Does Mathematics talk about the universe?
Table of Contents
What is the debate?
I was debating with a person on the internet, about whether, Mathematics is about the universe. I am of the belief that Mathematics is not about the universe. Exploring the universe is the job of Science. Then there is the deeper debate, is Mathematics Science?
Why is Mathematics not a Science?
My argument
Science is a neutral, rigorous, systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
This is the definition on Wikipedia's Science article. As one can clearly see Mathematics doesn't fit into this definition. Mathematics by itself doesn't talk about the real world because they don't make testable hypothesis about the universe, they don't do experiments. They explore abstract concepts which can very well exist in a vacuum.
For reference, we can look at this article Mathematics - Wikipedia.
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory,[1] algebra,[2] geometry,[1] and analysis,[3][4] respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.
Opponent's objections and my reply
My opponent's main objections seems to be that, if mathematics is not about the universe, or the language of the universe. Then how come we use it in Physics to find things about the universe.
I feel like this is an attempt to straw-man my argument. They are talking about Physics which totally falls into the definition 1. Sure, Mathematics can be used in Science for describing the universe and its various facets. But that doesn't mean that Mathematics as a field of study is about the universe.
Their rebuttal seems to be, Well, the Mathematics used in Physics is also Mathematics, right?.
Yes, the Mathematics used in Physics is also Mathematics, but I think there is some distinction that needs to be made clear.
Distinction between Mathematics and Mathematics in Science.
I am sure all of you and my opponent are aware of the Kinematic equations of motion. I will use two of them.
\[v = u + at\] \[s = ut + \frac12 at^2\]
Mathematically this system of equations is completely valid. So, is that why it's accepted? No, that's not the case. It is accepted because it has been experimentally verified. To further illustrate this, let's take another system of equations.
\[v = u + at\] \[s = ut + \pi at^2\]
This system of equation is also 100% valid mathematically. But we know in reality kinematics doesn't work like this. This shows that to make a claim about the universe, we need empirical evidence and because Mathematics is not empirical as I have just demonstrated, it's not Science.
Opponent's weak argument
After being confronted with this, my opponent claims that Mathematics is an exception to this and is about the universe. This is not even an argument. By this logic, I can argue that the world was made in 7 days. But let's not get there.
Opponent's post
My opponent asked me to review this post on their channel, and this is supposed to be relevant to debate. So I will go through it in its entirely.
Here is the entire post.
"The word that gives us a lot of Pleasure. The first part is our most dear. The second Part is related to rank, but is not used for prank." What is it? I often use this riddle of mine to describe the language of the universe: Math.(For the riddle: Our most dear is our Mother or Ma and "th" is the suffix of ranks like 4,5,6,9 and so on and adding them we get Math.)
Mathematics, the most important part of astrophysics is often referred to as the Language of GOD, but why is that let's find out today!! “Mathematics is the language in which God has written the universe. ” — Galileo Galilei There are infinite examples why Maths is the language of God. One of them is the Fibonacci Sequence!! The sequence is the most interesting sequence! In the sequence we add the previous 2 nos. to get the next no. 0 1 1 2 3 5 8 13 21… The nos. in the sequence are found everywhere. Like the the no. of petals in the flowers and the no. of spirals in a sunflower a typical Fibonacci nos. Now if we continue looking at the patterns and take the squares of each no. we get 0 1 1 4 9 25 64 169… Now what if we add the squares: 0+1+1+4= 6(2*3) 0+1+1+4+9= 15(3*5) 0+1+1+4+9+25= 40(5*8) 0+1+1+4+9+25+64=104(8*13)… Interesting isn't it? But why does it work? The answer can be proved by constructing a giant rectangle using squares with sides as the Fibonacci nos. and finding the areas in 2 different ways and equating it!! Now, if we connect the squares vertices using circle like things, a spiral is obtained: THE GOLDEN SPIRAL. The golden spiral is in everything we see, from us eating an apple to a galaxy!! One more observation is that if we take the ratios of the Fibonacci nos, like: 13:8= 1.625 21:13= 1.615 34:21= 1.619… We get closer to the GOLDEN RATIO: 1.618. The golden ratio? Yes, the ratio that if found in any of our body parts, the part is considered beautiful!!
There is much more to the beauty of MATHS!! To summarize my post in one sentence: "Maths, can be considered greater than the feeling of being considered just a subject, but should be considered as a language, confirmed by GOD."
Thank you everyone for reading! Stay tuned for the next post, till then keep learning and keep exploring SPACE!! Follow @spacemathsphysicslearners for more!
First paragraph
"The word that gives us a lot of Pleasure. The first part is our most dear. The second Part is related to rank, but is not used for prank." What is it? I often use this riddle of mine to describe the language of the universe: Math.(For the riddle: Our most dear is our Mother or Ma and "th" is the suffix of ranks like 4,5,6,9 and so on and adding them we get Math.)
This is paragraph just makes a claim, Math is the language of the universe.
Language of GOD?
Mathematics, the most important part of astrophysics is often referred to as the Language of GOD.
Again, sure, Mathematics is integral to Astrophysics, but its Science because
it's empirical. This doesn't mean that Mathematics is a science. No comments,
on the language of GOD thing.
Quote by a famous scientist
“Mathematics is the language in which God has written the universe.” —- Galileo Galilei
We should only look at the work of scientists. Keep in mind, using the argument, This scientist said so, therefore its true is a logical fallacy. But my opponent doesn't commit this logical fallacy, he will give us more examples.
Fibonacci sequence and the Golden ratio
One of them is the Fibonacci Sequence!! The sequence is the most interesting sequence! In the sequence we add the previous 2 nos. to get the next no. 0 1 1 2 3 5 8 13 21… The nos. in the sequence are found everywhere. Like the the no. of petals in the flowers and the no. of spirals in a sunflower a typical Fibonacci nos. Now if we continue looking at the patterns and take the squares of each no. we get 0 1 1 4 9 25 64 169… Now what if we add the squares: 0+1+1+4= 6(2*3) 0+1+1+4+9= 15(3*5) 0+1+1+4+9+25= 40(5*8) 0+1+1+4+9+25+64=104(8*13)… Interesting isn't it? But why does it work? The answer can be proved by constructing a giant rectangle using squares with sides as the Fibonacci nos. and finding the areas in 2 different ways and equating it!! Now, if we connect the squares vertices using circle like things, a spiral is obtained: THE GOLDEN SPIRAL. The golden spiral is in everything we see, from us eating an apple to a galaxy!! One more observation is that if we take the ratios of the Fibonacci nos, like: 13:8= 1.625 21:13= 1.615 34:21= 1.619… We get closer to the GOLDEN RATIO: 1.618. The golden ratio? Yes, the ratio that if found in any of our body parts, the part is considered beautiful!!
I think it's the same thing as in this section Why is Mathematics not a Science? . And no, not everything is in the golden ratio. There are many other ratios. Which may be as prevalent.