#entropy of a closed system cannot decrease

"you will exist only as an abstract idea" yeah girl that's the dream!!!

So when I was in college, I noticed something a bit concerning: a rather large portion of people involved in hard sciences were totally unfamiliar with even basic philosophy of science. For example, when I talked to other science majors I discovered that the majority of them seemingly didn’t know the difference between a theory and a law. The most frequent definition I got was that theories are still somewhat uncertain, whereas laws have been proven to be true and are more or less never wrong. This is incorrect – first of all, a scientific law can absolutely be wrong. Throughout history, even well-established scientific laws often end up being modified or thrown out entirely as new evidence comes to light. For instance, it turns out Newton’s Laws of Motion are only accurate for large objects moving slowly; things that are extremely small or moving close to the speed of light behave by entirely different rules. The actual difference between a theory and a law is that a law has to be a concise description of how something in nature behaves that can usually be stated in full in one or two sentences, or more ideally an equation. For example, the Second Law of Thermodynamics states that the entropy of an isolated system never decreases, or simply ∆S≥0. A theory, on the other hand, is an interconnected collection of ideas that attempts to explain a natural phenomenon or range of phenomena, and will make multiple falsifiable predictions. It’s possible for a scientist to devote their entire lives to improving humanity’s understanding of a single scientific theory – biology’s theory of evolution is a good example.

Now at this point you might be saying “So what? You’re just nitpicking at semantics.” I would argue that misunderstanding the theory/law distinction betrays a more fundamental lack of grasp on the scientific method. Once we start conceptualizing certain ideas, even implicitly, as infallible or otherwise not worth questioning anymore, we start veering away from the realm of science and into the realm of dogma. I have a strong suspicion that a lot of the weird STEM elitism that’s so prevalent these days is a result of widespread illiteracy as to what science itself is at a basic level – otherwise it would become obvious how ultimately inseparable hard science is from soft science, from philosophy, from art. I could go on about this for ten more pages but this isn’t really the topic I want to talk about right now. My essential point is that it’s very easy for people who are otherwise highly intelligent and highly competent in their field to lack proper understanding of its underlying philosophy.

The reason I bring this up is because I am about to argue that almost everyone is interpreting Gödel’s Incompleteness Theorems wildly inaccurately. More specifically, I’m aiming to demonstrate that the idea that a mathematical conjecture can be “true but unprovable” is tautologically false. This is a misconception that stems from confusion over what constitutes mathematical truth – which is actually a philosophy problem, not a math problem. If you want to be able to say anything at all about truth or falsehood in this context, first you’re going to need a coherent and precise definition for mathematics itself.

Let’s start by trying to answer a narrower question: what are numbers? In what manner can numbers be said to exist? Can you look at a number? Can you touch a number? I can draw the numeral “4” on a sheet of paper, but that’s not really the number four, it’s just an arbitrary symbol we chose to represent it. If tomorrow everyone decided that we were going to switch the numerals for four and five (such that “5” now means four and vice versa), nothing about how math works would change, it would just look slightly different on paper. So then a number definitely isn’t a physical object like a proton or a chair or a planet. Now at this point you could argue that perhaps numbers are a property that things in the real world can have – for example, if an H+ ion has a positive electric charge, most people would agree that its charge is something that that exists in the physical world despite the fact that it can’t exist independently from the ion. Analogously, you can count a group of apples and always get the same results; if there are four apples then there are four apples. You can even use arithmetic to make accurate predictions about how many apples there will be if you add more, remove some, or divide them into groups. So you could claim: therefore, numbers must be real i.e. they must somehow exist in the universe independent of human thought.

However, this line of argument fails pretty quickly once you consider the fact that the all the rules of arithmetic change relative to how you happen to be looking at the problem. For instance, suppose you’re trying to figure out how many people you can fit in an elevator. You’re inevitably going to end up using the natural numbers – we can all reasonably agree you can’t have a fraction of a person (you could cut a human being in half, but they would cease to meaningfully be a person at this point). You decide you can cram about eight people in before running out of room, but then realize you forgot to consider the elevator’s weight capacity. If it can safely lift about two tons, then you’re also going to have to measure the combined weight of everything it’s carrying in terms of fractions of tons. Suddenly the math you have to use changes from discrete to continuous, which is a really important difference; there’s no way to have between one and two people, but you can easily measure a weight between one and two tons (say 1.5 tons), and then if you want you theorize a possible weight that’s between one and the weight you just measured (say 1.25 tons), and so on and so on indefinitely. This is all fairly straightforward, but it presents a significant problem if you want to contend that these numbers exist independently of human cognition. Which set of rules is correct? If numbers objectively exist then it logically must follow that any given number either can be divided into arbitrarily smaller parts, or cannot be. Do negative numbers really exist? As far as we’re aware it’s impossible for an object to have negative mass, and you certainly can’t have a negative number of people. Do complex numbers exist?

Another problem: the number we get when we determine the mass of a given object will be different depending on what units of measure we’re using. If we switch from using kilograms to pound-masses, none of the physical properties of the object have changed, but we’re now measuring completely different numbers. This is because mass is an objective physical property, but numbers are simply a system we’ve come up with to help us describe this. An object inherently has mass, but does not inherently have two-ness or four-ness or the like. Mathematics, then, is not an objective reality but merely a human invention we sometimes use to describe objective reality, somewhat conceptually akin to a natural language like English or Mandarin. Once we grasp this, it becomes possible to define math in a precise and consistent matter (and hence mathematical truth). All mathematical systems can be ultimately be characterized in terms of sets of symbols, axioms, and rules of inference. Mathematics, therefore, is simply the study of axiomatic systems.

In this context, Gödel’s Incompleteness Theorems are less “existential crisis inducing mind-screw” and more “fairly intuitive idea that perhaps should have been obvious in retrospect.” The second incompleteness theorem can be approximately stated as: “for any consistent system F within which a certain amount of elementary arithmetic can be carried out, the consistency of F cannot be proved in F itself.” How could any system of axioms conceivably prove itself consistent? By the logical principle of explosion, we know that in any inconsistent system we can prove literally any proposition that the system can express, meaning an inconsistent system would necessarily be able to prove itself consistent according to its own rules. Therefore, it would be impossible for us to distinguish a hypothetical consistent math system that could somehow prove its own consistency versus an inconsistent system that could prove its own consistency due to some internal contradiction we haven’t yet discovered.

 The basic powers of Witches

There six original witches each one born with a certain element

Nether Witches

The magic of the underworld other known as nothingness witches born with this type of ability can serve people souls from their bodies bring others back to life, not all nether witches are necromancers but are more likely to be one.

The user can create, shape and manipulate Nether, the “Chthonian Element” that flows through the realms of the living, and the Dead. Nether is most known as the substance that makes up the Underworld, a subterranean dimension where all souls go when they pass on. Nether is very similar to Aether “the Celestial Element” in that it is from a Plane that exists between the planes of both matter, and energy. However, although it can partake in the nature of either substance, Nether is neither of these things.

Despite being often considered “Death-Force” Nether is more than the source of what drains life away from living things, it is the destructive aspect of reality, the source and very concept of entropy and destruction, disasters, and all degeneration in the matter, energy, and concepts. It is the power that makes possible and ensures severing the soul’s connection to their mortal body so they can pass onto the afterlife. It is also the power that summons and controls the souls of the deceased. Users of this power acknowledge that Nether exists in Elemental, Cosmic, and Spiritual forces. Nether exists in the cosmos as sort of a gateway between the land of the Living and the Dead, stretching out to anywhere where death has potential to occur.

Like Aether, Nether is a Spiritual Element, which means it cannot be perceived by any physical sense. The only way Nether can be seen is if it were mixed with an Element of the Physical Realm (Most often Darkness, Fire, or Earth).

Aether (Spirit)

Main specialties for aether witches Travelers of other dimissions dream walkers users of the Arcane craft.

these are the type of witches who are more likely to have Stronger Psychic abilities among the other Six.

The user can create, shape and manipulate Aether, a powerful and unique “Celestial Element” that flows through the Universe. There have been many claims/theories made by alchemists, natural philosophers, and very early modern physicists that confirm Aether’s power. One claim is that it was the pure essence that the Mythological gods lived and breathed in the same way humans did with air. Another claim is that Aether is the force used by God himself to create the Universe. Another reference would be the Hermeticist book “Kybalion” that not only explain its nature but the plane it comes from. As mentioned in the Astrology page, Aether is from the “Ethereal Plane”, a Physical Plane that exists between the ones of both matter and energy. However, although it can partake in the nature of either substance, Aether is neither of these things.

Despite its title as “Life-Force”, Aether encompasses more than the essence of living things. Users of this power will realize that Aether exists in Elemental, Cosmic, and Spiritual forces. This is also proven by the Kybalion’s entries. According to the texts, there are at least three levels of both matter and energy each with Aether in the middle. The first level of matter comprises the common forms of matter like solid/liquids/gases. The second level consists of matter that is at a more high level, and subtle. The third level is comprised of the most subtle, and tenuous forms of matter that scientists don’t even know about. Concerning energy, the first level consists of the common forms such as heat and light. The second level consists of “Nature’s Finer Forces”, higher forms of energy that is undiscovered by scientists. The third level consists of energy that is unrecognizable by human beings, and available only to beings of the Spiritual Plane. This form of energy can be considered as “the divine power” with the users being considered “gods”.

With this stated, each level of matter/energy refers to the one of the three mentioned forces. The first level means the elemental forces because the text refers to common forms. The second level means cosmic forces as they are referring to higher forms of matter/energy. The third level refers to spiritual/divine forces because the text referred to forms of matter/energy that is unrecognizable by mortal life-forms and only available to transcendent life-forms. This is supported by the fact that spirits are believed to be ethereal beings that are basically made of Aether. Needless to say, users of this power will be extremely powerful, and essentially invincible.

Fire Witches

Witches of fire can do more than controlling the element they are one of three that can steal/absorb others energy (by touch) and store them within themselves or use their magic type against them.

Fire witches immunity to fire

Fire mimicry

Sub-Ability

Fire witches can also create, shape and manipulate energy, the capacity to cause change: one of the most basic quantitative properties of a system, such as an object or a field of energy. Energy can be transformed (converted) among a number of forms that may each manifest and be measurable in differing ways. The law of conservation of energy states that the (total) energy of a system can increase or decrease only by transferring it in or out of the system, thus the total energy of a system can be calculated by simple addition when it is composed of multiple non-interacting parts or has multiple distinct forms of energy.

Common physical forms of energy include the kinetic energy of a moving object, the radiant energy carried by light and other electromagnetic radiation, and various types of potential energy such as gravitational and elastic.

Water Witches

The user can create, shape and manipulate water, an inorganic compound with liquid, gas (steam, water vapor), and solid (ice) states, including changing them from one state to other.

just because a water source is not near them water witches can summon (teleporting water from the seven seas or any water source close by) at any time and place. No matter in a dessert.

Water witches can communicate with water-related creatures and breath underwater.

Water mimicry

Air Witches

can cause storms fly and walk on air

The user can create, shape and manipulate air, the common name given to the layer of atmospheric gases and various compounds (mostly oxygen and nitrogen) surrounding the planet Earth that is retained by Earth’s gravity, and wind, movement of air relative to the surface of the planet. It is an important factor in determining and controlling climate and weather, and the generating force of most ocean and freshwater waves. Wind occurs because of horizontal and vertical differences in atmospheric pressure, and include breezes, squalls, gusts, whirlwinds, zephyrs, gales, tempests, and hurricanes.

Since air cannot be seen by conventional methods, neither can the attacks and derivatives formed by/from it, making it an invisible and versatile weapon that is very difficult to block and dodge.

Air Fire mimicry

Earth Witches

They can do more than manipulate the earth around, they also ability to commune with animals

Earth witches can use nature to blend or become one with their surroundings  with nature, they become instantly familiar, their connection is so deep that the earth can respond to one’s emotions and desires (blossoming with flowers and calming weather when happy, making skies stormy or cause earthquakes when angry, shifting the landscape to gain the advantage in a fight, etc.)

The user can purify, heal and generally influence the health of nature, and be considering the fact that they’re helping the environment, plants and animals act favorably towards the user. They have access to every living species of animal on Earth and can also draw strength from them and acquire their abilities. Nature obeys users every command and operates on a “hive mind”, meaning users can control an entire army of animals.

Earth mimicry

Extra

Witches typically Have longer lifespan than humans people can tell what element their kind possesses by the changing of their eye color and veins that glow when they are about to use their powers.

Fire; Orange

Water; Blue

Earth; Greenish-brown

Air; White

Nether; acid Green

Aether; Purple

Witches can still manipulate the other elements just to a lesser extent. There are exceptions though

 Bonding Magic; 

Witches can bond their souls to another to draw power from other supernatural beings, typically from another Witch, there is a price if the bonded person dies they well too. there’s an alternate brand created by a Nether witch instead of dying along with the person who is killed the other well only feel immense pain.  

“It seems like you have awoken, Ms. Kurihara Misato.” As Misato regained her consciousness, a youth about 20 years old was looking down upon her lying on the ground. “This here is… If I’m not mistaken, I was sent flying by the truck…” With a miserable face, the youth said to Misato who was mumbling while standing up. “Yes. And then, you died.” “Huh…”