When Going Gets Rough
Thu, 09/18/2008 - 03:38 — Mark NadalIt is in times like these that a person's character shines the most, in the moments of chaos and depression that those few spirits lift others up, transcending from the mortal world and piercing through the clouds above into God's presence. Though clouds may cast a darkness upon the land, the shadow only proves the sunshine.
Hi, I am Mark Nadal, and I am a product of the American 21st century. I live, I breathe in a time where the very structure of society breaks down individuals, pushing them to the brink of sanity and confusion, till it leaves people in chaos and destruction. I am a witness to the fall of a once great nation, and I leave you a message about the decay of a civilization. If we, the zeta generation, do not rise up and alter the course of our nation, then the only hope that remains is in the phoenix; if this be our destiny, then receive this message so that you too will not make the same mistake. We live in dire times, and we require a heroic response. But all too soundly and silently, heroes have passed into fiction. We are an invisible nation.
Such a voice is loss in the mingling meaningless crying sobs, such a voice is to justify such cries, we are generation crying, a generation dying, and no hero is arising. Amidst the chaotic sounds and confused souls screaming for somebody to care, somebody to love, a silent wake is left rippling in history. These voices must be heard, if not for their own sake, but then for the sake of those to follow.
I tread upon tears, they are the burden I have taken on, they are the cries I shall voice, a generation lost at heart. Some will scream for the unborn, I shall scream for the born. Let this weeping be heard, I shed tears for I cannot take the weight, but only God can, let my tears turn to blood and ash if I may bear these iniquities, this generation’s sin, if no one shall come, let me take them so that I may be guilty before my savior – for he has saved me once, assuredly he may save me twice. My heart trembles and weeps.
Forgive us our sins, cleanse us our iniquities, and let us not be forsaken. This generation needs a hero, and let heroes arise. Let our generation become legacy’s legends, so that they too, shall not forget. Though our age may come to an end, let the phoenix thrive, and remember us not as myth, but as Truth. We serve God, and we will His Will. That we may represent Christ, as He is a mediator to our Lord, let us be mediators to our Savior. Though darkness comes, we transcend. I hold a teardrop, timeless shed, but eternal grace I bless. Let us forget not our place, bearing our humility, as the prophets of a place, nation once so great. Our fall shall not be without a fight. Darkness may prevail for the while, but God’s light is the now. Move beyond the clouds, but forget not the trials. Forget not the Graveyard World, these bloodstained paws, give me your honest dead, to grapple with this beaming redemption, embrace it tightly, a breath away, the lighted way.
I mourn. I cry. I weep. I shed tears. For my friends, for my generation. Let me be a voice, if I may, even a hero, to bear these burdens, show the transcendental glory, breaking through the clouds of an overcast world, that happiness and joy can sustain, that these people may see. So that they too, may believe, and rejoice in the Truth. Embrace the Lighted way, a beaming crucifix. Love exists.
Love
On Love, Sex and Betrothal
Love is totality. Love is the basis of reality, the essence of human, the meaning of philosophy. It is the expression of your life, your breath, your motion; it consumes you and intoxicates your wholeness. You can no longer be a villain, yet human, with or without love. And a hero no longer can be real without it. Love is not carnal.
Zero
Of [Numbers], [Dimensions], and The Universe
by ©: Mark Nadal
The mathematical discrimination against zero has caused an obstruction to man’s scientific understanding of the universe. An affirmative action is necessary in order to counter this detrimental cause. This trilogy essay, thuswise written, intends to restore the scientific and mathematical application of operations on the ZERO number, and duly note the important ideals that it represents through first correcting the exception in Numbers, then explaining its importance in Dimensions and finally how it applies to The Universe.
On Numbers
The Definition.
The numerical symbol “0” represents the known English word “zero” which has a meaning of “”, however, “” can also be referred to as “Nothing”, “Null”, “Nil”, “Empty”. Aptly put in a literal fashion: “0=”, or otherwise “0=0”, “0=’Nothing’”. Zero, is a complicated concept to comprehend, as any representation of Nothing is obviously something, the representative does a poor job reflecting the attributes and characteristic of Nothing. So keep in mind that the words above listed all are symbolic representation of . However, the previous statement does not make sense without proper words: “…representation of nothing.”
The Crisis.
Mathematicians have mistakenly discriminated against zero because of its unique property, this however is subsequently dangerous because once we disallow, declare illegal, reject, and ignore the unique attributes of zero, we are less inclined to understand all that it represents and can formulate. The cause is not without reason, however; yet, in many practical ways, making particular operations involving zero “un-desired” is wise (these reasons will be addressed later). But making it illegal and disallowed is foolish for the important reasons of the philosophical answers that the nature of zero and its operations has to offer.
The Basis.
The elemental basis for numerous operations is addition. Subtraction is only the addition of the inverse of the number. Multiplication is only the addition of the number for a specified variable times. Division is the inverse of multiplication, which is based on addition. Exponent are based on multiplying (which is rooted in addition) a number for a specified variable times. Therefore, it is reasonable to say that Addition is the Mother of Operations; other operations are shortcuts through a rather lengthy process of addition.
The Binary.
Technically, only two states exist: 0 and 1, which is also commonly represented as FALSE and TRUE, or otherwise Nothing and Something. Other numbers, like 2 and 3 or 56 are just representations of 1+1, 1+1+1, (I’ll spare you 56, as I assume you are intelligent and understand the point).
For the following, as commonly used in computer science, “!” will mean “not” or “no”.
0 = 0 (Zero Equals Zero)
0 != 1 (Zero Not Equal to One)
0 = !1 (Zero Equals Not One)
1 = 1 (One Equals One)
1 != 0 (One Not Equal to Zero)
1 = !0 (One Equals Not Zero)
FALSE = FALSE
FALSE != TRUE
FALSE = !TRUE
TRUE = TRUE
TRUE != FALSE
TRUE = !FALSE
Nothing = Nothing (Nothing Equals Nothing)
Nothing != Something (Nothing does Not Equal Something)
Nothing = !Something (Nothing is Equal to No Something)
Something = Something (Something Equals Something)
Something != Nothing (Something does Not Equals Nothing)
Something = !Nothing (Something Equals No Nothing)
On the last one, notice the use of a double negative. In fact, “Nothing” is “no thing”, which could be represented as !thing, and “Something” could be just ‘thing’. Something that exists is the same as if there were no non existent things, because the existence of an object categorically denies nothingness, as something does in fact exist. It is black and white.
The Proposition.
x/0 = 0
1. By Law. Numerous laws exist in mathematics, because that is the scientific and absolute nature of it. These laws were not created, they were discovered; these laws were not conceived, they were revealed. These laws are universal and apply to all numbers. Making an exception for zero, so that it is illegal, is absolutely un-scientific and contrary to the very nature of mathematics. In fact, that is why it is called an “exception”, it is making an exception of the law of mathematics. This is significant because if we accept the exception, that means we have immediately departed from mathematics – we are no longer performing math. It is completely contrary to any kind of logical sense to use math while not performing it.
Inverse Law of Multiplication and Division: If x*b=a then a/b=x
Multiplication Law of Zero: If x*0=0
Therefor:
Division Law of Zero: If x/0=0
This is true because of the mathematical relationship between multiplication and division; in division, if a or b happens to be zero then the x will be zero.
On top of the inverse relationship, there is also a commutative law of multiplication. Using “|” to depict “either, if not already chosen” (x*b=a then a/b=x) + (x*b = b*x) = (x|b*x|b=a then a/x|b=x|b). Stating that 0/5=0, but then saying 5/0=Illegal contradicts the mechanics of the commutative law.
These are mandatory laws and no mathematician can ignore them without denying his profession.
Examples:
2*3=6, 6/3=2
(1+1)*(1+1+1)=(1+1+1+1+1+1), (1+1+1+1+1+1)/(1+1+1)=(1+1)
0*5=0, 0/5=0 (legal)
0*(1+1+1+1+1)=0, 0/(1+1+1+1+1)=0 [legal]
5*0=0, 5/0=0 (“illegal”)
(1+1+1+1+1+)*0=0, (1+1+1+1+1+)/0=0 [“illegal”]
(This last example also illustrates a violation of the commutative law if the preceding example is true)
2. By Reason. All operations other than division are defined with zero, it is illogical to leave a critical operand left out as being illegal, especially when it is already defined by the commutative law and is also required by the inverse relationship law. It is unreasonable to avoid mathematics while performing mathematics.
Additionally, if all numbers can be represented by either 0 or 1, and 1 is fully defined and its properties and attributes are accurately understood, making particular important properties of zero be illegal is detrimental to the mechanics of mathematics.
3. By Mathematics. Division can be read as, “How many‘b’s go inside of ‘a’?” the answer x is the amount.
10/1 = How many Ones are in Ten? = 10 = (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1)
10/5 = How many Fives are in Ten? = 2 = (5 + 5)
10/10 = How many Tens are in Ten? = 1 = (10)
Thus, it is mathematically accurate to state that No Nothings go into Something (see Binary Examples). The following example will be repeated in numerous different ways so the understanding between the literal and figurative perspectives of Zero makes adequate sense.
5/0 = How many Zeros are in Five? = None = ()
5/0 = How many Zeros are in Five? = Null = (Empty)
5/0 = How many Zeros are in Five? = Nil = (None)
5/0 = How many Zeros are in Five? = 0 = (Nil)
5/0 = How many Zeros are in Five? = Empty = (0)
5/0 = How many Zeros are in Five? = = ()
It is true to state that there are 0 “0”s in Five; there are NO “0”s in Five. The existence of Something empirically denies Nothingness; Something and Nothing are mutually exclusive. It is correct to state that there are 0 (the figurative amount) of “0”s (the literal meaning). Due to the figurative and literal meaning of zero, understanding the division expression is easier to comprehend if it is substituted with synonyms – as the previous example illustrated.
The following test will visually represent the concept.
1+1+1+1+1=5 [TRUE] [FALSE]
Does the zero “0” character appear anywhere in the following: “1+1+1+1+1”? [YES] [NO]
It is stated, that if division by zero was legal then it would be undefined because one can add any number of Zeros to Zero and it would still be Zero.
It is true that: 0+0+0+0+0+…=0. In fact: x+0=x, this is the Identity Property of Addition with Zero (same law applies to its inverse, subtraction).
This Identity Property of Addition with Zero reflects why it would not be undefined. The Identity Property of Addition with Zero states that “Any number + 0 is the same number.” The reason why is best illustrated by working through it mathematically:
The Opponent:
5+0=5, 5+0+0=5, 5+0+0+0+…=5
Therefore 5/0 would mean there is an undefined (or infinite) amount of “0”s in 5.
The Mathematics:
((5+0) = 5) = 5
This is a more accurate description of what happens, it is the SUM of 5 and 0 that equals 5, before you continue to the next operation you first perform the operation prior to it (in the order of the operations themselves, naturally).
(1+1+1+1+1)+0=1+1+1+1+1
1+1+1+1+1=1+1+1+1+1
1+1+1+1+1=1+1+1+1+1
That way, by the time you divide 5 into 0, 5 = 1+1+1+1+1, not 1+1+1+1+1+0+0+…, because you have already performed the identity test and it now equals itself which is 5 (or 1+1+1+1+1).
The conclusion that x/0=Undefined is mathematically faulty, as it is based on performing the operation prior to performing the operations within the grouping symbols (which take higher precedent).
Second, even while ignoring the hierarchy, adding an undefined amount of zeros to the number is not specified in the formula, meaning that the “answer” they draw is only based on tampering with the original formula to modify its behavior – which naturally results in a changed formula and thus an inaccurate depiction of the first.
The conclusion that x/0=Undefined is incorrect because it violates the law of Operational Hierarchies as well as expressly corrupts the original formula.
_______________________________________
0/0 = x
The reason why 0/0=x is a conclusion based on the combination of numerous mathematical laws.
If x/0=0
But if x/x=1
Then 0/0={0,1}
However x*b=a then a/b=x
In multiplication: if a or b or x = 0
(For purpose of clarity, assume a = 0)
Then Multiplication Property of Zero applies. x or b or x and b = 0
(For purpose, let: x != 0, then b=0)
Then in division: (a/b) 0/0=x
Then 0/0={…-5,-4,-3,-2,-1,0,1,2,3,4,5…}
More simply:
Because x*b=a then a/b=x, if x*0=0, then 0/0=x.
Then 0/0={…-5,-4,-3,-2,-1,0,1,2,3,4,5…}
Examples:
For x*b=a and a/b=x
|
1. x = 0
b = 0
a = 0
0*0=0
0/0=0
|
2. x = 0
a = 0
b = {…-5,-4,-3,-2,-1,0,1,2,3,4,5…}
0*{…-5,-4,-3,-2,-1,0,1,2,3,4,5…}=0
0/{…-5,-4,-3,-2,-1,0,1,2,3,4,5…}=0
|
|
3. b = 0
a = 0
x = {…-5,-4,-3,-2,-1,0,1,2,3,4,5…}
{…-5,-4,-3,-2,-1,0,1,2,3,4,5…}*0=0
0/0={…-5,-4,-3,-2,-1,0,1,2,3,4,5…}
|
4. x = 0
b = 5
a = 0
0*5=0
0/5=0
|
|
5. x = 2
a = 0 b = 0
2*0=0 0/0=2
|
6. x = 0
a = 0 b = 0 0*0=0
|
|
7. x = -5
b = 0 a = 0 -5*0=0 |
8. x = -5
b = 2 a = -10 -5*2=-10 |
_______________________________________
Origin of the Crisis.
Mathematics is appreciated because of its rigid, absolute framework. Two plus two will always equal Four, all numbers work in an orderly, perfected fashion. There are many good reasons why division by zero is undesired, however these are reasons that can be easily resolved.
1. Relativism. If 0/0 can be equated to anything then mathematics becomes completely meaningless, 0/0 = 0/0 could be substituted for 6 = 22. Mathematics becomes devoid of all meaning if 0/0 can be equated to anything.
This is mathematically false because it ignores the principle that “any operation may be performed only if it is done on both sides of an equation.” Mathematically, pairs of the operation 0/0 must have the same result for both sides, and naturally, 0/0 cannot be used to violate mathematical laws.
2. Computation. For practical purposes, if 0/0 can equate to any answer, this would expand into infinity, and a processing machine would get stuck in an infinite loop.
This is true, since a machine operates in a linear fashion it is unable to analyze complex abstractions (namely, infinity) unlike the human counterpart which can. In this situation since a randomly selected number could give rise to an unequated and thus false solution, the best practical answer is to prompt the human for input (since, currently, the human already is prompted with a supposed error message), if that input is available then the computer can finish the equation, however if not then the process should be terminated so a possible inaccuracy is not generated.
(Note from author: just as randomness, being an abstraction like infinity, cannot be calculated by a machine, humans have developed clever algorithms that accurately generate pseudo-random numbers. With this in mind, I speculate that it is not too tedious of an application that human wit cannot overcome and algorithmically produce accurate pseudo-0/0 numbers. This, I foresee, as the best alternative.)
The Importance of Being 0/0.
The applications of 0/0 is the greatest driving force to the necessity of abolishing the unmathematical exception. Here listed is only the beginning of numerous applications that prove important to the unifying structure of math. In fact, the results of some of these are so significant that they will further explained in the following essays Dimensions and The Universe. While at first these unifying results may not seem significant, this is because it explains quite common concepts that are already understood, what is important is to see how 0/0 is actually the application that defines these concepts. It is revolutionary to think that 0/0 is used all the time, yet it has been declared as meaningless, unimportant and illegal. Humans instinctively think in 0/0 and they are surrounded by 0/0, 0/0 is an important property that defines not only this world but also beyond. Now credit is given where it is due.
1. Variables. Variables are used all the time in real world mathematics, all formulas consist of variables, from F=M*A to C2 + B2 = C2. But until now, variables themselves could never be a mathematical expression. Variables can now relate to distinct processes of 0/0, just as a variable is a placeholder, so is 0/0. F=M*A actually is (0/0)=(0/0)*(0/0), as is the nature of formulas, if you select an answer for two of the “0/0”s, then you will immediately have the answer to the third. As is accustomed, you cannot manually ascribe all three variables, because a formula is used to solve for one of them.
The existence of 0/0 allows for variables to be mathematically defined, this highlights the unifying nature of mathematics.
2. Randomness. Any randomly selected number can also be identified in 0/0 and since 0/0 can be a placeholder for any unknown specified number it can namely be equated to randomness.
3. Infinity. Since 0/0 can express any number, 0/0 is the mathematical definition of infinity, since its solution includes all conceivable and inconceivable answers.
4. Unity Point Between Concretes and Abstracts. Realistically, numbers are finite, because we live in a physical (and thus finite) world. There are only 10 fingers and 10 toes on your hands and feet, the numbers 37 and 2,691 do not exist because you cannot exceed past a count of 20. There is a discrete amount of pages in a book, and a number beyond that does not exist for that object. Yet, theoretically we know that these numbers do exist, we know that if we can add up all of our fingers, we can always find a new number after that. As mentioned prior to this, we can hypothetically count into infinity. Because of this, 0/0 is the unity point between discrete and continuous numbers, it explains how in a world that has absolute, finite, integral values that undeterminable, infinite, continuous values are also possible. In other words, 0/0 expresses the relationship between concrete realities and abstract ideas, which subsequently explains how a human mind contrives such complexity.
Example: 0/0 explains the interaction between the Platonic form of a chair and physical chair itself. The physical chair expresses the discrete existence of a tangible, absolute object which consequently results in a ubiquitous, infinitely generic form that is what defines a chair as a chair. The real is what allows us to comprehend the abstract, but it is the abstract that allows us to define the real, this relationship is united because of 0/0.
5. Dimensions. Continue to the second essay. Note: This essay will also address the issue of reaching infinity as you graph towards dividing a number by zero.
6. The Universe. Continue to the third essay.
7. Beyond. 0/0 is such a defining attribute that its application surpasses that which is listed in this essay; namely 0/0, as its nature is unexhaustive, this list is not exhausted. Since mathematics is something that is superfluous to any one particular thing and can be applied to an exceedingly diverse amount of topics, whether logic or concretes or abstracts, it would be unwise to ever state that its case is closed.
8. God. Finally, 0/0 is a mathematical operation that can accurately describe the infinite attributes of God himself, it is fascinating to realize that the mastermind who constructed these mathematical, scientific and logical laws, which are absolute themselves, all reflect the nature of their Divine Creator.
This essay was originally published August 26th, 2007 on my older blog. NVision
Mon, 08/25/2008 - 23:35 — Mark NadalCurrently in: Silicon Valley, San Jose, CA.
Currently at: NScene, Nvidia NVision 2008.
Currently on: William's sweet computer.
Currently adoring: William's graphic tablet.
Currently made:
w00t!
Sun, 01/27/2008 - 21:20 — toxicstinaHaha yesterday I went to Alei's house played DDR for a few hours then went to cloverfeild. I got high off of ketchup!! Oh yea, I ran around the theater twice, and everyone thought I was crazy.
w00t!
