Is mathematics the queen of sciences? Yazan physicist.
Is mathematics the queen of sciences? Yazan physicist.
By Don Lincoln | Published: 2025-01-16 14:34:00 | Source: Hard Science – Big Think
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Social media can be a tricky place, where people are trapped in an endless game of one-upmanship. And, I’m sorry to say, this behavior can also be seen among science enthusiasts when discussing which disciplines are more important. People often take a reductionist view in these arguments, claiming that sociology is just applied psychology, psychology derives from biology, biology arises from chemistry, and of course chemistry is applied physics. As a physicist, I can support this way of thinking. In my opinion, physics is the queen of sciences.
However, one school of thought goes so far as to dismiss all of science as merely a repetitive application of applied mathematics. If physics is the queen of sciences, then mathematics is the empress. there Comedy xkcd This illustrates the debate in a humorous way, and some prominent physicists have made similar claims.
For example, in 1960 physicist Eugene Wigner published Research paper entitled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” While his position is often exaggerated among online fighters, he comments on the uncanny similarities between mathematics and physics, marveling at how well mathematics works. Physicist Max Tegmark said supposed This reality is not only parallel to mathematics; But reality He is Mathematics, and all mathematical structures, are representations of a variety of facts. In his proposal, different mathematics describe real universes embedded in a larger multiverse. This proposal is controversial—there’s a reason some in the theoretical community refer to Tegmark as “Mad Max”—but there are certainly some who would argue in favor of the primacy of mathematics over physics.
There is also no denying the value that mathematics adds to professional physicists. I devoted much of my undergraduate years to learning mathematical skills and how to apply them to the theories needed to solve specific research problems. actually, Single representation The equation that governs all known subatomic phenomena should be written down on a full page. This is just to write the equation, not to do anything with it. Given the centrality of mathematics in modern physics, it is quite understandable that some might think that this centrality implies priority. While these individuals may respect all sciences, for them mathematics is just that Primus between Paris.
I have a different point of view. I would argue that those who dispute the relative status of science versus mathematics understand neither.
Science is the study of the natural world. Physics – especially fundamental physics, which is my specialty – is the study of the deepest rules of nature. When we exaggerate, my colleagues might say that we investigate the foundations of physical reality by delving deeply into the laws of matter and energy, space and time. Particle physicists and cosmologists search for connections between the known behaviors of matter and energy, hoping to show how what appear to be completely dissimilar phenomena are actually different manifestations of the same thing. One example of this is how physicist James Clerk Maxwell showed that electricity and magnetism are two ways a common phenomenon called electromagnetism affects the world.
In contrast, at least fundamentally, mathematics has nothing to do with physical reality. Alternatively, mathematics can be called a subset of logic. With some liberties that might offend professional philosophers, mathematics can be widely regarded as the logic of numbers and quantities.
Now, when I say “mathematics,” I don’t mean arithmetic, geometry, or calculus. These are examples of mathematical disciplines, but I have a more abstract meaning in mind. I’m talking about intellectual constructs where one chooses a set of things (usually numbers) and a list of rules that govern them and then uses logic to figure out the implications of those choices. Use symbolic language, and you have a form of mathematics.
For example, basic arithmetic operations can be described as the rules governing integers along with addition and subtraction. Mathematics determines what happens if you take this set of numbers and apply those operations. Add or subtract two integers, and you get another integer. Add a zero to a number, and you get the same number. The form of mathematics that covers this kind of thing is called “group theory.”
If you need to represent objects that are not complete units – for example, half a pie – this primitive form of mathematics does not work. You need to add multiplication and division to the mix. When you do this, you invent additional numbers, specifically fractions.
One can go on and add other numbers to form the real numbers (which are all conceivable numbers ranging from minus infinity to plus infinity). You can imagine additional processes and rules governing the ever-growing list of numbers.
Mathematical processes and rules don’t have to be familiar. Using ordinary mathematics, if you add 11 and 4, you get 15. However, there is a form of mathematics – colloquially called “clock mathematics” – where 11 + 4 = 3. No doubt you have used this form of mathematical reasoning without appreciating it for what it is. If it’s 11 a.m. and something happens four hours later, it will happen at 3 a.m. This is correct mathematical logic; It is not the method that governs the normal way of counting.
So, how do these definitions of science and mathematics mix? After all, there is no denying that mathematics is deeply embedded in the world of contemporary science. It starts with two deeper thoughts.
The natural world is what it is. It is independent of humanity and governed by rules arising from root causes currently unknown to us. Water falls when it rains. The stars move across the sky on a clear night. The galaxy rotates slowly over eons. The laws of the universe are what they are, and there is nothing we can do about them.
Science is an attempt to understand those behaviors. We propose models that have assumptions. We carefully select the subset of mathematical logic that best represents the assumptions embedded in our model, and then use them to perform calculations. These calculations are not the physical world. It is a manipulation of models, using the logic of applied mathematics.
Not all mathematics is suitable for all scientific models. For example, if we are trying to understand the behavior of water, we usually think of it as something that we can break down into ever smaller amounts. For such a model, we choose to use continuous mathematics for high school algebra and introductory calculus.
However, when we get down to small enough scales, we encounter individual water molecules that cannot be cut in half and remain water. Here, continuous mathematics is not the best option; Instead, we should use the logic of discrete mathematics. If we do not change the mathematical formalism used, we will make predictions that are inconsistent with the behavior of the natural world.
My position is first that mathematics is an exercise in pure logic. It is not a human construct. Second, the universe is governed by all the rules that govern it, and these are not human constructs either.
Modern science creates models based on assumptions and uses any subset of mathematical logic that appears to parallel the rules governing nature. this He is A human build and a powerful one at that. If the model is validated by comparing its predictions to measurements, we hope to use this model and mathematical logic to predict untested phenomena. If that happens, we have some hope that our model guess is a reasonable representation of reality.
A good example of this is Albert Einstein’s theory of general relativity. Released in 1915, it was quickly validated by accurately predicting movement Orbit of Mercury And distortion The apparent location Of the stars during a solar eclipse. As predicted by theory Black holes and Gravitational wavesThese are two ideas that took nearly a century to validate. Mathematics has allowed researchers to conduct quantitative investigations into the implications of a theoretical model and the mathematical logic that governs it.
But mathematics is not a science. Mathematics is a field in itself, and can exist without science. From a scientist’s perspective, mathematics is a powerful tool that can be used to create a series of theories that more precisely shape reality. If the implications of each model turn out to be more easily determined through interpretive dance, scholars will ditch the math and lace up their dancing shoes.
There is no denying the brilliance of generations of mathematicians who enjoy playing with numbers and diving deeply into the consequences of the assumptions of each form of mathematics. My hat’s off to those who do all the heavy lifting. Indeed, when I was young, I was one of them, as I obtained a university degree in mathematics.
But as my career progressed, it became clear that I was not a mathematician. I am a scientist. Understanding the laws of nature attracts me much more than understanding the consequences of logic. So I’ll leave the math to the mathematicians, and I will remain grateful for their work because it makes it easier for scientists to investigate how the universe works.
So, for those enthusiasts who argue on the Internet about the hierarchy of sciences, I would say that they are all interesting (although I think physics underlies all the other sciences). Mathematics exists outside the realm of science, but is a purer realm. It simplifies the work of scientists to achieve this most ambitious goal of trying to understand everything.
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