# K theory of finite fields (mod l homology)

Recently I have been reading about K theory of finite fields. Here I write some summaries about this calculation and calculate the homology ring of $F\psi ^q$ which is one step in the computation of finite fields, see section 4, {Mitchell}. This post may be continued.

This post has been continued on A Summary of Quillen’s K-theory of Finite Fields (Oct 16, 2021).

# Thoughts on Physics, Maths and Reality (Part II)

This is a rethink of the same topic and I realised that at this point of my life I have corrected my definitions and philosophical system ever since I’m concerned about the issue of reality. I remember that when I wrote down these thoughts in part I, I used lots of parenthesises to indicate that these words are not well-defined and the discussion is loose and casual. What I’m trying to convey here is my current view on this topic and my personal systemising.

Given the advance of physical sciences, the temptation is to downgrade the subjectivity of mental entity. Yet subjectivity is an undeniable part of the definition of reality. By saying that it’s undeniable I mean incorporating the subjectivity of mental state into the definition of reality is an inevitable part of developing a more consistent philosophical theory. Some attempts to define reality without account for subjectivity of mental entity include:

1. defining reality as concrete existence that is consistent for everyone.

2. defining reality as an existence of something independent of observations, the so called “outside world” as in part I.

The first one is a raw definition and has already been refined or abandoned by most people gradually in their cognitive development. Mathematical theory, together with concrete existences (experiments, observations etc.), are intrinsically accepted by most people as reality. People accept a later established definition and build their theories upon it until at some points they realised this contradicts their raw definition of reality and posted the question what reality is. When this contradiction arises, it’s the raw definition to be abandoned.

The second one is a very common one among physicists: Reality is something existing independent of observation which reflects its existence on our perception. Such existence is a very fascinating part of our worldview that motivates discovery and exploration . This is a very sound standpoint and would not contradict anything that I try to establish. To resolve some unsolvable problems like whether multiple universes exist, whether god exists, we want to incorporate subjectivity of mental entity in such way that this questions become either solvable or turned into a systematic investigation of our own mental states. Take thinking bear as an example. For me, my thinking bear is a soulmate since they fit into the several defining properties of a soulmate. Physically, most of my bear’s body is a bunch of cotton and fabrics, eyes are made of plastic. These materials are arranged in such a way that the materials in bear’s facial area stimulate the part of my brain responsible for facial recognition which in turns activate a series of mental activities and other brain activities. Bear’s fur casting shadow on their facial area results in different perceived facial expressions under different lighting and viewing angles. This gives an impression of changing moods. Bear’s long limbs have greater velocity than other parts of the body when the whole bear is given a small amount of momentum. Such movements of the limbs are perceived as activities of the bear. So far this can be summarised as personification based on concrete characters of bear’s appearance. To get a complete figure, my imagination fills in the nonconcrete parts based on my preference. Bear’s personality, interests and emotional states are created by me. All these imaginations together with concrete characters created a figure matching the defining properties of a soulmate. There can also be such an argument in terms of whether god exists. I would need to define god as I did not get a predefined definition of god from the community where I grew up.

One thing that I need to clarify at this point is when I say a word is not defined, it doesn’t mean it’s not defined in dictionary, in society or in general discussion. I mean this word is not incorporated into my philosophical system. Indeed any generally well defined word could end up having various definitions for different people. Most of the time when we make arguments, we could work with others to try to agree on the objective aspects of the definitions but what’re mostly neglected are the definition on the aspect of mental state. For example, people who doubt whether god exists are likely those that define god based on concrete properties. Yet for those who believe in god, the spiritual existence of god is in the definition hence their answers would be positive. When an atheist try to argue with an theist that god doesn’t exist. Almost both sides try to explicitly define god by concrete properties and based on their arguments from there. But what make their arguments diverge is the difference of the mental aspects of the definition of god. Hence in most cases, to resolve such a problem is to analyse the mental aspect of a definition. Such analysis is usually not easy, it can be personal, requires some kind of self-awareness and systemising. But by inspecting and systemising the mental aspect of our definitions, we incorporate subjectivity of mental entity in such way that many potentially disturbing questions become either solvable or turned into a systematic investigation of our own mental states.