What is the relationship between the abstract world of mathematics and the material universe?

[Blinky]

I’ve read posts from non-theists saying that the universe is an accident, that it is without purpose or meaning. Is math an accident?

 

[empther]

I’ve read posts from non-theists saying that the universe is an accident, that it is without purpose or meaning. Is math an accident?

---

The universe has a purpose. God uses it as a launching platform to get people to Heaven.
But math is an accident in the sense that God does not determine every speed and direction of every subatomic particle all the time. He lets the world act contingently.

 

[WinterLight]

But math is an accident in the sense that God does not determine every speed and direction of every subatomic particle all the time.

What you’re describing, however, isn’t mathematics. Mathematics is the study of certain kinds of conditional statements; there’s nothing “contingent” about it (presuming, of course, that its foundations are true). As it turns out, such a study has ready applications in arithmetic and science.

 

[Alan_Wostenberg]

As Kronecker quipped “God created the natural numbers; all the rest are the work of man” .

The relationship depends on which mathematical entities we’re talking about. Saying “there are 2 cows” is one thing; but good luck pointing to -2 cows. Here is how Anthony Rizi, a student of Jacques Maritain, himself a student of Aquinas, explains the relation:

"mathematics: second level of abstraction that leaves behind all accidents of material things, save their extension. It consists of geometry, which leaves behind universal quantity, and arithmetic, which leaves behind all qualitative aspects of figure. By making analogies, the mind comes to understand the field of analysis, which builds the bridge between the two realms

Since they are abstracted from the mathematical real world, mathematical entities are real, even though they are conceived in an idealized condition not found in the world (they are, after all, abstractions from the particular). Following Jacques Maritain’s excellent terminology, we call the world of mathematics the world of the mathematical preter-real. However, mathematical beings can be conceived in ways in which they cannot exist in the real world. Asking “where are those -2 cows?” manifests such a case. Again, all mathematical entities are reductively real; that is, they can be decomposed into real pieces, but as entities they can be beings of reason. “-2” is an operation of taking away followed by a number.

• Rizi, the science before science, page 374.

 

[Pfaffenhoffen]

I couldn’t let this nonsense rest…

Total hogwash. Makes math look to be God.

Nature goes about its business without referring to math about which it knows nothing.

A two mile wide asteroid crashing into earth will cause more damage than a one mile wide asteroid, but not because it’s two miles wide instead of one. Number means nothing except to the human mind.

Was it Newton that said that Maths was the Language of God?
Nature goes about its business and not a single step of it goes forward without a reference to Mathematics.

What? Is this hoghogwashwahwash?

A two mile wide asteroid crashing into earth will cause more damage than a one mile wide asteroid, but not because it’s two miles wide instead of one.

Sorry, you know nothing about maths if you keep this sentence:

Number means nothing except to the human mind.

Maths are much more than algebra, the science of numbers…

 

[Pfaffenhoffen]

I’ve read posts from non-theists saying that the universe is an accident, that it is without purpose or meaning. Is math an accident?

No accident.
How come that a purely mental invented problem with a pure mental solution finds a practical purpose?

 

[Pfaffenhoffen]

The universe has a purpose. God uses it as a launching platform to get people to Heaven.
But math is an accident in the sense that God does not determine every speed and direction of every subatomic particle all the time. He lets the world act contingently.

I agree to you.
Though I tend to believe that God drives every particile. You know particles have got laws. Humans have freedom.

 

[Pfaffenhoffen]

As Kronecker quipped “God created the natural numbers; all the rest are the work of man” .

The relationship depends on which mathematical entities we’re talking about. Saying “there are 2 cows” is one thing; but good luck pointing to -2 cows. Here is how Anthony Rizi, a student of Jacques Maritain, himself a student of Aquinas, explains the relation:

The mistake of Kronecker is thinking that God created only visible things and not invisible. For instance, integrals were invented or discovered by men? Ant the irrational numbers? And trigonometry?

My view: they were discovered, not invented.

• Rizi, the science before science, page 374.

 

[empther]

agree to you.
Though I tend to believe that God drives every particile. You know particles have got laws. Humans have freedom.

I have an itch on my nose. I can scratch it or not. I decide to scratch it.
I raise my hand to scratch. Light bounces off my hand and radiates out to space. These photons of light will eventually hit atoms in space altering their speed and direction. These atoms will similary change the speed and direction of other atoms they hit. The effect will eventualy change the whole universe no matter how minutely.

My contingent decision to scratch my nose shows that God lets the universe act contingently.

 

[Alan_Wostenberg]

Does Kronecker think “God created only visible things and not invisible”? It seems to me if he thought that, he could not even say “God created the naturals”. For the naturals are invisible: what color is 2? What shape?

All of the mathematical entities were discovered, you say? None invented?

We discover cows, we discover 2 of them, but where are those -2 cows? Is not -2 as much an invention as the hamburger, the telescope? To say it is an invention is not to embrace idealism. Inventions such as the telescope or the negative numbers are helpful in understanding the world in a certain way.

We take something we find (cow) apply our skills, and make hamburger. We take raw material (sand), apply our skills, and make lenses for the telescope. We take raw material (the natural numbers) apply operations like “take away”, and get a manmade thing: -2. Apply additional operations, we make rationals, irrationals, and so on for all the wonderful beings of reason in mathematics.

From the things God creates, we make new things, we subdue the earth and fill it. What a privilege!

 

[Alberti_Devoveo]

Mathematics in and of itself has no meaning, but it can be extrapolated to the physical world by representing things, such as relating acceleration to velocity through the time-derivative or using vectors to derive conservation of momenta & energy. If I’m not mistaken, this is much like the position that Anthony Rizzi (cf. Alan Wostenberg’s posts) holds.

 

[tdgesq]

Mathematics in and of itself has no meaning, but it can be extrapolated to the physical world by representing things, such as relating acceleration to velocity through the time-derivative or using vectors to derive conservation of momenta & energy. If I’m not mistaken, this is much like the position that Anthony Rizzi (cf. Alan Wostenberg’s posts) holds.

I wouldn’t go so far as to say mathematics has no meaning in itself. It is ultimately based upon quantity and extension, accidents that do exist outside of the mind. The human intellect can and does abstract from material reality only the aspect of quantity, which is why we can speak about such things as natural numbers. I suppose the the major limitation of mathematics is that it can only describe extension, which is only a part of what we experience of the reality of the material universe. It does so with great success in that regard though.

 

[karbear]

Letters and syllables have no meaning in and of themselves but sentences paragraphs and books sure can. Meaning is a tricky word when talking about math anyway. Why not ask, instead, what is the significance? Or better yet, just as the OP did, what is the relationship,? Someone above mentioned Vectors, others mentioned integers. These things arent really that interesting by themselves. They are like letters of an alphabet. We give arbitrary symbols to sounds which form words, just like we give arbitrary symbols to numbers and to abstract mathematical concepts and operations. Disclaimer I’m no mathematitian, I made it through calc 3 and some 400 level abstract geometry - matrix class that was taught by a guy who used to crack codes for the cia (really interesting stuff). Sill, when you get beyond basic building blocks and get a glimpse ( I just got far enough to get a glimpse) into the world of putting basic things like vectors and derivatives and matrices and the like together, its hard not to be awed by it all. When you sart combining abstract concepts (words) the sentence becomes meaningful and numbers do start having shapes and colors. Someone asked above, what shape is 2? I would ask back; what is the literary meaning in a book containing only the letter L?

 

[tonyrey]

I wouldn’t go so far as to say mathematics has no meaning in itself. It is ultimately based upon quantity and extension, accidents that do exist outside of the mind.

A very important point! Water consisted of** two** molecules of hydrogen combined with one molecule of oxygen gas before human beings existed. Numbers are not fictions but facts.

 

[jimrob]

I don’t normally barge into this section, but I feel a few words from a mathematician might be in order.

Mathematics is mainly not about numbers - that’s just the bit we learn at grade school. Mathematics is not abstract: it applies itself to every aspect of the universe. Mathematics is about the laws to which the universe complies. It didn’t start with a bunch of school teachers writing down a load of numbers and making stuff up - it all comes from observation, experiment, theory and proof.

To a mathematician, God didn’t need to create our world and to fling stars into space (that doesn’t necessarily mean he didn’t). All God needed to do was invent the rules of mathematics, provide the initial source of energy and let the universe do the rest. (But why did he have to make quantum mechanics so mind-blowingly difficult?)

From my own experience, I can tell you that mathematicians tend to be a down to earth and fairly religious bunch. Atheists tend to study quasi-sciences like zoology (not much maths there). Mathematics and theology are the only two sciences that encompass the infinite and I’m privileged to be qualified in both.

 

[karbear]

A very important point! Water consisted of** two** molecules of hydrogen combined with one molecule of oxygen gas before human beings existed. Numbers are not fictions but facts.

Wow, maybe our human language is the construct. We know that the qualtily quantity and availability of words affects and limits literary exploration. When we find a new concept, we have to give it a new word. Although, things like wisdom actually exist. But our language and unserstanding of the term might affect our understanding of the concept of wisdom. Math almost seems to be more exact. Either we get it right or its completely wrong. If you add another oxygen to water it becomes hydrogen peroxide. Since math writes the laws of the natural world, and the natural world speaks volumes to us about the Creator (through analogy, beauty, metaphor - helps us understand concept and derive language), it seems like the created world is a pysical manifestation of his Word, and the language used is math.

 

[rmills1]

mathematics is a language, or set of languages, devised to explain and describe various realities about the universe.

And the Lord our God is the most eloquent speaker of this language. At the same time we’re still trying to learn how to conjugate verbs.

 

[karbear]

I don’t normally barge into this section, but I feel a few words from a mathematician might be in order.

Mathematics is mainly not about numbers - that’s just the bit we learn at grade school. Mathematics is not abstract: it applies itself to every aspect of the universe. Mathematics is about the laws to which the universe complies. It didn’t start with a bunch of school teachers writing down a load of numbers and making stuff up - it all comes from observation, experiment, theory and proof.

To a mathematician, God didn’t need to create our world and to fling stars into space (that doesn’t necessarily mean he didn’t). All God needed to do was invent the rules of mathematics, provide the initial source of energy and let the universe do the rest. (But why did he have to make quantum mechanics so mind-blowingly difficult?)

From my own experience, I can tell you that mathematicians tend to be a down to earth and fairly religious bunch. Atheists tend to study quasi-sciences like zoology (not much maths there). Mathematics and theology are the only two sciences that encompass the infinite and I’m privileged to be qualified in both.

Wow, please but in. I was hoping this discussion would become interesting. I have not much to contribute but my intuitive impression, but it is a worthy topic.

 

[tonyrey]

Wow, maybe our human language is the construct. We know that the qualtily quantity and availability of words affects and limits literary exploration. When we find a new concept, we have to give it a new word. Although, things like wisdom actually exist. But our language and unserstanding of the term might affect our understanding of the concept of wisdom. Math almost seems to be more exact. Either we get it right or its completely wrong. If you add another oxygen to water it becomes hydrogen peroxide. Since math writes the laws of the natural world, and the natural world speaks volumes to us about the Creator (through analogy, beauty, metaphor - helps us understand concept and derive language), it seems like the created world is a physical manifestation of his Word, and the language used is math.

I’m sure you have hit the nail precisely on the head!

 

[tonyrey]

I don’t normally barge into this section, but I feel a few words from a mathematician might be in order.

Mathematics is mainly not about numbers - that’s just the bit we learn at grade school. Mathematics is not abstract: it applies itself to every aspect of the universe. Mathematics is about the laws to which the universe complies. It didn’t start with a bunch of school teachers writing down a load of numbers and making stuff up - it all comes from observation, experiment, theory and proof.

To a mathematician, God didn’t need to create our world and to fling stars into space (that doesn’t necessarily mean he didn’t). All God needed to do was invent the rules of mathematics, provide the initial source of energy and let the universe do the rest. (But why did he have to make quantum mechanics so mind-blowingly difficult?)

From my own experience, I can tell you that mathematicians tend to be a down to earth and fairly religious bunch. Atheists tend to study quasi-sciences like zoology (not much maths there). Mathematics and theology are the only two sciences that encompass the infinite and I’m privileged to be qualified in both.

A warm welcome. You are the very person we need on this forum! I’ll send you a pm the next time I think your services are required…