In this document, I use the top-down apprach to draft an essay on the Universe.
This exercise is for homework 2 of the summer course EMSE 768 on scientific writing.
The most recent draft 2 is in the next section. The initial draft and the brain storming process are in the other sections.
The Universe
Yuhao
Broader than the continent is the ocean. Broader than the ocean is the sky. Broader than the sky is the Universe. Broader than the Universe is the breadth of an open mind.
The level of difficulty in understanding something is related to the width of the content in it. Understanding the Universe is very challenging because the Universe is so broad. Another task as challenging as understanding the Universe is to understand the mind, with the mind. It does not mean the land and the ocean are all understood. It does not mean the land and the ocean are easier to understand.
Here, I’m going to discuss how to understend the evolution of the Universe. It sounds weird to talk about the evolution of the Universe. How do we even know? What are the key observations that support the theories? What are the key theories that support the framework?
To begin with we start from relativity. Relativity is a weird theory. Or not. Relativity is inspired by the observation in the Michelson-Morley experiment (Einstein said it is not).
What was the initial goal for the Michelson-Morley experiment? The Michelson-Morley experiment was designed to find aether, the medium that light is supposed to travel through. In what sense? Light has wave properties. For other waves the wave feaure is from the oscillation of a medium. Why should light be an exception?
From the Michelson-Morley experiment and other experiments, the speed of light is the same in reference frames at different velocities. Under the constraint of the speed of light staying constant in reference frames at different velocities, space and time would need to correlate. When the space and time correlate, the space and time are not independent. It’s against intuition to have space and time correlated.
If space and time are correlated instead of independent, it becomes possible to model the effect of gravity by correlating the space and time. In the daily observations and observations in astronomy, we see the effect of gravity is related to mass. If we assume mass can lead to a specific way of correlation in space and time that creates the effect of gravity, we can develop a theory, the GR (General Relativity).
The application of GR is about solving the Einstein equation. In the Einstein equation the left hand side is a four-dimentional quantity related to the geometric properties in space-time, the right side a four-dimentional quantity related to the distribution of energy and momentum. Solving the Einstein equation for homogeneous and isotropic mass distribution, we will find a solution. What properties does the solution have? The solution shows that the space is expanding.
If we look at the Universe from the large scale, it is not crazy to assume the Universe is isotropic and homogenous. Is the Universe expanding? Hubble made some observations on the speed of galaxies in the direction away from the Earth and the distance of the galaxies away from the Earth. The result is that the farther a galaxy is away from the Earth, the faster the galaxy is receding from the Earth. So the Universe is expanding.
Another piece of evidence supporting the hypothesis of a Universe isotropic and homogeneous at the large scale is the observation of the CMB (Cosmic Microwave Background). The CMB at large scale is isotropic, indicating that the Universe was isotropic when the CMB was generated and that the expansion of the Universe has been isotropic since the CMB was generated. The power spectrum of the CMB follows the power spectrum of the so-called black-body radiation. The CMB power spectrum is the most perfect black-body radiation spectrum measured to date. The black-body radiation is the electromagnetic radiation from a system in thermal equilibrium with the environment.
If the Universe was in a state of thermal equilibrium when the CMB was generated, was the Universe infinite when the CMB was generated? Is the Universe mathematical? Contrary to common thought, math is not logically perfect. Gödel found that the natural number based systems are not logically complete. I do not know how the Gödel incomplete theorems work. I can give one example of a paradox in the natural number system. Suppose
Broader than the continent is the ocean. Broader than the ocean is the sky. Broader than the sky is the Universe. Broader than the Universe is the breadth of an open mind.
The level of difficulty in understanding something is related to the width of the content in it. Understanding the Universe is very challenging because the Universe is so broad. The only other task as challenging as understanding the Universe is to understand the mind, with the mind. It does not mean the land and the ocean are all understood. It does not mean the land and the ocean are easier to understand.
What we’re going to talk about is how to study the Universe using the scientific approach. It sounds weird to talk about the evolution of the Universe. How do we even know? What are the key observations that support the theories? What are the key theories that support the framework?
To begin with we start from relativity. Relativity is a weird theory. Or not. Relativity is inspired by the observation in the Michelson-Morley experiment (Einstein said it is not).
What was the initial goal for the Michelson-Morley experiment? The Michelson-Morley experiment was designed to find aether, the medium that light is supposed to travel through. In what sense? Light has wave properties. For other waves the wave feaure is from the oscillation of a medium. Why should light be an exception?
From the Michelson-Morley experiment and other experiments, the speed of light is the same in reference frames at different velocities. Under the constraint of the speed of light staying constant in reference frames at different velocities, space and time would need to correlate. When the space and time correlate, the space and time are not independent. It’s against intuition to have space and time correlated.
If space and time are correlated instead of independent, it becomes possible to model the effect of gravity by correlating the space and time. In the daily observations and observations in astronomy, we see the effect of gravity is related to mass. If we assume mass can lead to a specific way of correlation in space and time that creates the effect of gravity, we can develop a theory, the GR (General Relativity).
The application of GR is about solving the Einstein equation. In the Einstein equation the left hand side is a four-dimentional quantity related to the geometric properties in space-time, the right side a four-dimentional quantity related to the distribution of energy and momentum. Solving the Einstein equation for homogeneous and isotropic mass distribution, we will find a solution. What properties does the solution have? The solution shows that the space is expanding.
If we look at the Universe from the large scale, it is not crazy to assume the Universe is isotropic and homogenous. Is the Universe expanding? Hubble made some observations on the speed of galaxies in the direction away from the Earth and the distance of the galaxies away from the Earth. The result is that the farther a galaxy is away from the Earth, the faster the galaxy is receding from the Earth. So the Universe is expanding.
Another piece of evidence supporting the hypothesis of a Universe isotropic and homogeneous at the large scale is the observation of the CMB (Cosmic Microwave Background). The CMB at large scale is isotropic, indicating that the Universe was isotropic when the CMB was generated and that the expansion of the Universe has been isotropic since the CMB was generated. The power spectrum of the CMB follows the power spectrum of the so-called black-body radiation. The CMB power spectrum is the most perfect black-body radiation spectrum measured to date. The black-body radiation is the electromagnetic radiation from a system in thermal equilibrium with the environment.
If the Universe was in a state of thermal equilibrium when the CMB was generated, was the Universe infinite when the CMB was generated? Is the Universe mathematical? Contrary to common thought, math is not logically perfect. Gödel found that the natural number based systems are not logically complete. I do not know how the Gödel incomplete theorems work. I can give one example of a paradox in the natural number system. Suppose
Title: The Universe
The Universe is the place we live in. What do we know about the Universe?
Scratch that. I need to write following the outline I had.
What is this essay for? This essay for a practice using the Top-Down approach for doing writing. What is the Top-Down approach? The Top-Down approach is to make an outline and then fill in the content.
What is the topic in this practice essay? This essay is about the Universe. How much do we know about the Universe? Hard to say. (Shall we follow the outline? Where is the outline? The outline is in this web page. Looks good. What’s next on the outline?)
What is the origin of the universe? For the origin of the universe, check the article in this link, origin of the universe.
What’s the next item on the outline? The next item is the Standard Cosmological Model. It’s citing another material on line in this link, cosmological model.
What’s next? The next one is the existential problem. Sometimes people feel small because the Universe is supposed to be very big.
The next section is about the CMB.
Some may feel small because the Earth as a planet looks much bigger than a single person. But the Earth as a planet looks small compared to the Sun. The Sun as a star looks small compared to the solar system. The solar system looks small compared to the galaxy. The galaxy looks small compared to the galaxy cluster. The galaxy cluster looks small compared to the other bigger galaxy clusters. No matter how big a galaxy cluster is, it looks small compared to the… finally…the universe.
(Check this article on scientific American.)
Then how does a single person compare to the universe?
It’s hard to say. A person is small in space and time compared to the universe. But a person can perceive the universe. The volume of the mind doesn’t seem to have limit.
Existential crisis could be a philosophical question. Existential crisis is a recognized clinical condition. See What is an existential crisis?
To resolve existential crisis, need to seek help from experts or seek self-help. The best self-help resources for existential crisis is the Wikipedia page on existential crisis.
The CMB is a background signal in space. The discovery of the CMB is a fun story.
The CMB is measured with bolometers sent in space. The bolometers measure the temperature fluctuations.
Questions: How does Spider work?
The CMB is isotropic and homogeneous. Isotropic means that it’s uniform across all directions. Homogeneous means pretty much the same thing.
The size of the universe appears to be infinite.
Read the Nobel lecture on the discovery of the CMB THE COSMIC MICROWAVE BACKGROUND RADIATION by Robert W Wilson. Highly recommend.
Gödel’s theorem said math is not going to be complete
There are statements in math that you can either prove or disprove
If the universe is logically complete
Math is not ever going to describe the universe fully
In that sense, math could be a science
It’s better to have a logical universe than a mathematical universe
It’s beyond science to deduce the truths of the universe. Science is to provide description of predictions in a certain scope.
I would like to think that math is true and reflects in some way how the universe works.
But mathematics is logically in complete.
So either the universe is mathematical but not logical or universe is logical but not mathematical
Two things in math are fun to do:
Calculus in different context
Solving differential equations
Math could not describe physics perfectly
(Brain storm by Zhen Zhu Nan Da and Zhen Zhu Qu Qi)
https://github.com/rksm/org-ai
Check Launch a GitHub Page.