Mathematics

[Perpetual Student]

Ontological dribble!?!?!? A more succinct explanation is required.

Human beings create math…numbers…etc. They (we) do this in our minds…somehow. Nobody knows how. Nobody knows what variety of thing meaning (human consciousness) is either. To you it may be ontological dribble…but to the horde of cognitive scientists around the globe, it is the holy grail.

The universe creates…the universe. There appears to be mathematical precision to this universe thing. But…from the POV of the universe…it may be some other variety of thing entirely. We have NOT located math in this universe outside of our minds. How do we KNOW this? We KNOW this, in part, because we don’t even know what math is (or consciousness)… and we KNOW this because we don’t know what this universe is.

You insist that this thing you call ‘number’ has some variety of definitive phenomenology …but you refuse to substantiate this position (except by ridiculing the notion of phenomenology). Until you do so, you do not have one (a position).

...and to answer your question. No...ozone does not exist in nature. Something we call ozone exists in nature ( …how is an ozone molecule explicitly defined???...by where its relevant electromagnetic-strong nuclear – weak nuclear – gravitational forces begin / end ????). Does the color 'red' exist in nature? Obviously not.

Humans do not create number any more than we create all the other attributes of the universe. Do humans create gravity? The various attributes and features of the universe are there and we discover these attributes: number, gravity, charge, spin, fundamental forces, etc.
Your confusion is what I call ontological dribble which, frankly, seems to border on solipsism.

 

[annnnoid]

Humans do not create number any more than we create all the other attributes of the universe. Do humans create gravity? The various attributes and features of the universe are there and we discover these attributes: number, gravity, charge, spin, fundamental forces, etc.
Your confusion is what I call ontological dribble which, frankly, seems to border on solipsism.

My confusion???? You have yet to define this thing you call ‘number’. You have yet to explain how it works. You have yet to explain what it is. You have yet to explain a single thing about it. All you have done is wave your hands about like an epileptic on an ant hill and complain that anyone asking for more is ignorant.

You insist that ‘number’ is some kind of feature of reality. Wonderful! If you’re going to make these extraordinary claims you’d better be prepared to back them up. Define ‘number’. Until you do, your argument is not just wrong, it simply doesn’t exist.

 

[Brian-M]

Is 1 + 1 = 2 a property of the universe or just a concept of our own creation?

It's a tautology.

The number 1 is just a way of referring to a thing.
The number 2 is just a convenient way to refer to a thing and another thing.
The + symbol means and, while the = symbol means is.

So what the expression "1 + 1 = 2" actually says is...

A thing and a thing is a thing and a thing.

So far, no one has a clue what the relationship between the brain and 1+1=2 actually is.

The relationship is that 1 + 1 = 2 represents abstract concepts and our brains are capable of understanding, processing and generating abstract concepts.

….just ?!?!?!?!?!? As Perpetual Student quite accurately pointed out…mathematics somehow corresponds to, describes, represents, and / or predicts every fundamental feature of this universe we live in to one degree or another. It is not too much of a leap to wonder if mathematics actually IS this universe …except that no one anywhere has any idea how such a thing could be possible (then again…no one has any idea what this universe actually is)

Mathematics is a system of logic that our brains create to describe the behavior of the universe. We've been working on adapting mathematics to better describe the behavior of the universe for thousands of years, so it's hardly surprising to find that mathematics as it exists today is very good at describing the behavior of the universe.

New variants of math are created all the time when the need arises.

For example, Boolean algebra wasn't invented until the mid 19th century, and Bra-ket notation was introduced by Paul Dirac in 1939 in order to describe quantum physics.

This also raises the question of whether mathematics is merely one of an infinite range of conceptual systems. One that is conducive to our particular ability to comprehend.

What we call mathematics includes lots of different conceptual systems. For example, Boolean algebra is a completely different conceptual system than matrix math.

But if it’s merely random how to explain the obvious fact that the mathematical systems that are discovered / created have such a vast range of practical applications

I don't think it's random, but I do explain it by the fact that the universe behaves in a consistent way, therefore some consistent systems of logic are necessarily going to have practical applications.

Does ozone exist in nature? How many oxygen atoms does one molecule of ozone have? Is it different from one ozone molecule to another?

An ozone molecule has an oxygen atom connected to an oxygen atom that's also connected to a different oxygen atom.

If you want to apply the concept of "3" to this arrangement, you're free to do so, but the "3" exists in your own mind, not the group of oxygen atoms you're conceiving of.

 

[psionl0]

It's a tautology.

The number 1 is just a way of referring to a thing.
The number 2 is just a convenient way to refer to a thing and another thing.
The + symbol means and, while the = symbol means is.

So what the expression "1 + 1 = 2" actually says is...

A thing and a thing is a thing and a thing.

We can do a little better than that.

1, 2, 3 etc are counting numbers.
Take one thing and start counting and you will stop at 1.
Bring another thing together with the first thing and count and you will stop at 2.
So the + symbol means bring together while = is the final count.

If you think that this is abstract then count the number of children you take out on a trip and count them again when you return. You won't be able to convince anybody that it doesn't matter if the two counts are different.

 

[Brian-M]

If you think that this is abstract then count the number of children you take out on a trip and count them again when you return. You won't be able to convince anybody that it doesn't matter if the two counts are different.

You don't need numbers for small enough groups of children. Our brains are able to distinguish differences in quantity of small groups of things without having to rely on human-created abstract concepts such as numbers.

If you started off with a kid and a kid and a kid, but now only have a kid and a kid, you've obviously misplaced a kid. No counting required.

We (our distant ancestors) invented counting as a way of keeping track of far larger quantities than our brains evolved to handle with exact precision.

The numbers exist as concepts within our minds, not in the objects we apply them to. (This isn't to say that there isn't an enormous utility value in numbers, just that they're a conceptual tool we use as a means of dealing with certain aspects of reality, and not an inherent part of the reality we're dealing with.)

 

[annnnoid]

The relationship is that 1 + 1 = 2 represents abstract concepts and our brains are capable of understanding, processing and generating abstract concepts.

Yer missin da pointttt! You’re talking about the relationship between mathematics and ‘mind’. I’m talking about the relationship between mathematics (what is created by the mind) and the physical activity of the brain. A complete mystery at the moment.

What we call mathematics includes lots of different conceptual systems. For example, Boolean algebra is a completely different conceptual system than matrix math.

No…I’m talking about one conceptual system. The one that generates the capacity to comprehend the dimensions and patterns within which intelligible human meaning occurs. As an example…I would refer to experiences I have had ( and I have heard documented [to the degree that such things can be]) within dream states. Almost like perspectives into alternate conceptual systems (which may explain, to some degree, the difficulty in remembering them […to use an analogy…that which cannot see ‘in color’ cannot describe what occurs ‘in color’]) . Points of view that can only be recognized from within their own systems. This may sound somewhat esoteric…even mystical…but such experiences are far from unprecedented and, it must be noted, our own conventional point of view implicates others by its very existence.

I don't think it's random, but I do explain it by the fact that the universe behaves in a consistent way, therefore some consistent systems of logic are necessarily going to have practical applications.

And that is the point. What explains syntax and semantics (mathematical and otherwise). How is it not random…and why do we see such explicit evidence of pattern everywhere. Not to mention…that pattern implicates intelligence (and we all know what that means [don’t we?]).

 

[psionl0]

You don't need numbers for small enough groups of children. Our brains are able to distinguish differences in quantity of small groups of things without having to rely on human-created abstract concepts such as numbers.

It doesn't matter if you say, "one", "two", "three", ...... or "tom", "dick", "harry", ...... you are still counting.

The numbers exist as concepts within our minds, not in the objects we apply them to. (This isn't to say that there isn't an enormous utility value in numbers, just that they're a conceptual tool we use as a means of dealing with certain aspects of reality, and not an inherent part of the reality we're dealing with.)

Concepts such as "quantity", "more", "less" etc are real concepts that have a real effect on the universe. They don't just exist in our minds.

 

[Perpetual Student]

My confusion???? You have yet to define this thing you call ‘number’. You have yet to explain how it works. You have yet to explain what it is. You have yet to explain a single thing about it. All you have done is wave your hands about like an epileptic on an ant hill and complain that anyone asking for more is ignorant.

You insist that ‘number’ is some kind of feature of reality. Wonderful! If you’re going to make these extraordinary claims you’d better be prepared to back them up. Define ‘number’. Until you do, your argument is not just wrong, it simply doesn’t exist.

In physics, fundamental concepts are defined by their characteristics and behavior. For example, that's how physicists define an electron or a magnetic field. This is also how we define number in nature. Claiming that numbers do not exist in nature unless they can be "defined," is like claiming that electrons do not exist unless they can be "defined." Just like you cannot define an electron without describing its characteristics and behavior, you cannot describe an ozone molecule without describing the number of its oxygen Atoms. Number is simply in fundamental concept in nature and is consistent with THIS.
Your take on this seems to be more metaphysical than scientific.

 

[Perpetual Student]

<...>
Concepts such as "quantity", "more", "less" etc are real concepts that have a real effect on the universe. They don't just exist in our minds.

Clearly, if the above were not true there could be no physics. Even a cursory study of Maxwell's equations, general relativity, Newton's laws of motion or quantum mechanics reveals the deep connection that exists between mathematics and the universe.

 

[Jules Galen]

Mathematics is a discipline which exists entirely independent of
conception for while the symbols may be human it itself is not
But what do the honourable members here think of this though

I think you need better medication.

 

[Brian-M]

Yer missin da pointttt! You’re talking about the relationship between mathematics and ‘mind’. I’m talking about the relationship between mathematics (what is created by the mind) and the physical activity of the brain. A complete mystery at the moment.

Why should it be any more mysterious than the relationship of other abstracts systems to the physical activity in the brain?

Language, art, chess... don't they all relate to the physical activity of the brain the same way that math relates to the physical activity of the brain?

No…I’m talking about one conceptual system. The one that generates the capacity to comprehend the dimensions and patterns within which intelligible human meaning occurs. As an example…I would refer to experiences I have had ( and I have heard documented [to the degree that such things can be]) within dream states. Almost like perspectives into alternate conceptual systems (which may explain, to some degree, the difficulty in remembering them […to use an analogy…that which cannot see ‘in color’ cannot describe what occurs ‘in color’]) . Points of view that can only be recognized from within their own systems. This may sound somewhat esoteric…even mystical…but such experiences are far from unprecedented and, it must be noted, our own conventional point of view implicates others by its very existence.

After reading all that, I no longer think I know what you mean by "conceptual system" anymore.

Although, I have a vague suspicion that what you're talking about might be better described as an experiential or perceptual system.

And that is the point. What explains syntax and semantics (mathematical and otherwise).

We do. We create them.

How is it not random…and why do we see such explicit evidence of pattern everywhere.

They're not random because we need them to be useful, and in order to be useful they need to be consistent, not random.

We see patterns everywhere because:

1. Patterns are the consistent products of consistent systems
2. Our brains are hardwired to act as pattern-recognition devices

Not to mention…that pattern implicates intelligence (and we all know what that means [don’t we?]).

I don't. In what way does pattern imply intelligence?

 

[Brian-M]

It doesn't matter if you say, "one", "two", "three", ...... or "tom", "dick", "harry", ...... you are still counting.

I'm not talking about relying on names or other indirect forms of counting.

Let's move away from using kids as an example, and instead use things that don't normally have names attached, like cookies.

If you notice a very small quantity of cookies on a table, and then look at the table again a few minutes later, you can tell whether or not the quantity of cookies has changed, even if you haven't counted them.

Even animals and small children who don't know how to count can tell the difference.

Concepts such as "quantity", "more", "less" etc are real concepts that have a real effect on the universe. They don't just exist in our minds.

They're "real" concepts as far as any concept can be regarded as "real". But they don't have a "real" effect on the universe, they're an abstract way of representing certain aspects of the universe.

It's the things the numbers represent that have a real effect on the universe, not the numbers themselves. The numbers exist entirely in our minds.

 

[Dessi]

We can do a little better than that.

1, 2, 3 etc are counting numbers.
Take one thing and start counting and you will stop at 1.
Bring another thing together with the first thing and count and you will stop at 2.
So the + symbol means bring together while = is the final count.

Let's define a counting function, which simply returns the successor of its input: S

Let's define 0 a constant where S = 0 is false for all n.

Let's define addition function, n + m, which applies the successor function S to n by whatever is represented by m.

0 + n: n
n + 0: n
S(n) + S(m): S(n + m)

Let's define the equality function, n = m, which evaluates whether the two inputs represent the same input:

0 = 0: true
S(n) = 0: false
0 = S(n): false
S(n) = S(m): n = m

Let's assign some human-readable symbols to our counting function:

0: 0
1: S(0)
2: S(1): S(S(0))
3: S(2): S(S(1)): S(S(S(0)))
etc

Let's evaluate 1 + 1 = 2:

1 + 1       = 2
S(0) + S(0) = S(S(0))
S(S(0) + 0) = S(S(0))   // reduce left operand using addition rule
S(S(0))     = S(S(0))   // reduce left operand using addition rule
  S(0)      =   S(0)    // reduce both operands using equality rule
    0       =     0     // reduce both operands using equality rule
            true        // terminal case, stop recursion

QED.

Same train of thought as counting on one's fingers, but abstracted and formalized a little more.

 

[barehl]

Mathematics is a discipline which exists entirely independent of
conception for while the symbols may be human it itself is not
But what do the honourable members here think of this though

I have a question. Does the color green or the smell of cinnamon exist independent of conception?

 

[psionl0]

I have a question. Does the color green or the smell of cinnamon exist independent of conception?

That is a classical argument about the meaning of words.

If by "colour" we mean the wavelength of a particle of light then it exists independently of observation and depends only on the particle of light existing. OTOH if "colour" is defined by the way it is perceived by the human mind then it exists only if there is a human observer.

Ditto for smelly gasses.

 

[psionl0]

Let's define a counting function [ .......... ] but abstracted and formalized a little more.

You win.

 

[annnnoid]

In physics, fundamental concepts are defined by their characteristics and behavior. For example, that's how physicists define an electron or a magnetic field. This is also how we define number in nature. Claiming that numbers do not exist in nature unless they can be "defined," is like claiming that electrons do not exist unless they can be "defined." Just like you cannot define an electron without describing its characteristics and behavior, you cannot describe an ozone molecule without describing the number of its oxygen Atoms. Number is simply in fundamental concept in nature and is consistent with THIS.
Your take on this seems to be more metaphysical than scientific.

Clearly, if the above were not true there could be no physics. Even a cursory study of Maxwell's equations, general relativity, Newton's laws of motion or quantum mechanics reveals the deep connection that exists between mathematics and the universe.

I happily avert my gaze when there is one utterly absurd post on the science forum…but two (three…look, there’s three of them [which means….what????]) requires some kind of response.

You both seem to want to insist that something called ‘number’ is a fundamental part of reality. You both utterly refuse to provide any substantiation for this position…beyond some variety of vague ‘…but look…there are two of them…’

…and you call this science?????

Ok then…so ‘number’ is a fundamental feature of reality. Like electrical charge, spin, gravity, fundamental forces, etc. etc. What differentiates all of those things from this thing you call ‘number’?

… and the answer is…

…they are all explicitly defined!!!! (I hope I don’t actually need to provide links to establish this). I can google any one of those terms and immediately locate thousands of pages of material that consistently and coherently explains and substantiates their meaning and how they are understood to occur in space-time.

If I google the term ‘number’ I cannot locate a single definition that is remotely consistent with your description of it.

…not…one (…go ahead, give it a try). What do you suppose is the reason for that? Either you’re both wrong, or you have stumbled upon an utterly unprecedented discovery. I’ll put my money on the former.

Why should it be any more mysterious than the relationship of other abstracts systems to the physical activity in the brain?

Language, art, chess... don't they all relate to the physical activity of the brain the same way that math relates to the physical activity of the brain?

It never ceases to amaze not just that so many so-called skeptics are wrong about these issues…but just how wrong so many are. This science-explains-everything fairy-tale is as pervasive as any popular religion. Actually, that is exactly what it most resembles… a religion.

The facts: When it comes to language, art, chess (and / or math) nobody has a clue how they are created by the physical activity of the brain. Actually, nobody has a clue how anything is created by the physical activity of the brain. We are, essentially, in the dark ages when it comes to this subject.

After reading all that, I no longer think I know what you mean by "conceptual system" anymore.

Although, I have a vague suspicion that what you're talking about might be better described as an experiential or perceptual system.

We live in a four dimensional universe (apparently). Our reasoning / understanding is some kind of reflection of this experience. Imagine if you could ‘see’ time the same way you can see the other three physical dimensions (the fact that you can’t is the point [and don’t bother asking me to describe what that might be like…I can’t imagine it anymore than you can]). That is how fundamental a change of conceptual systems is. A more familiar, and modest, example might be a savant who I recently read about who describes experiencing mathematics as colors.

We do. We create them.

Not an answer. The question is…how? There are two possibilities: Either there are an infinite number of variations and we merely locate the syntax and semantics that work…somehow for some reason (how, for what reason…how / why do some things work and other things don’t). Or…there are parameters that govern the operation of what works and we function within those parameters.

I don't. In what way does pattern imply intelligence?

Remember…long ago and far away…in the movie 'Contact'. The character played by Jodie scans the infinite amount of data pouring in from ‘out there.’ What was she looking for? ….patterns. Why?....because patterns are an all-but definitive sign of intelligence. Those who insist that the universe ‘is’ mathematics…are basically saying that the universe ‘is’ intelligence. From there…it’s only a tiddlywink to the existence of whatever-it-is-that-a-God-is. Of course…you can always insist that the universe doesn’t function according to any rules. But that would be rather stupid wouldn’t it. There is certainly nothing definitive about the universe=intelligence=God thing ('except' that it has a variety of consistency to it). It’s just another of those inevitably inexplicable conclusions that our particular variety of cognitive condition manages to generate. If you’re going to insist that universe=mathematics…then our particular variety of cognitive condition invariably equates mathematics with intelligence (so far intelligence [ours] is the only thing capable of experiencing math). Thus, we have a universe that is intelligent. IOW….God!

…bah! Metaphysics.
What is it good for?
…ab..so..lute…ly…
…
…..nuthin!!!

…say it again.

(except…[for example] science).

 

[Brian-M]

It never ceases to amaze not just that so many so-called skeptics are wrong about these issues…but just how wrong so many are. This science-explains-everything fairy-tale is as pervasive as any popular religion. Actually, that is exactly what it most resembles… a religion.

Nobody's claiming that science explains everything. In fact, there's a very good chance that it's impossible, even in theory, for science to be able to explain everything.

But I suspect that you're unintentionally creating a strawman here by getting your terms confused.

I think what you meant to accuse us of was assuming that everything has a naturalistic cause or basis. Something I'll happily plead "guilty" to.

Assuming that everything has a naturalistic cause or basis in the absence of evidence to the contrary is a perfectly rational position in a world where there is no verifiable evidence demonstrating that anything supernatural exists.

There's nothing resembling religion about it. In fact, it's pretty much as opposite to religion as you can get.

The facts: When it comes to language, art, chess (and / or math) nobody has a clue how they are created by the physical activity of the brain. Actually, nobody has a clue how anything is created by the physical activity of the brain. We are, essentially, in the dark ages when it comes to this subject.

Let me digress for a moment and explain the Rule 110 cellular automation. (There's a point to this, I promise).

The rules for each cell are pretty simple, but I'll give a somewhat nonstandard explanation of it here...

• The automation consists of a single row of cells.
• This means each cell has an adjacent cell to the left and an adjacent cell to the right.
• Each cell has two possible states, "off" or "on".
• The state of the cells can change at regular time intervals, which I'll refer to as "instants".
• If both adjacent cells are "on" this instant, then the state of the cell between them will be different next instant.
• If both adjacent cells are "off" this instant, then the state of the cell between them will be the same next instant.
• If the adjacent cell to the left is "on" this instant and the adjacent cell to the right is "off" this instant, then the state of the cell between them will be the same next instant.
• If the adjacent cell to the left is "off" this instant and the adjacent cell to the right is "on" this instant, then the state of the cell between them will be "on" next instant.

With this cellular automation we now have a system, our own micro-universe, whose behavior is not dependent on numbers or mathematics. Each cell simply changes state (or fails to change state) depending on the states of it's neighbors.

But this setup has been demonstrated to be Turing Complete. It can function as a computer, which means it can perform numerical calculations, play chess, ect.

This shows that even a system that has no basis in numbers is capable of possessing structures capable of utilizing numbers. So if a cellular automation can do it, why not a neural net, such as the human brain?

We don't need to know exactly how the brain does it. All we need to know that it's physically possible for the brain to do it, and the observation that the brain appears to do it in order to be justified in concluding that the brain is actually doing it.

Remember…long ago and far away…in the movie 'Contact'. The character played by Jodie scans the infinite amount of data pouring in from ‘out there.’ What was she looking for? ….patterns. Why?....because patterns are an all-but definitive sign of intelligence.

She was looking for signs of ARTIFICIAL patterns. Natural patterns are all around us.

Do you think that the patterns of ripples and dunes in the desert sand is a sign of intelligence? That the patterns of ripples of water in a pond when a pebble falls in are a sign of intelligence? The patterns in the structure of a crystal or snowflake? The patterns of radio signals from a pulsar?

 

[Perpetual Student]

I happily avert my gaze when there is one utterly absurd post on the science forum…but two (three…look, there’s three of them [which means….what????]) requires some kind of response.

You both seem to want to insist that something called ‘number’ is a fundamental part of reality. You both utterly refuse to provide any substantiation for this position…beyond some variety of vague ‘…but look…there are two of them…’

…and you call this science?????

Ok then…so ‘number’ is a fundamental feature of reality. Like electrical charge, spin, gravity, fundamental forces, etc. etc. What differentiates all of those things from this thing you call ‘number’?

… and the answer is…

…they are all explicitly defined!!!! (I hope I don’t actually need to provide links to establish this). I can google any one of those terms and immediately locate thousands of pages of material that consistently and coherently explains and substantiates their meaning and how they are understood to occur in space-time.

If I google the term ‘number’ I cannot locate a single definition that is remotely consistent with your description of it.

…not…one (…go ahead, give it a try). What do you suppose is the reason for that? Either you’re both wrong, or you have stumbled upon an utterly unprecedented discovery. I’ll put my money on the former.

Can you define space and time? Give it a try. Are these concepts unscientific if you cannot do so?

It never ceases to amaze not just that so many so-called skeptics are wrong about these issues…but just how wrong so many are. This science-explains-everything fairy-tale is as pervasive as any popular religion. Actually, that is exactly what it most resembles… a religion.

The facts: When it comes to language, art, chess (and / or math) nobody has a clue how they are created by the physical activity of the brain. Actually, nobody has a clue how anything is created by the physical activity of the brain. We are, essentially, in the dark ages when it comes to this subject.




We live in a four dimensional universe (apparently). Our reasoning / understanding is some kind of reflection of this experience. Imagine if you could ‘see’ time the same way you can see the other three physical dimensions (the fact that you can’t is the point [and don’t bother asking me to describe what that might be like…I can’t imagine it anymore than you can]). That is how fundamental a change of conceptual systems is. A more familiar, and modest, example might be a savant who I recently read about who describes experiencing mathematics as colors.




Not an answer. The question is…how? There are two possibilities: Either there are an infinite number of variations and we merely locate the syntax and semantics that work…somehow for some reason (how, for what reason…how / why do some things work and other things don’t). Or…there are parameters that govern the operation of what works and we function within those parameters.




Remember…long ago and far away…in the movie 'Contact'. The character played by Jodie scans the infinite amount of data pouring in from ‘out there.’ What was she looking for? ….patterns. Why?....because patterns are an all-but definitive sign of intelligence. Those who insist that the universe ‘is’ mathematics…are basically saying that the universe ‘is’ intelligence. From there…it’s only a tiddlywink to the existence of whatever-it-is-that-a-God-is. Of course…you can always insist that the universe doesn’t function according to any rules. But that would be rather stupid wouldn’t it. There is certainly nothing definitive about the universe=intelligence=God thing ('except' that it has a variety of consistency to it). It’s just another of those inevitably inexplicable conclusions that our particular variety of cognitive condition manages to generate. If you’re going to insist that universe=mathematics…then our particular variety of cognitive condition invariably equates mathematics with intelligence (so far intelligence [ours] is the only thing capable of experiencing math). Thus, we have a universe that is intelligent. IOW….God!

…bah! Metaphysics.
What is it good for?
…ab..so..lute…ly…
…
…..nuthin!!!

…say it again.

(except…[for example] science).

Your own incredulity notwithstanding, even something as simple as a single diatomic hydrogen atom cannot exist without number.
Number is as much an aspect of the universe as are all the other fundamental concepts involving space, time, matter and energy. Centuries of discovery have revealed that at every every aspect and at all scales the universe is demonstrably mathematical. Sorry, claiming otherwise demonstrates ignorance.

 

[marplots]

Your own incredulity notwithstanding, even something as simple as a single diatomic hydrogen atom cannot exist without number.
Number is as much an aspect of the universe as are all the other fundamental concepts involving space, time, matter and energy. Centuries of discovery have revealed that at every every aspect and at all scales the universe is demonstrably mathematical. Sorry, claiming otherwise demonstrates ignorance.

Is the part I highlighted begging the question?

How might the universe appear to us without the concept of discrete, or ordered ranking, or "more-than/less-than?"

What does it mean to say I cannot imagine it so, other than a statement about how I conceptualize the world around me?