That is at least a contentious point of view. It would probably require some form of Platonism to be true and that seems pretty hard to defend.
still, i hold it would be more 'hard to defend' abstract concepts fail to exist.. regardless of 'where'
beyond the scope of humanity or human curiosity, look at chemistry
the universe is rather predicated on relations to the abstract concept of quantity
and those distinguishing identities exist within a hadron and in far flung galaxies
To you point about quantity. There are grains of sand. Does that mean that there are also numbers? I obviously argue no. You have to take some of the grains and set them aside to count them. You have to split your pile into two and recombine the two piles to add them. You have to line the grains up in order to number them.
By itself there are only grains of sand, mathematics only emerges when you impose additional structure on them and perform operations with them. There is no addition in a thousand grains of sand, it is the act of separating and combining them. Or at least imagining to do so.
You can build a huge part of mathematics on top of set theory but that does not mean that all of mathematics is already contained in every large enough set of things, at least not in any meaningful way. Only when you decide what to with the things in the set, what kind of manipulations you are willing to consider, that the structures mathematics describes emerge.
And while physics looks very mathematically, I see no problem with this. The most simple rules can give rise to staggering complex math. I find it much more reasonable to think - gross oversimplification ahead - that photons travel in straight lines in a three-dimensional space and therefore the electric field follows an inverse-square law instead of assuming that the universe already contained the mathematics needed to deal with electric fields.
There are just photons moving around, only after deciding how to measure distances and to look at spherical shells around charges we find a particularly simple way to describe electrical fields. But we could have made a lot of different choices leading to wildly different descriptions.
numbers exist without sand, sand needs numbers to exist
you can count apples instead of sand
yet physical phenomena, such as the formation of sand or apples, depends on quantity
chemistry shows that how many particles in what structure determine how it interacts physically with its environment
a hadron with three quarks is a baryon, a hadron with a different number is fundamentally different
There is an infinite number between 0.1 and 0.00000000000000000000000001
The only reason we can grable with these things in mathematics is because we are conscious minds who create symbolic meaning.
There aren't any numbers "out there".
"Out there" there are no perspectives only everything at once.
..edit.. I'm unable to reply again so I'll clarify what I mean here: for me physics is behavior, mathematics is existence
Only when you reduce reality (like humans do) and you start manipulating with symbols do you get mathematics.
This manipulation with symbols (and it's foundation of a quantifiable universe on top of a quantum universe) is the foundation of math, not the other way around.
Math is simply a way this underlying reality gets expressed, it is not what the reality is.
Why would sand need numbers to exist? I can pile up sand without ever knowing how many grains of sand are in the piles. I can not see how combining several things requires numbers, it only requires several things, i.e. you have to define what the different things are, where the boundaries between them are.
you can count apples instead of sand
Obviously, that was just an example. You need several objects.
yet physical phenomena, such as the formation of sand or apples, depends on quantity
It does only insofar as you need several distinct objects, it does not depend on numbers. Also note that you have to arbitrarily decide to count apples or grains of sand. Why apples or grains, why not atoms or quarks? There is a bunch of stuff and you have to divide into several distinct objects before you can even start to count them. The fact that you decide to divide all the quarks and electrons into things you call apples is an arbitrary decision and imposes a structure on top of the things that are there by itself. Only with this imposed structure and your [imagined] action of dividing and combining subsets of the things does something like counting, and numbers and addition emerge.
a hadron with three quarks is a baryon, a hadron with a different number is fundamentally different
Arbitrary definition. There are quarks, calling collections of them baryons or mesons or tetraquarks is an arbitrary definition made by humans, albeit a useful one.
But those grains of sand you are piling already exist ;P
In a universe where quarks only collect in groups of four sand would fail to exist
it needs baryons.. or whatever name you want to ascribe, yes it is scientifically known and recognised that naming conventions are arbitrary and often localised but naming stems from consistent behaviour
In a universe without baryons to claim sand exists would be making up a new substance that uses 3 quarked particles
Or if you add a fourth quark to one proton in a grain of sand it would cease to be sand
So the number of quarks that collect and how they structure determines the existence of sand
Similar to how a beach is formed based on the number of grains of sand
anyway the root of the issue is confounding to me.. how often has physics been disproven and replaced by implementing mathematics?
for me physics is behavior, mathematics is existence
if you are sincerely asking.. i suppose i'd answer: well the same as the state of the universe: empty; now what would be the meaning of the concept that the term, or symbol, seven refers to? well, still 7, but such a universe would lack the necessary representations to express it
my mathematical research begins in an 'empty universe' and questions the most base of assumptions necessary to get to a representation of, for instance, 7
an empty universe actually contains enough information to express all information utilising mathematics: the current empty 0, and the potential any state replacing the empty state 1; if time.. when emptiness begins and ends.. is allowed to be considered
(o) http://materlakes.enschool.org/ourpages/auto/2013/2/25/50973...
> "Someone just dumped a whole garbage can of orange peels out the window." ... "They float very nicely," he said without turning around. "That's interesting." ... "I don't mean it's interesting that they float," Teddy said. "It's interesting that I know about them being there. If I hadn't seen them, then I wouldn't know they were there, and if I didn't know they were there, I wouldn't be able to say that they even exist. That's a very nice, perfect example of the way--"
I want to argue that whenever you think that there is some math already contained in the universe, it is actually you accidentally introducing it without noticing it. Look, trees! One, two, three, ... See? There are numbers in the universe. And look, I can add the number of trees in this wood and that wood.
It is of course tempting to conclude that the math was already there. But I argue that it was not, that it is you inventing it. It is your concept of object identity that defines what a tree is and when two trees are the same or different trees, you divide the world into different objects. It is your concept of grouping objects into sets. It is your concept of pairing the elements of two different sets to compare their cardinalities. It is your concept of including one more element in a set that defines what counting means. It is your concept of combining two sets that defines what addition is.
That are all things you can do with objects in the universe, but nothing of that is inherent. If you look carefully enough, all the things that look like math already exists in the universe actually require you making use of a lot of abstract man-made concepts. Many of them, like object identity and counting, are just so deeply ingrained in us that you don't notice that you are using them if you don't pay careful attention.
That is I asked for the empty universe, I wanted to take away all the objects on which you could accidentally impose structure. If math were truly fundamental, if Platonism were true, then seven should still exist in an empty universe. I don't see how this would be true in any meaningful way.
If we added a mathematician to our empty universe, he could invent math. He could come up with the idea of objects and identity and set of objects and he could think about operations with those objects and consequences of the definitions he made. But it would all have no relation to the otherwise empty universe, it would be a game of formal rules, mostly manipulating strings of symbols. If the mathematician had great imagination, maybe he could imagine actual things existing in the universe, how he could label them with those numbers he invented, and how he could visualize addition by moving things around.