Actual philosophy

[Computergeek01]

I understood Duoas here, when he says numbers he is referring to the symbols we choose to represent them. He isn't saying that the data numbers represent isn't real, he is saying that the character set is fungible.

I also think he is going a step further and saying that the base of those numbers is arbitrary. You could calculate a function in decimal, binary, hexadecimal etc. The answer will always be the same, the only difference is how it appears due to how those integers get promoted and what character set they use. For example, in the decimal system 'F' is not a number but '15' is. They both represent the same value, they only differ in appearance due to their radix and character set.

[oSGzwA7f]

Let me rephrase that, how is mathematics not a human construction, but numbers are?

[htirwin]

Numbers and mathematics can be used to make abstract models of things in a physical universe (assuming it exists) because a physical universe exists.

Math and numbers can be used as tools for abstractly describing primitive notions of existence along with relationships between existing things.

I don't know if it makes sense or not to say that numbers and mathematics exist naturally. Numbers and mathematics can describe in some abstract way, anything that exists. We apply them to things that exist. Basically what I am saying is that existence itself is enough of a per-requisite for mathematics application.

What is interesting is that there are complex forms of existence, patterns and relationships in the real physical universe. That we can use abstract tools and ideas to represent them and investigate them is inherit to the fact that these tools and ideas are made for those purposes.

So I would say that numbers and math are both human constructs, and because things exist, they have applications.

[Lowest0ne]

I've very much in agreement with htirwin. Humans invented numbers.

A number is a representation of an amount. If there are a certain amount of marks on a piece of paper, one can make the same amount of ( or less or more ) marks on another piece of paper without knowing how many marks there are. One can do simple arithmetic with amounts figure out if there is enough of something.

I would be more inclined to believe that the act of the wolf giving birth physically changed its brain. The wolf doesn't know how many cubs it has, but it does know the difference between the correct and incorrect amount.

People began to use amounts and counting so much that they started to name the amounts. Evidence of this is the general lack of the number zero in many cultures that were otherwise using numbers a lot. I believe the Mayans were the only 'ancient' civilization using zero. Even then, the number zero wasn't even understood as a number, more like a placeholder ( 10 is ten ones, 100 is ten tens ).

I would recommend checking out "Zero: The Biography of a Dangerous Idea Paperback", or anything else by Charles Seife.

Counting and amounts only work for whole numbers ( or whole pieces ), and have little to do with measuring. I can measure something with a meter stick and say it is three meters long. You might be able to measure centimeters and call it 305 centimeters long. Someone else has an even more precise measuring tool, and will find a different measurement. This will continue infinitum ( yes, even with an electron microscope ).

However, if someone wanted a table to rest a coffee mug on, then the yard stick will be just as valid a measuring tool as an electron microscope.

"What is the least amount of money someone needs to be called a millionaire? five hundred thousand dollars."

[Mats]

This will continue infinitum ( yes, even with an electron microscope )

However, it will not continue infinitely if gravity is quantized, which it surely will be as all other forces being quantized and gravity not being quantized doesn't work, as well as non-quantized gravity leading to many problems just on its own.

Mathematics certainly seems to be an inherent property of the universe and numbers are part of makes up mathematics, so...

[Ispil]

Well, numbers are just one aspect of mathematics. Quantum states have nothing to do with numbers- you can completely deal with them as hilbert spaces, and no numbers are required. So maybe there's just an illusion of the necessity of numbers in the universe- in reality, we just haven't broken it down into mathematics beyond numbers yet.

[Mats]

You can't do anything which is real with a Hilbert space without having some values to calculate with. I mean, when you make the real-life measurements, how are you doing them without numbers? How are you going to do any calculus or measure any lengths or describe angles or anything? It's all very nice to say you can just manipulate equations without using any numbers, but in reality, you need a value to substitute in to start doing anything.

[Lowest0ne]

I'll be honest and say that when you talk about quantized gravity and Hilbert space I just get lost.

Mats wrote:

Mathematics certainly seems to be an inherent property of the universe and numbers are part of makes up mathematics, so...

Wikipedia says mathematics is the study of numbers ( quantity ), but I was going to say that numbers describe the mathematical nature of the universe. You don't need numbers to have a universe, just the description of it. The idea of something existing without an observer is a little twisty, but I'll let myself slide on that one.

I don't know where I am going with this next bit. My idea is that number quantify the universe and allow us to make measurements. However, such measurements are not necessary for the universe to "act" upon its physical differences.

I have no right or wrong, just playing with thoughts.

[Ispil]

Mats, not necessarily. Sure, calculating direct values requires numbers, but the proof of the no-communication theorem? None whatsoever. I'm not saying that you can take direct measurements without numbers, I'm saying that to demonstrate important concepts in physics and such do not require such numbers. When you take math and make it abstract, you at don't need numbers to demonstrate concepts more important than the numbers themselves.

[Mats]

Think of it this way. An electron is orbiting a hydrogen atom, when a photon comes along and interacts with it. How does the universe itself know things such as the energy of the electron, the energy of the photon, the position of the electron etc...?

The only reasonable way is to say that the electron and photon fields have values which describe these things. We represent these values with numbers and we get correct answers, so whatever the real universe is doing to 'know' what these values are, even if it is not a number, should be equivalent to a number anyway.

[Duthomhas]

Let me rephrase that, how is mathematics not a human construction, but numbers are?

I think we are getting twisted on definitions.

You are treating mathematics as our human understanding of the universe. (I think.)
I am treating mathematics as the intrinsic nature of the universe, of which we humans have some small understanding.

That is, the universe is mathematical. Likewise, 'numbers' are themselves a universal construct. (Aliens will have numbers too, that work just like ours.)

I guess I'm arguing that our perception of them is a human construct. But they exist without us.

(Silly segue: remember "Contact"? The 'gods' had to give us humans their number system before anything else they gave us would make sense.)

Mathematics is knowledge (of things as they are). It is hubris to believe we need to comprehend that knowledge for it to exist -- which would make for circular reasoning indeed.

I also think that Ispil is making an equivocation here. Unknown quantities != no numbers. And, impossible-to-communicate != no numbers. (It only means that the observers are not necessarily working with the same number representations.)

Unless I've missed something... (I admit I am a rank amateur in quantum mechanics.)

[htirwin]

We can use mathematics and numbers that that does/do not have any correlation to reality ( outside the human mind ). This tempts me to say that math and numbers are human constructs.

When I think of mathematics, I imagine there are three main components. There are systems ( collections of rules, symbols and definitions ) that we have constructed. There are ideas and exploration ( science? ). And there is truth.

When it comes down to it, maybe mathematics is 2 parts a human construction and 1 part intrinsic.

[helios]

We can use mathematics and numbers that that does/do not have any correlation to reality ( outside the human mind ). This tempts me to say that math and numbers are human constructs.

First, suppose mathematics is not wholly a human invention. Would we be unable to come up with maths that are unrelated to reality? If not, then the fact that mathematics can study physically meaningless objects is irrelevant to the question of where mathematics as a whole comes from.

Second, just because we haven't found an application to all forms of math doesn't mean they don't exist.

Third, until someone discovers the source code for the universe, the best we can say about the relation between mathematics and the universe is that mathematical models work. We don't know if this is by accident, by design of human mathematics, or because the universe is indeed mathematical.
In other words, in principle all forms of mathematics are unrelated to reality.

[Mats]

Second, just because we haven't found an application to all forms of math doesn't mean they don't exist.

Out of interest... Name a form of mathematics without an application?

In other words, in principle all forms of mathematics are unrelated to reality.

Dirac has something to say about this:

It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.

[htirwin]

I don't agree with the paradigm that there is some hidden set of expressions or laws that exist in and of themselves as part of the mechanism god uses to give cause and effect.

Or that there is or was some form of grand blueprint of the universe designed with mathematics.

My views are that physical properties of things themselves give rise to cause and effect. Assuming that there is consistency to cause and effect based, on physical properties, I think that true statements about quantity, geometry and relationships between existing things in the physical universe are inevitable. And this is our mathematical universe. The fact that the complexity or beauty of existence is awesome doesn't mean it must be God's design or be due to some math machine that controls everything.

I don't know how probability waves fit into all of this though.

[Duthomhas]

We can use mathematics and numbers that that does/do not have any correlation to reality ( outside the human mind ). This tempts me to say that math and numbers are human constructs.

LOL. I'm done here.

[htirwin]

LOL. I'm done here.

Because you are not intelligent enough to comprehend my arguments, or because there is something wrong with them?

I would like to hear what you think is wrong with them if that is the case?

Or maybe you have some grudge or hatred of me personally?

[helios]

Out of interest... Name a form of mathematics without an application?

I don't know whether there currently is one. My argument holds, either way.

My views are that physical properties of things themselves give rise to cause and effect. Assuming that there is consistency to cause and effect based, on physical properties, I think that true statements about quantity, geometry and relationships between existing things in the physical universe are inevitable. And this is our mathematical universe. The fact that the complexity or beauty of existence is awesome doesn't mean it must be God's design or be due to some math machine that controls everything.

If that math machine existed, what form would you gather it would have? For example, I imagine a universal cellular automaton.
I ask because I'm not sure how you can reconcile the end that paragraph with its beginning.

[htirwin]

If that math machine existed, what form would you gather it would have? For example, I imagine a universal cellular automaton.
I ask because I'm not sure how you can reconcile the end that paragraph with its beginning.

So you imagine that the universe itself is the math machine. But does this machine actually do math? Does it calculate? Does one particle know the velocity of another and use this information to determine how it reacts when it comes into contact with it? I think the universe is a collection of dumb fundamental particles. The fact that their collective behavior and existence is predictable is intrinsic to the nature of existence as we know it.

What I was getting at is that I don't believe that calculations are done to decide outcomes. Outcomes happen and it so happens we can model them with calculations.

I realize that religion is a huge hidden factor. If you believe in god, then you are forced to believe in an external force that decides cause and effect, and it would be natural for a human being to think of this as a calculator or a program that calculates and decides what happens; one that can be intervened to perform miracles.

It is from this paradigm where the philosophical opinions, in this context, from Dirac, Einstein, and many other highly distinguished religious physicists, come from.

[helios]

So you imagine that the universe itself is the math machine. But does this machine actually do math? Does it calculate?

Yes. State changes are forms of calculation.

I think the universe is a collection of dumb fundamental particles. The fact that their collective behavior and existence is predictable is intrinsic to the nature of existence as we know it.

You're simply moving the question, not answering it. "The particles behave the way they do because of the nature of existence, not mathematics." Okay, so is the "nature of existence" mathematical? If not, then what is it, and why does it make things behave as if it was?