a different "unicorn universe" in their heads, and each of those universes operates on our own mind's whims rather than any rules we can describe to each other.
Re: What Even Is a Number?
#165Earlier quoted context omitted.
> You're just confusing the map for the territory. I am not at all! We do math with symbols and diagrams, but those symbols and diagrams are about something: they are maps, and there is a territory that they are about. When I say "math", I include the concepts, not just the symbolic, graphical and other representations. So what I'm saying is that if/when mathematics provides a complete map to that territory which is…
The concepts are also just symbols, just in different media. They are also a map. >if/when mathematics provides a complete map to that territory which is "the world", Then it will encode all the information that exists in the universe. Which will not fit in your head, and thus will not be mathematics. Just because a territory is trivially a map of itself doesn't mean it is useful to call it a map. >The description of…
>Reality isn't just the initial rules. It has state. That state must be described for you to have a complete description of reality.
If reality is deterministic, then all the state is derivable from the rules and the initial state, and it's possible we could figure out the rules and initial state and become relatively sure of them. (We probably wouldn't be able to calculate the future, since evaluating the rules within reality probably necessarily takes more steps than reality takes during that time. But we might be able to calculate enough to see that it matches up with what we think the early universe must have looked like. We might notice that even the smallest of tweaks to the rules or initial state creates an avalanche of changes that doesn't line up with what we believe the early universe looked like, so we can be sure there are no free parameters.) It's fully possible that the rules and initial state could fit in someone's head. They might be ridiculously simple, like Conway's game of life in a few more dimensions.
(If you think "reality can't be deterministic because true randomness or quantum events exist", well you can fit true randomness into a deterministic theory by having the world branch of every random event outcome. The Many-Worlds Interpretation could be viewed as doing something like this for quantum events; it's a deterministic theory.)
Re: What Even Is a Number?
#166Earlier quoted context omitted.
We have very well-developed representations of the number universe that we can embed into our own universe. These things are governed by precise axioms. By contrast, we don't have such well-developed "unicorn universe". Indeed. The current better known attempts at a "unicorn universe" have problems with power scaling and the square-cube law. https://www.reddit.com/r/mylittlepony/comments/mrs81/accordi... Do you have…
>Do you have a good definition of what constitutes a "well-developed" universe? An easy definition would be one where everyone agrees on the exact mechanics and sequence of states. The fibonacci sequence is well-developed: it has an exact definition that every competent simulator can simulate the same way. If I say my favorite number is the 1000th item in the sequence (starting with 0, 1, 1 as items #1, #2, #3), then…
If we all try to talk about what happens in the "unicorn universe", everyone has their own different ideas about that.
Homo sapiens has this issue with this universe. Even if you subset that group to just scientists, there are still differences of opinion.
Re: What Even Is a Number?
#167Earlier quoted context omitted.
That's not what reification means, it's more a form of Platonism (Idealism), plus. See The Meno and it's discussion of the forms (say, the "form" of a spoon.) Plato would reify democracy (although he hated it) but most of us certainly do not. A nominalist (even a Berkeley follower) could discuss democracy perfectly well.
I'm pretty well versed in what reification means. Fundamentally it entails taking a theoretical concept and treating it as if it were a tangible, almost embodied, thing. Maybe my example wasn't the best but this “democracy thing” gets discussed as if it has material properties: that it can expand, that it can be transported from one place to another, that it can be expelled from a locale, and so forth. Those are pret…
Now if you look up tangible...
I think you're caviling, at this point.
Re: What Even Is a Number?
#168Earlier quoted context omitted.
>Do you have a good definition of what constitutes a "well-developed" universe? An easy definition would be one where everyone agrees on the exact mechanics and sequence of states. The fibonacci sequence is well-developed: it has an exact definition that every competent simulator can simulate the same way. If I say my favorite number is the 1000th item in the sequence (starting with 0, 1, 1 as items #1, #2, #3), then…
If we all try to talk about what happens in the "unicorn universe", everyone has their own different ideas about that. Homo sapiens has this issue with this universe. Even if you subset that group to just scientists, there are still differences of opinion.
Reality itself is well-defined in that it acts consistently with itself. We as humans don't have a well-defined embedding of this universe into itself. We would need to know the complete underlying rules of physics for that.
Re: What Even Is a Number?
#169Earlier quoted context omitted.
I'm pretty well versed in what reification means. Fundamentally it entails taking a theoretical concept and treating it as if it were a tangible, almost embodied, thing. Maybe my example wasn't the best but this “democracy thing” gets discussed as if it has material properties: that it can expand, that it can be transported from one place to another, that it can be expelled from a locale, and so forth. Those are pret…
Now if you look up tangible... I think you're caviling, at this point.
“Tangible” means touchable and has a Latin root; “tangere” still means “to touch” (though somewhat archaic) in my native Italian. That
same Latin root is why we call linear equations that share the gradient of a given curve evaluated at the point where they cross to be “tangential”.
Look, we could go on with this all day. What’s your point? To show your terminology and grasp of topics is greater than mine? Is this some kind of passing match? Because I’m really not interested in these schoolyard antics.
Re: What Even Is a Number?
#170I had a fun mind-play with my kids; I asked them if numbers like "one" and "two" really exist. They said yes, of course. OK, I said, show me a plain old "one". Nope, that's one fork; nope that's one ball; nope, you get the idea. You cannot show just "one" unattached to anything else. The concept of "one" is an idea. It only exists as a "real" concept in your mind because it exists as the same concept in the minds of…
A coiuple of my favourites: - Child is put into perfectly sealed cube. They have a torch, which provides light. Since the light cannot escape the cube, what happens when they turn the torch off? Where does it go? - If you put a brain in a jar and wired up electrodes which pulsed up every nerve ending etc to simulate reality - would the brain know it was in a jar? How ? (The matrix being the modern representation) -
In the case of the cube the internal temperature would rise slightly. Th kid is also emitting some heat too so that would also contribute to the rising temperature. Eventually the kid would die from lack of oxygen. If you provide oxygen to the child and remove carbon dioxide the system would no longer be sealed: adiabatic expansion of added oxygen would lower the temperature and removal of carbon dioxide would extract some heat from the cube.
Observed externally the mass of the cube (assuming you didn’t provide a life-support system as I suggested) would remain unchanged because all mass energy is still within the cube. It has simply rearranged itself in a manner unobservable to an external observer.
When they turn the light off you have a black body cavity with an intruder. Ultimately all the light would get reflected back and forth until it fell on various parts of his body whose colour allows them to absorb the incident light waves. The child would get slightly, probably imperceptibly warmer. His surface molecules would move faster and thus he’d have more heat energy.